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This is to certify that the

dissertation entitled

Perpendicular Giant Magnetoresistance: Study
and Application of Spin Dependent Scattering
in Magnetic Multilayers of Co/Cu and
N184F816/Cu.

presented by

Paul Robert Joseph Holody

has been accepted towards fulﬁllment
of the requirements for

Ph . D . degree in PhYSiC S

 

 

Major professor

 

Date jl/l7/ (I (9

MS U is an Afﬁrmative Action/Equal Opportunity Institution 0-12771

 

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DATE DUE DATE DUE DATE DUE

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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MSU IoAn Nﬁrm‘tvo Action/E“ Opportunity Inotltwon
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Perpendicular Giant Magnetoresistance: Study and
Application of Spin Dependent Scattering in Magnetic
Multilayers of Co/Cu and Ni34Fe16 /Cu.

By

Paul Robert Joseph Holody

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1 996

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ABSTRACT

Pcrpendicular Giant Magnetoresistance: Study and
Application of Spin Dependent Scattering in Magnetic
Multilayers of Co/Cu and Nig4F815/Cll.

By

Paul Robert Joseph Holody

Perpendicular transport through magnetic multilayers has been successfully described
by the two spin channel model. In the limit where spin ﬂip scattering can be neglected, the
transport current is carried by parallel channels of spin up and spin down electrons. Large
negative magnetoresistances arise from spin dependent scattering occurring in these
channels. Electrons with spins parallel to the local magnetization undergo a diﬂ‘erent
amount of scattering from those with spins antiparallel to the local magnetization.
Consequently the multilayer’s resistance can be controlled by the relative orientation of the
ferromagnetic layers’ magnetizations. Usually with the relative orientation antiparallel
(parallel) the multilayer has a high (low) resistance.

In this dissertation, an analysis of perpendicular transport measurements in the context of
the two spin channel model provides quantitative information about the amounts of spin
dependent scattering at the Ferromagnetic/Normal metal interfaces and in the bulk

Ferromagnet metal for the Co/Cu and Nquem/Cu systems (Nque15=Py). This is essen-

 

 

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Paul Robert Joseph Holody
tial to the understanding of the scattering mechanisms involved in Giant
Magnetoresistance. Our results show a signiﬁcant bulk contribution to the spin dependent
scattering; but, it is the interfaces which make the larger contribution to spin dependent
scattering in these systems. A larger bulk spin dependent scattering asymmetry was
determined for the Py/Cu multilayers, but not as large as expected ﬁom data derived
previously from ternary alloys.

Measurements were made on several Co/CuX series (where X=Pt, Mn, Ge and Ni) to
study the transport properties of magnetic multilayers when signiﬁcant spin ﬂip scattering
is present in the system. Analysis was done using the Valet-Fort theory which generalizes
the two spin channel model to include ﬁnite spin diﬂirsion lengths. A sharp drop in the
magnetoresistance is observed when the spin diﬂirsion length :2 layer thickness. These
results justify the inﬁnite spin diffusion length assumed in the previous Co/Cu study.

The transport properties of magnetic multilayers have an enormous potential for
commercial applications. As a way of demonstrating the utility of multilayers, several
multilayer systems were designed to meet speciﬁc requirements. These included systems
which had positive magnetoresistances as well as systems which exhibited (AR/R)/AH as
high as lO%/Oe in very low magnetic ﬁelds at 4.2K. Several attempts were made to

extend such high sensitivities to room temperature.

T 0 my parents

ACKNOWLEDGMENTS

Many thanks go to my thesis advisor, Professor Peter A. Schroeder for his guidance and support for
the duration of this project I am especially grateful for his patience and encouragement during the writing
of this dissertation. I would also like to thank Professors Jack Bass and William P. Pratt, Jr. for their
helpful insights and enthusiastic discussions. It has been a very rewarding experience to be part of such a
dynamic research group.

A special thanks goes to Reza Loloee for his help and instruction. Thanks are due to T om Palazzolo,
Jim Muns and Tom Hudson for their input on design and to Vivion Shull and Carol Flegler for their help
with the EDX studies. Discussions with my co-workers: S.F. Lee, Q. Yang, L.L. Henry, W.C. Chiang,
S.H. Hsu and S. Steenwyk have contributed greatly to my understanding. Also, our collaborators in
Orsay: A. Fort, A. Barthélémy, J.L. Duvail, L.B. Steren and R. Morel have made many insightful
comments and suggestions on this project.

I am the most thankﬁrl to my parents and brothers for their generous love and support over the past 29
years. A big GWI goes to Pat, Rob, Duane, Tim and Mike for their invaluable friendship the past 13 years.
I would also like to thank Mike Franklin for getting me out of the PA building for some “hoops” on a semi-
regular basis.

I would like to acknowledge the Ford Scientific Laboratory for their generosity in funding my
assistantship. Additional ﬁnancial support for this project was generously provided by the National
Science Foundation through MR-SEC and the US-France Cooperative Program and by Michigan State

University’s Center for Fundamental Materials Research.

 

 

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TABLE OF CONTENTS

LIST OF TABLES. .
LIST OF FIGURES. .

1 Introduction to Giant Magnetoresistance. .

2 Sample Preparation and Fabrication. .

2.1 Introduction. . .

2.2 Preparation of the System.
2. 3 Substrates and Holders.
2.4 Vacuum. . . .

2.5 Cooling System. .

2.6 Fabrication.

2.7 Targets.

3 Sample Characterization and Experimental Procedures. .

Introduction . .

3.1 Compositional Analysis Using EDX..
3. 2 X-rays.. . .
3. 3 Cross-sectional Analysis”

3. 4 Nuclear Magnetic Resonance.

3.5 Resistivity of Single Films. .

3.6 Determination of CPP Area. .

3.7 CIP Measurements.

vi

xii

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20
20
23
24
26
28

31

31
31
34
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42
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3.8CPPMeasurements................46

4 Theory of CPP Transportin Magnetic Multilayers. .- . . . . . . 50

Introduction. . . . . . . . . . 50
4.1 Spin Dependent Scattering- A Simpliﬁed Picture. . . . . . . . 51
4. 2 The Two Current Model. . . . . . . . . . . . 54
4. 3 Spin-ﬂip Scattering for the CPP Geometry. . . . . . . . . . 6O
4. 4 Spin Accumulation in Magnetic Multilayers. . . . . . . . . 65
4.5 Spin ﬂip Scattering by Spin-orbit Interactions . . . . . . . . 71
4.6 Positive and Negative Giant Magnetoresistance. . . . . . . . . 73

5 Analysis ofCo/Cu&Py/Cu Multilayers. . . . . . . . . . . 76

Introduction. . . . . . . . . . 76
5.1 Spin Asymmetry Parameters in Cb/Cu Multilayers. . . . . . 77
Basis for Separating Bulk and Interface Spin Dependent Parameters. . . 82
Global Fit of the Co/Cu Data... . . . . . . . . 89
5.2 Spin Asymmetry Parameters 1n Py/Cu Multilayers. . . . . . . . 98
Global Fit of the Py/Cu Data... . . . . . . . . . . . 112
FitA....................115
Fit B. . . . . . . . . . . . . . . 118
Comparison of Fits A and B. . . . . . . . . . . . . 120
Comparison with Co/Cu Multilayers. . . . . . . . . . . 132

6 Complex Magnetic Multilayers. . . . . . . . . . . . . . 134

6.1 Finite Spin Diffusion Length Effects in Multilayers of Co and Cu Alloys. . 134

Co/CuPt(6%) Samples. . . . . . . . . . . . . . . 136
Co/CuMn(7%) Samples. . . . . . . . . . . . . . 138
Comparison with Valet-Fort Theory... . . . . . . . . . 143
Co/CuNi(l4%) Samples. . . . . . . . . . . . . . . 146

Reconsideration of the Co/Cu Data. . . . . . . . . . . . 151

vii

 

 

7 Sum

 

6. 2 Giant Magnetoresistancc in Hybrid Multilayers. .
CIP- MR 1n Hybrid Multilayers.
Blocking Temperature and Magnetic Anisotropy .
Raising the Blocking Temperature (a) Variation with (C0.
Angular Dependence of MR.
Measurement of Coupling F 1elds . .
Raising the Blocking Temperature (b) Addition of Sin.

Raising the Blocking Temperature (c) Growth 1n 3 Magnetic Field. .

GMR 1n CPP hybrid Multilayers”
6.3 Inverted Giant Magnetoresistance.

7 Summary and Conclusions. .

viii

155
157
164
169
175
176
179
184
188
200

214

 

 

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2.1

3.1
3.2

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

LIST OF TABLES

Target voltages and currents and the resulting deposition rates for sputtered metals

usedinthisstudy.. . . . . . . . . . . . . . . . . . . . 27
Measured impurity concentrations of targets. . . . . . . . . . . . 33
Observed x-ray structure peaks. . . . . . . . . . . . . . . . 37
Slopes and intercepts for equation 5.2 above. . . . . . . . . . . . 82
CPP and CIP values at H0, Hp and HS for [ Co(1 .5nm)/Cu(tCu) ]xN. . . . . 83
CPP and CIP values at H0, Hp and HS for [Co(6. 0nm)/Cu(tCu)]xN. . . . . 84
CPP and CIP values at Ho, Hp and HS for [Co(tCo=tC,,)/Cu(tc,,)]xN. . . . . 84
Slopes and intercepts of the three CPP Co/Cu series. . . . . . . . . 85

Summary of ﬁtted Ho parameters (see text for ﬁt description) and independent
measurements. A 2ARNWCO of 6.11’Qm2 was assumed in the ﬁt. . . . . . 93

CPP values at H0, Hp, HS and HD for the [Py(1.5nm)/Cu(tCu)]xN series. The data
above the blank row were used in Fits A and B, given later. . . . . . . 103

CPP values at Ho, Hp, HS and HD for the [Py(6.0nm)/Cu(tc,)]xN series. The data
above the blank row were used in the Fits A and B, given later. . . . . . 104

CPP values at H0, Hp, HS and HD for the [Py(tpy=tc,,)/Cu(tc,,)]xN series. The data
above the blank row were only used in Fit B, given later. . . . . . . . 105

5.10

5.11

5.12

6.1

6.2

6.3

6.4

6.5

6.6

6.7a

6.7b

6.8a

Summary of ﬁtted parameters for Fit A. A ZARNb/py of 65me2 and a pm, of 5.0
nan were assumed for each ﬁt. The uncertainties in Set 1 and Set 2 have
adjusted so that the x2 will match the degrees of freedom for each ﬁt, see the
text. 116

Summary of ﬁtted parameters for Fit B. A ZARNb/Py of 65me2 and a p0, of 5.0
nﬂm were assumed for each ﬁt. The uncertainties in Set 1 and Set 2 have
adjusted so that the x2 will match the degrees of freedom for each ﬁt, see the text.

. 119

Py resistivity measurements on ﬁlms made along with CPP samples in several

CPP values at HO, Hp and HS for the [Co(6. 0nm)/CuPt(tCuP,)]xN series. The total

sample thickness rs 720nm... . . . . . . . . . . .137
CPP values at H0, Hp and HS for the [Co(6. 0nm)/CuMn(tCuM,,)]xN series. The
total sample thickness IS 720nm. . . . . . . . . . . . .138
CPP values at HO, Hp and HS for the [Co(6. 0nm)/CuGe(tCuGe)]xN series. The total
sample thickness 15 360nm. . . . . . . . . . . . . .140
Estimated parameters for Cu alloys. . . . . . . . . . . . . . . 144

CPP values at H0, Hp, HS and HD for the [Co(6.0nm)/CuNi(tC,,N,.)]xN series. The
totalsamplethicknessis720nm.. . . . . . . . . . . . . . .147

Values of shape anisotropy for oblate spheroids of Co (MS=1422 emu/cm3). . 166

Magnetic quantities for [Co(tCJ/AgM. 0nm)/Py(4. 0nm)/Ag(4. 0nm)]x10 attributed
totheCoclusters. . . . . . . . . . . . .170

CIP Magnetoresistancc and sensitivity measurements at both liquid He and room
temperatures for the [Co(tCy/Ag(4.0nm)/Py(4. 0nm)/Ag(4.0nm)]x10 series. . 170

Magnetic quantities for [Co(tCJ/CuM. 0nm)/Py(4. 0nm)/Cu(4. 0nm)]x10 attributed
totheCoclusters. . . . . . . . . . . . . . . . .171

6.8b

6.9

6.10a

CIP Magnetoresistancc and sensitivity measurements at both liquid He and room
temperatures for the [Co(tCJ/Cu(4.0nm)/Py(4. 0nm)/Cu(4. 0nm)]x10 series. . 171

Measurements of the Py coercive ﬁeld, HC, and the coupling ﬁeld, HCP”. between
the Co and Py layers for the [Co(tCJ/NM/PyM. 0nm)/NM]><10 series. . . . 178

Magnetic quantities for [CoSm(tCoS,,,)/Cu(4. 0nm)/Py(4 0nm)/Cu(4 0nm)]x10
attributed to the CoSm cluster... . . . . . . .180

6.10b CIP Magnetoresistancc and sensitivity measurements at both liquid He and room

6.11

6.12

temperatures for the[CoSm(tCos,,,)/Cu(4. 0nm)/Py(4. 0nm)/Cu(4. 0nm)]x10 series.

Parameters used in ﬁtting the CPP [Co(O. 4nm)/Ag(4. 0nm)/Py(tp_,)/Ag(4 0nm)]x20
samples............. .........191

CPP-AR values for the [ Co(0. 4nm)/Ag(4. 0nm)/Py(tpy)/A g(4. 011m) ]x20 series. 199

xi

1.1

1.2

1.3

1.4

1.5

1.6

2.1

2.2

LIST OF FIGURES

Flow of the measuring current for the CIP and CPP geometries. . . . . . 2

The ﬁeld dependent resistance of a [Co(6. 0nm)/Cu(6. 0) ]><60 multilayer in the a)
CPP and b) CIP geometries. For comparison, c) the ﬁeld dependent CPP resistance
of a Nb/Co(9. 0nm)/Nb trilayer is shown. Note that the change in resistance for the
single thin ﬁlm of Co is orders of magnitude smaller than it is for the multilayer. .

A representation of the antiparallel (AP) and parallel (P) conﬁgurations of the F
layermoments......................7

Schematic representation of the density of states in the s and d bands of a) a non-
magnetic metal and b) a ferromagnetic metal, like Co. . . . . . . . . . 8

The sample shape used for measuring both the CPP resistance (R=V/1) and the CIP
resistance (R=v/i). The CIP resistance is dominated by the two narrow strips above
and below the circular region of the sample. . . . . . . . . . . . . 10

Pictured in a) is a schematic of prototype GMR sensor, using a lithographically
patterned Co/Cu multilayer. Plotted in b) is the output of such a sensor. The
narrower peaks are the teeth of the gear passes the sensor. The missing tooth is
clearly visible as it passes. The peak to peak voltage corresponds to a 25% drop 1n
thesensor’sresistance. . . . . . . . . . . . . . 13

A cross section of the triode magnetron sputtering gun used in fabricating the
samplesforthisstudy....................18

A schematic of the sputtering systems is shown. Chimneys are able to rotate over
the sputtering guns to block deposition (chimney without hole) or columnate a
deposition beam (chimney with hole). A computer controlled stepping motor

xii

 

 

 

 

 

 

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2.3

2.4

2.5

3.1

3.2

3.3

3.4

3.5

3.6

3.7

rotates a substrate into position. Only three of the four guns are shown for clarity.
l9

Diagram of the Sample Positioning and Masking Apparatus (SPAMA) plate
layout.........................22

Diagrams for the various substrate holders used during the course of this study.
Holder a) was used to make CIP multilayers and single layer thin ﬁlms. Holder b)
was used to make the CPP samples. Holder c) was used to sputter CIP multilayers
in a strong magnetic ﬁeld. Dashed lines indicate the shutters which are hidden from
view when looking down through the substrate hole. The shutters could be rotated
about their center by pulling on one of the pins for rotating with an externally
controlledwobblestick.. . . . . . . . . . . . . . . . . . . 23

Schematic cross section of the cooling system with CIP holder (Figure 2.4a). . 25

Schematic representation of both a) low angle and b) high angle x-rays incident on a
multilayer exhibiting columnar growth. . . . . . . . . . . . . . 36

9-29 spectrum for [Co(6. 0nm)/Cu(9. 0nm)]x48. The bulk values of Nb (110),
Cu(lll) and Co(0001)areshown forcomparison. . . . . . . . . . 38

0-20 spectrum for [Co(6.0nm)/CuPt(9.0nm)]x48. The bulk values of Nb (110),
Cu(lll)and Co(0001)areshown for comparison. . . . . . . . . . . 38

0-29 spectrum for [Co(6.0nm)/CuNi14%(9.0nm)]x48. The bulk values of Nb (110),
Cu(1 1 1) and Co(0001) are shown for comparison. . . . . . . . . . . 39

Nb strip proﬁled via Dektak, note the scale change from 11m to pm for the vertical
andhorizontal,respectively. . . . . . . . . . . . . . . . . 44

Schematic of CIP-MR measurement for CIP ﬁlm. H is typically applied
longitudinally, along the direction of the measuring current. . . . . . . 45

SchematicofSQUIDmeasuringcircuit. . . . . . . . . . . . . . 47

xiii

 

 

 

4.4

4..
i).

_l-
be

 

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

Schematic representation of the density of states for 3d transition metals. In a) there
are no unpaired spins so ferromagnetism would not be exhibited, however, b) does
have a spin-split density of states in the 3d band similar to Co which is a
ferromagnet.(afterRef.2).. . . . . . . . . . . . . . . . . . 53

Schematic representation of electrons propagating along the z-axis, perpendicular to

the layers for F l and F2 a) antiparallel and b) parallel. Here, or = p‘L/pT , is the
sameforallFlayers.....................54

Equivalent circuit forthe two channel model.. . . . . . . . . . . . 56

 

Theoretically predicted behavior of JZR(HO)[AR(HO)—AR(HS)] with the
bilayer number, N, using the Valet-Fort model for if; = co and several different

values of (’3‘ listed in the ﬁgure (1301:10an and pCo=86an). The total
multilayerthicknessis720nm. . . . . . . . . . . . . . . . . 63

 

Theoretically predicted behavior of JAR(H0)[AR(HO) - AR(HS)] with the
bilayer number, N, using the Valet-Fort model for KC“ = so and several different

values of If," listed in the ﬁgure ((10510an and pCo=86an). The 10000nm and
lOnm predictions are nearly indistinguishable. The total multilayer thickness is
720nm. . . . . . . . . . . . . . . . . 64

Effects of spin accumulation and relaxation at the interface of two ferromagnetic
metal, F. and F 2 on the chemical potential, Au, the pseudoelectric ﬁeld, F, and the
spin currents, Ji, for an AP alignment of the moments of F 1 and F2. . . . . 66

Schematic representation of spin accumulation and relaxation effects for a
multilayer on the chemical potential, u, the pseudoelectric ﬁeld, F, and the spin
currents, Ji for the AP state, a), b) and c); and the P state, d), e) and f). . . . 70

Spin dependent scattering of a) AP and b) P states for inverse (positive) GMR.

Scattering is schematically represented as taking place only at the F /N interface for
clanty74

xiv

 

 

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5.4

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5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

The ﬁeld dependence of a) the CPP resistance, b) the CIP resistance and c) the
magnetization of a [Co(6. 0nm)/Cu(6. 0nm) ]x60 multilayer. . . . . . . . 78

Magnetoresistancc of Fe(5nm)[Co(1.5nm)/Cu(tCu)]xN plotted as a function of tCu,
the copper thickness. AF indicates antiferromagnetic coupling. The lines serve as
guidestotheeye.. . . . . . . . . . . . . . . . . . . . . 81

 

Plots of a) ART vs. N-I and b) \BRT(HO)[AR,(HO) - ART(HS)] vs. N-I for
[C 0(1 . 5nm)/C 110C”) ]xN multilayers. In a) the lines represent
ART(H0) and ART(HS) and in b) the line represents
J ART(!-I0 )[ AR 7(H0) — AR 7-(H s )] using the parameters derived from the global ﬁt
to all three sets of data given in Table 5.6. Total sample thickness is 360nm. . 86

 

 

Plots of a) ART vs. NJ and b) JART(H0)[ART(H0) - ART(HS)] vs. N-I for
[ Co( 6. 0nm)/Cu(tc,,) ]xN multilayers. In a) the lines represent
ART(H0) and AR T(H s) and in b) the line represents
JART(HO )[ART(H0) — AR T(HS)] using the parameters derived from the global ﬁt
to all three sets of data given in Table 5.6. Total sample thickness is 720nm. . 87

 

 

Plots of a) ART vs. NJ and b) JART(H0)[ART(H0) - ART(HS )] vs. N-I for
[Co(tCo=tC,)/Cu(tCu)]xN multilayers. In a) the lines represent
ART(H0) and ART(HS) and in b) the line represents
JART(H0 )[ART(H0) — ART(HS)] using the parameters derived ﬁom the global ﬁt
to all three sets of data given in Table 5.6. Total sample thickness is 720nm. . 88

 

ART vs. the bilayer number N-l for the Fe(5nm)[Co(1.5nm)/Cu(tCu)]xN system.

The lines represent AR 4P and AR; using the parameters derived from the global ﬁt
to all three sets of data given in Table 5.6 with H0 as the AP and then Hp as the AP
state. . . . . . . . . . . . . . . . . . . . . . . . . . 95

The ﬁeld dependence of a) the CPP resistance and b) the magnetization for a
[Py(6.0nm)/Cu(8.4nm)]x25 multilayer. Note that the resistance changes over a
much smaller ﬁeld range then for the Co/Cu multilayer shown in Figure 5.1. . 100

The CPP-MR for Ho (squares) and Hp (diamonds) is plotted for the
Py(5.0nm)[Py(1.5nm)/Cu(tc,)]xN series. The CIP-MR for Hp (triangles) is plotted
for the slightly different Py(5. 0nm)[Py(1.5nm)/Cu(tc,,)]x 14 series to compare with

XV

5.9

Parkin4 (ﬁlled circles). Measurements were made at 4.2K except for Parkin’s which
weredoneat300K.....................102

The ['1 values for Co/Cu all three multilayers series. The lines indicate the average
I'Ivalueforeachseries.. . . . . . . . . . . . . . . . . . .107

5.10 The ratio II plotted as function of the bilayer number, N for a) the tpy=1.5nm series,

5.11

5.12

5.13

5.14

5.15

5.16

5.17

the (”=6.0nm series and the tpy=tcu series. Unﬁlled symbols are H0 values and
ﬁlled symbols are HD values. Generally IID points are directly above the 1'10 values
for the same sample. This is indicated in Figure 5.11a by arrows for a few

representative samples. . . . . . . . . . . . . . . . . . . . 109
The magnetization hysteresis curve for a multilayered sample with
[Py(30.0nm)/Cu(30.0nm)]x6 at T=5.0K. The coercive ﬁeld for this sample was
1.70e. The insert shows that the sample saturates quickly. . . . . . . . 112
The HO and HS data for the Py(5. 0nm)[Py(1.5nm)/Cu(tc,)]xN series. . . . . 113
The Ho and HS data for the [Py(6. 0nm)/Cu(tc,,)]xN series. . . . . . . . 114
The Ho and HS data for the [Py(tpy=tc,,)/Cu(tc,,)]xN series. . . . . . . . 114
AR1(HO) and AR1-(Hs) plotted as a function of the corrected bilayer number, N-l for

the Py(5.0nm)[Py(1.5nm)/Cu(tc,,)]xN. Total sample thickness is held constant at
360nm. Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11,
while Fits A and B in b) use Set 2 parameters ﬁom Tables 5.10 and 5.11. Points
withﬁlledsymbolswerenotusedinﬁts.. . . . . . . . . . . . .122

The square root data plotted as a function the reduced bilayer number, N-l for the
Py(5.0nm)[Py(1.5nm)/Cu(tCu)]xN. Total sample thickness is held constant at
360nm. Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11,
while Fits A and B in b) use Set 2 parameters from Tables 5.10 and 5.11. Points
withﬁlledsymbolswerenotusedinﬁts.. . . . . . . . . . . . .123

ART(HO) and ART(HS) plotted as a function of the corrected bilayer number, N-l for
the [Py(6.0nm)/Cu(tc,)]xN. Total sample thickness is held constant at 360nm. Fits
A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits A and
B in b) use Set 2 parameters from Tables 5.10 and 5.11. Points with ﬁlled symbols
werenotusedinﬁts.....................126

xvi

5.18 The square root data plotted as a function the reduced bilayer number, N-l for the

Py(5.0nm)[Py(1.5nm)/Cu(tCu)]xN. Total sample thickness is held constant at
360nm. Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11,
while Fits A and B in b) use Set 2 parameters from Tables 5.10 and 5.11. Points
with ﬁlled symbols were not used in ﬁts. . . .. . . . . . . . . . 127

5.19 AR1-(HO) and AR1(HS) plotted as a function of the corrected bilayer number, N-l for

the [Py(th=tCu)/Cu(tc,,)]xN. Total sample thickness is held constant at 360nm.
Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits A
and B in b) use Set 2 parameters ﬁom Tables 5.10 and 5.11. The Best Fit H5 line is
a least squares ﬁt to the HS data. Points with ﬁlled symbols were not used in ﬁts.
Hodatawasnotusedineitherﬁt” . . . . . . . . . . . . . . .128

5.20 The square root data plotted as a function of the corrected bilayer number, N—l for

6.1

6.2

6.3

the [Py(tpy=tCu)/Cu(tC,)]xN. Total sample thickness is held constant at 360nm. Fits
A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits A and
B in b) use Set 2 parameters from Tables 5.10 and 5.11. The Best Fit HS line is a
least squares ﬁt to the HS data. H0 data was not used in either ﬁt. . . . . . 129

Plotted are both the measured and predicted values using the Valet-Fert theory for
the quantity J AR (H0 )[AR (H0) — AR (HS)] as a function of N, the bilayer number.
The Valet-Fert predictions use (3’ = 00 and I?“ = 2.8nm, 8.0nm and co with the

appropriate Felix, given in table 6.4. The Co/CuGe samples have a total thickness
360nm, while all other samples are 720nm thick. The ﬁlled symbols have different
CuX thickness than those indicated on the top axis.. . . . . . . . . . 139

 

A comparison of AR7(H)-AR7(HS) versus H for samples with the same nominal
bilayer thickness a) [Co(6.0nm)/Cu(9.0nm)]x48, b) [Co(6.0nm)/CuGe(9.0nm)]x24
and c) [Co(6.0nm)/CuPt(9.0nm)]x48. The lines are guides to the eye. . . . 141

Plotted are H ratios as a function of the N, the bilayer number for Co/Cu, Co/CuMn,
Co/CuPt and Co/CuGe samples with tC0=6.0nm. The ﬁlled symbols have to“
different from those indicated on the t0p axis. The solid line represents the average
IIratiofortheCo/Cuseries. . . . . . . . . . . . . . . . . .143

xvii

 

 

6.4

6.6

6.8

6.9

 

6.4

6.5

6.6

6.7

6.8

6.9

Plotted are both the measured and predicted values using the Valet-Fert theory for
the quantity \/ AR (I-lo )[AR (H0) — AR (H5 )]as a function of N, the bilayer number.
The Valet-Fert predictions use (if z co and Kg.“ = 10nm and 00 with the

appropriate pCux, given in Table 6.4. The total thickness of multilayers from both
series is 720nm. The ﬁlled symbols have different Cu thickness than those
indicated on the top axis. . . . . . . . . . . . . . . . . . 148

 

Plotted are H ratios as a function of the N, the bilayer number for Co/Cu and
Co/CuNi samples with tCo=6.0nm. The ﬁlled symbols have to, different from those
indicated on the top axis. The solid line represents the average I1 ratio for the
Co/Cuseries.......................149

Valet-Felt predictions for the [Co(tCo=tCu)/Cu(tCu)]xN series using the Co/Cu

parameters from table 5.6 together with a) assumed values of If," :00 and

(3“ = 50nm, 75nm, 100nm and 00 ; and with b) assumed values of if,” = 00 and
€S}=l.0nm,2.5nm,5.0nmandoo. . . . . . . . . . . . . . .153

The ﬁeld dependence for a [Co(0.4nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4.0nm)]x10
sample of a) the CIP-MR and b) the magnetization at 4.2K. In b) the hysteresis of
the Co and Py is shown schematically. The curve label hybrid in b) is an actual
measurement......................159

Schematic illustration of a pinholes bridging Py and Co. With island-like Co
clusters only a small fraction of the Co ferromagnetically couples to the Py layers.
. 161

The ﬁeld dependence of the CIP-MR at 300K for a hybrid sample with
[Co(0.4nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4.0nm)]x10. Superparamagnetism of the Co

clusters has drastically reduced the MR observed at 4.2K (compare with Figure
6.7a)..........................l62

6.10 The temperature dependence of the magnetization is plotted for the hybrid

[Co(0.6nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4.0nm)]x10. Initially the sample is cooled in
zero ﬁeld (ZFC) and then a lOOOe ﬁeld is applied to saturate the Py layers. For the
ﬁeld cooled (FC) curve the sample is allowed to cool in the lOOOe ﬁeld. The peak
in the ZFC curve deﬁnes the blocking temperature. . . . . . . . . . 163

xviii

ll

 

 

6.11

6.13 L

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COL.
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PHIL

6.11 The blocking temperature, T B, is plotted for [Co(tCJ/NM/PyM. 0nm)/NM ]x10
samples with NM=Ag(4.0nm) or Cu(4.0nm) as function of ’Co for both series. The
lines are guides to the eyes. . . . . . . . . . . . . . . . . . 172

6.12 The a) CIP-MR and b) the maximum slope, S = AR / AH, of the CIP-MR are plotted
as a function of IQ, for samples of [Co(0. 6nm)/NM/Py(4. 0nm)/NM]x10 with
NM=Ag(4.0nm) or Cu(4.0nm). The lines are guides to the eye. . . . . . . 174

6.13 Comparing major and minor hysteresis loops of the magnetization shows a weak
coupling ﬁeld between the Py layers and the Co clusters. The minor loop extends
zi450e from the Py coercive ﬁeld. The displacement of the minor loop from H=0
represents the coupling ﬁeld. Here the coupling is ferromagnetic. These hysteresis
loops are for [Co(0.4nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4.0nm)]x10. . . . . . 177

6.14 The coupling ﬁelds for samples of [Co(tCJ/NM/PyM.0nm)/NM]x10 plotted as a
function of tCo, where NM=Ag(4. 0nm) or Cu(4.0nm). The open (ﬁlled) symbols are
measurements of the coupling taken from resistance (magnetization) hysteresis
loops. Nearly every sample shows ferromagnetic coupling. Plotted along with the
coupling ﬁelds is the Py coercive ﬁeld for each sample. . . . . . . . . 178

6.15 The ﬁeld dependence of a) the CIP-MR and b) the magnetization at 4.2K for a
[CoSm(0.6nm)/Cu(4.0nm)/Py(4.0nm)/Cu(4.0nm)]x10 sample. . . . . . . 181

6.16 The a) CIP- MR and b) the maximum slope, S: AR / AH, of the CIP- MR are plotted
as a function of tF for samples of [F (IF)/Cu(4 0nm)/Py(4. 0nm)/Cu(4. 0) ]x10 where
F -—C0 or CoSm. Lines are guides to the eye... . . . . . . . .182

6.17 The blocking temperatures of [F (IF)/Cu(4. 0nm)/Py(4. 0nm)/C u(4. 0) ]x10 samples
plotted as function of t,.—, where F =C0 or CoSm. Lines are guides to the eye. . 183

6.18 The magnetization hysteresis curves along (squares) and normal (circles) to the in-
plane easy axis for a multilayer of [Py(4.0nm)/Ag(4.0nm)]x20 at T=5.0K. The
direction of the induced easy axis in the Py layers was deﬁned during growth by a
2.6kOe magnetic ﬁeld (see Figure 2.6).. . . . . . . . . . . . . . 185

6.19 The magnetization hysteresis curves along (circles) and normal (triangles) to the in-

plane easy axis for a multilayer of [Co(6.0nm)/Ag(6.0nm)]x20 at T=5.0K. The
direction of the induced easy axis in the Co layers was deﬁned during growth by a

xix

6.20

6.21

6.22

6.23

6.24

6.25

6.26

6.27

2.6kOe magnetic ﬁeld (see Figure 2.6). A similar sample without an induced
anisotropy is also shown for comparison (squares). . . . . . . . . . 186

In a) AR(H) for [Co(0.4nm)/Ag(4.0nm)/Py(10.0nm)/Ag(4.0nm)]x20 is plotted. The
large saturation ﬁeld is indicative of island-like Co layers. Plotted in b) is AR(H) in
the vicinity of the ﬂipping Py moments after the trapped ﬂux has been released (see
text). The slope, AR/R, is a factor of 10 greater in b) than in a) the region where the
Pyﬂips.........................189

In a) AR(HP) and AR(HS) are plotted as a function of tpy. Plotted in b) as a function
of tpy is AAR=AR(Hp)-AR(HS). In both a) and b) the lines represent the values

predicted by the two channel model assuming ta, =04, 0.6 and 0.8nm along

want/gum”.....................192
Equivalentresistormodelforfff’ﬁO.. . . . . . . . . . . . . .193

In a) AR(HP) and AR(HS) are plotted as a ﬁlnction of IF). Plotted in b) as a function
of tpy is AAR=AR(HP)-AR(HS). In both a) and b) the lines represent the values

predicted by the two channel model assuming t'Co = 0.4, 0.6 and 0.8nm along with
r3=o.........................l9o

In a) AR(I-Ip) and AR(HS) are plotted as a function of tpy. Plotted in b) as a function

of tpy is AAR=AR(HP)-AR(HS). In both a) and b) the lines represent the values

predicted by the two channel model assuming {Co = 0.6nm and either [5” = 0

oriffy=oo........................198

Schematic representation of the structure of [M ,/Cu(tCu)/M/Cu(tCu) ]x5 where
M,=Fe(1.2nm)/Cr(0.4nm)/Fe(1.2nm) and M2=Fe(1.5nm). . . . . . . . 201

The low ﬁeld behavior at 300K of a) the CIP-MR and b) the magnetization for
[M,/Cu(1.6nm)/M/Cu(1.6nm)]x5. . . . . . . . . . . . . . . . 203

The variation of the MR with the Cu spacer thickness for a) Fe/Cu multilayers ﬁom
Petroﬁ‘, et al.42’43 and b) [M ,/Cu(t(~,,)/M/Cu(tc,,) ]x5 samples where M, consists of
an Fe(1.2nm)/Cr(0.4nm)/ Fe(1.2nm) trilayer and M2 is a single Fe(1.5nm) layer. .

XX

6.28 The high ﬁeld behavior of a) the CIP-MR and b) the magnetization of the sample in
Figure 6.28. The hysteresis is not seen on this scale. . . . . . . . . . 207

6.29 The ﬁeld dependence of the CPP resistance is plotted for a multilayer of
[Co(0.4nm)/Cu(2.3nm)/Fe V(6.0nm)/Cu(2.3nm)]x20. The V concentration is 27%.
Here the HS resistance is the high resistance state. The MR of these samples are
lessthan3%.......................210

xxi

Chapter 1:

Introduction to Giant
Magnetoresistancc

Magnetoresistancc is the change in electrical resistance of a material in response to a
magnetic ﬁeld. All metals, pure or alloyed, have a magnetoresistance (MR) due to the
Lorentz force which arises from the motion of electrons in a magnetic ﬁeld. This effect
increases a material’s electrical resistivity with an applied magnetic ﬁeld. The effect is
very small at room temperatures1 and will not be of concern in this work. In very pure
metals, the MR changes monotonically with increasing applied ﬁeld, and the MR is
deﬁned relative to the initial H=0 resistance.

Some ferromagnetic alloys such as permalloy (N isoF e20) exhibit an enhanced MR due
to the spontaneous resistivity anisotropy of the material. (Permalloy will be represented
by the symbol Py unless otherwise stated.) With this type of magnetoresistance (AMR)
the resistance of a material depends on the relative orientation of the current through the

material and the magnetization of the materialz. Typically this effect gives MR’s of a few

2
percent. The AMR of permalloy ﬁlms has been utilized since 1991 by IBM for read

heads in hard disk drives3.

Technological advances during the past decade have allowed almost atomic control of
the deposition process in making thin metallic ﬁlms. This has allowed the study of
artiﬁcially grown layered metallic structures. Of great interest both academically and
technologically, is the recently emerging ﬁeld of magnetic multilayers. A magnetic
multilayer is composed of a single, repeated unit cell, typically a ferromagnetic (F) layer
such as Co and a “normal”, non-magnetic (N) layer like Cu, written as F/N or Co/Cu.
The unit cell may indeed be more complex4, as will be demonstrated later, and recently
the properties of magnetic multilayers composed of only F metals5 have been explored.
These structures exhibit large changes in resistivity in response to a magnetic ﬁeld. This

type of magnetoresistance is called Giant Magnetoresistancc (GMR).

CIP direction

CPP direction

 

F/N interface

Figure 1.1: Flow of the measuring current for the CIP and CPP geometries.

 

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For layered GMR structures there are two types of MR measurements. The resistance

is measured with either the current ﬂowing along the plane of the layers or perpendicular
to the plane of the layers. These are, respectively, the so called current-in-plane or CIP
resistance and the current-perpendicular-to—plane or CPP resistance, illustrated in Figure
1.1.

Graphs of CIP and CPP resistance as a function of ﬁeld for a Co/Cu sample are
shown in Figure 1.2. One of the differences between the MR of metals and that of
magnetic multilayers is that the MR of magnetic multilayers usually saturates at a
saturation ﬁeld of HS as in Figure 1.2. The saturated resistance represents a better deﬁned
state of the system than the H=0 state since the magnetic conﬁguration of the sample in
the HS state is known. (Further discussion of this is given later.) Consequently it is more

useful to deﬁne the MR by equation 1.1.

R(Hs)

 

Where R(I-I) is the resistance in ﬁeld H.

This study will focus on three speciﬁc states of a multilayer’s CPP resistance. As
deﬁned in Figure 1.2, these states are: (1) The initial, as prepared, state of the resistance,
Ho, usually the sample’s highest resistance state. (2) The saturated state, HS, the sample’s
resistance after all the F layer moments have been aligned. (3) The peak state, Hp, the
highest sample resistance aﬁer saturation. A demagnetized state, HD, will also be brieﬂy

discussed.

R(‘PP (11(2)

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L 1

 

 

 

' -1 .01-0.8 L -0.6 L 0.4-0.2. 0.0 L 0.2 A 0.4 A 0.6 L 0.8 L 1.0
H (kOe)

Figure 1.2: The ﬁeld dependent resistance of a [Co(6.0nm)/Cu(6.0)]x 60 multilayer in the
a) CPP and b) CIP geometries. For comparison, c) the ﬁeld dependent CPP resistance of
a Nb/Co(9.0nm)/Nb trilayer is shown. Note that the change in resistance for the single
thin ﬁlm of Co is orders of magnitude smaller than it is for the multilayer.

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Although unusual MR effects in magnetic multilayers were reported earlier6, the
discovery of MR in magnetic mulilayers is attributed to Albert Fert’s group at the
Université of Paris-Sud in Orsay, France7, who observed large changes in the resistivity
of artiﬁcially layered F e/Cr ﬁlms. Upon saturating these Fe/Cr multilayers in a 20kOe
applied ﬁeld, they observed a reduction of up to 50% in the resistivity. This effect was
given the name Giant Magnetoresistancc (GMR) because the magnitude of the MR is
much larger than the MR observed in the isolated F metal. Since then numerous groups
have reported GMR effects in many different F/N systems. Most notably Stuart Parkin of
IBM Almaden has provided a systematic study of the elements as a function of their
position in the periodic tables.

The Fe/ Cr multilayer experiments done in Fert’s groups were prompted by
Griinberg’s 1986 discovery of antiferromagnetic exchange coupling between the Fe
layers in trilayer sandwiches of Fe/Cr/Fe for a Cr thickness of 1.0nm. Later in 1990,
Parkin found that this exchange coupling oscillated between antiferromagnetic and
ferromagnetic depending on the thickness of the non-magnetic spacer layer").
Oscillations in the MR accompanied the oscillations in the exchange coupling (see Figure
5.2 for an example of such oscillations). The strength of the coupling also diminished

s,10,1 1 12
and others

with increasing spacer thickness. Subsequent investigations by Parkin
showed that this oscillating exchange coupling existed for several different F/N
multilayered systems.

The mechanism responsible for GMR is the spin-dependent scattering of the

conduction electrons at the F/N interfaces and in the bulk F layers. In a ferromagnetic 3d

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transition metal, the d band is shifted in energy becoming asymmetric for spin-up and
spin-down electrons. Later we will show that this leads to conduction electron scattering
which depends on whether the electrons have their spins oriented parallel or antiparallel
to the local magnetization. Neglecting spin-ﬂips, these two spin channels independently
cany the current in parallel.

In a multilayer, the magnetization of each F layer deﬁnes up and down for the
electron spins. For an appropriate choice of the thickness of the N metal, exchange
coupling will magnetically order the multilayer antiferromagnetically (AF )8’10’11’12 , as
shown schematically in Figure 1.3. Strong AF coupling forces adjacent F layer
magnetizations to be antiparallel. (This antiparallel conﬁguration of F layer
magnetizations will be designated as the AP state of the sample.) Therefore conduction
electrons that were spin up in one layer are now spin down in the next. As a way of
keeping track of each spin channel, an absolute spin direction may be deﬁned as the
direction of the applied ﬁeld. In this absolute ﬁame, the scattering rates now depend
upon whether electrons have their spins oriented either parallel or antiparallel to the local
magnetization, i.e. the magnetization of a particular F layer. In the AP state, electrons in
both the spin up and spin down channels undergo the same amount of scattering over the
length of the multilayer. With a sufﬁciently large applied ﬁeld the exchange coupling
can be overcome, forcing every F layer to be parallel to one another. (The parallel
conﬁguration of F layer magnetizations will be designated as the P state.) In the P state,
electrons in one spin channel (down for example) will be scattered less than electrons in

the other spin channel throughout the entire multilayer. This in effect short circuits the

7

current through one of the spin channels (down in this example) resulting in a lowering of
the sample’s overall resistance. The resulting change in resistivity is generally negative
(the resistance drops), but later in this study a positive GMR will be discussed in detail,

with the main point that multilayers may easily be designed to meet speciﬁc needs.

H:

 

F/N interface

Figure 1.3: A representation of the antiparallel (AP) and parallel (P) conﬁgurations of the
F layer moments.

There are at least two possible causes for spin dependent scattering. The ﬁrst cause
will be treated in detail in section 4.1 and reﬂects that electron scattering from impurities
depends on the density of states of the spin up and spin down electrons. In Figure 1.4 a

schematic representation of the density of states is shown for a) a normal metal and b) a

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ferromagnetic metal like Co. The scattering of an electron depends upon whether its spin

is parallel or antiparallel to the local magnetic moment, a result of the spin-split density
of states in F metals like Fe, Co and Ni. This spin dependence in the d band causes
different scattering rates for spin up electrons and spin down electrons as they propagate
through the sample. The second cause of spin dependent scattering is that the multilayer
potential is itself spin dependent so that electrons in the spin down channel experience a
potential different from those electrons in the spin up channel. Applying a ﬁeld to the
sample changes the potentials in each channel which correspond to changes in the

scattering rates of both spin up and spin down electrons.

Density of states

       
     
 

    

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Figure I. 4: Schematic representation of the density of states in the s and d bands of a) a
non-magnetic metal and b) a ferromagnetic metal, like Co.

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Experimentally the CIP resistances typically range from 0.010 to 1.00 while those

for the CPP depend critically on the cross sectional area of the sample since the length of
a multilayer is typically between 100-1000nm. In these studies an in-situ masking system
gives a sample area of z 1.2 m2, illustrated in Figure 1.5, resulting in CPP resistances of
lO-lOOnQB. The current is injected into the Nb pads labeled by I in Figure 1.5. At 4.2K
the Nb strips are superconducting, forming an equipotential surface above and below the
multilayer. Since the superconducting Nb leads are equipotentials the current distribution
will be uniform over the cross sectional area of the sample, which is important for a direct
measurement of the intrinsic MR. The current takes the path of least resistance from the
top Nb lead, perpendicularly through that section of multilayer sandwiched between the
Nb strips and into the bottom Nb lead. The multilayer is not superconducting and a
potential drop occurs across the multilayer. The large cross sectional area of the
multilayer relative to its total thickness requires attaching a sensitive detector, namely a
SQUID circuit, across the Nb pads labeled V in Figure 1.5 to measure the potential dr0p.
Recently, M.A.M. Gijs, et al.14 used complex lithographic techniques to reduce the
sample’s area to a few umz, giving a CPP resistance of 0.010. Another group at the
Naval Research Laboratory headed by G. Prinz has also used lithographic techniques to
create pillars with small cross sections (less than 5 pmz) for CPP-MR measurements of
Spin valves”. CPP-MR measurements have also been made on electro-chemically

deposited multilayers of Co/Cu in nanopores 100nm in widthw'n’ls.

10

 

 

i V I Sample

 

 

Top Nb

 

CPP Area, A

Bottom Nb

 

 

Substrate

 

 

 

 

 

Figure 1.5: The sample shape used for measuring both the CPP resistance (R=V/I) and
the CIP resistance (R=v/i). The CIP resistance is dominated by the narrow strips above
and below the circular region of the sample.

In the CIP geometry, the separation of the bulk asymmetry parameters (deﬁned in
chapter 4) from the interface asymmetry parameters is quite difﬁcult. This is due to the
non-uniform current distribution throughout the multilayer, both layer to layer and within
each layer. The current canied by both the F layers and the N layers is connected through
the transmission of electrons at the F /N interfaces. Spin-polarized electrons emerging
from one F layer undergo spin-dependent scattering at the F /N interface or in the bulk F
material of the adjacent F layers. This requires that an electron be able to sample at least

two F layers before being scattered, meaning that it is heavily dependent upon the elastic

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mean free path (mfp) of the electron. For sputtered samples the elastic mfp is generally

less than 10nm. For samples with tp (the F layer thickness) or tN (the N layer thickness)
greater than the elastic mfp, the CIP-MR decreases because the spin polarized electrons
are no longer able to propagate to the next F layer and therefore the fundamental length
scale in the CIP geometry is deﬁned by the elastic mfp.

The CPP geometry is not plagued by this problem, all the electrons must propagate
through the entire multilayer and thereby sample each F layer. It is the chemical potential
(or the eﬁ’ective electric ﬁeld) within a multilayer which varies from layer to layer
causing a build-up of spin at the F/N interfaces. The new phenomenon of spin
accumulation at the PM interfaces only exists for the CPP geometry”. Working to
equilibrate the spin asymmetry at the interfaces are spin relaxation processes. Spin
relaxation may occur by either spin ﬂip scattering”, which mixes the two spin currents
locally, or domain structure in the F layers2 1 , which tends to drive spin currents transverse
to the driving current. It is the interplay between the spin accumulation and spin

relaxation processes that determines the length scale over which large MR’s may be
observed. This length is called the spin diffusion length, (Sf, a measure of the length over
which an electron’s spin remains polarized. The spin diffusion length is typically much
longer than the elastic mfp in the CPP geometry and therefore [sf becomes the
fundamental length scale of the systemzo’zz. Since the current is the same throughout the

sample in the CPP case, it is now possible to experimentally access the spin dependent

scattering parameters which we will refer to as the asymmetry parameters both at the F/N

interface
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interfaces and in the bulk F layers. The CPP geometry is also advantageous from an

applications point of view because the CPP-MR is typically double that of the CIP-MR.
Many in industry have recognized that GMR has a great potential for sensor
applications including read heads in hard disk drives. Experiments done in conjunction
with Dr. H. Holloway of the Ford Scientiﬁc Laboratory in Dearborn, Michigan have
demonstrated the ability of GMR multilayers to detect magnetic ﬁeld pulses of z3000e
up to frequencies of 1.0kHz. Figure 1.6 shows schematically, the layout of the simple
sensing circuit and the timing gear used. A constant current of 1.0mA is put through a
GMR sensing resistor speciﬁcally made by lithography to give a high 1.0kQ resistance.
A biasing ﬁeld supplied by a small magnet puts the sensor in an intermediate resistance
state. As a tooth on the gear rotates past the GMR ﬁlm, the biasing ﬁeld is modiﬁed and
detected by an oscillation in the ﬁlm’s resistance. The changing resistance causes a
voltage ﬂuctuation easily measured with an oscilloscope. Each valley in the output
voltage corresponds to the closest approach of a tooth on the gear to the GMR ﬁlm. The
output clearly shows when the missing tooth has rotated past the sensor. The signal
magnitude is independent of ﬁequency, an advantage compared with induction coil
sensors whose response varies with the frequency of the ﬂuctuations in the ﬂux. GMR
sensors surpass currently used Si Hall effect sensors by at least one order of magnitude in

sensitivity and should be comparable in production cost in the near future.

V (nIV)

\J

 

 

 

 

 

 

 

Sample
Magnet
. . .|
Tlmlng gear
7 I i 1 L
gear tooth passes L_missing gear tooth passes
5 L
L .
3 -L
E 1 ~
> ' .
-1 _ 1
-3 _ _
-5 - a
0 25

t (ms)

Figure 1.6: Pictured in a) is a schematic of prototype GMR sensor, using a
lithographically patterned Co/Cu multilayer. Plotted in b) is the output of such a sensor.
The narrower peaks are the teeth of the gear passing the sensor. The missing tooth is
clearly visible as it passes. The peak to peak voltage corresponds to a 25% drop in the
sensor’s resistance.

14

The spin-dependent scattering processes can in principle take place both at the F/N
interface and in the bulk F metal. The main goal of this study will be to both separate and
quantify the amount of spin-dependent scattering at the F/N interfaces and in the bulk F
layers for Co/Cu and NiMFeIG/Cu multilayers (N i84Fe16 will from here on be referred to as
Py or permalloy unless otherwise noted).

This study utilizes techniques pioneered at MSU to measure the CPP-MR of several
magnetic multilayer systems”. Chapter 2 deals with the fabrication of both CIP and CPP
sputtered magnetic multilayered ﬁhns. Chapter 3 describes the characterization of these
sputtered ﬁlms by several methods including: X-Ray Diffraction (XRD), X-Ray
ﬂuorescence (EDS), Cross-sectional Transmission Electron Microscopy (XTEM) and
Nuclear Magnetic Resonance (NMR). Chapter 4 describes the theory of CPP GMR used
in deriving the spin asymmetry parameters. Chapter 5 contains the measurements and
analyses of the CPP-MR data for the relatively simple Co/Cu and Py/Cu systems to
determine the spin asymmetry parameters of these two systems. Chapter 6 contains
measurements made on more complex multilayer systems including: (1) The variation of
the spin diffusion length of Cu via impurity scattering in Co/CuX multilayers where

=Pt, Mn, Ge and Ni. (2) The creation of large MR’s (both CPP and CIP) at low
temperatures for the Co/Ag/Py/Ag system by utilizing the different coercive forces of Co
and Py, instead of exchange forces, to form an AP state. (3) The ﬁrst measurements of a
positive GMR in both CIP and CPP geometries using layers of Fe, Cr and Cu (CIP) and
Co, Cu and FeV (CPP). All of these are aimed to show the predictability of more

complex systems based on measurements of previously simpler magnetic multilayer

it}; 1111': ~

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15

structures as well as demonstrate that new materials may be engineered to meet very

speciﬁc requirements.

 

' P.M. Levy, Solid State Physics, edited by D. Turnbull and H. Ehrenreich, Vol. 40, p.
397(1995)

2 LA. Campbell and A. Fert, Ferromagnetic Materials, Vol. 3, edited by ER Wohlfarth,
North Holland, p. 752 (1982).

3 K. Derbyshire and E. Korczynski, Solid State Technology, Sept, 57 (1995).

‘ T. Valet, J.C. Jacquet, P. Galtier, J.M. Coutellier, L.G. Pereira, R. Morel, D. Lottis and
A. Fert, Appl. Phys. Lett. 61, 3187 (1992); P. Holody, L.B. Steren, R. Morel, A. Fert, R.
Loloee and PA. Schroeder, Phys. Rev. 850, 12999 (1994); Q. Yang, P. Holody, R.
Loloee, L.L. Henry, W.P. Pratt Jr., P.A. Schroeder and J. Bass, Phys. Rev. B51, 3226
(1995)

5 B. Dieny, V.S. Speriosu, B.A. Gurney, S.S.P. Parkin, D.R. Wilhoit, K.P. Roche, S.
Metin, D.T. Peterson and S. Nadirni, J. Magn. Magn. Mater. 93, 101 (1991); J.M.
Gallego, S.K. Kim, T.J. Moran, D.L. Lederrnan and I.K. Schuller, Phys Rev. B51, 2550
(1995); L.L. Henry, M. Oonk, R. Loloee, Q. Yang, W.C. Chiang, W.P. Pratt Jr. and J.
Bass, submitted to J. Magn. Magn. Mater. (1995).

’ H. Sato, P.A. Schroeder, J.M. Slaughter, W.P. Pratt Jr. and W. Abdul-Razzaq,
Superlattices Microstruct. 4, 45 (1987); E. Velu, C. Dupas, D. Renard, J .P. Renard and J.
Seiden, Phys. Rev. B37, 668 (1988).

7 MN. Baibich, J.M. Broto, A. Fert, F. Nguygen Van Dau, F. Petroff, P. Etienne, G.
Creuzet, A. Friederich and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
' S.S.P. Parkin, Phys. Rev. Lett. 67, 3598 (1991).

9 P. Grunberg, R. Schreiber, Y. Pang, M.B. Brodsky and H. Sowers, Phys. Rev. Lett. 57,
2442 (1986).

'° S.S.P. Parkin, N. More and KP. Roche, Phys. Rev. Lett. 64, 2304 (1990).
“ S.S.P Parkin, R. Bhadra and KP. Roche, Phys Rev. Lett. 66, 2252 (1991).

'2 D.H. Mosca, F. Petroff, A. Fert, P.A. Schroeder, W.P. Pratt Jr. and R. Loloee, J. Mag.
Mag. Mat. 94, L1 (1991).

 

L .4. Bond

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Referen.

magnetic I

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11993).
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l6

 

‘3 W.P. Pratt Jr., S.F. Lee, J.M. Slaughter, R. Loloee, P.A. Schroeder and J. Bass, Phys.
Rev. Lett. 66, 3060 (1991).

” M.A.M. Gijs, S.K.J. Lenczowski and IE. Giesbers, Phys. Rev. Lett. 70, 3343 (1993).

'5 W. Vavra, S.F. Cheng, A. Fink, J.J. Krebs and GA. Prinz, Appl. Phys. Lett. 66, 2579
(1995).

'6 T.M. Whitney, J.S. Jiang, P.C. Searson and CL. Chien, Science 261, 1316 (1993).
‘7 A. Bondel, J.P. Meier, B. Doudin and J .P. Anserrnet, Appl. Phys. Lett. 65, 3019 (1994).

" L. Piraux, J.M. George, J .F. Despres, C. Leroy, E. Ferain, R. Legras, K. Ounadjela and
A. Fert, Appl. Phys. Lett. 65, 2484 (1994).

‘9 Reference 21 has shown that spin accumulation may occur in the CIP geometry if the
magnetic layers are not single domain.

2° T. Valet and A. Fert, Phys. Rev. B48, 7099 (1993); J. Magn. Magn. Mater. 121, 378
(1993)

2‘ S. Zhang and P.M. Levy, Phys. Rev. B50, 6089 (1994).

22 H. Camblong, et al., Phys. Rev. B47, 4735 (1993); S. Zhang and P. Levy, Phys. Rev.
B47, 6776 (1993).

Chapter 2:

Sample Preparation and
Fabrication

2.1 Introduction
The multilayered ﬁlms fabricated for this study were deposited here, at Michigan

State University, using the computer controlled ultra high vacuum DC magnetron
sputtering system located in the basement of the Physics & Astronomy Building. This
system allows deposition from up to four different L.M. Sirnard “Tri-Mag” sputtering
sources in a single run.

During sputtering, Ar ions ﬁ'om an Ar plasma bombard the target material causing
atoms of this material to be ejected. A basic description of the sputtering mechanism is
illustrated in Figure 2.1. Electrons are thermionically emitted from the tantalum ﬁlament.
A positive 50-60V potential between the ﬁlament and anode pulls these electrons away
from the ﬁlament and to the anode. Ar gas is injected inside the gun housing near the
target at a rate of 45cm3/min. The Ar becomes ionized through electron collision and
forms a plasma limited to the region just above the target by two powerful magnets and a
conﬁnement shield. This results in the creation of a stable plasma current of 5-7A. A
negative 200-600kV potential applied to the target accelerates the ionized Ar to strike the
target, knocking atoms off the surface. This produces a beam of target atoms, typically

17

l8

0.5-1 .0A. A substrate placed ~12cm above the target collects the material from this beam
at a rate determined by the target voltage and the plasma current.

Although the plasma easily ejects material ﬁom the target surface, most of the kinetic
energy from the Ar ions is deposited as heat in the target. To avoid melting, the target
was water cooled. After the Ar ions hit the target, they capture an electron from the
surface of the metal and are reemitted as neutral Ar atoms. Electrically conducting

targets must be used to provide these electrons.

Magnetic .. Aluminum gun
conﬁnement housing
shield

Ar Plasma

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=- E— r r j ‘
NWLL
Tantalum TCooling waterl

ﬁlament

Figure 2.1: A cross section of the triode magnetron sputtering gun used in fabricating the
samples for this study.

 

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stepping motor

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atmosphere

 

SPAMA plate Shaﬁ

 

 

 

 

 

Chimney ‘ Chimney
with hole - w1thout
hole

 

sputtering
gun

 

 

 

 

 

 

 

 

 

 

Figure 2.2: A schematic of the sputtering systems is shown. Chimneys are able to rotate
over the sputtering guns to block deposition (chimney without hole) or collirnate a
deposition beam (chimney with hole). A computer controlled stepping motor rotates a
substrate into position. Only three of the four guns are shown for clarity.

The four sputtering guns are situated on the bottom of a cylindrical vacuum chamber,
as illustrated in Figure 2.2. Above each gun is a set of two chimneys, one without a hole
to block the deposition beam ﬁom reaching the substrate and the other with hole in the
top to allow deposition. After deposition, the chimney without the hole is rotated back
over the gun to prevent deposition of unwanted material before an exposed substrate can
be protected. A computer controlled stepper motor rotates the substrate above the

selected gun until the preset thickness, determined by the deposition rate, has been

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deposited. Multilayers are grown by sequentially rotating the substrate between two or

more sources.

2.2 Preparation of the System

The system was prepared in the same manner for each run to limit sample variations
from run to run. The gun parts for each source were cleaned in an acid bath containing
roughly 1 part HF, 9 parts HNO3 and 3 partsdistilled H20. Each gun part was scrubbed
with a stainless steel wire brush and then rinsed in distilled H20 to remove material ﬁom
the previous run. Each target material had its own gun to help minimize chemical
impurities in the samples. For example, parts used to sputter Co were used to sputter Co
exclusively. To remove any small particles loosen by scrubbing a 6 minute ultrasonic
cleaning was done, ﬁrst in acetone and then in ethyl alcohol. All substrate holders and
masks as well as the sample positioning and masking apparatus (SPAMA) plate were
subject to the same cleaning procedure.

The limited number of chimneys forced their reuse in every run even though different
materials were being sputtered. To help prevent cross contamination from previous runs,
the chimneys were wrapped in Al foil each time a new material was to be sputtered. The
magnetic shields were not cleaned. However, each gun had its own magnetic shield

which was only used for a speciﬁc target material.

2.3 Substrates and Holders

All samples made for this study were grown on (001) oriented Si substrates. The
substrates were cut into half inch squares from 3 inch, 0.5mm thick, boron-doped, silicon
wafers of resistivity 109-cm purchased from Silicon Quest International. Care was
taken to see that the substrates ﬁt snugly into the sample holders to prevent sliding as the

SPAMA plate rotated. They were then sequentially washed ultrasonically in the

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following: alconox and deionized water, deionized water, acetone, and alcohol. Samples
prepared for CIP measurements were then hydrogen terminated by etching in
concentrated HF for one minute followed by dips in deionized water and alcohol. All
substrates were stored in alcohol until loading occurred. Prior to loading into the holders
on the SPAMA plate, the substrates were blown dry using N2 gas.

Loading was performed quickly just before the system was closed to minimize the
buildup of atmospheric hydrocarbons. The number of samples made during each run
could be varied according the conﬁguration of the SPAMA plate. The plate has positions
for eight substrate holders and two for ﬁlm thickness monitors, as shown in Figure 2.3.
Two types of substrate holders were used for the bulk of this study. The ﬁrst was
designed to hold two substrates, as illustrated in Figure 2.4a. A single holed shutter
permitted each substrate to be exposed separately. Films made with these holders
covered an area slightly less than the half inch square of the substrate itself. The second
holder was designed to hold a single substrate. A manually rotatable masking system
allowed the ﬁhn to be patterned in situ as the run progressed, as shown in Figure 2.4b. A
third holder used near the end of this study was designed for sputtering samples in the
presence of a magnetic ﬁeld. These hold a single half inch square substrate centered
between two NdFeB magnets so that the direction of the ﬁeld lies in the plane of the
substrate, as indicated in Figure 2.4c. A shutter was manually slid back and forth to

expose an area slightly less than the substrate.

Sam

p051:

 

22

Sample holder
positions (SH)

 
  

Fihn thickness monitor

positions (FTM) Substrat

radius

Figure 2.3: Diagram of the Sample Positioning and Masking Apparatus (SPAMA) plate
layout.

23

 
  

~
‘Q

 
      
   
   
     

pin for rotating
shutter

   
 

 

shutter screw- “ . .
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substrate

'-. , hole for
Pin for rotating . ‘ z.) :3; (3 "."\ shutter screw -
masks “. - 't ,o' ° x" shutter and maskrng

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Figure 2.4: Diagrams for the various substrate holders used during the course of this
study. Holder a) was used to make CIP multilayers and single layer thin ﬁlms. Holder b)
was used to make the CPP samples. Holder c) was used to sputter CIP multilayers in a
strong magnetic ﬁeld. Dashed lines indicate the shutters which are hidden from view
when looking down through the substrate hole. The shutters could be rotated about their
center by pulling on one of the pins for rotating with an externally controlled wobble
stick.

2.4 Vacuum

The sputtering chamber is UHV compatible reaching an ultimate background pressure
of between 1 and 2 x10‘8 torr. A high speed CTI Cryo Torr 8 cryopump is used to pump
down the system. A pressure of 5 x10'6 torr is achieved just 15 minutes after closing but
to go lower the system is baked overnight (~12 hours) at 60 °C. Upon cooling to room

temperature, the gate valve is opened completely and a pressure of roughly 8 x10'3 torr is

new:
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24

measured. The system is then left to pump for 24 hours ﬁnally reaching 2 x10:8 torr.
Cooling the substrates with liquid N2 for one hour prior to sputtering tends to lower this
pressure somewhat but generally the ﬁnal background pressure never dips below 1 x10-8
torr. The system is capable of lower background pressures but the viton gasket sealing
the ﬂange between the top and the main parts of the chamber would have to be replaced
with a metal gasket such as copper or indium and then be bolted tight.

The partial pressures of the background gases inside the chamber are measured using
the M100 Quadrapole Gas Analyzer purchased from Dycor Electronics. These gases are
He, H20, N2, 02 and Ar. Partial pressures of between 10'8 and 10'9 torr are measured for
H20 vapor and N2 gas. The other gases have pressures at least an order of magnitude

lower.

2.5 Cooling System

The cooling system for the SPAMA plate was designed and built by C. F ierz and
WP. Pratt, Jr. is illustrated in Figure 2.5. An external heat exchanger has high pressure
(1000 psi) N2 gas ﬂowing through a l/l6 inch stainless steel tube welded inside a length
of l/4 inch copper tubing, through which liquid N; is constantly ﬂowing. The high
pressure gas is then forced into a capillary that runs inside the length of the shaft holding
the SPAMA plate, into a second heat exchanger consisting of a tiny copper reservoir
located at the bottom of the shaft. The second heat exchanger is thermally connected via
four copper rods to the SPAMA plate. The constriction caused by the capillary forces
the high pressure N2 gas to condense into liquid N2 as it travels to the reservoir where it
evaporates and retums via the capillary up the shaft to a second stainless steel tube and is
vented to the outside. The larger copper tube carrying the liquid N2 in the ﬁrst heat
exchanger continues on to a large internal ring (Meissner trap) around the top of the

chamber before being vented to the outside. This helps to ﬁeeze out impurities inside the

.3“
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25

chamber. A thermocouple is placed on this loop to conﬁrm that liquid N2 is ﬂowing. An
important part of this design is the use of small capillaries which permit the whole
assembly of the 2ml heat exchanger and SPAMA plate to rotate.

 
     

N2 gas thermocouple pressure
bridge SCI'BW
L I capillaries
. substrate

sample
AK / First Heat holder \
‘ ]/ Exchanger \
k

 

 

 

 

 

 

\ SPAMA plate
A, “it shutter
Cu block
‘IH Cu rod shutter
- OFHC Cu

 

 

f

A Second Heat
Exchanger

 

Figure 2.5: Schematic cross section of the cooling system with CIP holder (Figure 2.4a).

the lam?
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26

A small copper block is placed behind each substrate and bolted ﬁrmly to the
SPAMA plate. This serves two purposes: (a) It keeps the substrate from moving as the
SPAMA plate rotates from source to source. (b) It thermally anchors the substrate to the
SPAMA plate so the heat from the growth process is transferred to the reservoir, as
shown in Figure 2.5. The temperature of the substrate is monitored by a thermocouple
mechanically held in place by a screw to the back of the copper block. From run to run
the temperature range in which the samples are grown is kept between ~40C° and 25°C to
minimize effects due to growth conditions. Should the temperature increase above this
range, the guns are shut down and the system is allowed to cool.

The only modiﬁcation to the cooling system concerned the source for liquid N2. The
two 30 liter dewars previously used were replaced with a single 100 liter pressurized
dewar. A typical run required about 50 liters of liquid N2, therefore the need to switch
the 30 liter dewars in the middle of a run was eliminated. This prevented the possible

release of impurities frozen out inside the chamber on the cooling ring.

2.6 Fabrication

Just before sputtering, the pressure is brought up to 2.5 mtorr, the ambient sputtering
pressure during each run, by backﬁlling the chamber with high purity Ar (99.999%) gas.
As a further protection against impurities, the Ar is passed through an oxygen scrubber
and then through a liquid N2 trap. The Ar pressure is held in dynamic equilibrium
throughout the run by ﬂowing Ar at a constant rate through each gun and then opening
the gate valve just enough to maintain 2.5mtorr.

The run begins by turning on all the sputtering sources and letting them equilibrate
which takes no more than 10 minutes. The target voltages and currents are ﬁxed from
run to run for each material so that the deposition rates are similar for samples made in

different runs, this again helps minimize effects due to growth conditions. The deposition

rites ;

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27

rates are measured using quartz crystal ﬁlm thickness monitors. A 3% correction is
added to the measured rate, the result of comparing nominal bilayer thickness to those
obtained from x-ray measurements. The values for target voltages, currents and

deposition rates are listed in Table 2.1.

Table 2.]: Target voltages and currents and the resulting deposition rates for sputtered
metals used in this study.

 

 

 

 

 

 

 

 

 

 

 

 

 

Metal Target Voltage Target Current Deposition Rate
(V) (A) (nm/ S)

Ag 200 0.500 1.10i0.10“
Cu 400 0.700 1.30:0.106
CuGe 400 0.700 1 .07i0.02"
CuMn 400 0.600 1.13:0.01”
CuNi 500 0.800 0.90i0.05"
CuPt 400 0.700 0.80:0.05"
Cr 500 0.700 0.55:0.02”
Nb 600 1.010 0.80:0.05"
Co 500 0.800 0.85:0.05“
Fe 500 0.500 0.53:0.01“
FeV 500 0.700 0.45:0.02”
Py 500 0.800 0.80i0.05“

 

 

 

 

 

 

a The uncertainties represent ﬂuctuations ﬁ'om run to run in deposition rate.
b The uncertainties represent ﬂuctuations in the deposition rate during a run. Each of
these metals is used in only one or two runs.

A two position shuttering system helps prevent cross contamination by manually
rotating either a short open chimney or a short Al foil covered chimney above each
source. The open chimney has a 5cm diameter hole cut in the Al foil covering the top,
thereby narrowing the region exposed to the particle beam to just the desired substrate
holder; while the covered chimney blocks the beam entirely. Note that the present system

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28

either has all sources open or all sources blocked. A modiﬁcation by Reza Loloee is
currently underway to selectively open or block each source.

Typically in a single run, 6 CPP samples and 4 single layer 300nm ﬁlms (one for
each source) were produced. The 300nm ﬁlms were done as checks to see if the
resistivity and/or composition (in the case of alloys) signiﬁcantly deviated ﬁom previous
runs. The procedure for making a CPP sample was as follows:

1. Measure deposition rates for each material (masks closed).

2. Open mask for bottom Nb strip and deposit 350 nm of Nb.

3. Rotate to mask for sample and deposit the multilayer.

4. Rotate to mask for top Nb strip and deposit another 350 nm of Nb.

5. Close mask.

The time to deposit an entire CPP sample varied from approximately 30 to 60 minutes
depending on the sample. The Nb strips each took roughly 7 minutes to deposit and the

multilayer itself varied depending on the desired sample from 15 to 40 minutes.

2.7 Targets

Three different types of targets were used as sputtering sources: ready-made,
commercially produced, in-house alloyed and in-house composite. Targets of 99.999%
pure Cu, 99.999% pure Ag, 99.95% pure Co, 99.9% pure Fe and 99.95% pure Nb were
ordered ﬁom Angstrom Scientiﬁc. Permalloy (Nileelg) was also ordered from
Angstrom Scientiﬁc because the melting temperatures of Ni-Fe alloys are above 1400°C,
beyond the operational range of the quartz chamber on the induction fumace. Of these,
only the Nb was received in the form required for immediate use, disks 5.72cm in
diameter and 0.64 cm thick. The rest were received as bars and were cut to the ﬁnal
dimensions using the computer controlled traveling wire electrical discharge machine

(EDM) by the staff of the physics shop at MSU.

29

Alloyed targets of CuX were made in the rf induction furnace at MSU. These were
made from 99.999% pure Cu and; 99.999% pure Pt, 99.999% pure Ge, 99.99% pure Ni
and 99.9% pure Mn. The procedure listed below was followed :

1. The appropriate amount of each material was lightly etched in HNO3.

2. Components were placed in a cylindrical, boron nitride coated, graphite crucible

slightly larger than the intended 5.72cm target diameter.

3. The quartz chamber was pumped down to 10*5 torr for several hours and then

backﬁlled with a gas mixture of 10% H2 and 90% Ar to eliminate any oxidation.

4. Materials were heated until a good convection ﬂow was observed, to ensure a

homogeneous composition.

5. The target was allowed to cool for several hours before opening to the atmosphere.
Some targets such as the CuPt alloy were ﬂipped over and remelted in a similar manner
to better ensure homogeneity. The alloy target was then machined to the proper
dimensions by the physics shop.

Composite targets were used for FeV and CoSm. The F eV target was constructed by
cutting seven 1.28cm diameter holes (at the comers and center of a hexagon) in an Fe .
target with the EDM. Vanadium plugs were used to ﬁll the holes. The CoSm target was
made by putting a rectangular piece of Sm on a Co target. The Sm was held in place by
a screw through the backside of the Co target.

During a run, the sources are water cooled to prevent overheating. For good electrical
and thermal contact with the target, they are mounted on copper holders and bolted to the
copper base through which the water ﬂows. For good conductors such as Cu and Ag the
targets are merely set on top of the holder. Magnetic targets must be held in place with In
solder because of the strong magnetic ﬁelds needed to conﬁne the plasma inside the
source. Originally the Nb target was treated like a Ag or Cu target; but the power used
for deposition heated the Nb target until it glowed. This limited the number of CPP

samples made before shutting down to cool to just two. Soldering the Nb to the holder

mill 1

n11: b

30

with In provided much better thermal contact and allowed several CPP samples to be

made before cooling down again.

Chapter 3:

Sample Characterization
and Experimental
Procedures.

Introduction

This chapter lists and describes the results of sample characterization analyses done
on sputtered multilayers made at MSU. These include a qualitative discussion of
compositional studies using energy dispersive x-rays (EDX) and standard 0-20 x-ray
diﬁ'raction techniques at both low and high angles done by the author. Additional studies
were performed by others using cross-sectional electron microscopy (XTEM) and nuclear
magnetic resonance (NMR) provide more insight into the sample structure.

The chapter ends with a discussion of the different techniques used in measuring the

resistance of a CPP sample, a CIP sample or a single layer thin ﬁlm.

3.1 Compositional Analysis Using EDX
Films of alloyed targets were examined for both impurity concentration and
uniformity of composition using energy dispersive spectroscopy (EDS or EDX). This

procedure involves bombarding the sample ﬁlms with electrons and analyzing the energy
31

spam
facilir}
results
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32

spectrum of ﬂuorescent x-rays. These studies were done at the Center for Electron Optics
facility located here at MSU in the basement of the Pesticide Research Center. All EDX
results were obtained using a JEOL JSM-35C Scanning Electron Microscope (SEM)
equipped with a Tracor Northern x-ray detector. A dedicated PC running Noran Inc.
commercial software performed the necessary calculations for the compositional analysis.
Vivion Shull (now retired) and then Stan and Carol F legler operated the SEM.

Fluorescent x-rays are produced after core electrons are ejected ﬁ'om various atoms
within the sample via inelastic collisions with a beam of incident electrons from the
SEM‘. The core vacancies are then immediately ﬁlled by another higher level electron
within each atom. These transitions release x-rays of a characteristic energy.

Since the electron energy levels depend on the atomic number, a characteristic x-ray
spectrum exists for every element. This x-ray "ﬁngerprint" can then be used to identify
the constituent elements in the sample. The concentration is obtained by comparing the
count rate of a particular transition series, either K,Jl or La, for each constituent element in
the sample. Three factors must be taken into account before comparing the rates: (a) The
element with higher atomic number has a larger cross section and will produce more x-
rays (Z correction). (b) The probability an x-ray will be absorbed before it escapes the
sample (A correction). (c) The probability an x-ray will create a secondary x-ray by
ﬂuorescence in the sample (F correction). Together these form the ZAF correction factor
which is close to 1.0 for the materials studied here.

If the ZAF corrections are calibrated to scans of pure samples taken at the same
electron energy then the accuracy of the concentration c for this method is (c i 0.03c).
This calibration was not done so the error is approximately (c :1: 0.07c) for all impurities
in this study 2. Table 3.1 lists both the nominal and measured impurity concentrations for
single layer sputtered 300nm ﬁlms used for the work described in this thesis. The
system is sensitive enough to detect impurities of less than 1 at.%, but low counting

statistics make quantitative analysis difﬁcult and generally unreliable. In all analyzed

33

ﬁlms no detectable unintended impurities were seen. It should be noted that the detector

is not sensitive to the lower Z elements ﬁom oxygen on down.

Table 3.1: Measured impurity concentrations of targets.

 

 

 

 

 

 

 

 

 

Host metal impurity nominal c (at.%) measured c (at.%) thickness (nm)
Cu GeI 4 4.9103 200
Cu Mni 7 71-05 200
Cu Ni 6 5.9-1:04 300
Cu Ni 14 13.71-1 300
Cu Pt 6 59:04 300
C0 Sm 10 10.3:t0.7 100
Fe V 30 27:2 300
Ni Fen 19 161:1 100-500

 

 

 

 

 

 

 

1 Target made by M. Wilson.

T Target made by L. Hoines.

D Fe impurity concentrations of 19 at.% were measured in the purchased Py targets,
consistent with manufacturer’s speciﬁcations, however, Py ﬁlms (both single and
multilayered) repeatedly measured near 16 at.%.

3.2 1

1113130

ﬁlm-.1

Ki

.

r
L..
'11
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93.12::

DEBIT.

1.3
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34
3.2 X-rays

Multilayer properties are very sensitive to structure. Many very sophisticated
methods such as XAF S, XTEM and NMR are used to probe the structure of multilayers
at many different scales. Although results from more sophisticated studies done on
samples made at MSU and studied by others will be reviewed, they are not the focus of
this study. Simple 0-20 x-ray diffraction (XRD) was used to probe the perpendicular
structure of each multilayer. From these scans, the bilayer thickness and crystallographic
orientation could be measured.

The sample spectra were obtained using the Rigaku rotating Cu anode diffractometer
housed on the fourth ﬂoor of the Chemistry building at MSU. For a concise description
of the setup used, see the dissertation of M.L. Wilson3._ The divergence angle of the x-ray
beam was limited to (1/6)° by a set of divergence slits placed before and after the sample.
A graphite monochrometer placed between the sample and the detector ensured that only
Cu-Ka radiation (0.15418nm) was detected. The sample alignment was good to :0.l°,
which may have introduced small errors in the peak positions for angles less than ~10°.
This was of little consequence since most samples failed to produce any peaks in this
region.

For reﬂected x-rays in the 0-20 geometry, the momentum transfer vector is always
perpendicular to the atomic planes in the sample and therefore only probes the structure
along this direction. Peaks observed in these spectra correspond to periodicities along the
sample's grth direction and give a measure of the lattice spacing of each material in the
multilayer, the crystallite size and the bilayer spacing.

The Bragg condition describing the relationship between the diffraction spacing and
the peak angle is given equation 3.1

m}. = 2d sin 0 3.1
where m is the order of the intensity peak, I is the wavelength of the source (Cu-Ku
radiation) and d is the spacing which produces the peak angle, 0. The largest repeated

ll
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Vﬁr‘.

anti
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35

spacing in each multilayer comes from the bilayer thickness, A. So for d=A, Bragg peaks
should be seen at angles of less than ~ 10°. These peaks are almost never seen in the
Co/Cu and Py/Cu samples used in this thesis. For rather thick bilayers, A>20nm, this is
understandable since the most intense peaks would be observed in the region where the
detector is saturated by the beam line, however, peaks from thinner bilayers should still
be detectable. A combination of similar electron density between the two materials and
columnar growth could partially account for the absence of low angle superlattice peaks.
At low angles the x-ray beam illuminates a larger area of the sample and therefore is very
sensitive to the ﬂatness of the illuminated area, Figure 3.1a. Although the interfaces
within a column might be atomically ﬂat, kinks form in the bilayer between neighboring
columns which reduce the coherence of the scattered x-rays and may reduce the low angle
superlattice peaks. If the column widths are much smaller than the illuminated area of the
sample, then the x-rays would experience a large number of these kinks at low angles so
that x-ray peaks ﬁ'om the bilayer spacing should be very hard to see. At high angles,
where the x-rays begin to probe the lattice structure of the constituent materials, the kinks
between neighboring columns are not as important since a greater portion of the x-ray
beam may now sample the columns, themselves, Figure 3.1b.

At best however, this can only be a contributory factor, since others4 have observed

low angle peaks in similar sputtered Co/Cu samples.

1.0

561

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36

a) 13) High angle
x-rays sense

Low angle x-rays ﬂat interfaces.

sense rough interfaces.

l l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/ \ / \__
Column: 1 ' 2 3 I 4 l 5

 

Figure 3.1: Schematic representation of both a) low angle and b) high angle x-rays
incident on a multilayer exhibiting columnar growth.

High angle peaks are due to the lattice spacing of each constituent material. The
observed structure peaks for each material is given in Table 3.2. These were expected
since ﬁlms grow with the most densely packed atomic planes oriented parallel to surface
of the substrate in order to minimize energy. These planes are <111> for fee lattices and
<110> for bcc lattices. The side peaks next to the main lines of both multilayer
constituents arise from a modulation of the constituent spectra by the spectra resulting
ﬁ’om the bilayer thickness. The intensity of these satellites tends to be enhanced with the
addition of heavy Z impurities into the spacer layer such as Pt, ﬁgures 3.2-3.4.

R“ til!
‘0

illi‘ p;

37

Table 3.2: Observed x-ray structure peaks.

 

 

 

 

 

Metal Structure peak 9-29“
Nb 1 10 38
Cu 1 l l 43
C0 0001 48
Py _1 11 44

 

 

 

 

 

a Peak angle for a bulk ﬁlm 300nm thick.

Crystallite size may be estimated from the structure peaks, although it is complicated
by the presence of satellites in some cases. The average crystallite size perpendicular to

the plane of the layers is given by Scherrer’s equation:

_ 10.
B cosB

 

3.2

where S is the crystallite size, B is the FWHM of the diffraction peak at angle 9 and K is a
constant related to the crystallite shapes. If K is taken to be unity then S becomes the
volume average of the crystallite dimension normal to the reﬂecting planes, th6. The
volume averaged crystallite size estimated from equation 3.2 (K =1 . 0) was approximately
30nm. For all but the thickest interlayers, this was greater than the bilayer thickness for
each sample.

Not considered here is the effect of strain on the linewidth broadening of the lattice
structure peaks. The lattice mismatch from one material to another undoubtedly strain
each sample. Also, defects (both structural and chemical), which are inherit in sputtered

samples, probably increase the amount of strain in a given multilayer.

ry..—... >h.::£-_:v >:7.:U:.—

«7.7.2: thhzﬁhﬂy >JT£CD~Z~

38

 

0’“ 1” Co(0001)

Nb(l 1 0)

 

 

 

 

Intensity (arbitrary units)

 

 

 

 

 

 

3o 40‘ i i so i 60
29

Figure 3. 2. 9-29 spectrum for [Co(6.0nm)/Cu(9.0nm)]x48. The bulk values of Nb (110),
Cu(111) and Co(0001) are shown for comparison.

 

T

1 Cu(111) Co(0001)

 

Nb(l 1 0)

 

 

 

 

 

Intensity (arbitrary units)

 

.— 4‘— —l

 

 

 

 

 

30 4o 50 6O
29

Figure 3.3. 6-29 spectrum for [Co(6.0nm)/CuPt(9.0nm)]x48. The bulk values of Nb
(110), Cu(111) and Co(0001) are shown for comparison.

 

3‘11- nu”

4 .t
AvamC-a hhﬁhemLLSV %~.mCO-C- Tu. «UL.
. . well

39

 

f Cu(111) Co(0001)

l
A i A . A

 

lmlLl

 

Nb(l l 0)

 

 

 

Intensity (arbitrary units)

f/S
l
l
l

 

 

 

 

 

 

30 40 so 60
29

Figure 3. 4. 6-29 spectrum for [Co(6.0nm)/CuNi14%(9.0nm)]x48. The bulk values of Nb
(110), Cu(111) and Co(0001) are shown for comparison.

40
3.3 Cross-sectional Analysis

Cross-sectional electron microscopy (XTEM) was used to study a limited number of
samples. Studies at MSU were done on Co/Ag CPP samples by D. Howell et al.7, while
other XTEM studies were done on Co/Cu CIP multilayered ﬁlms by P. Galtier et al.8 at
Thomson in Orsay, France. Results for NiFe/Cu and Co/Cu CPP samples are hard to
analyze because the materials have similar atomic numbers so the Z contrast is rather
poor. Galtier was able to image these materials by using a technique know as Fresnel
contrast9 which enhances the contrast between the materials by defocusing the electron
beam. Some inferences can be made about the structural properties of NiFe/Cu and
Co/Cu CPP samples by comparing the work done on Co/Ag with Galtier's on Co/Cu.

In the MSU studies, the layering is quite good for the ﬁrst few bilayers, but thereafter
dark-ﬁeld micrographs show a columnar structure at least 20nm in width for the average
column. Although layering is still uniform within each column, layering between
neighboring columns does not always register and kinks form from one column to the
next.

The Galtier study showed similar trends in the layering. However, the samples had a
small number of thin bilayers so the layering was quite good, and although the beginnings
of columnar growth are visible, well deﬁned columns were not observed. Galtier did
observe well deﬁned columns for multilayered ﬁlms sputtered in Orsay when the total
sample thickness exceeded 50nm. The MSU samples he received had total thickness less
than 50nm.

The Nb strip necessary for transport measurements in CPP samples had little effect on
the smoothness of the layering within a column, but did seem to provide nucleation sites
for the growth of columns. Dark-ﬁeld micrographs show crystallites in the Nb at the
Nb/ferromagnet interface correlating nicely with the columns in the multilayer.

Comparing the results of Galtier to those of Howell leads to the following conclusions
about CPP NiFe/Cu and Co/Cu samples. They most likely have columnar growth

V .
(‘10 CL:

331693;

‘A

4]

probably nucleated by Nb crystallites near the Nb/ferromagnet interface. The layering
within a column is probably quite good. The ﬁrst few bilayers are smooth but as the

sample grows the neighboring columns become mismatched.

3.4 Nuclear Magnetic Resonance

Nuclear magnetic resonance (NMR) studies were done on Co/Ag and Co/Cu samples
sputtered at MSU and sent elsewhere for analysis. The Co/Ag series was studied by van
Alphen et 01.10 in Eindhoven while samples of Co/Cu were studied by Mény et al.11 in
Strasbourg.

The Co/Ag results are detailed in the thesis of SF, Lee”. By comparing the ratio of
interface Co signal to bulk Co signal, this studylo found that for ’Co>1-0"m continuous Co
layers are deposited in the sample. Below this value the Co layers consist of island-like
structures. Behavior consistent with purely granular Co/Ag samples is seen for the
thinnest Co thickness, 0.2nm. This will be important when considering the hybrid
samples in Chapter 6.

The Co/Cu results11 indicate that the structure of the Co layer depends upon the
thickness of both Cu and Co. If the Cu thickness is held constant, the Co remains fcc
until a tCo~3.0nm. Near this thickness the Co contains a mixture of hop and fee
structures. Further increases of ta, will eventually lead to the detection of only the hcp
structure. Increasing the Cu thickness will tend to increase the amount of fee Co in the
Co layers. Comparing the NMR data with interface models indicates that for thin Co up
to 3 monolayers could be intermixed at the Co/Cu interfaces. For thicker Co, model
comparison suggests only one intermixed layer. The thicker Co NMR spectra are also

consistent with 9.0nm wide columnar grains.

,n‘m
5~ALI

I...
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....
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42

3.5 Resistivity of Single Films

In most sputtering runs, single layer ﬁlms of multilayer constituents were made as
both a check of sample variability from run to run and as an independent measurement of
the resistivity of each material. These ﬁlms were measured using the van der Pauw
technique13 .

The resistivity for ﬁlms of arbitrary shape may be measured using the van der Pauw
technique, if the ﬁlm fulﬁlls the following conditions: (1) The contacts are located on the
circumference of the sample. (2) The contacts are sufﬁciently small. (3) The sample
thickness is uniform over the entire sample. (4) The sample must be simply connected,
i.e., it has no isolated holes within the ﬁlm. When these conditions are satisﬁed, equation

3.3 is used.

 

p = “d (RABCD + RBCDA)f[ RABCD) 3.3
ln2 2 RBCDA

In equation 3.3, d is the ﬁlm thickness and f is a ﬁmction of the ratio RAECDARBQDA
where RARCD is the potential difference measured between contacts D and C divided by
the current through contacts A and B. Values of f are tabulated in Ref. 13.

The resistivity of each ﬁlm was measured by attaching the leads to the sample with In
and cerralloy 117 solder. The holder was then slowly lowered into a dewar of liquid
helium, the same environment in which CPP measurements are made. R Aim, is obtained
by putting 1.000 mA from a Kiethley 224 current source through leads A and B while the
potential difference across leads C and D is measured with a Kiethley 181 nanovoltrneter.
Similarly, Room is found by putting current through B and C while measuring the
potential across A and D. The ﬁlm thickness is measured using a Dektak IIA surface

proﬁlometer. The resistivity of the sample is then calculated using equation 3.3.

43

The uncertainty in the resistivity of these ﬁlms is almost entirely due to measurement
of the ﬁlm's thickness, i5-10%. Typically six different locations are scanned and
averaged together for the ﬁlm's height. Substrate curvature and discontinuities in the Nb

strip proﬁle can make determination of the ﬁlm's height much harder.

3.6 Determination of CPP Area

The quantity of interest in the CPP geometry is the conductance per unit area, G/A.
Experimentally it is easier to measure its inverse, AR, the product of the sample area and
the total sample resistance. The effective sample area is the region of overlap between
the crossed Nb strips, asi shown in Figure 1.5. This area is determined by the width of
each Nb strip. A Dektak IIA surface proﬁlometerl4 with horizontal and vertical
resolutions of 50nm and 0.5nm, respectively, is used. Figure 3.5 shows a typical scan of
a Nb strip.

The procedures followed for each scan are detailed in the thesis of SF. Lee”. The
only difference here is that all samples were deposited on Si <100> substrates which had
no noticeable curvature compared to the sapphire substrates used by SF. Lee. Here the
width was always deﬁned by ﬁnding the point 10nm above a sharp increase in the slope
of the Nb proﬁle on either side of the strip. Reasons for the 10nm given by SF. Lee
concern the suppression of TC in thin superconducting ﬁlms. The average width of the
Nb leads was ~1.1mm making the sample area ~ 1.2mm2. Uncertainties in the effective

CPP areas were i2-5%.

Height nn1

 

 

 

 

 

 

 

 

 

400
300 ~
E
G 200 ~ -
3 Sr substrate ,
on Nb strrp
’5
m 4 >
100 ~
0 ..
0 1000 2000 3000

Width ,um

Figure 3. 5. Nb strip proﬁled via Dektak, note the scale change from nm to m for the
vertical and horizontal, respectively.

3.7 CIP Measurements

Two different types of CIP measurements were made over the course of this study.
The ﬁrst will be designated as just CIP and will refer to those measurements made on the
CIP part of the CPP samples, see Figure 1.5. For these measurements both voltage and
current leads were soldered to each of the CIP pads on the sample. The sample’s
resistance is dominated by the two thin sections connecting the CIP pads to large circular
area. Typically the sample’s conductance was measured using a SHE model PCB
potentiometric conductance bridge which has a range of 0.050 to 100. Occasionally it
was necessary to measure the resistance directly using a Fluke 8502A multimeter in four

terminal mode which is capable of measuring resistances down to 0.01mQ. For ﬁrrther

details see Ref. 12.

Sub:

45

The other type will be designated as a “CIP ﬁlm” since these were multilayered ﬁlms
made without a mask (Figure 2.4a) and so only CIP resistances could be measured in
these samples. The resistance of these samples is also measured using a four terminal
method. For these CIP samples the leads are attached in a row along the sample using Ag
paint as shown schematically in Figure 3.6. The samples were then loaded into a
Quantum Design Magnetic Property Measurement System (MPMS) for temperature and
ﬁeld dependence studies. The computer controlled MPMS was interfaced with a
Kiethley 224 programmable current source and a Kiethley 181 nanovoltmeter using the
external device control (EDC) routines written by R. Loloee15 . The potential difference
between the inner leads is read while a 1.000mA current is put through the outside leads.

Measurements for :tl .000mA are averaged together to eliminate any thermal EMFs.

V

 

Ag paint
contacts

 

 

 

CIP ﬁlm 0 O

Substrate

 

 

 

 

 

m
V

Figure 3. 6: Schematic of CIP-MR measurement for CIP ﬁlm. H is typically applied
longitudinally, along the direction of the measuring current.

.- J
Le.

46

3.8 CPP Measurements

The apparatus used for measuring CPP resistances is based on the ability of a
superconducting quantum interference device (SQUID) to detect extremely small
voltages (~10’15v). Three different SQUID based systems were used in the course of this
study. The low ﬁeld apparatus, described in SF. Lee’s thesis” and elsewhere“, was used
mainly to measure Co/Cu, Co/CuPt, Co/CuMn and Co/CuGe samples. The highest ﬁeld
achievable in this system was 1.0kG. The high ﬁeld apparatus was built by SF. Lee and
is similar to the low ﬁeld system except for the ST superconducting magnet and the heavy
Fe shielding around the SQUID. This system was seldom used except for samples with
strong antiferromagnetic coupling which required 1-2T for saturation. The Quick Dipper
(QD) system was designed and built by professor W.P. Pratt, Jr..

All three systems use the same basic design for the sensing circuit. The SQUID is
used as a null detector to determine the ratio of sample current to reference current
necessary to maintain the same potential drops across both the sample and the reference
resistance. The SQUID is linked inductively to a circuit loop containing the sample and
reference resistances, Figure 3.7. First a known current, 13, is put through the sample side
of the circuit loop. Since RS and Rnfare in parallel, a small current will ﬂow through the
inductor next to the SQUID. The ﬁeld generated by this inductor causes the SQUID to
go out of balance. To null out this current (and hence the SQUID), another current, Inf,
is put through the reference side of the circuit loop. The reference current is increased
until the potential across Rm] exactly balances the potential across R s- As this happens,
the current through the inductor decreases, reducing the ﬂux through the SQUID loop
bringing it back into balance. RS is found using equation 3.4.

ﬁx _ A
R"! — 1., 3.4

. .me
P....

.2?

i

”It.

3,.
“Y

‘1

47

SQUID

sample reference
_—’ ‘—

 

AA
VVVT

 

AAAAAA
VVVVVVV

sample referenc

AA
VV

AAA
VVV

 

 

 

Figure 3. 7: Schematic of SQUID measuring circuit.

The difference between the QD and the other two systems is that the SQUID
controller for the QD has a feedback circuit in which I", is adjusted automatically; so that
instead of manually adjusting and recording the current ratio IS /I,ef through Rs and Rn},
only IS and V0, the feedback output voltage of the SQUID are measured. For the QD
equation 3.5 is used.

 

R; = 9.461(AV") 3.5
AI

3

m

‘vvnv

&_LL

is V8

lu:
“A ‘~‘

48

where R5. is the effective sample resistance in n!) and AVO is the change in V0 measured
in volts when IS is changed by AIS measured in Amps.

Superconducting wire is used for sample/reference circuit loop to eliminate any other
resistive sources. Both the current leads and the two superconducting voltage leads are
soldered to the Nb pads with In. The small contact resistance associated with these In
solder joints is not important for the following reasons: (1) A constant current is
maintained through the sample so a slightly higher resistance will not change IS. (2)
There is no current ﬂow from the sample to the reference (and the reverse) when the
circuit is balanced, so the In joints cannot drop any of the voltage. Also the In resistance
is very small when compared with the 94.5uQ reference resistor.

The magnet on the QD is a superconducting solenoid hand wound using
multiﬁlarnent NbTi (Cu matrix) wire. It is designed for a maximum of 30A, which gives
~1.6T of ﬁeld. The calibration is given below in equation 3.6.

B = 0.05265 x I 3.6
where B is the strength of the applied ﬁeld in Tesla when a current of 1 Amps is put
through the solenoid. The sample is always mounted in the same position with the

current perpendicular to the applied ﬁeld.

49

 

‘ I.A. Watt, “The Principles and Practices of Electron Microscopy”, Cambridge
University Press, Cambridge, UK. (1985).

2 L. Hoines Ph.D. Dissertation, Michigan State University (1994).
’ M.L. Wilson, Ph.D. Dissertation, Michigan State University (1994).

‘ H. Holloway, private communication.

’ H.P. Klug and LE. Alexander, X-Ray Diﬂraction Procedures For Polycrystalline and
Amorphous Materials, Wiley-Interscience, New York, NY (1974) p.659.

6 Ibid. p. 657.
7 D. Howell M.A. Crimp, unpublished.
’ P. Galtier, unpublished.

’ P. Galtier, T. Valet, O. Durand, J.C. Jacquet and J .P. Chevalier, Mat. Res. Soc. Symp.
Proc., 313, 47 (1993).

‘° E. A. M. van Alphen, P.A.A. van der Heijden and W.J.M. DeJonge, J. Appl. Phys. 76,
(1994).

” C. Mény, P. Panissod and R. Loloee, Phys. Rev. B45, 12269 (1992).
'2 S.F. Lee, Ph.D. Dissertation, Michigan State University (1994).

'3 L.J. van der Pauw, Philips Research Reports 13, 1 (1958).

“ Sloan Technology Corp., Santa Barbara, CA.

’5 R. Loloee, unpublished.

‘° D. Edmunds, W.P. Pratt Jr. and J.A. Rowlands, Review of Scientiﬁc Instruments 51,
1516 (1980).

Chapter 4:

Theory of CPP Transport
in Magnetic Multilayers

Introduction

This chapter begins with a much simpliﬁed picture of spin dependent scattering.
Then the two current model for electron transport in F/N multilayers is used to derive
equations used in the analysis of CPP data given in chapters 5 and 6. This is followed by
a discussion of the Valet and Fert equations which allow for ﬁnite spin diffusion lengths
in both the F and N metals. Next the CPP phenomenon of spirr accumulation at the PIN
interface is examined along with spin ﬂip scattering by spin orbit interactions. Finally the
chapter closes with a section that theoretically shows GMR could either be positive or
negative depending upon the spin asymmetry of adjacent F layers. For an introductory
discussion of magnetism see Cranglel ; for a more detailed discussion of magnetism see
Bozorthz, Chikazumi’ or Cullity". Also articles by 1.13. Cookes give results which include

exchange interactions and spin waves in Co, Ni and Fe.

50

“hr
'ruc

(7“
.v

51

4.1 Spin Dependent Scattering - A Simpliﬁed Picture

This section is to give a crude idea of where spin dependent scattering arises. The
spontaneous magnetic moments of Fe, Co and Ni are a result of the unpaired 3d electron
spins. For isolated Co atoms the 3d orbital only contains 7 electrons out of the 10 that
could be accommodated. Electron interactions favor an arrangement that maximizes the
total spin, and so in accordance with Hund’s Rules 5 electron spins point in the same
direction while the remaining 2 electron spins point in the opposite direction. Since each
electron may contribute one Bohr magneton (us) to the macroscopic magnetization, the
total magnetic moment of a Co atom is 3113. For isolated atoms there is also a
contribution from the orbital angular momentum of the electrons to the total magnetic
moment, however, in a crystal the orbital moment is quenched and therefore will not be
of concern here.

As atoms are brought close together to form a crystal electron orbitals overlap
allowing electrons to hop from atom to atom. The electrons are no longer bound to a
particular atom but are shared by all the atoms in the crystal. The 3d and 4s atomic levels
spread into energy bands. The 43 orbitals overlap much more than do the 3d orbitals,
which results in a wider 4s band with mobile low effective mass electrons. The 3d band
does not overlap as much resulting in a narrow band of higher effective mass electrons.
In a highly simpliﬁed s-d picture, the 4s electrons are largely responsible for the transport
properties of these metals, while the less mobile 3d electrons are responsible for the
magnetic properties. (This picture is oversimpliﬁed since massive hybridization occurs.)

The density of states Ds(E) and Dd(E) in the s and d bands of nonmagnetic transition
metals are shown schematically in Figure 4.1a for both spin directions. The area under
each D(E) curve equals the total number of states of each spin available to electrons. For
a crystal with N atoms, this is N and 5N for s and d electrons, respectively. Since the (1
band is narrow (d electrons are less mobile) and must accommodate ﬁve times the

number of electrons than the 5 band, Dd(E)>>Ds(E).

52

Current propagating through a ferromagnet is mainly carried by equal numbers of
spin up and spin down 45 electrons. The resistivity depends on the amount of scattering
the electrons undergo as they travel through the ferromagnet. This is proportional to the
number of available states into which electrons can be scattered. This simplistic picture
is shown schematically in Figure 4.1. As is done in the next section, one may deﬁne a
resistivity for the spin up electrons, pT , and similarly a p” , for the spin down electrons.
Each resistivity depends on the density of states near the Fermi surface. The metal shown
in 4.1a has the same density of states for each spin, and therefore the scattering is
independent of the electron’s spin. Figure 4.1b shows the density of states for a
ferromagnet which does depend on the electron spin. Here, pT cc DT (E) while
p’ ocDJ'(E) and at the Fermi surface D’(EF)>DT(EF) which gives rise to an
asymmetry in the scattering of spin up and spin down electrons. Therefore in Figure

4.1b, there is spin dependent scattering and p¢ / pT > 1.

l‘

P.

14

Lu
I4

‘-
..~, A

53

Density of states

 

  

 

 

   
 

      

  

III] A
III
-m””/////////////,::::: 1: ‘3
III I
I’ll "
till I]

  

 

/////,
. //

 

4,,””///////////////£- 1::

- I III/’I/l/l/l/l/ll/lﬂ - II
‘ r ' 'III/////////////////,5:5

 

 

4s 3d 43 3d

Figure 4.1: Schematic representation of the density of states for 3d transition metals. In a)
there are no unpaired spins so ferromagnetism would not be exhibited, however, b) does

have a spin-split density of states in the 3d band similar to Co which is a ferromagnet.
(aﬁer Ref. 2)

54

4.2 The Two Current Model

Initially we assume there is no spin ﬂip scattering. Then the current through a sample
can be thought of as ﬂowing through two independent channels deﬁned by the spin of the
electron relative to some deﬁned axis. Consider a multilayer with the plane of the layers
lying in the xy plane and a current, J, applied along the z axis (CPP geometry). Taking
the magnetization of the ferromagnetic (F) layers as being in either the +x direction or the
-x direction makes the x axis the spin quantization axis. This deﬁnes the absolute spin
direction as + or -, where + electrons remain spin up as they pass through the multilayer
and - electrons remain spin down as they pass through the multilayer. In each
ferromagnetic layer one spin channel undergoes more scattering than the other spin
channel. As the + electrons pass through the sample they undergo more scattering in F

layers that have their magnetizations pointing down, schematically shown in Figure 4.2.

Both a1 >1 and a2>1.

3) b)

Fl N F2 F1 N F2
6'0) 6"(0‘\
/' \/7
€(l)/\// e'(1) /\./

 

 

 

 

 

 

 

 

L

Figure 4. 2: Schematic representation of electrons propagating along the z-axis,
perpendicular to the layers for F, and F2 a) antiparallel and b) parallel. Here,

a = p‘|'/p‘r , is the same for all F layers.

CL

3::
0'31
e1;
CCU

fro:

55

Taking the concept of majority and minority carriers from electron transport in semi-
conductors, one may say that the + electrons are majority carriers for F layers in which
the magnetization is in the + direction and minority carriers for F layers with the
magnetization in the - direction. Similarly, for the other channel - electrons parallel to the
F layer magnetization are majority carriers and are minority carriers for - electrons
antiparallel to F layer magnetizations. The channels will carry current independently
when the amount of spin—ﬂip scattering in the sample is negligible. Figure 4.3 shows the
equivalent circuit for the two channels. The resistance of each channel is a series
combination of RN, Rm, RF and Rm where these are the contributions to the resistance

from the normal metal, F/N interfaces, ferromagnetic metal and S/F interfaces. We use

the following deﬁnitions:
T _ 2PF
PF 1+3
l _ 29F
PF 1‘3
RT = 2RF/N
F/N —l+'y 4.1
2R
Riv/v = —1 FIN
‘7
pi = Plv = 291v

T
RS/F = RAE/F = ZRS/F

Here p;- (pIJE) is the resistivity for an F layer with its local Mi parallel (antiparallel) to
the electron spin. Similarly, 11;,” and Rt, N are the F/N interface resistances. pp and pN
are the bulk resistivities of the F-metal and N-metal measured independently on thin
ﬁlms. [3 and y are thus deﬁned as the spin asymmetry parameters of the bulk F-metal and
the PIN interface, respectively. 2R5, F is the boundary resistance between the

superconducting Nb and the ferromagnet (Co6’7’8’9or Pym) measured on a series of S/F/S

ex...

18‘
:A

56

sandwiches. It is assumed that R5,; is the same for each spin channel and therefore makes
no contribution to the change in a sample’s resistance in going from an AP state to a P

state.

Spin Up Channel (+)

_RT RT 1 R1,, _

F/N

 

 

Spin Down Channel (-)

Figure 4.3: Equivalent circuit for the two channel model.

The resistances of the (+) and (-) channels are multilplied by the area, A, of the
sample so that the bulk resistances may be directly compared with the interfacial
resistances. The expression for adjacent F-layer magnetizations aligned antiparallel (AP)

to each other is given by1 l:

my.

> .
u
NV. :40...

57
N l T l
ARl‘+)(AP) = ZARg/F + Elpl‘tF + Plr’F + Piv’N + PN’N + 2ARF/N + 2ARF/Nl

2N 2N
=4ARS/F+1_Bz thF‘l'ZNleN‘l'l 22ARF/N

 

 

= AR(T”(AP)

The parallel combination of AR)” (AP) and AR(T"( AP) is just AR,(AP) given in

equation 4.2:
ART(AP) = 2ARS,F + Neg, + NpNtN + N2 1412;,” 4.2

where p;- = pF/(l—BZ) and 12;,” = RHN/(l—yz). If the total sample thickness,
T =N(tF+tN), is constant, equation 4.2 is linear in the bilayer number, N. The parameters
for the slope and intercept of ART versus N are then given in terms of the p;- and Riv/1v
instead of p,- and Rpm.

The resistance of a sample that has adjacent F-layers parallel (P) to each other is
straightforward to calculate but more complex since AR§+)(P) #3 AR}')(P). As in the

derivation of equation 4.2 each channel is added in series ﬁrst.

ARi+)(P) = ZARSIF + N(Plr’F + Plv’lv + ZARFIN)

t + 2N
lump” (1+7)

= 4141:,”r + mm” + 2(1- 13)Np}t; + 4(1—1)NARi~/~

 

 

ZARF/N

Similarly, the resistance for (-) channel is obtained by replacing B and y with -B and -y.
AR}"(P) = 4.4a” + 2NpNtN + 2(1+B)Np;z, + 4(1+ y)NAR ,1”,

Adding AR‘T+’(P) and AR)" (P) in parallel results in equation 4.3.

58

c c 2
N t + 2NAR .
ART(P)=ART(AP)-[B p” Y m] 4.3
ART(AP)

 

The spin asymmetry parameters may be extracted by ﬁrst obtaining p} and R}, N using
equation 4.2. Then B and y are obtained using equation 4.4. Rearranging terms in

equation 4.3 gives a more useful quantity experimentally.

 

AJRT(AP)[RT(AP)—RT(P)] = N[Bp;-tp+y2AR;,N] 4.4

This equation makes the interesting prediction that the square root should be independent
of pN, the normal metal resistivity. Results which conﬁrm this prediction and thereby
support the two channel model are presented later. In equation 4.4, quantities measured
experimentally, the CPP resistances, are grouped on the left side. The right side of
equation 4.4 may be used to determine [3 and y by choosing two sets of data with
tp=constant and ﬁtting the data to this equation. Choosing tF=tN= T/2N gives equation

4.5 which has the bulk spin asymmetry independent of the number of bilayers.

 

AJRT(AP)[RT(AP) — RT(P )1 = lip-25: + Ny2AR},N 4.5

Plotting the tF=tN data as a function of the bilayer number results in a positive intercept,
proportional to the bulk spin asymmetry parameter, and a positive slope, proportional to
the interface spin asymmetry parameter. In either case IF=tN or tF=constant, p;- and R}, N

must be determined from ﬁts of equation 4.2.

59

A commonly used asymmetry parameter may be deﬁned by the ratio of the spin down

resistivity to the spin up resistivity in the bulk F material and at the PIN interface, these

are:
l
_ PF
aF ' 7
PF
l
or _ RF/N
FIN " T
RF/N

With the deﬁnitions given previously in equations 4.1, these spin asymmetry parameters

may be related to the scattering parameters in the bulk, 13, and at the interface, 7.

...=_;+g
1 4.6

+7

aF/N =I-—Y

The expressions in 4.6 are used to relate B and y to the asymmetry coefficients used
extensively in the literature.

The two current model can also be used for more complex multilayer structures with
two different magnetic components F1/N/F2/N. Here the AP state is produced by
choosing ferromagnetic materials F 1 and F2 with signiﬁcantly different saturation ﬁelds,
H51>>H32. The AP state is formed aﬁer saturating the sample at H31 and then taking the
ﬁeld back through zero to just beyond -Hsz. The ART for each state (AP and P) is just the

parallel combination of the spin up and spin down channels similar to that shown above.

AR(+)(AP) = 4ARN,,CO + N[4p NtN + agate, + mg“, + plytpy + 2AR,iy,Ag] 4.7a
ARH (AP) = 4ARN,,CO + N14pNtN + para, + 21mg, Ag + plytpy + 2.412;, Ag] 4.7b

exp:
010

AR

 

60

Substituting the deﬁnitions listed in 4.1 into equations 4.7 gives AR in terms of B and y
for each ferromagnetic material. The resistance of the AP state for samples of
Co/Ag/Py/Ag (where Py=Ni34Fe16) is obtained from the parallel addition of equations
4.7a and 4.7b. The P state for these samples is found in a similar fashion. A simpliﬁed
expression for the AP state similar to that given in equation 4.2 for the AP state of the
two component system does not exist for this three component system, since

AR‘*’(AP)¢ AR"’(AP).

4.3 Spin-ﬂip Scattering for the CPP Geometry

In the previous section, it was assumed that the spin-ﬂip scattering was negligible.
Relaxing this condition leads to a very complicated set of equations derived by Valet and
F ert'z. In their theory, they showed that for multilayers the Boltzmann equation reduces
to macroscopic transport equations if the spin diffusion length (a measure of the spin ﬂip
scattering length to be deﬁned in equation 4.14) is much longer than the elastic mean ﬁ'ee
path (mfp), regardless of the ratio of the mfp to the layer thickness. They analyzed a two
component system with single domain F-layers. Simplifying assumptions of: (1) single
parabolic conduction bands, (2) same effective mass, m, and (3) same Fermi velocity, VF,
were made for each metal. The m and v; simpliﬁcations may be relaxed without an
essential change in their conclusions. They have included both spin dependent scattering
in the bulk material and at the interfaces but limit themselves to low temperature to
eliminate spin-ﬂips from magnon-electron collisions. The spin-ﬂip events they allow
arise from spin-orbit interactions or exchange scattering associated with defects or
impurities in either metal. The steady state spin dependent electrochemical potential ([4),
electric ﬁeld (F), and current densities (J) are found in each layer by matching the
solutions to the transport equations at each interface. Continuity of the current across an

interface leads to spin accumulation at each interface.

1w
'5 uh'
.

61

The Valet and Fert model give the following equations for ﬁnite spin diffusion
lengths in both the F and N layers:

R(P,AP) = N[ro 4424/1401 4.8
where

r0=(1_l52)p.r+P;/t~4320-72)”: 4-9

(ti-ll)2 - t 72 t 132
.(N com??? + ,gpcothz—[F +—,—
13st cf stf sf rb

rs, —
4.41 — _,_.... t—r... +1. 441414.444]
pNisf 2Z3! pFZJ 24,, rb lev 23!, pplsf 22,,

equation 4.10

 

 

(P) _

equation 4.1 1

 

 

_ 2 2 2
(B . z”) tanhl:i%vﬁ:l+ I F coth[—t—Ff:|+ p:—
(AP) _ pN Sf sf p

rs, — .
1 t 1 t l 1 t l t
—:e~‘““*‘I#l—'r°°‘h —— +—. —*i~‘a“h[§irl7°° —
Plvsf sfPrs/ sf ’1: 13st sprsf sf

In the limit where the spin diffusion length is much longer than the layer thickness,

 

equations 4.8 to 4.11 will reduce to 4.2 for the AP state and 4.3 for P state shown in the
previous section. If the spin diffusion length is approximately the layer thickness then the
diﬁ’erence in the resistance between the AP and P states will be reduced by the spin-
ﬂipped conduction electrons, invalidating equations 4.2 and 4.3.

The effects of ﬁnite spin diffusion lengths are illustrated in Figures 4.4 and 4.5 where
J [ AR (AP ) — AR (P)]AR (AP) is plotted as a function of N, the bilayer number for the

 

Valet-Fert equations (4.8-4.11). The deviation from inﬁnite spin diffusion length is

expected to be the greatest for smaller bilayer number when ta, is held constant. In this
region the normal metal interlayer is thicker so the ratio of IN to I; has the greatest

‘1
“111..

1.7”"
dud“

62
value. Comparing ﬁgures 4.4 and 4.5 reveals a greater sensitivity to [5 than to 85’}. For

further illustrations see Q. Yang’s dissertation”.
The Valet-Fert equations are valid only when 6:; >> 71.8,. Recently Valetl4 has

extended the analysis to second order in AIL/EC} and found a correction term

~% (’3‘; (My / £2} ). Further analysis must show if this correction holds to all orders.

If; ..
‘ ig‘ul‘

bilay

'51.

'f“ 'r
: .dnl

 

100
“F:- 90
E
v 80
e
5 70
r..
ﬁ 60
g 50
5 40
E 30
g; 20
<1
; 10
0

63

tCu (nm)

 

 

   
    

 

 

 

30.0 12.0 6.0
- {Co(6.0nm)/Cu(tCu)} N ~
3 20.0nm
” 10000nm \
O 10 20 30 40 50 60 70 80

Bilayer Number N

 

Figure 4.4: Theoretically predicted behavior of J AR (Ho )[AR (H0) - AR (115)] with the
bilayer number, N, using the Valet-Fert model for (if? = no and several different values of
[5; listed in the Figure (pCu=10an and pC°=86an). The total multilayer thickness is

720nm.

 

 

5‘

I
Du

predli

64

 

 

 

 

tCu (nm)
30.0 12.0 6.0
100 2 . . . w - .

a; 90 u {Co(6.0nm)/Cu(tCu)}N a
c: . «
“CL 80 _ s
a; _

:5, ' 7o — e
F. , 4
SE 60 ~ 4
g 50 l 10000nm ~
r: i &10.0nm ~
M 40 _ 1.0nm 2
<' h \ \ 4
A 30 — —
EC: - 0.1nm ~
5,; 20 . ~
5 > 4
v 1" i .

0 r 1 a l . ' . 1 l 1 i i u i %

 

0 l 0 20 30 40 50 60 70 80
Bilayer Number N

 

Figure 4.5: Theoretically predicted behavior of \/ AR (H0)[AR (H0) - AR (115)] with the
bilayer number, N, using the Valet-Fert model for if; = no and several different values of

25’; listed in the Figure (pCu=10an and pCo=86an). The 10000nm and 10nm
predictions are nearly indistinguishable. The total multilayer thickness is 720nm.

65
4.4 Spin Accumulation in Magnetic Multilayers

Although spin-dependent scattering is responsible for both CIP-MR and CPP-MR,
there are fundamental differences concerning the mechanisms through which the spin
diffusion length (SDL) is manifested. The most important distinction between them
comes from spin accumulation which occurs only in the CPP geometry. Spin
accumulation refers to the buildup of a particular spin at an interface where the current of
a given spin is suddenly forced to become smaller. Balancing spin accumulation are spin
relaxation effects which relax the polarization of the electron spin.

To illustrate these effects on the transport properties at an interface, consider the
boundary between two semi-inﬁnite, identical ferromagnets (except for reversed
magnetizations) shown in Figure 4.6. This closely follows the calculations of Fert, Valet

5. The current in each ferromagnet can be thought of as having two

and Barnasl
channels“. Here conduction electrons with spin parallel to the F1 magnetization form the
+ spin channel while those with spin antiparallel to the F1 magnetization form the - spin
channel (or<1 for both ferromagnets). For transport ﬁ'om F1 to F2, the + spin electrons
(majority carriers) carry more of the current in F 1 than do the - spin electrons (minority
carriers). After crossing the boundary into F2 the spin channels switch roles because the
magnetization is reversed, the - spin channel in F 1 is now the majority carrier in F2. As a
result, the ﬂux of + spin electrons incident from the left of the interface is less than the
outgoing ﬂux of + spin electrons on the right. In effect the + spin electrons are being
accumulated at the interface. This results in an out-of-equilibrium polarization and an

increase in the chemical potential (u) near the boundary for the + spin electrons. The

opposite is true for the - spin electrons.

Figure 4' 6: El;
imminent 111

“Pm Cum

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4. 6: Effects of spin accumulation and relaxation at the interface of two
ferromagnetic metal, F, and F2 on the chemical potential, Au, the pseudoelectric ﬁeld, F,
and the spin currents, Ji, for an AP alignment of the moments of F, and F2.

llle
tamer
1110mm
distant:

bﬂoul

This Sp
down a
1115 £113
been d:

30n. 8:

mlCTOSi

With 1.

“here 1

dﬁfdsic

67

The spin relaxation process balances spin accumulation by allowing spins to change
carrier channels. The spin relaxation time, 15f, is generally much longer than the
momentum relaxation time, 1,, and so spin accumulation will diffuse a signiﬁcant
distance away from the interface. The diffusion of the spins away from the interface

modiﬁes the chemical potential in this region. The potential difference now obeys the

following diffusion equation.
_ 62
Qi+——'”—-l=D—,(11.—11.) 4.12
rd 62

The solution to 4.12 is a simple exponential provided the spin bands are symmetric,
differing only in their scattering rates.

urn, =A11+ = Ae

Ap+ = Ae—m" z > 0

2H,, Z<O

This spatially changing potential (pseudoelectric ﬁeld) will force + spin electrons to slow
down and the - spin electrons to accelerate. Since the current is proportional to a u/a 2,
it is also modiﬁed by these interface effects as indicated in Figure 4.6. This problem has
been dealt with macroscopically by Johnson and Silsbeel7 and also independently by van
Son, et a1. 1 8.

Valet and F ert12 have justiﬁed this macroscopic picture by starting from the
microscopic Boltzmann equations and taking the limit that the spin diffusion length is

much longer than the mean free path. From Ref. 12:

 

13:36.92
8 67' 413
La]: = (“s—u-s) .
o, 62 £23!

where for spin, 5, the current density is J, , the conductivity is os=nse213 /m and the spin

diffusion length (SDL) is 4 deﬁned by

1/2
I, = vF[t,f (13;! + 13"!)4 /3] z vF(t,,t, /3)1/2 4.14

The equations
second says 1h.
spill relaxation

for the chemic

the SDL of ea.

in Ref. 18.

In the C I?
conduction ele
layer before it
critically on 1]
adjacent mag,
though the SD
is lhe elastic ,
thickness he“
ﬁnd it harden

68
The equations in 4.13 give two simple expressions. The ﬁrst is just Ohm’s law. The

second says that the spin accumulation due to the divergence of the current is balanced by
spin relaxation through spin ﬂips. Combining equations 4.13 gives the diﬁusion equation

for the chemical potential in equation 4.12, if Dtsf is replaced by (if; which is related to

the SDL of each spin channel by lg} = if + 212, the kind of “average” SDL alluded to

in Ref. 18.

In the CIP geometry, the elastic mfp determines the length scale. A spin polarized
conduction electron must be able to travel from one magnetic layer to the next magnetic
layer before its spin relaxes. For CIP, travel between adjacent magnetic layers depends
critically on the elastic mfp. Electrons will tend to stay in a particular layer, isolating
adjacent magnetic layers, if the layer thickness is much larger than the elastic mfp. Even
though the SDL is typically at least one order of magnitude greater than the elastic mfp, it
is the elastic mfp which determines where the electrons travel. Therefore as the layer
thickness becomes on the order of the elastic mfp, spin polarized electrons in one layer
ﬁnd it harder to propagate directly to the adjacent magnetic layer. If the layers are several
elastic mfp’s then very few spin polarized electrons enter the adjacent magnetic layer
before their spin relaxes, even though the layer thickness may be much less than the SDL.
This will severely reduce the MR in CIP samples and limit layer thicknesses to of the
order of 1.0-5.0nm for reasonable MR changes. In the CPP geometry, propagation
between adjacent magnetic layers does not depend on the electron’s elastic mfp since all

electrons must travel through every layer. It is the SDL of the material that determines

whether or no
the main requi
In a multil
metal and fer
interface will
nature of a :
hmrbolic ex
currents. Figu
in Ref. 12 fo
16411510 the g:

1’Iﬂagnetic cc

69

whether or not an electron will remain spin polarized relative to the next magnetic layer,
the main requirement for GMR.

In a multilayer where the SDL is much longer than the thicknesses of both the normal
metal and ferromagnetic metal, the spin accumulation and relaxation effects for each
interface will interfere resulting in complex expressions for the resistance. The periodic
nature of a multilayer modiﬁes the simple exponential solutions given above to
hyperbolic expressions for the chemical potential, the pseudoelectric ﬁeld and the spin
currents. Figure 4.7 gives a schematic representation of detailed calculations carried out
in Ref. 12 for these three quantities. Matching the boundary conditions at the interfaces
leads to the general expressions for the resistance of a'CPP multilayer in both the AP and

P magnetic conﬁgurations given in equations 4.8-4.11.

 

 

 

r
l

l
l

 

 

 

 

70

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Z

Figure 4. 7: Schematic representation of spin accumulation and relaxation effects for a
multilayer on the chemical potential, u, the pseudoelectric ﬁeld, F, and the spin currents,
Ji for the AP state, a), b) and c); and the P state, (I), e) and f).

4.5 Spin

Increasin
hill of magn
impurities v
paramagneti.
4.3K elimin:
detailed desc
claim. Spll

lntroduc:

elements adt

Hereti', is l
impurities.
impuﬁb’ ato
For Iran:
0f the 45 C0
“ﬁnal bOun
5110111 lie “it
would have
[he COIlducti
111 the 3d in
Slates ClOse
msonanCe is
in energy an

the 3d impur

71
4.5 Spin Flip Scattering by Spin-orbit Interactions

Increasing the spin relaxation rate will signiﬁcantly reduce the SDL and lower the
MR of magnetic multilayers. Spin ﬂips may result from three different sources: (a) from
impurities with strong spin-orbit scattering, (b) from exchange interactions with
paramagnetic impurities or (c) ﬁom electron-magnon collisions. Measurements made at
4.2K eliminate the electron-magnon interaction as a signiﬁcant source of spin ﬂipping. A
detailed description of paramagnetic exchange interactions ﬂipping spins is given by Fert
e! 01.19. Spin-orbit interactions are considered here.

Introducing impurities with strong spin-orbit coupling such as Pt, Au or other 5d

elements adds an extra term, 1: 3:, , to the spin relaxation raters].
l 1 1

0 I
‘s/ W Ts!

Hererg, is the spin relaxation rate due to spin-orbit scattering by defects and residual

impurities. The impurity term is proportional to the number of intentionally added
impurity atoms per unit volume in the host metal.

For transition metal impurities, spin-orbit scattering is attributed to the hybridization
of the 4s conduction band states in the host with the 3d states of an impurity atom. A
virtual bound state is formed when empty electron states in the 3d shell of an impurity
atom lie within the conduction band of the host”. Normally the 3d state of the impurity
would have a speciﬁc energy and an inﬁnite lifetime, but since the state now lies inside
the conduction band it mixes with the conduction electron states. Therefore an electron
in the 3d impurity state is now able to escape into the continuum of conduction band
states close to the energy of the 3d impurity. The lifetime is no longer inﬁnite and a
resonance is seen in the density of states near the impurity state forming a state broadened
in energy and extended in space. The width of the state depends on both the strength of

the 3d impurity potential and the degree of coupling with the conduction electron states.

10 caleula‘
section. A 511:
of the d state .

number of 0’ e1

The spin flip c

“here .1, is ti:
I'ElOCll)’. £111;
The spin diff;

Neglecting the

The 5le dlfllhl
51in channel"

m the fE‘rromaL

311d 11) [he fem)

EquallOns ,

 

72

To calculate the relaxation rate of the impurities, one must ﬁrst ﬁnd the spin ﬂip cross
section. A simple expression given by Yafet21 relating the spin ﬂip cross section in terms
of the d state spin-orbit constant, M, the width of the virtual bound state, A (zleV), the

number of d electrons, Z, and the Fermi wave ntunber, k;, is

2
0;, = i"¥I:Q] sin’(rr Q) 4.15
k, A 10
The spin ﬂip cross section is related to the spin ﬂip relaxation by
i, = N,v,.o,j. 4.16
Ts!

where N, is the concentration per unit volume of impurity atoms and v; is the Fermi
velocity. Equations 4.15 and 4.16 are for nonmagnetic 3d transition metal impurities.
The spin diffusion length may be calculated once the spin relaxation time in known.

Neglecting the residual term in equation 4.14 gives the spin ﬂip mean free path as
1

it = v r I = ——

Sf F 3f 10.3}
The spin diffusin length depends on the spin ﬂip mfp, Ad, and the elastic mfp, 71, in each
spin channel”. The elastic mfp in the nonmagnetic layer is the same in each channel but

in the ferromagnetic layer this is not true. In the nonmagnetic layer the SDL is given by19

 

l/2
hN1”
ti} =[ ‘I ] 4.17
6
and in the ferromagnetic layer by
A A 1". NZ
e; = ———T i ‘1 4.18
30cT + M)

Equations 4.17 and 4.18, together, deﬁne the length scales over which the spin

polarized channels can exist as separate currents.

73

4.6 Positive and Negative Giant Magnetoresistancc

Giant magnetoresistance refers to the change in electrical resistance with applied
magnetic ﬁeld brought about by spin dependent scattering of the conduction electrons.
The difference between positive and negative GMR lies in the conﬁguration of the
multilayer with respect to the spin asymmetry coefficients of either the F layer, (1,; , or at
the PIN interface,aF/N , or both. A two component multilayer has one F component so
that the spin asymmetry parameter is the same in every F layer and at every F/N interface,
either all 01>] or all or<1. At zero ﬁeld exchange forces between the F layers maintain an
antiparallel state, which results in each channel undergoing the same amount of scattering
as indicated in Figure 4.2a Applying a ﬁeld overcomes the exchange interaction and
aligns adjacent F layer moments parallel to each other. This P state causes the same
preferential scattering for one of the channels at every F layer leading to a shorting of the
current by one of the channels, Figure 4.2b. This produces a negative GMR since the
resistance drops as the ﬁeld increases.

A multilayer with two ferromagnetic components, F, and F2 , may be constructed in
such a way that or,>1 for F, while a2<1 for F2. In this way adjacent F layers will have
reversed spin asymmetries. At zero ﬁeld, exchange forces will again maintain an
antiparallel alignment between F, and F2. In the AP state a spin up electron weakly
scattered in F, is also weakly scattered in F 2 because: (1) the magnetization of F2 is
antiparallel to that of F, and (2) the spin asymmetry has changed ﬁ'om or,>1 to a2<1, as
indicated in Figure 4.8a. Applying a ﬁeld to align F, with F 2 leads to a higher resistivity
because now only the spin asymmetry is alternating from F, to F2 so electrons from each
channel now scatter the same amount, Figure 4.8b. This produces a positive GMR since
the resistance increases with applied ﬁeld.

Actually the exchange force is not essential to obtain a positive GMR. However, the
ability to form AP and P states together with alternating spin asymmetries is required.

Whether the AP state is formed by exchange forces or large differences in saturation

(\ﬁ

.7:-

74

ﬁelds between F, and F2 is not important. Positive GMR should be observable for both

the CIP and CPP geometries .

 

For 011>1 and 012<1,

 

 

N F21 b) F,
\i €(r)\l
/\/' e(,)/\‘/P

 

 

\
/'

 

 

Figure 4. 8: Spin dependent scattering of a) AP and b) P states for inverse (positive)
GMR. Scattering is schematically represented as taking place only at the F /N interface
for clarity.

75

 

‘ J. Crangle, Solid State Magnetism, Van Nostrand Reinhold, New York, NY (1991).
2 R. M. Bozorth, F erromagnetism, D. Van Nostrand, New York, NY (1951) p. 423.
3 S. Chikazumi, Physics of Magnetism, Wiley, New York, NY (1964) p. 60.

‘ B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading, MA
(1972) p. 117.

’ J .F. Cooke,
6 C. F ierz. et al., Phys. Cond. Matt, 2, 9701 (1990).

7 C. Fierz. et al., Physica B 165-166, 4553 (1990).
' C. Fierz. et al. (unpublished).

9 J .M. Slaughter, et al., Proceedings of LT-l 8 [Jpn. J. Appl. Phys. 26, Suppl. 263, 1451
(1987).

'° P. Holody, et al. (unpublished).

” S.F. Lee, Ph.D. Dissertation, Michigan State University (1995).

'2 T. Valet and A. Fert, Phys. Rev. B 48, 7099 (1993).

'3 Q. Yang, Ph.D. Dissertation, Michigan State University (1995).

" T. Valet (unpublished).

'5 A. Fert, T. Valet and J. Bamas, J. Appl. Phys. 75 (10), 6693 (1994).

‘6 I.A. Campbell and A. Fert, in Ferromagnetic Materials, edited by HP. Wohlfarth,
(North Holland, Amsterdam, 1982), Vol.3, p. 769.

‘7 M. Johnson and RH. Silsbee, Phys. Rev. B 35, 4959 (1987).
" P.C. van Son, H. van Kempen and P.Wyder, Phys. Rev. Lett. 58, 2271 (1987).
'9 A. Fert, T. Valet and J.L. Duvail, Phys. Rev. B 52, 6513 (1995).

2° J .S. Dugdale, The Electrical Properties of Metals and Alloys, Edward Arnold
(Publishers), London, England (1972) p.137.

2‘ Y. Yafet, J. Appl. Phys. 39, 853 (1968); J. Appl. Phys. 42, 1564 (1971).

Introdu.

For the C11
multilayers 1
Parameters

PerPendicule
aCCESS to [h
interfaCes “.

““1111, t
[0 CU based

CW“ and c
Champ, “,1 l

mumal'ers.

Chapter 5:

Analysis of Co/Cu & Py/Cu
Multilayers

Introduction

For the CIP geometry, derivation of the spin asymmetry parameters in magnetic
multilayers is difficult and often requires one to appeal to a model with a few adjustable
parameters. Measurement of the resistance of a multilayer with the Current applied
Perpendicular to the Plane of the layers, the CPP geometry, allows one to gain direct
access to the spin asymmetry parameters both in the bulk F layers and at the F/N
interfaces without adjustable pararnetersl’z‘3’4’5’6. An extensive study of Ag/Co CPP
multilayers was done by SF. Lee."8 and was further extended to AgX/Co (X=Pt, Au, Sn
and Mn) by Q. Yangg. This study was done to extend the works of both Lee and of Yang
to Cu based multilayers. In this chapter results for the ﬁrst measurements done on CPP
Co/Cu and CPP Py/Cu multilayers will be given and analyzed. Section 6.1 of the next
chapter will explore the role that ﬁnite spin diffusion length (SDL) plays in Co/CuX

multilayers.

76

 

5.1 A8!“

The CO L
ﬁt the data.
(11.111 11» ‘Co' ‘
C001 interfi
and (171150101
we“, produce
both the C0 «1

A prelimi
ﬁxed at 360m
bilayers. San
the presence c
for Samples W
hat the Fe bu
fe buffer were
CofCu multilt:
oscillatory c0;
also provided

Measurements

 

1ire Started h,

(lithe CPP and

 

77

5.1 Asymmetry Parameters in Co/Cu Multilayers

The Co/Cu system was investigated by preparing three different series. To pr0perly
ﬁt the data, equations 4.2 and 4.3 together require information about six quantities:
(a)AR ”NCO, the Nb/Co interface resistance; (b)pCu, the Cu resistivity; (c) AREMCH, the
Co/Cu interface resistance; (d)p2.0, the Co resistivity; (e)BCo, the bulk spin asymmetry
and (Gym/Cu, the Co/Cu interface spin asymmetry. Three different series of samples
were produced, two with constant Co thickness and one which varied equal thicknesses of
both the Co and Cu. The multilayer’s total thickness was kept constant in each series.

A preliminary Co/Cu series was produced with ta, held at 1.5nm and total thickness
ﬁxed at 360nm. The Cu layer was limited to thicknesses which gave integer numbers of
bilayers. Samples were made with and without a 5nm Fe buffer. Parkin10 showed that
the presence of a Fe buffer layer increased the amount of coupling between the Co layers
for samples with thin Cu spacer layers. Our experiments conﬁrmed this, but also showed
that the Fe buffer had little effect on samples with tCu> 5. Own. The samples without the
Fe buffer were therefore used for the global ﬁtting (to be described) to obtain B and y for
Co/Cu multilayers. A series of 1.5nm Co with an Fe buffer was made to verify the
oscillatory coupling seen by others11 for CIP samples of Co/Cu. We will see that this
also provided valuable information on the magnetic state of the as prepared samples.
Measurements of an extensive series of samples with ta, ranging from 0.7nm to 14nm
were started by S.F.Lee and ﬁnished by the author. Figure 5.1 shows the ﬁeld dependence

of the CPP and CIP resistances and magnetization for a typical Co/Cu multilayer with the

78
ﬁeld applied along the direction parallel to the layers. The resistance of each was

measured by starting at zero ﬁeld (H0) and then increasing the ﬁeld until the resistance
saturates at H5. The sample is then cycled once between H5 and -HS. During this cycling
the resistance peaks in two places, :th, near the coercive ﬁeld of the multilayer, shown
in Figure 5.1c. Comparing the ﬁgures in 5.1 reveals that the hysteresis loops in a), b) and
c) are well correlated and features from each curve occur at approximately the same
ﬁelds. Although the Hp state of the CPP in Figure 5.1a) is close to the coercive ﬁeld, He
of Figure 5.1c), a close examination of other samples shows that the Hp state of the CPP
resistance is generally not identical to HC. In fact, M(Hp) may be an appreciable fraction
of M(I-Is)12 . The HS values are perhaps the most well deﬁned states since saturation

occurs when all the moments are aligned. The magnetoresistance is deﬁned as:

RU!) ‘ R(Hs) x 100% (5.1)
R(Hs)

 

MR(H)=

where ROI) and R015) are the resistances at H and at HS (the ﬁeld at which the resistance

saturates) respectively.

79

H (kOe)
-I.0 ~Q.8 -Q.6 -Q.4 —Q.2 0:0 0:2 0:4 0,6 0.8 1 0
90 H0 “,9 -

a) i

 

RCPP (110)
q on
O O
‘\
etc a

at
o
I.
:1
U1

 

50.1....

 

 

 

 

M (l 0‘3 emu)
O

 

 

 

 

_20 ' i L' ~ I l l l l I
-1.0 -0.8 -0.6 -o.4 -o.2 0.0 0.2 0.4 0.6 0.8 1.0

H (kOe)

Figure 5.1: The ﬁeld dependence of a) the CPP resistance, b) the CIP resistance and c)
the magnetization of a [Co(6.0nm)/Cu(6. 0nm)]x60 multilayer.

80
Figure 5.2 shows the MR plotted as a ﬁmction of Cu thickness. The CPP zero and

peak data are plotted along with CIP peak data to show that the effect is generally
doubled in the CPP geometry. The CIP data in Figure 5.2 are typical of those reported
elsewhere”. Bothtthe CPP and CIP samples exhibit oscillatory behavior in the MR.

The oscillatory behavior of the saturation ﬁeld of CIP samples has also been observed
by others”. The coupling constant can be calculated from the saturation ﬁeld of an AF
coupled sample. The oscillating saturation ﬁeld therefore implies an oscillatory behavior
in the strength of the coupling which is usually described as an oscillatory exchange
interaction. In both MR and H5 measurements the oscillations decay with the Cu
thickness until they become negligibly small for Cu thicknesses greater than 6.0nm. In
this work the variation with Cu thickness is studied in the region tCu>6.0nm where the
analysis is uncomplicated by the presence of the oscillatory exchange ﬁeld. The
assumption is made that R(H=0)=R(AP). We will see some experimental evidence
supporting this assumption and further note the prediction of Zhang and Levy15 for the
CPP geometry. Their work‘5 predicts the same AP resistance for a CPP sample
regardless of whether the F layer magnetizations are perfectly antiferromagnetically
aligned or are collinear with a random, statistically uncorrelated (SU) conﬁguration so

long as the multilayer’s total moment is zero, 2 M,- = 0, assuming that each F layer is a
i

single domain.

Mugnetorcsi stance (96)
C)
0

58100.2: 11
[Cr the Copp-

 

81

 

200 . ,
130 ’ AF! Fe(5.0nm){Co(l .5nm)/Cu(tCu)]N j

l

 

l
—e
l

160
140 AF 0 CPP-MR, Ho ;
. 2 A CPP-MR, HP
120 , AF3 [:1 CIP-MR, H0

1 00 ,, _

T V

I
l

 

 

 

V T Y

W
C
l
1

Magnetoresistancc (96)

.h
C
lﬁT'

 

N
O
, ,

 

 

 

 

 

 

 

Figure 5.2: Magnetoresistancc of Fe(5nm)[Co(1.5nm)/Cu(tCu)]xN plotted as a function of
tCm the copper thickness. AF indicates antiferromagnetic coupling. The lines serve as
guides to the eye.

Basis for St
Equa:
.11, F. Bl

thickness. 8:

there the sI
used to deter
.\'-1 is on
SUperconduc
eliminates 11
Small but 111'

next section.

Towel],- Si

’1' and .'

1 [EC
1\

”festive”, a

 

133‘ 54a and

 

82
Basis for Separating Bulk and Interface Spin Dependent Parameters

Equation 4.2 gave ARﬂAP) as a function of four quantities p},pN,AR;/N and
AR s/ r- By constraining the relationship between IN and tp, ﬁxing t,, the total sample
thickness, and ignoring the differences between N and N-l , equation 4.2 becomes:

ART(AP) = Intercept+ Slope x N 5.2

where the slopes and intercepts are given Table 5.1 below. These relationships can be
used to determine values for p}, p N , AR ;, r and AR S, F. The difference between N and
N-l is only important for small numbers of bilayers. It arises because the
superconducting proximity effect in the Cu layer directly underneath the top Nb lead
eliminates the resistance of one Cu layer and one Co/Cu interface. This correction is
small but will be taken into account in the global ﬁt of all three sets of Co/Cu data, in the

next section.

Table 5.1: Slopes and intercepts for equation 5.2 above.

 

 

 

 

 

 

tN and t; relations Intercept Slope
t,:=constant ZARSIF‘l'PN’r (p}—pN)tF+2AR;-,N
t,.-=t,,, ZARS/f "'(Pir +PN )tr /2 2141?;le

 

 

The data for tC0=I.5nm, tCo=6.0nm and tCo=tCu are listed in Tables 5.2, 5.3 and 5.4,
respectively, and are plotted as a function of the reduced bilayer number (N -l) in Figures

5.3a, 5.4a and 5.5a, respectively. The AR, values for ﬁelds H0, Hp and HS are shown. In

83

each case there is a linear relation between ART and N-l. Assuming that the true AP state
of a multilayer corresponds with the highest resistance, it would appear that the H0 data

approximate the AP state better and ﬁts to AR,(AP) should use the H0 data. According to

Table 5.1 the slope of the t~=tp data directly measures 2AR ,1, N, the F/N interface
resistance. The appreciable slope in Figure 5.5a clearly indicates this quantity contributes
signiﬁcantly to the overall resistance of each multilayer. The Nb/Co interface resistance
was determined independently on series of Nb/Co/Nb sandwiches with varying ta, ’6.
Interestingly, the Nb/Co interface resistance remained the same for a series of sandwiches
with the Co grown on a 5.0nm Fe buffer”. With knowledge of the Nb/Co interface

resistance, the intercept of the ﬁxed ta, data is used to estimate the Cu resistivity which

can then be compared with resistivity measurements done on 300nm thick Cu ﬁlms. The

value of p} can then be determined from either of the remaining two relationships in
Table 5.1. Table 5.5 lists the slopes and intercepts obtained from a least squares ﬁtting of

the H0 data shown in Figures 5.3a, 5.4a and 5.5a.

Table 5. 2: CPP and CIP values at H0, Hp and HS for [Co(1.5nm)/Cu(tCu)]xN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tCu nm N CPP AR (MI) CIP (o)
#
H0 HP H8 H0 HP I'Is

343-A1 28.5 12 20.71 19.32 17.40 1.4318 1.3968 1.3517
343-08 28.5 12 20.09 18.14 16.28 1.2207 1.1869 1.1416
343-04 18.5 18 27.09 23.61 20.01 1.6731 1.1869 1.5011
343-01 13.0 25 32.15 29.22 23.56 --------

357-07 10.5 30 41.61 34.47 26.74 2.5920 2.3883 2.1650
342-A2 8.0 38 47.40 39.37 28.59 3.1230 2.8217 2.4845
343-03 8.0 38 48.22 39.17 28.25 3.2852 2.9300 2.5760
342-05 6.0 48 59.67 49.21 34.34 4.0193 3.5817 3.0893

 

 

“ _ ‘A...ﬂ

 

 

 

84

Table 5.3: CPP and CIP values at H0, Hp and HS for [Co(6. 0nm)/Cu(tCu)]xN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tCu nm N CPP AR (me1) CIP (Q)
#
HO Hp H5 H0 Hp HS
357-01 54.0 12 30.96 29.26 27.27 0.3858 0.3840 0.3818
343-03 30.0 20 41.37 37.95 31.93 0.7426 0.7234 0.6982
357-03 24.0 24 45.69 40.71 33.86 0.9675 0.9628 0.8934
393-01 22.8 25 45.69 42.65 34.67 1.0196 0.9958 0.9474
325-05 20.0 28 51.54 47.29 37.74 0.9309 0.8979 0.8506
325-04 15.0 34 54.74 48.06 36.89 --------- 0.7341 0.6908
325-03 12.0 40 65.01 57.20 42.77 1.1703 1.1208 1.0191
325-02 9.0 48 75.95 64.26 46.50 1.5873 1.4444 1.2783
434-06 7.1 55 91.61 74.66 52.69 1.6332 0.9360 0.7166
325-01 6.0 60 100.39 76.59 63.67 --------- 2.2341 1.8663
Table 5. 4: CPP and CIP values at H0, Hp and HS for [Co(tC0=tC,, )/Cu(tc,)]xN
Sample to, nm N CPP AR (film‘) CIP (Q)
#
Ho Hp Hs Ho H, Hs
392-03 20.0 18 46.99 41.06 36.04 0.7894 0.7850 0.7728
342-04 18.0 20 51.96 46.27 39.84 1.1188 1.0770 1.0336
378-06 14.4 25 59.03 53.71 47.11 0.7144 0.7111 0.6984
319-04 12.0 30 66.24 57.50 48.99 1.4939 1.4522 1.3605
342-03 12.0 30 67.98 57.88 47.69 0.9741 0.7917 0.7704
342-02 9.0 40 76.47 64.62 50.47 0.6846 1 .5473 1 .4037
376-03 8.0 45 74.88 61.41 45.69 1.6375 1.4684 1.2660
342—01 7.2 50 88.42 76.49 59.73 2.3116 2.2170 2.0186
318-01 6.0 60 l 13.52 93.74 73.25 2.4826 2.2743 2.0475
328-01 6.0 60 104.27 79.74 64.87 2.2660 2.1820 1.9369

 

 

 

 

 

 

 

 

 

 

 

 

85
The quantities p}, p N , AR ;, r and AR 5, F may all be calculated using the values for

the slopes and intercepts given in Table 5.5, but the values obtained this way give some
inconsistent results depending on which pair of conditions are chosen from Table 5.1. In
the next section a global ﬁt using all three sets of H0 data along with the HS data which

we now examine will be used to obtain more representative values.

Table 5.5: Slopes and intercepts of the three CPP Co/Cu series.

 

 

 

 

t; Intercept (me‘) Slope (ern‘)
1.5nm 7.9:t0.5 1.06i0.02
6.0nm 13511.4 1 3210.5

t,.-=tN 24.6il.S 1.29r0.04

 

 

 

 

 

 

86

 

 

 

 

 

 

   

   

   

 

 

 

 

 

 

tCu (nm)
a) 15.6 7.3 4.4
120 - -
0 Ho data
100 L A HP data
0 Hsdata
g: 80
E
C:
‘b-I
V 60 ~
[—
at
<
40
20
{C00 .5 nm)/Cu(tCu)} N
0 A; I 1 r l A l r 1 I
0 10 20 3o 40 50 60 70 80
DH
b) tCu (nm)
15.6 7.3 4.4
100 - r . r
'5 90 *- {Co(l.5nm)lCu(tCu)}N j
3:" 30 _ s
8 .
a 70 — -
t- » «
5 60 - e
a L Q
..E? 50 1
15 40 ~ —
2'; 30 — Q
a 1
i 20 - “
O
3 10 ~ ~
0 1 t 1 . L A; A t . . l .
0 10 20 30 40 50 60 70 80

Figure 5.3: Plots ofa) AR,- vs. NJ and b) JART(H0)[ART(HO)- ART(HS)] vs. N-I for
[Co(1.5nm)/Cu(tc,,)]xN multilayers. In a) the lines represent ART(H0) and ART(HS)
and in b) the line represents JART(H0)[ART(H0)-ART(HS)] using the parameters
derived from the global ﬁt to all three sets of data given in Table 5.6. Total sample

N-l

 

 

thickness is 360nm.

87

 

 

 

 

 

 

 

 

 

 

 

 

 

tCu (11111)
a) 28.3 11.6 5.8
120 ~ T ‘ i . V ‘ ~
0 H0 data .
100 _ A HP data 0 A
. :1 H8 data 0
(cg 80 r o A A ‘
c .
2: 6o - O ' A D —
. I
g .c A A ' [j
40 ’— O “ 1:1 I ‘ T
1- ‘; D d:
20 e r
{Co(6.0nm)/Cu(tCu}N
0 r i r ' r I i 1 t 1 1 t 1 A
0 10 20 30 40 50 60 70 80
N-l
b) to: (am)
28.3 11.6 5.8
100 I ' I ' T Y I ' I I T
"A r- 4
g 90 j {Co(6.0nm)/Cu(tCn)}N j
’ 2: 80 c
3 ,
a 70 -
E.‘ -
g 60 — o O -
g 50 r l
v 1
5 40 h 1
2'; 30 ~ 0 -
a . ~
5 20 f ‘
g 10 e a
O r L u_ l L l A A 1 l t l 4 r
0 10 20 30 40 50 60 70 80

N-l

 

Figure 5.4: Plots of a) ART vs. N-I and b) JAR,(H,)[AR,(H,) — AR,(HS)] vs. N-I for
[Co(6.0nm)/Cu(tc,)]xN multilayers. In a) the lines represent ART(H0) and ART(HS)
and in b) the line represents JAR,(H,)[AR,(H0)-AR,(HS)] using the parameters
derived from the global ﬁt to all three sets of data given in Table 5.6. Total sample
thickness is 720nm.

 

88

 

 

 

 

 

 

 

 

 

tCu (nm)
a) 17.1 8.9 5.9

E

C

b

t—

a:

<

20 ~ 4
{Co(tCo=tCu)/Cu(tCu)}N
o t 9 t L I r 1 1 . 1 t 1 m
0 1 0 20 30 40 50 60 70 80
hLl
b) tCu (nm)
1 7.1 5.9 8.9
l 00 T I ' 1 ' l f r, , v , Y

 

90 T {Co(tCO=tCn)/Cu(tCu)}N

 

 

 

\/{AR1‘(Ho)-ART(H8))ART(HO) (mmz)

 

 

0 . I r L A I # 4 4 l A I A I L
O 10 20 30 4O 50 6O 70 80
bLl

 

Figure 5. 5: Plots of a) ART vs. NJ and b) JART(H0)[ART(H0) — ART(HS)] vs. N-I for
[Co(tCo=tC,, )/Cu(tCu)]xN multilayers. In a) the lines represent ART(H0) and AR,~(HS)
and in b) the line represents JART(H0)[ART(H0)—ART(HS)] using the parameters
derived from the global ﬁt to all three sets of data given in Table 5.6. Total sample
thickness is 720nm.

 

89

The spin asymmetry parameters may be estimated once the resistivities are known.
This is done by using equation 4.4 which is linear in the bilayer number and groups
experimental quantities on the left and the two unknoWns B and 7 on the right. For ﬁxed

ICU equation 4.4 becomes:

 

At/RtHonRtHo) — R(Hs)l = NIBP'COICO +r24Ré.,e.1 5.3a

and for tCO = t Cu:

 

AJR(Ho)[R(Ho)- R(Hs)1 = 13920 tr/z + erAREae. 5.3b
The slope of the right hand side of equation 5.3a (ﬁxed too) versus N contains both B and

7 while equation 5.3b (tCothu) separates B and y by intercept and slope. The data are

displayed in Figures 5.3b, 5.4b and 5.5b.

Global Fit of the Co/Cu Data

Fitting all three sets of data simultaneously helps eliminate inconsistencies in the
data. The same procedure used for the analysis done by S.F.Lee3 on Co/Ag is applied
here to Co/Cu. Analysis is now done for all the data at once.

The N-l corrected versions of equations 5.2 for the AP state and equations 5.3 for the
square root quantity are given below as equations 5.4 and 5.5, respectively.

For tC0=constantz

ARI?!) = 2ARNb/Co + N pCutT + pz’otCo + (N — 1)[(p2'o — pCu)tCo + 2ARCo/Cu] 54a

 

 

AJR(Ho)[R(Ho) - R(Hs)] = (N —1)llip2.re. + 724R£.,e.l+ Boats. 5.4b

90

 

and tCo=tCuz
’4pr = ZARNb/Co + (960 '*' Poultr " Pcu’ Cu + (N ‘1)2AR6o/Cu 5-53
AJR(H0)[R(H0) - R(Hs)l = pro ’r/2 + (N ‘1)1’ZAR6c/Cn 55b

First AR NW0 is regarded as an independently determined quantity8 and the three sets
of Ho data (tC0=I.5nm, tC0=6.0nm and tCo=tCu) are simultaneously ﬁt18 to equations 5.4a

and 5.5a. The x2 for each data set is found and summed together. The total x2 is then

minimized using p20,pCu and AR 50,0, variable parameters. A similar ﬁt is done for all

 

three sets of square root data, JAR(H0)[AR(H,)—AR(H,)], to equations 5.4b and
5.5b to obtain the parameters 136013 and yZARéNCu. Now the spin dependent parameter B

and y can be determined using Pbc and 2AR2‘30,Cu given by the H0 ﬁts.

The (Co=tc,,=6.0nm samples have been listed as either belonging to the tCo=6.0nm set
or the tCo =tC,, set but not both which would weight them more heavily than the other
points in the ﬁt. The uncertainties quoted here have been adjusted so that the x2 is
reduced to the number of degrees of freedom for each ﬁt. The number of degrees of
ﬁeedom is just the difference between the number of data points and the number of
unknown parameters in the ﬁt. There are 28 data points in both ﬁts with 3 unknowns in
the Ho ﬁt and 2 unknowns in the HS ﬁt. Therefore the H0 ﬁt has 25 degrees of freedom

while the HS ﬁt has 26 degrees of freedom. The uncertainty of each data point is

increased by a factor of ,le /25 for H0 and ,le /26 for H5. This procedure is based on

the admission that there are uncertainties in the data whose nature is not known.

The results of the Ho ﬁt are given below:

91
pCu = 7:3 an
pg, =75r5 an
AR50,C, = 0.51:0.02 trim2

The x2 was 83 for degrees of freedom 25, before uncertainties were adjusted.
The HS ﬁt gave:

no}, = 34:3 norn
yARgm = 0.39:0.01 m2

The x2 was 250 for degrees of freedom 26, before uncertainties were adjusted. The spin

asymmetry parameters may now be calculated. They are:

B=0.46i0.05
y =0.77r0.04

Using Poo = p2,,(1- B2) and RC0,“ = Raw-”(1 — 72 ) , the best values for the Co resistivity
and interfacial Co/Cu resistance are:

pa, = 601 10 nﬂm
ARGO,“ = 0.2032002 m2

The asymmetry ratio between the spin down channel and the spin up channel may be

 

calculated using the following:
p‘ (1+9)
C0 = ——$—‘-’- = = 2 7 ﬂ: 0 3
pCo (1- B)
l
ace/Cu = RCO/Cu = (1+7) = 7.7 i 1.3

Rgo/ Cu (1 - 7)
Comparing the resistance ratios of the spin down to spin up channels for bulk Co and
Co/Cu interfaces gives a measure of which contributes more to the MR of the system.

The resistance of the Co/Cu interface gives the same resistance as 7.0nm of Co. For

92

Co/Cu samples with tCo=7.0nm the a’s calculated above indicate that the interface
contribution to the spin dependent scattering is 2.8 times more than the contribution from
bulk Co. Therefore the spin dependent scattering most responsible for GMR must be
located near the Co/Cu interface.

Although the Ho state seems to be more representative of the true AP state, it suffers
from the fact that once the saturation ﬁeld is applied the H0 state can never be recovered.
More will be said in the Py/Cu section about trying to recover the original HO
measurement. The Hp (and HS) measurements are quite stable and very reproducible with
both ﬁeld cycling and thermal cycling. In the same measurement run, the Hp and HS data
for the initial ﬁeld cycle are identical to Hp and HS values obtained in later cycles.
Thermal cycling between room temperature and 4.2K produces little difference between
the original Hp and HS values and those taken after cooling to 4.2K again. Even
measurements of the same sample taken months apart agree within mutual uncertainties,
demonstrating that oxidation is not a problem.

The N-l correction changes the relations in Table 5.1 in two way. (a) First, the
equations are now linear in N-l (if N is large) and the resistance of the extra (Nb) Co
layer is added to each of the intercepts. (b) Second, the Cu term, Pct/r: in each intercept
is no longer a constant, but proportional to (N-1)/N. In Figures 5.3a, 5.4a and 5.5a the
observed curvatures in the ﬁts are attributed to this non-linear Cu term. For large N the
Cu term becomes nearly constant since (ND/NM and the ﬁts appear linear in N-l. As

N—)1, the Cu term goes to zero resulting in a lower intercept than that expected from an

extrapolation from the high N data. For the tCo=6.0nm series Pch = 4.3 film2 (half that

93

for the other two series). Since pat, is small, we are unable to attribute any curvature in

our data to this non-linearity.

Table 5. 6: Summary of ﬁtted Ho parameters (see text for ﬁt description) and independent
measurements. A ZARNWO of 61me2 was assumed in the ﬁt.

 

 

 

 

 

 

 

 

 

 

 

independent measurements H0 ﬁt units
ZARNb/Co 6.1:0.6 fanz
pa, 6:1 7:3 an
pCO 60:10 60:10 an
Pbo 75:5 nan
B 0.46:0.05
ac, 2.7:0.3
ARGO/C, 0.20:0.02 me‘
A R20 / Cu 0.51:0.02 fan1
y ' 0.77:0.04
area/C, 7.7:1.3

 

 

 

 

 

 

To determine whether or not the parameters in Table 5.6 (obtained from ﬁtting data in
the uncoupled region of Figure 5.2) are consistent with the strongly AF -coupled Co
layers at the AF,, AFZ and AF, peaks of Figure 5.2, a plot of AR,(HO) and ART(HS) as a
function of the corrected bilayer number for the Fe(5.0nm)[Cu(tCu)/Co(1.5nm)]xN series
is compared with the values based on the ﬁtted parameters from Table 5.6. This is shown
in Figure 5.6. The ﬁtted parameters describe the Ho data quite well near the 1st and 2"d

AF peaks (tCu=0.9nm and 2.1 nm). The 3rd AF peak in Figure 5.6 is somewhat below the

94
H0 ﬁt. Since the coupling is stronger for thinner Cu layers, the ﬁrst AF peak should be

the closest to a perfect AP state. However, the strong AF coupling here is extremely
sensitive to ﬂuctuations in the Cu thickness19 so it is hard to determine whether or not the
sample is completely AF or contains some F coupled regions. The second AF peak is
less sensitive to Cu layer thickness ﬂuctuations and so easier to use for precisely locating
the peak AF coupling. Since the HO ﬁt directly connects AF, and AF 2 with the
uncoupled region, one may conclude that either: a) The as-deposited state of the F layer
magnetizations for samples in the uncoupled region must be aligned antiparallel,
possibly by magnetostatic interactions between the Co layers which may arise ﬁ'om the
layering or thickness ﬂuctuations in the sample. b) The as-deposited conﬁguration of the
F layer magnetizations is random in accordance with the theoretical prediction of Zhang
and Levyz. For the CPP geometry, they predict the AP resistance of multilayers with a
random arrangement of F layer magnetizations is equivalent to the AP resistance for
strongly AF coupled multilayers. Figure 5.6 may provide experimental evidence
supporting the theoretical prediction of Zhang and Levyz, however, further experiments
must be done to eliminate magnetostatic interactions as the cause of possible AP ordering
in the H0 state.

The H3 ﬁt represents the uncoupled HS data well but lies consistently above the HS
data in the coupled region. Some samples in the coupled region (near F, and F 2 in Figure
5.6) have their H0 data lying slightly above the HS ﬁt which is an indication that these

samples are strongly F-coupled.

200

180

160

140

ART (fflmz)

80

60

40

Figure 5. 6: AR,» vs. the bilayer number N-1 for the Fe(5nm)[Co(1.5nm)/Cu(tc,,)]xN

system. The lines represent AR ,4}, and AR; using the parameters derived ﬁ'om the global
ﬁt to all three sets ofdata given in Table 5.6 with Ho as the AP and then Hp as the AP

state.

95

tCu (nm)
3 . 0

1.5

 

 

E5
3'
s

DDO

 

 

 

120
100

l
Uncoupled *—-,

O
A

I DO

20

 

AF2

6

OA6

0

AF
OF2A
A

Q
a:

D

CID

1:1"119‘>

DD

‘16:.

F1

Fe(5 .Onm) {Co(l .5nm)/Cu(tCu)} N

l

 

N-l

80 100

120 140

 

96
As a side note, the ﬁrst AF peak has both H0 and Hp points overlapping, indicating

that the AF coupling is same for both states. The second AF peak shows a signiﬁcant
difference between the H0 and Hp resistances. The weaker AF coupling might be unable
to overcome pinning forces which cause some F layers to remain parallel to each other
after saturation.

To summarize, Co/Cu multilayers were analyzed in terms of the two channel model.
The spin asymmetry parameters for both bulk Co and the Co/Cu interface were estimated
by globally ﬁtting three separate series of H0 and HS data. Results from this ﬁt are given
in Table 5.6. It was found that the Co/Cu interfaces contribute signiﬁcantly to the
multilayers’ total resistance, one Co/Cu interface resistance is equivalent to the resistance
of 7.0nm of Co. In addition, (1Com, = 7.7 > a0, = 2.7 meaning that the Co/Cu interface
contribution to the spin dependent scattering is almost a factor three greater than the
contribution from bulk Co. Experimental evidence supporting the equivalence of

statistically uncorrelated and antiparallel states is given in Figure 5.6.

 

' S.F. Lee, W.P. Pratt Jr., Q. Yang, P. Holody, R. Loloee, P.A. Schroeder and J. Bass, J.
Magn. Magn. Mater. 118, L1 (1993).

2 BE. Camblong, S. Zhang and P.M. Levy, Phys. Rev. B 47, 4735 ( 1993).

3 WP. Pratt Jr., S.F. Lee, P. Holody, Q. Yang, R. Loloee, J. Bass and RA. Schroeder, J.
Magn. Magn. Mater. 126, 406 (1993).

4 G.E.W. Bauer, Phys. Rev. Lett. 69, 1676 (1992).
5 Y. Asano, A. Oguri and S. Maekawa, Phys. Rev. B 48, 6192 (1993).
6 H. Itoh, J. Inoue and S. Maekawa, Phys. Rev. B 51, 342 (1995).

7 SF. Lee, Ph.D. Dissertation, Michigan State University ( 1994).

97

 

' S.F. Lee, Q. Yang, P. Holody, R. Loloee, J. H. Hetherington, S. Mahmood, B. Ikegami,
K. Vigen, L.L. Henry, P.A. Schroeder, W.P. Pratt Jr. and J. Bass, Phys. Rev. B 52, 15426
(1995)

9 Q. Yang, Ph.D. Dissertation, Michigan State University (1995).
‘° S.S.P. Parkin, Z.G. Li and DJ. Smith, Appl. Phys. Lett. 58, 2710 (1991).

" D.H. Mosca, A. Barthélémy, P. Etienne, A. Fert, P.A. Schroeder, W.P. Pratt Jr. and R.
Loloee, J. Magn. Magn. Mater. 94, L1 (1991).

'2 P.A. Schroeder, S.F. Lee, P. Holody, R. Loloee, Q. Yang, W.P. Pratt Jr. and J. Bass, J.
Appl. Phys. 76, 6610 (1994).

'3 S.S.P. Parkin, R. Bhadra and KP. Roche, Phys. Rev. Lett. 66, 2152 (1991).

"S. S..P Parkin, Phys. Rev. Lett. 67, 3598 (1991); S. S.P. Parkin, N. More andKHP
Roche, Phys. Rev. Lett. 64, 2304 (1990).

‘5 S. Zhang and P. Levy, Phys. Rev. B 47, 6776 (1993).

'6 C. Fierz, S.F. Lee, J. Bass, W.P. Pratt Jr. and RA. Schroeder, J. Condens. Matter 2,
9701 (1990); Physica B 165-166, 453 (1990); J.M. Slaughter, J. Bass, W.P. Pratt Jr.,
P.A. Schroeder and H. Sato, Jpn. J. Appl. Phys. 26, Suppl. 26-3, 1451 (1987).

'7 P. Holody, et al., unpublished.
" S.L. Meyer, Data Analysis for Scientists and Engineers, Wiley, NY, New York (1986).

'9 F. Giron, P. Boher, P. Houdy, P. Beauvillian, K. Le Dang and P. Veillet, J Magn.
Magn. Mater. 121, 318 (1993).

98

5.2 Spin Asymmetry Parameters in Py/Cu Multilayers

To gain further insight into the differences between bulk and interface spin dependent
scattering in magnetic multilayers, three series of Py/Cu (Py=Nig4Fe,6) multilayers
similar to those prepared for the Co/Cu study were made. Unlike Co/Cu where the
impurities are concentrated near the F/N interface, a layer of permalloy will have Fe
atoms evenly distributed over the entire thickness of each Py layer, so that impurity

scattering (Fe in Ni) now takes place throughout the Py layers, which suggests that a large

bulk spin asymmetry will exist. Fert and Campbell1 have shown that or = p‘L / pT for

impurities of Fe in a Ni host is large for dilute alloys. One might therefore expect that
orpy> 010,. Furthermore if one considers the Py/Cu interface to approximate an alloy of Ni
in Cu, then the much lower or for Ni in Cu suggests that perhaps apy> orb/Cu. Part of the
motivation in performing measurements on Py/Cu was to see if these crude predictions
would be correct.

Measurement of the CPP resistance for a series of Py/Cu multilayers is the best way
of accessing the relative amounts of interface and bulk scattering in this system. Three
separate series of Py/Cu samples were made; two with constant tpy (1.5nm and 6.0nm)
and another with tpy=th Unlike the Co series all samples were limited to a total
thickness of 360nm in an effort to minimize the waviness of the layered structure2 which
may correlate with HC3 .

The ﬁeld dependence of the MR for a typical Py/Cu multilayer is shown Figure 5.7

along with the magnetization. The peaks in both CPP and CIP MRS after saturation occur

99

near but not at the coercive ﬁeld in the magnetization curve. The range of ﬁeld over
which the resistance changes is much smaller than that for Co/Cu in Figure 5.1. The
average Hp is 200e for tpy=1.5nm and 6.0 Oe for tpy=6.0nm, more than a factor of 20
smaller than the average Hp for Co/Cu. The saturation ﬁelds are nearly 10 times smaller

in Py/Cu than in Co/Cu.

100

H (kOe)
-0.2 -0.1 0.0 0.1 0.2

 

 
  

ARCPP (n0)

 

 

 

 

 

 

 

 

 

 

Figure 5. 7: The ﬁeld dependence of a) the CPP resistance and b) the magnetization for a
[Py(6.0nm)/Cu(8.4nm)]x25 multilayer. Note that the resistance changes over a much
smaller ﬁeld range then for the Co/Cu multilayer shown in Figure 5.1.

101
The data for each Py/Cu series, tp,.=1.5nm, the tpy=6.0nm and tpy=th is presented in

Tables 5.7, 5.8 and 5.9, respectively. As will be shown the Py/Cu system proved to be
much more difficult to analyze than the Co/Cu system for the following reasons: (a) The
scatter of the experimental points is much greater in the Py/Cu system than in the Co/Cu.
(b) The coupling between Py layers extends out to thicker Cu layers than did the coupling
between Co layers in Co/Cu. (c) The largest resistance measured for the Py/Cu system
was not always the Ho resistance as it was for Co/Cu.

Oscillations in the CIP-MR for Py/Cu multilayers were ﬁrst reported by S.S.P.
Parkin". The MR (deﬁned in equation 5.1) for our tpy=1.5nm samples is plotted in Figure
5.8 as a function of the Cu thickness. The CPP-MR and CIP-MR peaks occur at the same
Cu thickness and both MR’s exhibit the same oscillation length of 1.2nm. Peaks in both
the CIP-MR and CPP-MR indicate strong AF coupling between Py layers. The three
antiferromagnetic peaks seen by Parkin4 are also given in Figure 5.8 for comparison.
Evidence for the oscillatory coupling extending out to tCu=6. Gun: is seen in Figure 5.8 but
the 3rd, 4th and 5th AF peaks are somewhat diminished indicating that a signiﬁcant
portion of the sample is F -coupled. Only the 1st and 2nd AF peaks can be identiﬁed as
having strong AF-coupling. As was the case for Co/Cu, Figure 5.2, the CPP-MR is
roughly twice that of the CIP-MR. Samples with tCu>10.0nm have a monotonically
decreasing Ho CPP-MR, and therefore these samples are considered to be uncoupled.
The region between tCu=6.0nm and tCu=10.0nm has MR’s which are signiﬁcantly lower
than both the strongly AF samples for thin Cu layers and the uncoupled samples with

thick Cu layers. Several samples in this region also show the Hp CPP-MR higher than the

102
Ho CPP-MR. Unlike the Co/Cu system, the crossover from oscillating MR 10

monotonically decreasing MR is not well deﬁned in the Py/Cu system. However, cutting
off the data at a Cu thickness in which the CPP-MR is clearly monotonically decreasing
with Cu thickness will allow a direct comparison of 0er and awe“ with (loo and ago/Cu,

the major point in this study.

Py(5.0nm) {Py(l .5 nm)/Cu(tCu)}N

 

 

 

 

 

 

 

 

 

 

 

 

l 00 . r r r r . l
o CIP, Parkin ;
A CIP, HP .
D CPP, H0 _
A o CPP, HP .
SE a
o .
0
a _
g I!
O? =
3 N 0 d
5 .. <>
0 a A
S u 0 0
o .. 0 <3
8 I 0 1 2 14
ten (nm)

Figure 5. 8: The CPP-MR for Ho (squares) and Hp (diamonds) is plotted for the
Py(5. 0nm)[Py(I.5nm)/Cu(tc,)]xN series. The CIP-MR for Hp (triangles) is plotted for the
slightly different Py(5. 0nm)[Py(1.5nm)/Cu(tc,,)]x14 series to compare with Parkin" (ﬁlled
circles). Measurements were made at 4.2K except for Parkin’s which were done at 300K.

103

Table 5. 7: CPP values at H0, Hp, HS and HD for the [Py(1.5nm)/Cu(tCu)]xN series. The
data above the blank row were used in Fits A and B, given later.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tcu N Area CPP-AR(H) fQ-ml
# nm mm2 Ho Hp HS HD

432m 435 8 1.304 18.11 16.65 14.35

410‘" 345 10 1.253 20.29 19.34 17.11

417"“ 285 12 1.276 22.00 20.38 17.07

417‘” 225 15 1.261 25.80 23.64 20.38 25.44
409‘” 185 18 1.306 29.94 28.07 22.56

425“1 149 22 1.416 31.92 27.72 22.35 31.77
403‘” 129 25 1.272 41.38 35.83 28.27

432‘” 105 30 1.174 44.18 34.86 28.10

425‘" 94 33 1.175 41.42 40.78 32.02

377‘” 80 32 1.327 37.48 37.97 30.13

378‘" 80 38 1.259 43.95 45.08 35.84

509‘” 75 40 1.209 36.66 38.66 30.03 41.49
504‘" 70 42 1.323 37.39 40.12 30.04

42508 65 45 1.181 46.06 42.20 34.81

377m 60 48 1.225 46.95 47.47 36.38

509‘” 57 50 1.327 43.58 47.12 37.38 49.88
417‘" 53 53 1.326 49.48 46.84 36.35

5440* 51 55 1.313

54413F 47 58 1.288 56.76 58.68 54.72 60.81
403‘” 45 60 1.293 54.36 57.27 51.03 58.17
544‘" 45 60 1.293

377“1 40 65 1.261 49.63 49.37 48.26

425‘” 36 71 1.183 46.02 47.10 40.79

432‘” 35 72 1.126 47.02 44.88 41.29

509ms 33 75 1.347 48.70 53.19 39.41 54.85
544‘" 33 75 1.145 56.99 57.60 51.20 60.55
544‘” 32 77 1.323 52.75 52.90 50.97 53.80
503“ 30 80 1.466 63.12 63.42 60.50

491“ 20 100 1.625 102.25 99.00 73.43

509m 20 103 1.242 121.03 113.17 66.02

5090‘ 15 120 1.391 60.91 61.04 60.74

503‘“ 8 157 1.405 158.01 153.48 83.76

 

 

104

Table 5.8: CPP values at Ho, Hp, HS and HD for the [Py(6.0nm)/Cu(tCu)]xN series. The
data above the blank row were used in the Fits A and B, given later.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tCu N Area CPP-AR(H) fQ-m‘
# nm rnrn2 H0 H. HS 14,,

432‘” 540 6 1.411 18.77 17.24 15.58

699‘" 454 7 1.284 24.24 24.32 21.53 25.54
425‘” 340 9 1.282 24.67 23.16 19.70

409‘” 300 10 1.369 28.11 27.73 21.64

613‘" 267 11 1.461 31.08 28.80 21.20 31.02
4,7‘” 240 12 1.212 38.09 30.35 28.01

580 240 12 1.250 33.13 24.63 21.96 32.50
433‘” 217 13 1.335 33.06 29.82 25.96

699‘” 217 13 1.186 29.71 30.97 23.98 35.15
580“1 197 14 1.393 37.01 31.40 28.31 41.97
699‘” 180 15 1.312 30.32 31.45 23.87 34.31
417‘” 180 15 1.321 40.00 31.36 29.24

58005 165 16 1.285 48.93 33.51 32.07 48.06
424‘” 165 16 1.234 51.93 48.20 40.64

373“ 150 17 1.185 36.26 32.77 27.60

613‘” 140 18 1.554 40.62 40.00 30.21 42.49
403‘" 130 19 1.300 43.46 45.02 33.06

373““ 110 21 1.181 33.07 32.04 29.65

613‘” 92 23 1.285 37.62 35.31 32.50 39.68
417‘” 84 25 1.211 46.35 45.46 42.40

578‘” 84 25 1.580 36.41 37.06 31.64 39.98
613‘" 78 26 1.613 36.82 34.89 32.83 36.71
377‘” 60 30 1.339 39.64 39.84 37.50

613‘” 49 33 1.293 40.73 40.95 39.28 41.52
3770* 40 36 1.151 43.20 43.18 42.51

425‘” 40 36 1.251 40.01 40.03 39.02

425‘” 35 38 1.195 43.32 43.27 42.77

40301F 30 40 1.265 53.49 - 53.42

5,0“ 30 40 1.356 40.02 40.05 39.52 40.05
510‘” 20 45 1.305 47.76 47.86 47.44 47.98
510‘” 15 48 1.210 46.20 46.15 46.04

510‘" 8 53 1.258 73.75 72.77 56.80 73.24

 

 

105

Table 5.9: CPP values at H0, Hp, HS and HD for the [Py(tpy=tCu)/Cu(tc,,)]xN series. The
data above the blank row were only used in Fit B, given later.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tCu N Area CPP-AR(H) fQ-ml
# nrn nun2 H0 Hp HS HD

628‘" 360 5 1.422 32.08 32.65 27.79 31.13

424‘" 300 6 1.135 35.63 34.31 31.81 38.07

627‘" 300 6 1.289 30.42 31.20 26.00 31.61

424‘” 225 8 1.173 30.58 32.01 28.88 32.70

628‘” 200 9 1.304 33.33 35.03 29.26 38.02

433‘” 180 10 1.218 40.05 37.65 35.63

438‘" 180 10 1.390 40.87 37.60 35.55 42.35

628‘” 164 11 1.513 33.71 33.32 27.42 35.40

424‘” 150 12 1.350 35.32 35.94 31.57 38.11

627‘” 150 12 1.640 35.59 34.82 30.70 37.74

424‘” 180 10 1.327 53.94 53.40 50.93

403‘" 120 15 1.382 40.15 39.36 37.28 41.73

438‘” 90 20 1.274 39.26 38.44 36.97 40.89

628‘” 90 20 1.517 34.25 33.03 30.01 35.22

404‘” 75 24 1.246 42.16 39.87 39.30 41.76

438‘” 67 27 1.212 37.24 37.35 36.31

403‘” 60 30 1.241 44.62 43.56 42.15

628‘” 60 30 1.427 37.47 36.53 33.64 38.06
‘ 433‘“5 56 32 1.274 38.02 37.98 36.92

404‘" 45 40 1.427 49.81 49.57 48.63

417‘” 45 40 1.194 43.54 -....- 42.58

403‘” 36 50 1.258 45.62 45.46 44.79

509‘” 15 120 1.391 60.91 61.04 60.74

 

 

106
As was argued previously, the H0 state is the best approximation to the AP state for

Co/Cu. For Py/Cu, the situation is less clear because of greater variability between
samples. In many cases the Hp resistance may equal or even surpass the as deposited, H0
resistance. A direct comparison of H0 and Hp resistances may be made by deﬁning the
ratio, IT, as follows:

n_ MR(Ho) _ R(Ho)-R(Hs)

- _ 5.5
M80!» R(Hp)-R(Hs)

 

The 1'1 ratio is used to determine whether or not the Ho resistance is signiﬁcantly
higher than the Hp resistance. Having l'l>1.0, i.e. between 1.5 to 2.0, indicates that the H0
resistance is signiﬁcantly larger than the Hp resistance. In cases where Hzl.0, it is
unclear which resistance best approximates the true AP resistance of the sample, since
AR(I-Io)zAR(Hp). While IT<1.0, i.e. below 0.90, indicates the Hp resistance is
signiﬁcantly higher than the H0 resistance.

The ratio IT is plotted as a function of N in Figure 5.9 for each Co/Cu series. In these
multilayers IT is well deﬁned and varies little for all three series: 1T=1.81:0.20 for
tCo=1.5nm, IT=1.71:0.32 for tC0=6.0nm and 1T=1.86:0.21 for tCo=th For Co/Cu the
values of IT for each sample indicates that the Ho resistance is always signiﬁcantly larger
than the Hp resistance.

For each Py/Cu series, the 11 values do not stay within a narrow range. The data for
Py/Cu are given in Figure 5.10. For the moment we concentrate on the unﬁlled H0
points. The average of the tpy=1.5nm series is IT=1.68:0.32 for samples with

tCu>10.0nm. As shown in Figure 5.10a, the IT values steadily decrease for samples with

107
tCu<10.0nm. The average of the tpy=6.0nm series has IT=1.45:0.66 for samples with

tCu>I6.0nm, neglecting extreme values (IT>3.0). Again as the Cu spacer becomes thinner
(tCu<16.0nm), the IT values steadily decrease as seen in Figure 5.10b. However for the
tpy=tCu series, the IT values are fairly constant at IT=0.99:0.40 over the whole range of

Cu thickness shown in Figure 5.10c.

 

 

 

 

 

lT=MR(Ho)/MR(HP)
/
/V
O
D
C] 0 DD»
[3
C]
D
D

 

 

 

 

tCo=6.0nm
1 - tCo=l.5nm ] a
, o too-1.5nm, Ho
1 Cl tapﬂmmuﬂo
! A. tosmuﬂo
o A r l r A r 1 g l
0 10 20 30 40 50 60

Bilayer Number N

Figure 5. 9: The IT values for Co/Cu all three multilayers series. The lines indicate the
average IT value for each series.

 

5.7

 

 

108
tCu (nm)
1 0.5

34.5

 

 

 

 

 

 

 

 

 

 

 

30 40 50 60
Bilayer Number N

20

10

 

 

a c a q u
OD T A 0
HH 0 O O 6 r 0
a. 11.1.. on.
.... 0 mm
a . a ..
t .110 AM 2 r t
O 1
O. 0. Av
o
o
.4110 r m N 8
o o r o
.m co
m t)
o 0 N m0 0 o
i r
3 W m 6.? o
m o.
o B o o o
o o o
r m r .o
o o o o o
0
6 r o o O o
0 ﬂ 0
0 0 r
o r 1 0 u o
o 3 P a
o
_ b 0 b p
2 l o 3 2 1..
)
AEVMEGIVMS—uc b AEVEGEVM—Zuz

109

 

 

 

 

 

 

 

C) tCu (nm)
18.0 6.0 3.6
3 .
O try=ton H0
0 try=tctt. Hr) %
A 0
Z . o O o O
G 9 .
E5 0 O o
M e . O . O O
2 . O O C
It 1 o 0
1:: 00 o
to 00 O
0 1 'R A 1 -
0 10 20 30 40 50 60
Bilayer Number N

Figure 5.10: The ratio IT plotted as function of the bilayer number, N for a) the tpy=1.5nm
series, the (5:6.01101 series and the tpy=tcu series. Unﬁlled symbols are H0 values and
ﬁlled symbols are HD values. Generally I'ID points are directly above the 1'10 values for
the same sample. This is indicated in Figure 5.10a by arrows for a few representative
samples.

The Co/Cu data clearly suggest that the H0 resistance is always the largest measured
for any sample independent of the thickness of either Co or Cu. The Py/Cu data only
suggest this is true when ’5, is relatively thin (1.5nm or 6.0nm) and is fairly thick. There
seems to be a fundamental difference between the H0 resistances measured for the tpy=tc,,

data and the H0 resistances measured for the constant tpy data.

110
The ambiguity between the H0 and Hp resistances for the (p).=tc,, samples lead to a

search for another resistance state; one in which the magnetization was also nearly zero
after the sample had been exposed to a saturating ﬁeld. Experimentally it is possible to
approach a state of zero magnetization after saturation by cycling the sample through the
hysteresis loop several times, progressively lowering the applied ﬁeld with each cycle.
This cycling randomizes the domains in the magnetic layers leaving the magnetization of
the ﬁnal state close to zero. Samples were demagnetized at 4.2K by starting at saturation
and cycling at least 12 times, each time reducing the ﬁeld. Nearly one third of the
cycling was done inside the peak ﬁeld of each sample. The resulting resistance state of
the sample is labeled, HD, the demagnetized resistance. 1'1 ratios substituting HD for H0 in

equation 5.5 will be denoted by ITD.

In Co/Cu multilayers, the HD resistances for a few representative samples5 always fell
between the Ho and Hp resistances. For these samples the HD resistances resulted in an
average I'ID ratio of 1.3. Clearly the H0 state for Co/Cu multilayers is a unique state
which is irreversibly changed once a saturating ﬁeld is applied.

In Figure 5 .10 1'10 values are shown by ﬁlled symbols. For the tpy=1.5nm multilayers
with ITzl.6, the HD resistance was larger than the Hp resistance but smaller than the HO
resistance. These points are not recorded in Figure 5.103. Figure 5.10a does show that
those tpy=1.5nm multilayers with H410 increased to I'IDzl.3. For the tpy=6.0nm
multilayers with Hz1.45, the HD resistance was also between Hp and Ho resistances.
'Those tpy=6.0nm samples (Figure 5.10b) with ITzl.0 increased to ITDz1.5. The

15:6. Onm samples with thin Cu thickness showed little change in their TI values upon

lll

demagnetizing, possibly because these sample are in the region of strong coupling.
Nearly every demagnetized tpy=tCu sample in Figure 5.10c showed I'ID>IT for the HD
resistance.

Since a majority of the tpy=tCu samples have Hz] .0, it seems likely that the H0 and Hp
resistances are related to each other. As noted earlier, Hp for the 1.5nm and 6.0nm Py
data becomes smaller as the Py thickness increases. Since Hp roughly corresponds to the
coercive ﬁeld, this is equivalent to the coercive ﬁeld decreasing with increasing Py
thickness. This is conﬁrmed by magnetization experiments. Figure 5.11 shows the
hysteresis curve of a [Py(30.0nm)/Cu(30.0nm)]x6 sample. The sample has a coercive
ﬁeld of 1.70e, much smaller than samples ﬁ'om~ the other two Py/Cu series with
comparable Cu thickness. The small coercive ﬁeld suggests that the magnetic
conﬁguration of the Py layers for tpy=tCu samples with thicker Py layers is very sensitive
to small magnetic ﬁelds. Samples are exposed to small stray ﬁelds during sputtering.
Powerful magnets used to conﬁne the plasma during the sputtering process are not
completely shielded from the sample and expose it to a ﬁeld possibly as high as 3.00e
during growth. As Figure 5.11 shows, this small ﬁeld could produce a signiﬁcant portion
of the saturation magnetization for this sample. Therefore, the measured Ho resistances

of tpy=tCu samples are similar to their Hp resistances because the samples have been

partially saturated before measurements were made.

112

{Py(30.0nm)/Cu(30.0nm)}x6

 

 

 

 

 

 

 

 

 

 

‘06‘02‘0’2’
1 1 1 . H (kOe) .
-0.02 -0.01 0.00 0.01 0.02

H (kOe)

 

 

 

 

Figure 5.11: The magnetization hysteresis curve for a multilayered sample with

[Py(30.0nm)/Cu(30.0nm)]x6 at T=5K. The coercive ﬁeld for this sample was 1.70e. The
insert shows that the sample saturates quickly.

Global Fit of the Py/Cu Data

Preliminary results based on a partial analysis of the tpy=1.5nm and 6. Onm are

published elsewhere“. These results will be commented on later. The analysis done
here represents a complete analysis of our Py/Cu data in the limit that (’3 >> t py. In

these ﬁts, for a given sample, the larger of AR(Ho) and AR(HD) was used for AR,(AP).
In Figures 5.12-5.14 all the data are plotted using this criterion. The data for all three sets

of Py/Cu multilayers were globally ﬁt following the same procedure outlined in the

113

previous section for Co/Cu multilayers. At ﬁrst a ﬁt was done using all the data in Tables

5.7-5 .9 above the cutoff (blank row), to minimize the effect of coupled Py layers. This ﬁt

of the Py/Cu data resulted in values for p15,, pa, and AR py/C, which poorly represented all

three series. To properly ﬁt the H0 data for the tpy=tc,, series, required pisy z 140an
much smaller than was required for either the 1.5nm or 6.0nm Py HO data. The previous
section also showed that it is difficult to interpret the H0 data of the tpy=tCu series as
being the closest approximation to an AP state. Because of the ambiguity of the Ho state

in the tpy=tC,, samples, two different ﬁts to the Py/Cu data were done.

 

 

 

 

 

 

 

 

tCu (nm)
7.2 2.9 1.5
160 ' Y i r r r . T , r w , v O T
140 7 0 Ho. data -
. D 2'18, data .
120 e 0 r
{g 100 — 0 ~
C: D l
’5 80 e ~
I- r DD
g 60 _ % SE8 0 s
4 o C’o Q) OCPO D 9 gr -
0 r 0 1:1 DODCDCB D
* 080:1 :1 ED
20 P $0 {Py(l.5nm)/Cu(tCu)}N
o r l r l A l n l r l n l I; J; A l
0 20 40 60 80 100 120 140 160

N-l

Figure 5.12: The H0 and HS data for the Py(5.0nm)[Py(1.5nm)/Cu(tc,,)]xN series.

 

 

 

 

 

 

to. (MI)
26.7 5.6 1-1
80 '
. 1 o
70 c 0 Ho, data I
5 D fundaur ’
60 ~ "
L D 1
o
a" 50 ~ 8 i
g r o O O Q Q g D l
t: 40 ~ 0 000 O 0 8 8 O 9 9 I
t- » 08 o O D o D 0
g 30 " 001:] CIDDDD D [p 7
00 El 1:1 ‘
20,_ CDDDij ‘
t a
10 . {Py(6.0nm)/Cu(tCu)lN
0 A . . A A r l r
0 10 20 30 40 50 60

N-l

Figure 5.13: The Ho and HS data for the [Py(6.0nm)/Cu(tCu)]xN series.

 

 

 

 

 

 

 

too (M)
16.4 5.8 3.5
80 . . . . . . - r
70 — -
60 i r
o .
a; so _ D O a _
_ 0
“g 40 — 8 O O 8 Q g g -
(— 0 00009 D 8 g g 8
00 Q
g 30 7 DC] a: C] D _
20 e e
0 Ho. data
* D Hsdm
’0 : {Py(th)/CU(tCu)lN I
o . 1_ A . r l . 1 . 1
0 10 20 30 40 50 60
N-l

Figure 5.14: The H0 and HS data for the [Py(tpy=tCu)/Cu(tc,)]xN series.

llS
Fit A
Fit A only includes the 1.5nm and 6.0nm Py data given in Tables 5.7 and 5.8 above

their indicated cutoffs. With only four sets of data, the HO and HS data for tpy==1.5nm and

6. 0nm, the ﬁtting procedure now treated p38,, AR jay/Cu, B and y as the only free
parameters. The Nb/Py boundary resistance and the Cu resistivity were constrained to
independently measured values. A Cu resistivity of pa, = 5.0 :10an was determined

by measuring 300nm thick Cu ﬁlms made along with the multilayers during the various
runs. The Nbe boundary resistance of 2AR NW5, = 6.5:].Ofnm2 was determined by

ﬁtting the resistance of a series of Nb/PY(tpy)/Nb trilayers as a ftmction of the Py
thickness. The intercept of the best ﬁt line through the trilayer data is a direct
measurement of the Nble boundary resistance. Similarly to the Co/Cu data , the Py/Cu

data is ﬁt in a two step process: (a) First the H0 data for (5:1.5’1’" and 6. 0nm series is ﬁt
to equation 4.2 to obtain p}, and AR ;.,,C,. (b) Second both the H, and HS data are used to

ﬁt equation 4.4 to obtain values for B and y. The results for ﬁtting procedure A are listed
in Table 5.10. The columns labeled Set 1 and Set 2 contain the best parameters for
slightly different cutoffs in the data. The cutoff for the 15:1.5’1’" data is the same for
both Set 1 and Set 2. The cutoff choice for the tpy=6.0nm Ho data is less clear. The
square root data peaks at N-1=15, so data beyond N-1=15 are likely to be affected by
coupled Py layers. The samples with N=16 may be suspect because it is not known
whether they are on the coupled side or the uncoupled side of this peak. One of the N=16

samples is eliminated from Set 1 and Set 2 since the HS resistance is much larger than the

1 16
HS values of the neighboring points in Figure 5.13. The other N=16 point of Figure 5.13

is included in Set 1 but not in Set 2.

Table 5.10: Summary of ﬁtted parameters for Fit A. A 2ARNb/py of 65me2 and a pg, of
50an were assumed for each ﬁt. The uncertainties in Set 1 and Set 2 have adjusted so
that the x2 will match the degrees of freedom for each ﬁt, see the text.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

independent Fit A
measurements Set 1 Set 2 units
2ARWP, 65:10 meI
pC, 5.0:1.0 an
pp, 137:35 147:22 140:22 nﬂm
p}? 218:19 211:19 nﬂm
B 0.57:0.07 0.58:0.07
up, 37:03 38:03
Apr/C, 0.16:0.06 0.17:0.06 fnml
A R :5” Cu 0.45:0.04 0.44:0.04 film‘:
7 0.79:0.08 0.79:0.08
orb/Cu 8.7:0.7 8.4:0.7

 

 

The uncertainties in the parameters (under Fit A for columns 3 and 4) in Table 5.10
have been adjusted so that the x2 will equal the number of degrees ﬁeedom for the ﬁt, N A-
2. (Here N A is the number of data points used in ﬁt A and 2 is the number of adjustable
parameters.) Comparing Set 1 and Set 2 in Table 5.10 reveals only minor differences in

all the parameters. For the ﬁt of the H0 data, Set 1 of Fit A had a x2 of 71 and with

N A=21 for Set 1 the uncertainties in p}, and AR Iowa, were increased by a factor of

 

\/ x2 / (N A — 2) = 1.93. For Set 2 of Fit A the H0 ﬁt resulted in a slightly smaller )8 of 60,

117

and with N A=20 the uncertainties in p‘Py and AR INC" were increased by a factor of

 

73,2 /(N, — 2) = 1.83. It is fair to say that both Set 1 and Set 2 give reasonable ﬁts to the

Ho data of the 1.5nm and 6.0nm Py data. The x2 per degree of freedom is only slightly

 

less for the choice of Set 2. The ﬁt of the square root data, AJR(H0)[R(HO) — R(HS)] ,

resulted in a x2 of 239 for Set 1. The uncertainties in B and y are increased by a factor of

 

7x2 /(NA -2) = 3.54 for Set 1. Similarly for Set 2, the x 2 of the square root ﬁt is 209

 

and the uncertainties in B and y are increased by a factor of JxZ/(NA —2) = 3.41. Again
for Fit A both Set 1 and Set 2 ﬁt the data reasonably well, with the reduced x2 for Set 1

being slightly greater than that for Set 2 (12.6 to 11.6, respectively).

The largest difference between Set 1 and Set 2 occurs for the Py resistivity. The

value of p}, for both sets differs by less than 5%, which considering the uncertainty in

p}, for each choice, makes them more or the less the same. The value of AR is,“ in Set

1 and Set 2 are even closer, differing by only 2.2%. All other parameters in Table 5.10
for Set 1 and Set 2 are virtually identical, especially when taking into account their

uncertainties.

”8

Fit B

Fit B uses the same 1.5nm and 6.0nm Py data as Fit A along with the HS data above
the cutoff from the tpy=tc,, series. Although the H0 resistance state of the tpy=tcu data
may be signiﬁcantly altered by the magnetic ﬁeld of the sputtering system, keeping the
HS data of the tpy=tC,, set seems justiﬁable in that the saturation state of a sample has the
same magnetic conﬁguration (and therefore the same resistance) each time the sample is
saturated. However, keeping only the HS data will only affect the Py spin asymmetry
parameters, B and 7, since the H0 data is used to ﬁt p}, and AR A“. The Fit B procedure
is as follows: (a) First, the Ho data for tpy=1.5nm and 6. 0nm series is ﬁt to equation 4.2 to
obtain p}, and AR;y,C,,. (b) Second, the Ho data for the tpy=1.5nm and 6. Onm series are
used to estimate H0 values for the tpy=tc,, series. (c) Third, the H0 and H5 data for the
tpy=1.5nm and 6. 0nm series along with the estimated Ho values and HS data for the
tpy=tCu series are ﬁtted to equation 4.4 to obtain values for B and y. The results for ﬁtting
procedure B are listed in Table 5.11. The columns labeled Set 1 and Set 2 have the same

meanings as in Fit A. The estimated H0 resistances for the tpy=tc,, series are based on the
ﬁtted values of p}, and AR Am, determined by ﬁtting the H0 1.5nm and 6.0nm Py data.

In Fit B the Cu resistivity and the Nb/Py boundary resistance are also constrained to the

same values given previously in Fit A.

119

Table 5.1]: Summary of ﬁtted parameters for Fit B. A 2ARNb,py of 6.5ern2 and a Den of
50an were assumed for each ﬁt. The uncertainties in Set 1 and Set 2 have adjusted so
that the x2 will match the degrees of freedom for each ﬁt, see the text.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

independent Fit B units
measurements Set 1 Set 2
2ARNMs, 6.5:] .0 fan1
pg, 5.0:1.0 an
pp, 137:35 116:22 114:21 an
pg 218: 19 211:19 nﬂm
B 0.68:0.07 0.68:0.07
up, 53:04 52:03
Apr/C, 0.22:0.05 0.22:0.05 film“
AR [ﬂy/Cu 0.45:0.04 0.44:0.04 mel
y 0.71:0.07 0.72:0.07
up,“ 60:04 6.21-0.4

 

 

The uncertainties in the parameters (under Fit B for columns 3 and 4) in Table 5 .11
have been adjusted so that the x2 will equal the number of degrees freedom (the
difference in the number of data points and the number of adjustable parameters, N 3-2)
for the ﬁt. Comparing Set 1 and Set 2 in Table 5.11 reveals only minor differences in all

the parameters. In ﬁtting the Ho data, the same data points used in Fit A are used in Fit B,
therefore the values of the parameters, pisy and AR :54“, and their uncertainties listed in

Table 5.11 for Fit B are the same as those given in Table 5.10 for Fit A. The ﬁt of the

 

square root data, AJR(H,)[R(H,) — R(HS)], includes the HS data often ip,=ic, samples

in addition to the points used in Fit A. This resulted in a x2 of 370 for Set 1. The

 

uncertainties in B and y are increased by a factor of sz/(NB—Z) = 3.57 for Set 1,

120
NB=31. Similarly for Set 2, the 12 of the square root ﬁt is 322 and the uncertainties in B

 

and y are increased by a factor of \/ x2 /( N B — 2) = 3.39 , Np=30. Again for Fit B both Set
1 and Set 2 ﬁt the data reasonably well, with the reduced x2 for Set 1 being slightly

greater than that for Set 2, 12.8 to 11.5, respectively.

The largest difference between Set 1 and Set 2 in Fit B also occurs for the Py
resistivity. The values of p}, and So}, for both sets are the same as those in Fit A, since
the same Ho data is used in both Fit A and Fit B. All other parameters listed for Set 1 and

Set 2 in Table 5.11 are virtually identical, especially when taking into account their

uncertainties.

Comparison of Fits A and B

As has been shown above choosing Set 1 or Set 2 within either Fit A or Fit B makes
no difference in the value of the ﬁtted parameters. However, comparing the parameters

derived with Fit A to those obtained with Fit B do show some signiﬁcant differences,
even though the same p}, and AR Am“ values are used in each ﬁt. In comparing the
remaining parameters for Fit A and Fit B, the parameters only overlap at the extremes of
their uncertainties, with the exception of the 01’s which do not overlap at all. Clearly the
tpy=tc,, series has an appreciable effect in modifying the parameters B and y. The 01’s for
Fits A and B show the largest disparities. In Fit A, up,“ is more than a factor of two

larger than up, for either Set 1 or Set 2, while Fit B gives cosy/C, and 01p, approximately

121
equal for Set 1 and Set 2. Fit B suggests that the bulk Py contribution to spin dependent

scattering is on par with the Py/Cu interface contribution to spin dependent scattering. Fit
A indicates that the bulk Py contribution to spin dependent scattering is only half the

Py/Cu interface contribution to spin dependent scattering.

The 1.5nm Py data is shown in Figure 5.15 and 5.16 along with lines representing the
parameters given in Tables 5.10 and 5.11. Figure 5.15a compares Set 1 values for both
Fit A and Fit B, while Figure 5.15b compares the Set 2 value for both ﬁts. In each ﬁgure,
the Ho ﬁts are identical, since the same p}, and AR Ly,“ values are obtained in both ﬁts.
The curvature of the ﬁts can be explained by the nonlinearity of the Cu term as N
approaches zero, see page 91. The HS ﬁts differ slightly with Fit B lying below Fit A.
The 1.5nm Py square root data is plotted in Figures 5.16a and 5.16b along with lines
representing the various values given in Tables 5.10 and 5.11. Differences between

Figure 5.16a and 5.16b are nearly impossible to distinguish.

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) tCu (nm)
60 31.2 15.6 10.1
i A & B i
. 0 Ho. data -
50 s 1 r3 Hs, data \ “
1 Ho, FitA-l . .
1 — Hs.FitA-1 ! o .
A 40 ~ 1 —— Ho.FitB-l 1 A —
(E > —— HS, Flt B-l \ ,
g 30 . . O —
[- D I /
a: * ' .
< 20 ~ . ‘ - -../f D B .
1 . ' '
10 . e
, {Py(l .5nm)/Cu(tCu)lN ,
o - - . 1 r .
0 10 20 30
N-l
b) tCu (nm)
60 31.2 15.6 10.1
t I i .
i A & B
' 0 H0, data
50 _ l 13 H8, «a \ _.
Ho,Fit A—2
— Hs,FitA-2 O ‘ .
A 40 - — Ho, Fit B-2 A a
N —— F't B-2
g r HS. 1 \ 4
‘43 30 — . ° -
[- D I /
ﬁ 20 . = ° ' "J D B ~
e - .
10 — 4
{Py(l .5nm)lCu(tCu)]N
o r 1 l r 1
0 10 20 30
PM

Figure 5.15: ART(H0) and ART(HS) plotted as a function of the corrected bilayer number,
N-l for the Py(5.0nm)[Py(1.5nm)/Cu(tc,,)]xN. Total sample thickness is held constant at
360nm. Fits A and B in a) use Set 1 parameters listed in Table 5.10s and 5.11, while Fits
A and B in b) use Set 2 parameters from Tables 5.10 and 5.11. Points with ﬁlled symbols
were not used in ﬁts.

123

tCu (nm)
31 .2 15.6 10.1

n)
v

 

40

{Py(l .5nm)/Cu(tCu)}N

 

\/{ART(Ho)-ART(H3))ART(H0) (mmz)

 

 

 

 

tCu (um)
31.2 15.6 10.1
40 . 1 . T , T

on
V

 

{Py(l .5nm)/Cu(tCu)}N

 

\/{ART(Ho)-ART(H8)}ART(HO) (mmz)

 

 

 

 

Figure 5. I 6: The square root data plotted as a ﬁmction the reduced bilayer number, N-l
for the Py(5.0nm)[Py(1.5nm)/Cu(tC,)]xN. Total sample thickness is held constant at
360nm. Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits
A and B in b) use Set 2 parameters from Tables 5.10 and 5.11. Points with ﬁlled symbols
Were not used in ﬁts.

124

The 6.0nm Py data is shown in Figures 5.17 and 5.18 along with lines representing
the various ﬁts. The ART(H0) and ART(H5) data and Set 1 parameters for Fits A and B
are plotted in Figure 5.17a while the Set 2 parameters for Fits A and B are plotted in
Figure 5.17b. The differences between the Set 1 parameters in Figure 5.17a and those of
Set 2 shown in Figure 5.17b are barely perceptible. In each ﬁgure the H0 ﬁts are
identical, while the HS Fit A parameters give values for ART(HS) slightly above those
obtained from Fit B parameters. The 6.0nm Py square root data is plotted in Figure 5.18

along with the square root ﬁts.

The tpy=tcu ART(HO) and ARI-(HS) data is plotted in Figure 5.19 along with the
various ﬁts. The differences between the ﬁts using the Set 1 parameters in Figure 5.1%
and those using the Set 2 parameters in Figure 5.1% are small but noticeable. In both
ﬁgures the H0 ﬁts are identical and both Fits A and B are well above the Ho data. This is
not too surprising given that the Ho data was not used in either of Fits A and B because
their I'I ratios in Figure 5.10c were approximately 1.0. The AR(HS) obtained with Fit B
parameters differ markedly from those obtained using Fit A parameters. Although both
Fits A and B lie above the best ﬁt line through the HS data, the parameters of Fit B come
signiﬁcantly closer to describing the HS data. It is a little surprising that Fit B does not do
a better job of ﬁtting the tpy=tcu saturated data, but in ﬁtting the HS data one must know
the values of the actual Ho data. For these data the H0 values were assumed, based on ﬁts
to the Py 1.5nm and 6.0nm Ho data. One could argue that the 1.5nm and 6.0 data have

been weighted more heavily than the tpyztcu data in Fit B since 1.5nm and 6.0 H0 data are

125
effectively acting as the H0 data for the tpy=th series. This would in effect skew the HS

values of Fit B closer to the HS values of Fit A. Fit B in both Figure 5.1% and 5.1% lies

roughly half way in between the HS data and the HS values obtained from Fit A.

The square root data for the tpy=tcu series is plotted in Figure 5.20. The AR(HO) data
has been estimated ﬁom the parameters for p}y and AR A,“ given in Tables 5.10 and

5.11. Although the data is quite scattered, the Set 1 parameters for both Fits A and B

represent the square root data better than the Fits using the Set 2 parameters.

126

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) to: (run)
66.0 34.0 21.7 15.2
60 1 . 1 r .
1 . .
50 - 0 Ho, data A & B 3 -
1 D Hs, data
1 H0, Fit A-l \ . A ~
40 _ . —- Hs, Fit A-l 1 0 g . ' _
gp —— H0, Fit B-1 1 o l
e —— Hs, Fit 3-1 1 , . o ' *
C3 1. 1’ , ‘ O 13
b 30 ~ ‘ . 4
l— . D r . I //
O O a
g C] 2/. D
20 ~ B ~
7. I
10 ~ , -
1 {Py(6.0nm)/Cu(tCu))N
o g _l_ m . - 1 ' 1_~ 1 1 1 1 ' 1
0 2 4 6 8 10 12 l4 l6 1 8 20
N-l
b) to: (nm)
66 0 34.0 21.7 15 2
60 V T ' I F T ' Vﬁ 1 ' 1 1 1 ﬂ 7 ﬁ
50 _ 0 Ho, data : d
0 113, data A & B
Ho, Fit A-2 \ . A
40 _ — Hs, Fit A-2 o . ' .
g; —-—- Ho, Fit B-2 0 i
5 ~ —— Hs, Fit 13.2 .. o '
E . " o I
v 30 e u
t- ‘ D . D I
a * ° ° . a . a
20 " 0 /¢ 0 B a
. If .
10 ~ -
{Py(6.0nm)/Cu(tCu)}N
0 . 1 L 1 1 A g. 1 . 1 . 1 1 g 1 1 . 1 .
O 2 4 6 8 l 0 12 l4 16 18 20
N-l

Figure 5.1 7: ART(HO) and ARﬁl-ls) plotted as a ﬁmction of the corrected bilayer number,
N-l for the [Py(6.0nm)/Cu(tc,,)]xN. Total sample thickness is held constant at 360nm.
Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits A and B
in b) use Set 2 parameters from Tables 5.10 and 5.11. Points with ﬁlled symbols were
not used in ﬁts.

127

tCu (nm)
66.0 34.0 21.7 15.2

93
v

 

40

{Py(6.0nm)/Cu(tCu)}N

 

x/{ARTmo)-ART(Hs)}ART(Ho) (mmz)

 

 

 

 

tCu (run)

66.0 34.0 21.7 15.2
40 ' 1 f I ' 1 ' T 1 T F T T j ' T ' 1

on
V

 

{Py(6.0nm)/Cu(tCu)}N

\ftAeroyAR-rmsnammo) (romZ)

 

 

 

 

 

N-l

Figure 5.18: The square root data plotted as a function the reduced bilayer number, N-l
for the Py(5.0nm)[Py(1.5nm)/Cu(tc,)]xN. Total sample thickness is held constant at
360nm. Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits
A and B in b) use Set 2 parameters from Tables 5.10 and 5.11. Points with ﬁlled symbols

were not used in ﬁts.

128

tCu (nm)
a) 36.0 20.0 13.8 10.6

 

60

  

 

 

 

«1‘

E

C

2':

t-

5 o

D -
Best Fit Hs 1 — H3: Fit A-l '
‘ — Ho. Estimate B l
10 ~ — Hs. Fit 3.1 1
1 {Py(th)/Cn(tCn)lN

 

 

 

 

 

ART (mmz)

20

1

Best Fit Hs

 

111100
15.
3'
1’.

Hs. Fit B-2 -

{PY(tPY)/Cu(tCn)} N 1

0 1 1 L 1 1 1 1 I . 1 1 .

0 2 4 6 8 l 0 l 2 l
N-l

1

 

10

 

 

 

 

16 18 20

#r—

Figure 5.19: ART(HO) and AR1-(HS) plotted as a function of the corrected bilayer number,
N-l for the [Py(tpy=tc,,)/Cu(tc,)]xN. Total sample thickness is held constant at 360nm.
Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits A and B
in b) use Set 2 parameters ﬁom Tables 5.10 and 5.11. The Best Fit HS line is a least
squares ﬁt to the HS data. Points with ﬁlled symbols were not used in ﬁts. H0 data was

not used in either ﬁt.

a)
v

 

\/{ART(Ho)-ART(HS)}ART(H0) (mmz)

on
V

 

x/{ARr(Ho)-ART(HS)}ART(HO) (mmz)

50

10

50

10

36.0

20.0

129

tCu (nm)
13.8

10.6

 

 

ﬁr

{Py(tpy=tCu)/Cu(ICu)} N

,_

 

 

 

10 12

l4 l6

18

20

 

 

N-l
to: (run)
36.0 20.0 13.8 10.6
{Py(th=tCu)/Cu(tCu)] N o

,—

4; L

 

 

 

10 12
N-l

14 16

18

Figure 5. 20: The square root data plotted as a function of the corrected bilayer number,
N-l for the [Py(tpy=tc,,)/Cu(tc,,)]xN. Total sample thickness is held constant at 360nm.
Fits A and B in a) use Set 1 parameters listed in Tables 5.10 and 5.11, while Fits A and B
in b) use Set 2 parameters from Tables 5.10 and 5.11. The Best Fit HS line is a least
Squares ﬁt to the HS data. HO data was not used in either ﬁt.

130

To choose the best set of parameters from those in presented Tables 5.10 and 5.11 a
comparison with independently measured values of the permalloy resistivity is necessary.
Table 5.12 lists the resistivities of Py ﬁlms 100-300nm thick, made in several runs along
with the CPP samples. Some of the ﬁlms were masked to provide a set four terminal
geometry from sample to sample, others were measured using the Van der Pauw
technique described in chapter 3. An average value for the Py resistivity was obtained by
weighting each measurement of p p, by the associated uncertainty in its geometry,
typically i5%. This gave p Py =137i9 nﬂm. However, the uncertainty in pp, did not
reﬂect the amount of scatter in the resistivity measurements which resulted in a reduced
x2 of 14.3. Adjusting the pp, uncertainties to bring the reduced x2 to 1.0 gave the value

listed in Tables 5.10 and 5.11, pp}, =137i35 nﬂm which reﬂects the range of Py

resistivites that were mearsured.

The parameters ﬁom Fit A-2 come the closest to the independently determined value
for pp, at 140i22an. Fit A-l gives a value for ppy slighly higher than the
independently determined value, but well within the uncertainties. Both sets of
parameters ﬁ'om Fit B are somewhat low when compared to the 137an value but the

uncertainty of each overlaps with the independent measurement.

As previously mentioned a partial analysis of the Py/Cu data have been published
elsewhere“. The analysis found in Ref. 6 represents our initial estimates for B and y (or
up), and aPy/Cu)‘ At the time of these estimates only samples with tpy=1.5nm and 6. Onm

were being examined. The parameters given in Ref. 7 are also results of an analysis done

131

only on samples with tpy=1.5nm and 6. 0nm. While this analysis uses the same tpy=1.5nm
data, about one third of the (5:6. Onm samples used in Fits A and B were made after this

analysis was done.

Table 5.12: Py resistivity measurements on ﬁlms made along with CPP samples in
several runs.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample # MN” tpy (nm) p (nﬂm) iﬁp (nﬂm)
43 1-01 M 950213 142 5
43 1-04 M 900i6 123 8
431-06 M 900i12 120 16
43 1-07 M 1091 6 148 8
43 8-06 M 841:1 133 2
438-07 M 85:1:3 1 l3 4
438-08 M 94i3 151 24
438-09 M 114i18 177 5
569-06 V 2441 25 107 1 1
570-09 V 298:1:12 126 5
571-10 V 280:1:16 115 7
605-10 V 32413 144 2
613-07 V 277i20 102 7

 

 

 

 

 

 

 

a M signiﬁes a masked ﬁlm and V signiﬁes Van der Pauw measurement.

132

Comparison with Co/Cu Multilayers

Based on resistivity measurements of impurity scattering in dilute ferromagnetic
alloys done by Campbell and Fenl, one might expect that permalloy would have a larger
on than Co. CPP-MR measurements done on Co/Cu multilayers in section 5.1 and Py/Cu
multilayers in section 5.2 show that this expectation is justiﬁed. The value of ac, given
in Table 5.6 is lower than the up, values given in Tables 5.10 and 5.11. At the extreme of
their uncertainties the Fit A value for apy=3.7i0.3 does not quite overlap with
aCo=2.7:t0.3, while the Fit B value of apy=5.3i0.4 is well above 010,. The interface
parameters are less clear. The value of aCdCu=7.7i1.3 lies between the Fit A value for
apymu=8.7i0.7 and the Fit B value for aPy/Cu=6.0i0.4. However, in comparing the ratio
of the contributions to the spin dependent scattering ﬁom the bulk F metal to that from
the F/N interface, one ﬁnds that the ratio of interface to bulk is larger for Co/Cu. Values
in Table 5.6 give eta/Cu /aCo=2.9 whereas aPy/Cu mp, is 2.4 for Fit A and 1.1 for Fit B,
both smaller than the Co ratio.

The resistivity of the Py is more than double that of the Co. This is expected since the
sputtered Py layers are most likely forming a disordered random alloy of Ni and Fe with
concentrations similar to the sputtering target. However, somewhat surprisingly the
interface resistances of Co/Cu, ARGO/Cu, and Py/Cu, ARPy/Cw are quite similar. One might
expect the Co/Cu interface resistance to be higher since Co prefers the hop structure,

while Cu and Py both prefer fcc. However, NMR studies8 on Co/Cu multilayers show

133
that the Co is fcc for Co layers less than 3.0nm thick, therefore the Co/Cu interfaces are

probably similar structurally to the Py/Cu interfaces.

 

‘ I.A. Campbell and A. Fert, in Ferromagnetic Materials, edited by RP Wohlfarth,
(North Holland, Amsterdam, 1982), Vol. 3, p.769.

2 XTEM pictures show good layering throughout the sample thickness, however, beyond
100nm the layers begin undulating. P. Galtier, T. Valet, O. Durand, J .C. Jacquet and J .P.
Chevalier, Mat. Res. Soc. Symp. Proc., Vol. 313, p. 47 (1993).

3 R.D.K. Misra, T. Ha, Y. Kadmon, C.J. Powell, M.D. Stiles, R.D. McMichaels and W.F.
Egelhoff Jr., in Magnetic Ultrathin Films: Multilayers and Surfaces, edited by EB.
Marinero, B. Heinrich, W.F. Egelhoff Jr., A. Fert, H. Fujimori, G. Guntherodt and R.L.
White, MRS Symposium Proceedings Vol. 384, Material Research Society, Pittsburgh,
PA., p.373 (1995).

‘ 8.8. P. Parkin, Appl. Phys. Lett. 60, 517 (1992).

5 RA. Schroeder, S.F. Lee, P. Holody, R. Loloee, Q. Yang, W.P. Pratt, Jr. and J. Bass, J.
Appl. Phys., 76, 6610 ( 1994).

‘ P.A. Schroeder, J. Bass, P. Holody, S.F. Lee, R. Loloee, W.P. Pratt Jr. and Q. Yang,
Mat. Res. Soc. Symp. Proc. Vol. 313, 47 (1993).

7 Q. Yang, P. Holody, R. Loloee, L.L. Henry, W.P. Pratt Jr., P.A. Schroeder and J. Bass,
Phys. Rev. B51, 3226 (1995); J. Bass, P.A. Schroeder, W.P. Pratt Jr., S.F. Lee, Q. Yang,
P. Holody, L.L. Henry, R. Loloee, Mater. Sci. Eng. B31, 77 (1995).

' C. Meny, P. Panissod and R. Loloee, Phys. Rev. B45, 12269 (1992).

Chapter 6:

Complex Magnetic
Multilayers

This chapter will focus on multilayer systems that are more difﬁcult to analyze. First,
Co/CuX multilayers, where CuX is a Cu based alloy, will be seen to exhibit ﬁnite spin
diffusion length effects in CPP-MR. Second, a system that uses two F-metals, Co and
Py, will show how GMR can be attained without relying on strong AF ~coupling. The
last part will investigate attempts at producing a reversed GMR, one in which the AP

state corresponds with the sample’s lowest resistance.

6.1 Finite Spin Diffusion Length Effects in Multilayers
of Co and Cu Alloys.

To better understand the transport properties of magnetic multilayers, it is necessary
to see how different types of scattering effect the resistance of a sample. In chapter 5 the
resistance of Co/Cu and Py/Cu multilayers was successfully described by a simple two

channel model. In this model, the electrons are divided into two parallel spin channels,
134

135

for each of which the resistances are summed in series. Inherent in this model is the
assumption that each spin channel carries current independently and therefore an electron
in the spin up channel will not ﬂip spin and join the spin down channel along the way.
Spin ﬂip events are enhanced by spin-orbit scattering from impurities, exchange
scattering by paramagnetic impurities and by electron-magnon scattering. Spin ﬂips may
be characterized by two different length scales, (V, the spin diffusion length and 13,", the
spin mixing length. The spin diffusion length is the distance an electron travels before
ﬂipping its spin, without transfer of momentum. The spin mixing length is the distance
the electrons travel before the two spin currents are mixed by scattering that
simultaneously ﬂips an electron’s spin and transfers momentum. The effects of electron-
magnon scattering producing spin ﬂips may be neglected for measurements made at
4.2K. Electron Spin Resonance (ESR) measurements1 of the spin ﬂip cross section
attributed to intrinsic defects in Cu indicate that the inﬁnite spin diffusion length assumed
in the two channel model analysis of the Co/Cu multilayers of chapter 5 was justiﬁed.

The Valet-Fert2 theory described in chapter 4 predicts measurable deviations from the

 

linearity of JAR(H0)[AR(H0)- AR(HS)]and NJ, as the spin diffusion length (SDL)
approaches the layer thickness. This theory showed that a Boltzmann equation model
reduces to macroscopic transport equations for spin diffusion lengths much longer than
the mean free path of the conduction electrons. Equations 4.8-4.11 are the Valet-Fert
results for the two channel model when ﬁnite SDL effects are taken into account for both

the F and N metals.

136
A systematic study of SDL effects in magnetic multilayers of the form Co/CuX where

X=Pt, Mn, Ni or Ge was begun. Each Co/CuX series was characterized by both high and
low angle diffraction. As was shown in chapter 3, these spectra revealed no change in the
lattice structure of the multilayer with the additions of each impurity. One difference
between the original Co/Cu series and each Co/CuX series exhibited here is the addition
of an extra “capping” layer of Co before the top Nb lead is deposited. This modiﬁcation
to the multilayer structure now leaves a C0 layer next to each Nb lead. The ferromagnetic
Co layers are intended to suppress the superconducting proximity effect in the multilayers
thus eliminating possible complications concerning whether or not the CuX layer next to
the Nb will become superconducting. To examine the sample variability from sputtering
run to sputtering run, two [Co(6.0nm)/Cu(tc,)]xN samples with 1cu=9-0 and 30. Onm
(N=20 and 48) were sputtered along with the Co/CuX samples. These Co/Cu samples
were fabricated before the CuX source was turned on preventing possible contamination

by the CuX gun.

ColCuPt(6%) Samples

Introducing a small amount of Pt into the Cu layers of the multilayer should
considerably shorten the SDL of the normal metal layer by providing an impurity with
strong spin-orbit scattering3. A dilute alloy containing 6 at.% Pt was chosen as a
compromise between substantial altering of the normal metal properties and being able to

reliably measure an effect. Multilayers of [Co(6. 0nm)/CuPt(tCuP,)]xN were made for

comparison with the [Co(6.0nm)/Cu(tCu)]xN series previously made for the Co/Cu study
in chapter 5. The total sample thickness of the CuPt samples was held constant at
720nm. To avoid complications with the alloy modifying the coupling between magnetic

layers‘, only samples with tCupg6.0nm were made. The data for the Co/CuPt(6%) series

is given in Table 6.1.

Table 6.1: CPP values at Ho, Hp and HS for the [Co(6.0nm)/CuPt(tCuP,)]xN

137

series. The total sample thickness is 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tCu N Area CPP-AR(H) fQ—mz
# nm mm2 Ho Hp HS
4901” 600 11 1.233 115.34 115.34 115.27
484 300 20 1.381 124.92 124.92 124.26
4900: 300 20 1.284 128.90 128.81 128.24
4900/ 300 20 1.380 118.89 118.81 118.20
508W 300 20 1.234 108.08 108.03 107.69
4846‘ 180 30 1.253 120.35 120.23 118.53
484W 90 48 1.591 147.07 145.52 138.03
49066 90 48 1.260 128.02 123.52 118.17
508"3 90 48 1.305 1 14.30 1 14.30 109.25
484“1 60 60 1.432 160.46 147.50 138.62

 

 

138
Co/CuMn(7%) Samples

A second series of multilayers that had a shortened SDL was made by alloying Cu
and Mn. For Mn the spin-orbit relaxation is small} and can be neglected so that the
primary source of spin ﬂip scattering at low temperatures is attributed to an exchange
scattering which does not directly relax the spin accumulation to the lattice but transfers
it to the paramagnetic impurity system5 which then relaxes to the lattice. This leads to an
exchange scattering relaxation term in addition to the spin-orbit contribution. A series of
samples doped with 7 at.% Mn in Cu was made similarly to the aforementioned Co/Cu
series. The resistances of the [Co(6.0nm)/CuMn(tCuM,,)]xN series are given in Table 6.2,

the total thickness was held at 720nm.

Table 6.2: CPP values at H0, Hp and HS for the [Co(6.0nm)/CuMn(tCuM,,)]xN
series. The total sample thickness is 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tcu N Area CPP-AR(H) fQ-m‘

# nm mm2 H0 11,. HS
478‘” 600 1 1 1.251 199.43 199.43 199.41
478‘” 300 20 1.204 196.17 196.19 196.17
479V 180 30 1.305 217.38 217.36 217.33
479‘” 120 40 1.423 186.95 186.79 186.42
478‘” 90 48 1.366 185.79 185.32 184.76
478‘" 60 60 1.326 177.28 174.35 172.01

 

 

139
The data for the above three systems Co/CuPt, Co/CuMn and Co/Cu are shown in

Figure 6.1. The Co/Cu samples made during the Co/CuX runs have the additional Co
“capping” layer and are denoted by the open circles in Figures 6.1, 6.3 and 6.4. These
newer Co/Cu agree, generally within the scatter of the data, with the Co/Cu samples
studied previously. Large departures from linearity similar to those predicted by Fert and
Valet are seen for the Co/CuPt and Co/CuMn samples. One further step is necessary to

conﬁrm these departures are indeed explained by the Valet-Fert theory.

 

   
 
 
  

 

 

 

 

 

 

 

 

tCu (nm)
30.0 12.0 6.0
70 I ‘ * ' 7 ’ ‘ T
{Co(6.0nm)/CuX(tCux)}N .9
A 60 ” . O
E
T; 0 Cu 0
g 50 7 A CuMn(7%)
a o CuPt(6%)
2:, 40 - . CuGe(4%)
E 30.
O
a .
52 20 ~—
35. .
3 1o —
L
0 1 . 1 , 1 1 . 1 1 A
o 10 20 30 4o 50 6o 70

Bilayer Number N

Figure 6.1: Plotted are both the measured and predicted values using the Valet-Fert
theory for the quantity JAR(H0)[AR(Ho)-AR (HS)]as a function of N, the bilayer
ntunber. The Valet-Fert predictions use IS!" = 00 and if,“ = 2.8nm, 8.0nm and 00 with

the appropriate Pcux, given in Table 6.4. The Co/CuGe samples have a total thickness
360nm, while all other samples are 720nm thick. The ﬁlled symbols have different CuX
thickness than those indicated on the top axis.

 

140

The normal metal resistivity does not enter explicitly into equation 4.4 reproduced

here with corrections for the extra Co layer.

 

JAR<H0)1AR(HO) — AR(HSH = N19p2.rc. +124Réo/cn +szorc.

Even so, the resistivity of the CuPt(6%) and CuMn(7%) is substantially higher than for
Cu, more than a factor of 20. To test whether the departures from linearity are caused by
the shortening of the SDL or the increase in the resistivity (which depends upon the
elastic mfp) a third series of Co/CuGe multilayers was made. An alloy of 4 at.% Ge in
Cu has roughly 20 times the resistivity of Cu but has a very small spin ﬂip cross section3
and therefore a large SDLz6lnm. If the Co/CuGe samples behave like the Co/Cu data
then it is the shortening of the SDL by the Pt and Mn impurities that cause the deviation
from equation 4.4. Signiﬁcant departures of the Co/CuGe data from the Co/Cu data
would have indicated that elastic mfp effects play a more fundamental role in CPP
electron transport than was previously thought. The resistances of the
[Co(6.0nm)/CuGe(tCuGJ]xN series are given in Table 6.3, the total sample thickness is
only 360nm because the CuGe(4%) sputtering target was thin. The results plotted in
Figure 6.1 for the Co/CuGe(4%) samples clearly indicate that the direct effect of
increased resistivity can only be a very minor effect.

Table 6.3: CPP values at Ho, Hp and HS for the [Co(6.0nm)/CuGe(tC,,GJ]xN
series. The total sample thickness is 360nm.

 

 

 

 

 

 

 

 

 

 

Sample tcu N Area CPP-AR(H) fQ-mr
# nm mm2 H0 Hp HS
4415W 300 10 1.313 82.70 80.98 80.67
44500 60 30 1.271 87.39 81.66 76.56
44505 90 24 1.227 94.15 90.79 87.1 1

 

 

 

 

50

40*

10*

20

ART(H)-ART(HS) (fﬂmz)

30

20*

10*

Figure 6.2: A comparison of ARKIﬂ-ARKHS) versus H for samples with the same
thickness a) [Co(6.0nm)/Cu(9.0nm)]x48,
[Co(6.0nm)/CuGe(9.0nm)]x24 and c) [Co(6.0nm)/CuPt(9.0nm)]x48. The lines are

nominal bilayer

guides to the eye.

 

30*

20*

 

 

 

16*

12*

Co/CuGe(4%) b)

llllllllllllllllll

 

 

 

Y I Y j v I v I V I Y 17* ‘‘‘‘‘‘

 

H (kOe)

 

142
Before ﬁnally comparing the data with the Valet-Fert theory, we consider evidence

that no major changes occur in the coupling of the system. If the coupling between Co
layers remains weak with the addition of impurities into the Cu spacer layer, then a
similar ﬁeld dependence of ART should be seen for samples of Co/CuX and Co/Cu with
the same spacer thickness. Figure 6.2 shows the ﬁeld dependence of ARﬂIﬂ-ARKHS) for
similar multilayers of Co/Cu, Co/CuGe(4%) and Co/CuPt(6%). All three multilayers in
Figure 6.2 exhibit similar ﬁeld dependent behavior. The as-deposited Ho resistance has
the largest value for each sample. Each sample saturates well before 1.0 kOe. The HP
resistance of each also occurs at approximately the same ﬁeld, near the coercive ﬁeld.
The magnitudes of ARrﬂﬂ-ARKHS) are also quite similar for each multilayer in Figure
6.2. (To correctly compare the magnitude of ARKID-ARKHS) for the Co/CuGe(4%)
sample to ﬁrst order, the difference must be doubled since the total thickness of the
CuGe(4%) samples is half that of the other series.) The similarities in forms and
magnitudes of the samples shown in Figure 6.2a, 6.2b and 6.2c allows one to conclude
that introducing Pt and Ge impurities into the Cu spacer layer does not modify the
coupling between Co layers such that these multilayers are no longer considered
uncoupled. As a further check, the ratio 1'] (deﬁned by equation 5.5) is calculated for
each Co/CuX sample and plotted in Figure 6.3. The values for T1 ﬂuctuate about 1.7 for
every series except Co/CuPt(6%). This suggests that the impurities also do not greatly
modify the relationship between ARﬁHo) and ART(HP). The 1'1 values for a majority of

the Co/CuPt(6%) data are closer to 1.2. Although this signiﬁes a smaller difference

143
between the H0 and Hp resistances, the H0 resistance is still the largest and therefore

should be used for the AP state‘s.

 

 

 

 

 

 

 

tCux (nm)
66.0 1 8.0 8 .4
3 * 1 '
0 Cu Old 0
1 0 Cu New 0
g A CuMn(7%) O
. O CuPt(6%) i A
A l I CUGC(4%) l .
i 2 P ‘L J I O 7
D
g . . 9 -
3 Cu ' . . z
a - o
M O
0
E l r O o O o _
{Co(6.0nm)/CuX(tCux)}N
0 1 - A , ' A l 1 ml 2 l
0 1 O 20 30 40 50 6O
Bilayer Number N

Figure 6.3: Plotted are 1'] ratios as a function of the N, the bilayer number for Co/Cu,
Co/CuMn, Co/CuPt and Co/CuGe samples with tCo=6. 071m. The ﬁlled symbols have
'cux different from those indicated on the top axis. The solid line represents the average
l'I ratio for the Co/Cu series.

Comparison with Valet-Fert Theory
For the constant 6.0nm Co data, a straight line through the origin is expected for

normal metals with SDL much larger than the layer thickness. This behavior was

144

observed for the constant Co series shown in Figures 5.3b and 5.4b of chapter 5.
Deviations from this behavior are attributed to spin ﬂips in the normal metal layer. The
largest deviations are observed for the Co/CuMn(7%) data. The Co/CuPt(6%) data show
a smaller but still measurable effect. The three Co/CuGe(4%) samples are well within the
scatter of the Co/Cu series and therefore must have a long SDL.

The data of each Co/CuX series were ﬁtted to the Valet-Fert equations (4.8-4.11)

assuming I?" = co and using I; as a ﬁtting parameter. These ﬁts used the same

parameters derived from the analysis of the three Co/Cu series examined in the previous
chapter. The only exception was that pa, was replaced by measured values of Pcux made

on 300nm CuX ﬁlms fabricated in each sputtering run with the CPP multilayers. Table

6.4 lists the parameters used in the analysis along with independent estimates of [2}.

Table 6.4: Estimated parameters for Cu alloys.

 

 

 

 

 

 

 

 

Metal 0r 9% p71 93!, 4’5, 4:} (um)
Alloy“ mam)" (nnmr (um)d <nm)° (nmf
Cu -- 5.51:1 110 11000 450

CuMn(7%) 310 270i30 2.1 24(6) 3(1.5)

CuPt(6%) 120 130110 5.5 50 7

CuGe(4%) 162 1821:20 4.0 5700 61

CuNi(l4%) 185 180130 3.5 250 12

CuNi(6%) 85 88i15 7.7 580 27

 

 

 

 

 

 

 

' Impurity concentrations in atomic %.

b Calculated ﬁ'om intended impurity concentrations and known resistivities per atomic %
impurity7.

c Measured on sputtered ﬁlms 300-500nm thick. Uncertainties are the largest deviations
ﬁ'om the average values.

d Calculated from p5,, (p’,’{, for Cu) and free electron equationss.
° The sputtered Cu value assumes a defect content of ~1% and a spin-orbit cross section
of 1x10'18 cmz. The CuPt value was calculated from a free electron conversion of ESR

145

cross sections”. The CuMn value was estimated by Fert5 from available information

about exchange coupling in this alloy, parenthetical value was calculated from a cross
section measured by Starr, et 01.9 using weak localization.

f Calculated using equation, 4.17 (if; = ,/(XC}KZ) / 6 also given inz’s’lo.

The data sup rt the estimates for [N given Table 6.4. The CuMn(7%) and
P0 sf

CuPt(6%) data both clearly lie below the straight line representing [if/{=00 in Figure 6.1,
with the CuMn(7%) showing the bigger effect. The best ﬁt curve through the CuMn(7%)

data yields 33M" = 2.8nm, in good agreement with the estimate of 3.0nm listed in Table

6.4. The best ﬁt curve through the CuPt(6%) data gives I?” = 8.0nm close to the
calculated value of 7.0nm.

Because both the Co/CuGe(4%) and Co/Cu data lie near the inﬁnite SDL line (Figure
6.1), one can eliminate the differences in the elastic mfp as the cause of the reduction in
CPP-MR. The reduction in the CPP-MR for the CuMn(7%) and CuPt(6%) multilayers
must arise ﬁ'om something other than the reduced elastic mfp. The CuGe(4%) samples
also show that changing the total thickness of the multilayer by half does not have a

measurable effect.

146
ColCuNi(l4°/o) Samples

The possibility of spin ﬂip scattering at the interfaces of Py/Cu multilayers has been

”'12 on GMR in these samples. This could profoundly affect

mentioned in several papers
the applicability of the f 3! = 00 Valet-Fert theory. To investigate this possibility, in
Py/Cu multilayers a series of Co/CuNi(14%) samples was measured. The magnetic
properties of CuNi alloys are well documented”. Cu has a ﬁlled 3d band and a half ﬁlled
4s conduction band, while Ni has vacancies in both the 3d and 4s bands. The unpaired
spins in the 3d band are responsible for ferromagnetism in Ni. Since Cu and Ni form a
solid solution over the entire concentration range, it is possible to make alloys of any
concentration. As Cu is added to Ni, it is energetically favorable for the 4s Cu electrons
to ﬁll in the 3d Ni band. Adding the proper amount of Cu will kill the ferromagnetism of
the CuNi alloy. This happens at 60 at.% Cu concentrations. With higher Cu content the
alloy becomes a Pauli paramagnet. Unlike Mn in Cu, the Ni atoms do not form magnetic
ions with the Cu host. The absence of a local magnetic moment should rule out spin ﬂip
scattering via the exchange interaction with paramagnetic impurities, leaving spin orbit

coupling as the mechanism for reducing the SDL.

A series of [Co(6.0nm)/CuNi(tCuN,-)]XN samples with total thickness 720nm was
measured at 4.2K and compared with similar Co/Cu samples described earlier. A 14 at.%
Ni concentration was chosen so that the resistivity of the alloy would be similar to the

other Cu based alloys in Table 6.4. The data are listed in Table 6.5 and plotted in Figure

147
6.4 with J AR (H0 )[AR (H0) — AR (HS)] as a function of N, the bilayer number, for both

 

Co/Cu and Co/CuNi(14%).

Table 6.5: CPP values at Ho, Hp, HS and HD for the [Co(6.0nm)/CuNi(tCuN)]xN series.
The total sample thickness is 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample tcu N Area CPP-AR(H) fQ-mz
# nm mmz H0 HP HS HD

637") 60.0 11 1.208 122.80 122.79 122.76

633"5 30.0 20 1.190 128.98 128.66 128.17 128.78
6376‘ 30.0 20 1.205 118.56 118.27 117.81 118.37
6440'5 30.0 20 1.309 98.46 97.86 96.87 98.04
6440’ 18.0 30 1.272 104.04 101.90 98.34 102.55
644W 12.0 40 1.259 108.30 104.32 98.77 105.62
633‘" 9.0 48 1.153 136.12 130.74 124.60 132.19
637"5 9.0 48 1.187 144.07 139.22 132.46 140.02
644"3 9.0 48 1.339 117.64 111.98 103.74 113.92
633” 6.0 60 1.201 134.99 124.90 116.23 126.81

 

 

 

 

 

 

70
A 60
O
5
5 so
‘5
a 40
5
A 30
O
E
3.2 20
S.
7 10

148

 

 

 

 

 

 

 

 

 

tCu (nm)
30.0 12.0 6.0
{Co(6.0nm)/CuX(tCux)}N .
>— . —
l 0 Cu
* A CuNi(l4%) A ‘
10nm

— 4
1
1
o 10 20 A 30 4o 50 60 7o

Bilayer Number N

Figure 6.4: Plotted are both the measured and predicted values using the Valet-Fert
theory for the quantity JAR(H0)[AR(Ho)-AR(HS)]as a function of N, the bilayer
number. The Valet-Fert predictions use [if = co and if!“ =10nm and 00 with the

appropriate Pcux: given in Table 6.4. The total thickness of multilayers from both series
is 720nm. The ﬁlled symbols have different Cu thickness than those indicated on the top

axis.

 

In Figure 6.4, the Co/CuNi(l4%) samples clearly fall below the line representing

inﬁnite SDL, therefore the spin diffusion length is shortened by the addition of Ni to the

Cu spacer layer. The open symbols in Figure 6.4 are Co/Cu samples made prior to the

149
Co/CuNi(14%) samples in the same sputtering run. The ﬁeld dependence of the

Co/CuNi(14%) samples was similar to those shown in Figure 6.2 in both form and
magnitude, so any modiﬁcation in the coupling between Co layers by the Ni impurities is
small4‘”. The ratio 11 is plotted as a function of N in Figure 6.5. Both sets of data are
evenly scattered about 1.7 over the whole bilayer range, indicating that the relationship

between the H0 and Hp resistances is the same for each series.

 

 

 

 

 

 

 

tCu (nrn)
66.0 1 8.0 8 .4
3 , . . , . r -
f 0 Cu Old
i 0 Cu New 5 .
i A CuNi(l4%) g
A A
a.
2 _ —<
E . A .
4; A
3 Cu Q A o . E
i A O ' O
"2‘
11 l - “
I:
{Co(6.0nm)/CuX(tCux)}N
o 1 l l 1 = 1 L » l 1 l
0 1 0 20 30 40 50 60
Bilayer Number N

Figure 6.5: Plotted are TI ratios as a function of the N, the bilayer ntunber for Co/Cu and
Co/CuNi samples with tCo=6.0nm. The ﬁlled symbols have tCu different from those
indicated on the top axis. The solid line represents the average 1'1 ratio for the Co/Cu

series.

150

Spin orbit scattering is suspected as the mechanism for ﬂipping spins for two reasons.

First, the CuNi(l4%) data are consistent with the Valet-Fert model using (gum = 10nm,

close to the predicted value in Table 6.4 based on the spin orbit cross section of Ni.
Second, comparing the CuNi(l4%) data with the CuPt(6%) data reveals that the Pt
impurities are much better at spin ﬂip scattering than are the Ni impurities. The Ni
concentration is more than double the Pt concentration, and yet has a longer spin
diffusion length. This is consistent with ESR data3 which show that 3d transition metals,
such as Ni, are much less efﬁcient at spin orbit scattering than are 5d metals, like Pt.
Furthermore, preliminary results for similar experiments on Co/CuN i samples currently
carried out at MSU by S.Y. Hsu's, in which the Ni concentrations are varied from 5% to
20%, show that the measured SDL for each Ni concentration agrees with calculated

values of the SDL based on spin orbit scattering.

Another possible mechanism for spin ﬂip scattering in Co/CuN i is the formation of
tiny Ni clusters in the Cu layer which possess a local magnetic moment. Electrons
scattering of? these clusters would likely undergo spin ﬂips, reducing the SDL of the
material. The possibility of Ni cluster formation in Cu is unlikely because Cu and Ni
form a solid solution at all concentrations. Also, the CuN i layers are sputtered ﬁ'om a
homogeneous target of CuNi(l4%) at rates of 1.0nm/s, presumably forming a random
alloy. Magnetic measurements on 300nm ﬁlms of CuNi(l4%) showed no evidence of

magnetic clusters forming in the ﬁlm.

151
Reconsideration of the Co/Cu Data

The scatter in the Co/Cu data presented in Figure 6.1 means that we cannot
distinguish between the (30" = 6lnm and {’5‘} = 00 in the normal metal. In these samples,
it was assumed that is!" >> 1C0 = 6.0nm. However for samples with thicker Co layers

one might expect to see the square root data deviate from a ﬁt based on this assumption.
Figure 5.5b shows small deviations between the square root tCo=tCu data and the ﬁt based

on the two channel model (where 63’ z co and ((33; = 00 are assumed). In Figure 5.5b the
low N data lie noticeably below the ﬁt. By assuming (3‘ = 00, justiﬁed by the Co/Cu data

in Figure 6.1, a ﬁt using the Valet-Fert model to the tCo=tCu data could give a possible
lower bound on the SDL in Co. The square root data for the tCo=tCu series is plotted in
Figure 6.6 along with predictions using the Valet-Fert model for ﬁnite SDL. Figure 6.6
shows the extreme cases for SDL’s in both the Cu and Co needed to explain the slight

curvature in the tCo=tCu data. As shown in Figure 6.6b, for (f; = oo, a C0 SDL of 2.5nm

could explain the curvature16 in the ’cf’a data as the Co thickness increases (N

decreases). Alternatively, these deviations could be explained by assuming 13%} = co and

a SDL of 75nm in the Cu as seen in Figure 6.6a. The two extremes put a lower bound of

If!" = 2.5nm and [3‘ = 75nm. The lower bound on the SDL in Cu is a factor of 6 smaller

than the 450nm given in Table 6.4 which is based on a measurement of the spin orbit

,17

cross section attributed to defects in Cu3 . The agreement between the estimated values

of (2’, and the ﬁtted values of £2} for each Co/CuX series implies that the SDL in Cu is

152
probably closer to 450nm than 75nm. Therefore the curvature in the low N tCo=tCu data is

probably due to a ﬁnite SDL in Co greater than 2.5nm.

Looking closely at Figures 6.6a and 6.6b one notices that the inﬁnite ﬁt crosses the
ﬁts for ﬁnite SDL. This discrepancy is attributed to the handling of the Nb/Co boundary
resistance in each model. In the two channel model presented in chapter 4, the Nb/Co
boundary resistance is included by adding 4ARNb/Co to the + channel and the - channel
before the + and - channels are added in parallel. For the case with ﬁnite SDL, the Valet-

F ert model has yet to be rigorously extended to multilayers with superconducting Nb

contact layers, and therefore the Nb/Co boundary resistance, 2AR NMCO = 6.1mm2, is
added in series to equation 4.8. Simply adding the Nb/Co boundary resistance to the
Valet-Fert predictions is only an approximation of the real resistance and as Figure 6.6
shows there are small inconsistencies. Fortunately they exist at a level below our ability

to measure.

m
v

70

60

50

40

30

20

 

\/{ART(Ho)-ART(HS)}ART(H0)

10

on
V

70

60

50

30

20

 

\/{ART(Ho)-ART(HS)} ART(H0)

10

153

tCu (nm)
17.1 8.8

5.9

 

}

T

T

 

{Co(tCo=tCu)/Cu(tCu)] N

infinite

J

  

100nm

     
   

 

 

 

40

 

 

 

50 nm
_ 75 nm _
0 1o 20 A 30 4o 50 6o 70
N-l
tCu (nm)
17.1 8.8 5.9
L {Co(tCo-ﬁtCu)/Cu(tCu)}N o
* 5.0 nm 7
'_ infinite _
- 1 \1.0 nm ‘
2.5 nm
0 10 20 30 40 so 60 7o
N-l

Figure 6. 6: Valet-Fert predictions for the [Co(tC0=tC,,)/Cu(tc,,)]xN series using the Co/Cu
parameters from Table 5.6 together with a) assumed values of (f; = no and [3‘ = 50nm,
75nm, 100nm and 00 ; and with b) assumed values of if} = 00 and KS; =1.0nm, 2.5nm,
5.0nm and 00 .

154

 

‘ F. Beuneu and P. Monod, Phys. Rev. B 13 (1976) 3424.

2 T. Valet and A. Fert, Phys. Rev. B 48, 7099 (1993).

3 P. Monod and S. Schultz, J. Phys. (Paris) 43, 393 (1982).

‘ S.S.P. Parkin, C. Chappert and F. Herman, Europhys. Lett. 24, 71 (1993).
5 A. Fert, J.L. Duvail and T. Valet, Phys. Rev. B 52, 6513 (1995).

‘ Demagnetizing a few representative Co/CuPt(6%) samples show that the AR(HD) is less
than the Ho resistance. The ratio I'ID is less than 1.2.

7 J. Bass, in Metals: Electronic Transport Phenomena, edited by K. H. Hellwege and J. L.
Olsen, Landolt-Bﬁrnstein, New Series, Group 3, Vol. 15 Pt.a (Springer-Verlag, Berlin,
1982)

' N. W. Ashcroft and N. D. Mermin, Solid State Physics (W. B. Saunders, Philadephia,
1976)

9 A. F. Starr, A. Nishida and S. Schultz (unpublished).
'° T. Valet - " A. Fert, J. Magn. Magn. Mater. 121, 378 (1993).
” B. Dieny, J. Magn. Magn. Mater. 136, 335 (1994).

‘2 V.S. Speriosu, J .P. Nozieres, B.A. Gurney, B. Dieny, T.C. Huang and H. Lefakis, Phys.
Rev. B 47, 11579 (1993).

'3 R.M. Bozorth, F erromagnetism, D. Van Nostrand, New York, NY (1951) p. 308.
" J.F. Bobo, L. Hennet and M. Piecuch, Europhys. Lett. 24, 139 (1993).
'5 S.Y. Hsu, et al., to be published.

'6 Data in SF. Lee, Ph.D. Dissertation, Michigan State University (1994) show deviations
from the ﬁtted quantities in similar multilayers of Co/Ag for tC0>15.0nm with more
signiﬁcant deviations for tC0>20.0nm. MR and magnetization studies on these thick Co
samples show complex magnetic behavior.

'7 A. C. Gossard, T. Y. Kometani and J. H. Wernick, J. Appl. Phys. 39, 849 (1968).

155

6.2 Giant Magnetoresistancc in Hybrid Multilayers.

Fundamental to large changes in a magnetic multilayer’s resistance is the ability to
form two very different magnetic states, where the moments of adjacent magnetic layers
are aligned either parallel or antiparallel to each other. In the previous chapter samples
with very thin Cu spacer layers exhibited an oscillatory MR. Peaks in the MR
corresponded to strong AF exchange coupling between F layers which formed the AP
resistance. Samples in the uncoupled region still behaved as if the adjacent F layers were
aligned antiparallel. (This could be explained by magnetostatic interactions between the
F layers or a random conﬁguration of the F layer magnetizations.) However, in this
section the alignment of the magnetic layers is governed by the differences in the
coercive forces between adjacent magnetic layers.

The term “hybrid” refers to a multilayer containing two distinct magnetic
components. Here the materials Py and Co are used to provide the magnetic contrast
necessary to produce an AP state. As mentioned in chapter 5, for the same thickness, the
coercive ﬁelds of Co are more than 20 times larger than those of Py. This large
difference in coercivity results in large resistance changes in the sample at low ﬁelds.
This section is divided into two parts: The ﬁrst deals with CIP-MR and magnetic
measurements on both Ag and Cu based hybrid systems. The second deals exclusively
with CPP transport measurements made on a series of Ag based hybrids in which the Py
thickness is varied.

In most of this section the magnetic contrast between discontinuous layers of ultra-

thin Co and thicker continuous layers of Py is used to produce the AP state necessary for

156
GMR. Prior measurements on Co/Ag multilayers indicated poor MR for Ag thicknesses

less than 5.0nml when thick continuous layers of Co were used. However, if the Co
thickness was reduced to less than 1.0nm then large MR’s were observedz'3 . These ultra-
thin Co samples exhibited larger saturation ﬁelds for both the resistance and
magnetization than those required for multilayers with thicker Co layers. NMR studies
by van Alphen et al.4 described in section 3.4 indicated that the Co existed as clusters
below nominal Co layer thicknesses of 1.0nm. As will be described, it is believed that
the clustering of the Co layers reduces the effect of pinholes thereby improving the MR.
In addition to improving the MR, samples with clustered Co layers exhibit larger coercive
and saturation ﬁelds than samples with continuous layers of Co of comparable thickness.
These properties are utilized in the hybrid structures that follow.

The magnetic properties of a system of ferromagnetic clusters can be somewhat
sensitive to temperature. Very simply, at low T, a cluster behave ferromagnetically.
However, as the thermal energy approaches the magnetic energy of a cluster, the cluster
begins to behave paramagnetically. This crossover from ferromagnetism to paramagnetic
behavior is sometimes referred to as superparamagnetism. Properties such as the coercive
ﬁeld of a system of clusters are reduced to zero as T increases. A more detailed

discussion of the temperature dependence of ferromagnetic clusters is given later.

157
CIP-MR in hybrid multilayers.

Although CIP—MR measurements are hard to interpret without complicated models
with several adjustable parameterss, this geometry is important technologically since it
allows MR measurements on samples with resistances of a few Q, instead of the en!)
encountered in the CPP direction". All of the resistance studies were carried out by L.B.
Steren in Orsay, France. The magnetic studies were done at MSU using Quantum Design
magnetometers. The studies were done independently on the same sample; after
sputtering, each half inch square substrate was cleaved into two equal parts. One half was
kept here for the magnetic measurements while the other was sent to Orsay for the
resistance studies.

The resistance and magnetization of each multilayer are well correlated. Figure 6.7
shows the ﬁeld dependence of both the magnetization and the resistance of a
[Co(0.4nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4.0nm)]x10 sample at 4.2K. The ﬁeld dependence
is typical for most hybrid samples. In the low resistance state, the applied ﬁeld aligns
both the Py and Co moments. As the ﬁeld is lowered the resistance stays roughly the
same until a small negative ﬁeld in reached. The small rise in the resistance after
saturation as the ﬁeld is reduced may be attributed to some of the more anisotropic
clusters. The C0 clusters will tend to orient themselves along their easy axes at low ﬁeld
minimizing their energy with respect to the applied ﬁeld; so that although the Co layer
magnetization points in a speciﬁc direction, the individual cluster moments are actually
distributed over some range of angles. As the ﬁeld is swept through HC for Py, the Py

magnetization ﬂips and a large change in the resistance is observed. The resistance levels

158
off after the Py layers are saturated forming a small plateau. Sweeping the ﬁeld further

in this direction begins to ﬂip the Co layer bringing the sample back into the low
resistance state. The initial H0 resistance is much smaller than the Hp resistance because
the Co clusters have not yet been polarized along the ﬁeld direction. Therefore only half
the Co clusters have moments antiparallel to the adjacent Py layers, creating a resistance
state which is deﬁnitely not an AP state. The magnetization plot for the same sample
shows a similar ﬁeld dependence as the ﬁeld is swept through the Py HC. In these
hybrids, most of the Py ﬂips with a change in ﬁeld of only S-ISOe. The MR associated
with the ﬂip of the Py is about 30% giving slopes (AR/AH) as high as 6%/Oe, much more

ﬁeld sensitive than MR devices now used in hard drives7.

159

 

 

C0—>

PY <— A/Rhigh

 

Reversal of NiFe

[f g
1 / 1

 

 

M antiparallel

M parallel
R 10W \

\

    

  

 

 

3)
30 ~
A L
§ 20
a:
2
10 ~
0
-5
b)
1.5
1.0 ~
0.5 —
g 0.0 .
-0.5 —
-1.0

 

 

 

 

 

 

 

 

 

 

 

 

 

-4 -3 -2 -1 0 1 2 3 4 5
H (kOe)
» Reducing H, M of NiFe F Hybrrd
with low coercive force -7a+~:<::v ;
changes sign first. r’V
Co islands l Py layers /
Co M slowly reversing ‘
w Large H, M of Py
// b
c : 2-“.4nj-jj &Co parallel.
‘— <—— Py —->
+— —> C0 —>
-5 -4 -3 -2 -l O l 2 3 4 5
H (kOe)

Figure 6. 7: The ﬁeld dependence for a [Co(0.4nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4. 0nm)]x10
sample of a) the CIP-MR and b) the magnetization at 4.2K. In b) the hysteresis of the Co
and Py is shown schematically. The curve label hybrid in b) is an actual measurement.

160

The thickness of each layer is chosen to be smaller than the elastic mfp of each
material. The thin 0.4mn Co layers are not thick enough to form a continuous layer,
NMR measurements by van Alphen et 01.4 indicate complete layers of Co form after
1.0nm of Co has been deposited. There are two advantages in having a layer of island-
like clusters of Co in these samples. Studies have shown that multilayers made with a Ag
spacer layer less than 5.0nm and continuous Co layersl'3’9’lo exhibit poor MR. This is
usually ascribed to ferromagnetic bridging (pinholes) between F layers. Further inquiries
showed large oscillatory MR effects in Co/Ag with ultra-thin Co layersz‘s. The ﬁrst
advantage is that the layer of Co clusters is then, less sensitive to ferromagnetic bridging
by pinholes or defects. Figure 6.8 illustrates that a pinhole connecting a Co cluster to a
Py layer, will only ferromagnetically couple a cluster near the bridging site, leaving the

rest of the Co layer uncoupled from the Py layer.

161

 

 

 

CO :QSﬂOLD

Ag 4— Ferromagnetic bridge

 

 

 

 

 

 

COCZDCDCDC

 

 

 

 

 

 

 

Figure 6.8: Schematic illustration of a pinholes bridging Py and Co. With island-like Co
clusters only a small ﬁaction of the Co ferromagnetically couples to the Py layers.

The second advantage is an enhancement in the magnetic contrast between Co and
Py. Within a layer of island-like ferromagnetic clusters, magnetostatic interactions
between the clusters increase the hysteresis and saturation ﬁeld of this layer, relative to a
similar continuous layerg. Therefore a layer of Co clusters is magnetically harder than a
comparably thick continuous Co layer. Also, the actual volume of Co present in these

hybrid structures is so small that the bipolar ﬁelds produced by the Co clusters have only

 

the slight
the Py”.
hybrids i

to Cu and

IQ

 

MR (%)

1.1

0.1

Figure 6.9
[CO/0 4mn

CIUSIEFS ha

162
the slightest effect on the Py coercive pr0perties, very effectively decoupling the Co from

the Pyl '. The Py layers also have a lower HC in the Ag based hybrids than in Cu based

hybrids ‘2’13’14 which may be attributed to the weaker miscibility of Ag and Py compared

to Cu and Pyls.

 

3.0

2.5 *

2.0 *—

MR (%)

 

 

 

 

H (kOe)

Figure 6.9: The ﬁeld dependence of the CIP-MR at 300K for a hybrid sample with
[Co(0.4nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4.0nm)]x10. Superparamagnetism of the Co
clusters has drastically reduced the MR observed at 4.2K (compare with Figure 6.7a).

 

The<

sensitivitj

 

as the 161

Evidence

that show

temperatt

distributit

Co cluste-

M (x10"8 emu)

Figme 6, 1 (
[CO/0.6""?
ﬁe“(ZFC
COOled {PC
Cline dEﬁn

163
The disadvantage of using Co clusters is the degradation of both the MR and

sensitivity with increasing temperature as shown in Figure 6.9. The reduction of the MR
as the temperature increases is attributed to superparamagnetism in the Co clusters.
Evidence for this is observed in temperature dependent magnetization measurements like
that shown in Figure 6.10. Cooling the sample in zero ﬁeld (ZFC) from room
temperature to 5K, freezes the moment of Co clusters in a certain (presumably random)
distribution. A small lOOOe ﬁeld is applied which saturates the Py layers but leaves the

Co clusters in their ZFC orientations.

 

   
  

1.90
' Field Cooled in 100 0e ,

 

1

1.85 i

Superparamagnetic
behavior in E
Co islands

    

1.80

 
 

Blocking .
Temperature

   

1.75

'Y Tvavvvvvryr vva

M (1:10”3 emu)

1.70 f"

  

Zero Field Cooled

 

 

 

1.65
0 100 200 300 400

T(K)

Figure 6.10: The temperature dependence of the magnetization is plotted for the hybrid
[Co(0.6nm)/Ag(4.0nm)/Py(4.0nm)/Ag(4.0nm)]x10. Initially the sample is cooled in zero
ﬁeld (ZFC) and then a lOOOe ﬁeld is applied to saturate the Py layers. For the ﬁeld
cooled (F C) curve the sample is allowed to cool in the lOOOe ﬁeld. The peak in the ZFC

curve deﬁnes the blocking temperature.

 

 

Blocking
The depel
measured
gll'lllg tilt
Since the
amount 01
than the e
magnetic .
to a the 1
be express

crystal an

Change in 1

 

The di
anismropy
the <100>
the anlsotrc
of me CD'S

between 1h:

164
Blocking Temperature and Magnetic Anisotropy

The dependence of a material’s magnetic properties on the direction in which they are
measured is known as the magnetic anisotropy. When measuring a sample. the direction
giving the lowest saturation ﬁeld in known as the easy direction or axis of the material.
Since the saturation ﬁeld is small along the material’s easy direction only a minimal
amount of energy is required for saturation. To saturate the material in a direction other
than the easy axis requires additional energy to overcome the anisotropy. Generally, the
magnetic anisotropy energy possesses the crystal symmetry of the material and is referred
to as the magnetocrystalline anisotropy. For a cubic system, this anisotropy energy can
be expressed in terms of the direction cosines of the magnetization with respect to the
crystal axes. The two lowest order terms are given in equation 6.1, where E0 is the
change in energy as the magnetization is rotated through some angle, 0.
Ea =K,(011012+01301§+01§0tl)+K;,_(otl2 a2a3)+-- 6.1

The direction of the easy axis for cubic systems is complicated and depends on the
anisotropy constants K, and K 2 for a particular material. For bcc Fe the easy axis is in
the <100> direction and in fee Ni the easy axis is the <1 1 l> direction. The expression for
the anisotropy energy of an hcp system is simpler since the easy axis lies along the c axis
of the crystal. In this case, the anisotropy energy depends only on a single angle, 0,

between the c axis and the magnetization.

15=1<l sin20+Kzsin40+~~ 6.2

 

 

The mag
magnetic
even dor

For:
the easy
poles at
than alt
produce
ferromz
geomei

magne

“here
Oblate

anisot

165

The magnetocrystalline anisotropy is intrinsic to the material but other extrinsic forms of
magnetic anisotropy may contribute to a sample’s anisotropy energy and in some cases
even dominates the magnetocrystalline anisotropy of the sample.

For example the geometry of a ferromagnetic material will also affect the direction of
the easy axis. Demagnetizing ﬁelds within the material act to limit the number of free
poles at the surface of the material. A demagnetizing ﬁeld along a short axis is stronger
than along a long axis. Therefore, a ﬁeld applied along a short axis must be stronger to
produce the same true ﬁeld inside the specimen. For example: (a) a long needle like
ferromagnet has its easy axis along the axis of the needle; whereas, (b) a thin disk
geometry will have the easy axis in the plane of the disk. The demagnetizing ﬁelds of a

magnetized sample have an associated magnetostatic energy which is given by
E=§HdM=-l-NdM2
Where HfNM is the demagnetizing ﬁeld and Nd is the demagnetizing factor. For an

oblate spheroid with semi-major axes c > semi-minor axis a and magnetization M5, the

anisotropy energy becomes:

E luv, — NC)M§ sin2 0 6.3

shape =
Which is of the same form as the ﬁrst term in equation 6.2 with KS = %(Na — NC)M§.
Therefore the shape ansiotropy of an oblate spheroid is dependent upon both the
magnetization of the sample and the ratio of the c axis to the a axis. With c>>a this
approximates a thin disk.

In many materials it is possible to induce anisotropy by special preparation or

treatment of the sample. As will be shown later, it is possible to induce a permanent easy

166

axis in a sample by depositing the sample in a strong magnetic ﬁeld. The induced
anisotropy is similar to other uniaxial anisotropies listed previously.

E = K" sin2 0
Where K, is the anisotropy constant and 0 is the angle between the magnetization and the
direction of the ﬁeld applied during growth.

The magnetization of a small, single domain particle will tend to point along its easy
axis in order to minimize its internal energy. In general the direction of the easy axis for
a small particle depends on both crystal structure and the macroscopic dimensions of the
particle and their relative orientations. Table 6.6 gives some values for the shape

anisotropy of an oblate spheroid of Co for comparison with K,=6.8x106erg/cm3.

Table 6. 6: Values of shape anisotropy for oblate spheroids of Co (MS=1422 emu/cm3).

 

 

 

 

 

 

 

 

 

 

 

c/a Na-Nc K s (10° erg/cm’)
1.0 0 0
1.1 0.472 0.477
1.5 1.892 1.913
5.0 5.231 5.289
10.0 5.901 5.966
20.0 6.165 6.233
00 211: 6.353

 

At low temperatures and in zero applied ﬁeld, the anisotropy energy of the particle,

K V, will dominate in holding its magnetization in place. (Here K represents the total

 

167
strength of the anisotropy which could be a complex function of the magnetocrystalline

and shape anisotropies.) As the temperature increases, the particle’s internal energy
increases by an amount, kAT. At a certain temperature, the particle’s thermal energy
becomes of the order of the particle’s anisotropy energy and the particle’s magnetization
no longer points in a particular direction. The temperature at which kT zK V is called the
blocking temperature, TB. When the particle’s anisotropy can no longer keep its
magnetization from spontaneously reversing then the particle acts paramagnetically. The
magnetization of paramagnets is governed by a Langevin Law which describes the
competition between thermal ﬂuctuations and an applied ﬁeld. The particle’s moment
will tend to align with an applied ﬁeld while the thermal ﬂuctuations will tend to disalign
the moment and ﬁeld. The major difference between a normal paramagnetic material and
one with clusters of magnetic atoms is magnitude of the magnetic moment. The magnetic
moment per atom of a paramagnetic material is just a few 1113 while ferromagnetic
particles above TB have moments of 103 113. For example a spherical Co particle only
5.0nm in diameter has a moment of 2510000113. These types of particles are said to
behave superpararnagnetically because of their large moments and their paramagnetic
behavior above TB.

To determine the blocking temperature of an assembly of superparamagnetic particles
one must examine the time required to relax the magnetization. The rate of decrease in
the magnetization is proportional to the initial magnetization of the system and the

probability that a particle has enough thermal energy to overcome the energy gap

168
presented by the anisotropy energy, AE =K V. The probability is given by the Boltzmann

sewn
factor e . Therefore,

dM -Kl'/kT = ﬂ

-————= Me 6.4
dz fo

I

Where ﬁerO’gsec'] is called the frequency factor. The constant 1 is the relaxation time of

the magnetization and is given in equation 6.5.

_l_=fOe-Kl'/kT 65
I

Since the temperature and the volume appear in the exponential, they are rather
insensitive to the choice of the relaxation time. An appropriate choice for the relaxation
is 100 sec. This is roughly the amount of time it takes to make a measurement of the
magnetization. Using this estimate for 1 one may estimate the blocking temperature of
the system.

KV

z 6.6
25k,

TB

 

As will be done later, the volume of the average superparamagnetic particle may also be
estimated using equation 6.6 if their anisotropy constant is known.

The nature of the MR above the blocking temperature is completely different from
that at 4.2K (compare Figure 6.7a with Figure 6.9). Above T3, the Co magnetization is
governed by a Langevin Law and the Co clusters lose their remanent magnetization, or
alternatively, HC for the Co layer goes to zeroz. With no remanent magnetization, the Co
clusters are randomly oriented near zero ﬁeld. Therefore in small ﬁelds where the Py

magnetization ﬂips, the relative orientation between the Co clusters and the Py layers

169
does not change; both before and after the Py ﬂips, roughly half the moments of the Co

clusters are parallel and half antiparallel. Since the relative orientation between the Py
and the Co is not changed, minimal change in the resistance is observed. As the ﬁeld is
increased, the Co clusters gradually become polarized, parallel to the Py layers, in the
direction of the applied ﬁeld. Since some of the Co was antiparallel to the Py near zero
ﬁeld, a small drop in the resistance is seen. The MR drops an order of magnitude within

20K of T3z60K for tCo=0.4nm.

Raising the Blocking Temperature (a) Variation with ta,

For commercial application, it is necessary to increase TB to above room temperature.
Three different studies were done to investigate how TB could be varied. The ﬁrst set of
experiments varied the Co thickness in both Ag and Cu based hybrids to study what
happens as the island-like Co layer becomes a continuous Co layer. NMR data by van
Alphen, et al.4 showed that continuous Co layers formed when the nominal thickness
reached ”1.0nm in Co/Ag multilayers. Magnetic measurements by R. Loloee2 also
indicated clustering in both Co/Cu and Co/Ag systems for tC0< 1.0nm, with TB in the Cu
samples almost four times that of the Ag ones.

Table 6.7a gives measurements of the magnetic properties due to the Co layers in the
[Co(tCJ/AgM.0nm)/Py(4.0nm)/Ag(4.0nm)]x10 samples. The MR and sensitivity of these
samples at room temperature and 4.2K are given in Table 6.7b. Similar measurements

for the [Co(tCJ/CuM.0nm)/Py(4.0nm)/Cu(4.0nm)]x10 series are given in Tables 6.8a and

6.8b. The blocking temperatures for both series are shown in Figure 6.11 as a function of
the Co thickness. Both series show an increase in TB with tCo less than 1.0nm. If the
strength of the anisotropy changes little with the volume, then a higher TB means that the
increased anisotropy energy (K V) is a result of larger average cluster voltunes as the Co

thickness increases. The Cu hybrids show TB a factor of two greater than the Ag hybrids,

170

consistent with the ﬁndings of Loloeez.

Table 6. 7a: Magnetic quantities for [Co(tCJ/AgM. 0nm)/Py(4. 0nm)/Ag(4. 0nm)]x10
attributed to the Co clusters.

 

 

 

 

 

 

 

 

 

 

 

 

 

tCo(nm) T B (K) MS (emu/cm? K (erg/cm?“ V (nm5)"
0.4 50 6.8)(10b 25
0.6 90 1137 6.8x10b 46
0.7 80 6.8)(10b 41
0.85 140 1154 6.6)(106 73
1.0 120 1189 6.7X106 62
1.15 120 1000 6.7x10" 62
1.3 140 1325 6.6x106 73

 

a From Reference 16.

b Calculated using equation 6.6.

Table 6. 7b: CIP Magnetoresistancc and sensitivity measurements at both liquid He and

room temperatures for the [Co(tCJ/AgM. 0nm)/Py(4. 0nm)/Ag(4. 0nm)]x10 series.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(C, (nm) MR (%)“ 5 (%)/0e)“ MR (%)” s (Va/0e)”
0.4 25.6 0.95 3.20 0
0.6 30.7 2.30 3.40 o
0.7 33.5 2.40 3.50 0
0.85 28.8 4.90 3.70 0.36
1.0 29.0 3.80 3.98 0.22
1.15 29.1 3.08 0.21
1.3 28.9 2.72 3.15 0.10

 

a Measurement made at 4.2K.
b Measurement made at 300K.

 

171

Table 6. 8a: Magnetic quantities for [Co(tCJ/CuM. 0nm)/Py(4. 0nm)/Cu(4. 0nm)]x10
attributed to the Co clusters.

 

 

 

 

 

 

 

 

tC0(nm) TB (K) M5 (emu/cmj) K (erg/emf)“ V (nm‘i)0
0.4 180 1150 6.2x 10° 100
0.6 200 1110 5.8x10° 120
0.8 260 1240 5.3x10" 170
1.0 270 1133 5.1x10" 180
1.3 280 1050 4.9x10" 200
1.6 290 985 4.4x10" 230
2.0 335 999 3.9x10" 300

 

 

 

 

 

 

 

a From Reference 16.
b Calculated using equation 6.6.

Table 6. 8b: CIP Magnetoresistance and sensitivity measurements at both liquid He and
room temperatures for the [C 0(tCo)/C u(4. 0nm)/Py(4. 0nm)/C u(4. 0nm) ]x1 0 series.

 

 

 

 

 

 

 

1C, (nm) MR (%)“ 5 (%)/0e)“ MR (%)” s (%/0e)b
0.4 24.7 1.50 3.80 0.38
0.6 29.1 1.40 4.50 0.35
0.8 27.8 2.42 5.90 0.67
1.0 28.6 2.34 6.30 0.41
1.3 25.4 0.78 6.20 0.39
1.6 25.6 1.10 6.50 0.53
2.0 23.1 1.11 5.85 0.23

 

 

 

 

 

 

 

 

a Measurement made at 4.2K.
b Measurement made at 300K.

172

As the Co thickness increases beyond 1.0nm, TB in each series levels off which

indicates a crossover to continuous Co layers. The volume of the average Co cluster may

be estimated from equation 6.6 using the measured values of TB and the temperature

dependent values of K, given for bulk Co in Cullityw. The average cluster volume is

given in Tables 6.7a and 6.8a. The Cu hybrids show signiﬁcantly larger Co cluster sizes

approximately twice the volume of the Ag hybrids. TEM studies have revealed that the

layering in thin-Co/Cu multilayers is much better than in thin-Co/Ag samples of

comparable nominal thickness”. The lattice parameter similarity and surface energy

considerationsl8 between Co and Cu suggest Co/Cu has a more stable superlattice

 

 

 

structure than Co/Ag.
300 *
A
200 L ‘
A .
M
v
1::
E-
100 *
l
+ Co(tCo)/A3(4)/NiP¢(4)/AS(4)XI0
+ Co(tcoyCu(4)/NiFc(4)/Cu(4)x1O

 

 

 

0.0 0.2 0.4 0.6 0.8 1.0
tCo (nm)

Figure 6.1 l : The blocking temperature,

1.2

TB,

is

1.6

plotted

1.8

for

[Co(tCJ/NM/PyM.0nm)/Nij10 samples with NM=Ag(4.0nm) or Cu(4.0nm) as function

of tea for both series. The lines are guides to the eyes.

173
The MR dependence on [Co is similar to that for the TB data for both types of hybrids.

Figure 6.12 plots both the MR and sensitivity (S in %/Oe) for both series at 4.2K and at
300K. At low temperatures, the Ag hybrids show much more sensitivity to ﬁeld than do

the Cu ones, even though the overall MR of both is nearly the same. This supports the

11.12.13.14
’ . At

idea that the Py layers in the Ag hybrids” are softer than in the Cu hybrids
room temperature, it is the Cu hybrids which show a better ﬁeld sensitivity. TB for the
thicker Co samples is close to room temperature so that some of the larger Co clusters in
these samples have not yet become superparamagnetic. The reduction in the MR at
300K is an order of magnitude in the Ag hybrids while the Cu hybrids are reduced only a
factor of 4. Similar reductions are observed in the sensitivity data. Interestingly, all the
data in Figure 6.12 exhibit features at 1C0z0.8nm. All the Ag data show peaks near or at
0.8nm of Co. For tC0<0.8nm the MR and hence the sensitivity increase as ((0 increases.
presumably because the larger Co islands present a greater area for the electrons to scatter
from. Thicker than 0.8nm, the Co forms continuous layers and ferromagnetic bridging by

pinholes decreases the MR and sensitivity. The same is true for the Cu samples except

that bridging is less of a problem with Cu.

174

 

 

 

 

 

 

 

 

 

 

 

 

30 . a)
g 20* —-—----———*——
M + Ag,4.21(
2 —e— Ag,3OOK

+ Cu, 4.2K
—-A- Cu, 300K

10 * ——‘ ’ ' *—

0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

[Co (nm)
5
4 F + Ag. 4.2K A
—9— Ag, 300K
"—4—- Cu.4.21(
Cu, 300K .

E3
K
g 2
U)

1

0 e

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

tCo (nm)

Figure 6.12: The a) CIP-MR and b) the maximum slope, S = AR / AH, of the CIP-MR
are plotted as a function of tCo for samples of [Co(O.6nm)/NM/Py(4.0nm)/NM]><10 with
NM=Ag(4.0nm) or Cu(4.0nm). The lines are guides to the eye.

 

Angular l

Thel
multilayer
magnetiza
c0nductior

Spin depe
the botton

between e

1"€d_\'a}'€\'.
menc

ll
:-

adjacent 11‘

observed 1
predicted
k; "k; at 1
A stud;
Conductivi
magnetic 1

 

 

 

175
Angular Dependence of MR

The large difference in coercive ﬁelds of Co clusters and Py layers makes the hybrid
multilayer an ideal system for studying the dependence of MR on the angle between layer
magnetizations. The mechanism for GMR is attributed to spin dependent scattering of the
conduction electrons and/or spin dependent potential barriers between successive layers.
Spin dependent potential barriers are due to the difference in Fermi energy with respect to
the bottom of the conduction band between adjacent materials. Exchange splitting
between electron subbands can cause the barriers to be spin dependent"). Calculations by
Vedyayev, et al.20 show that GMR varies linearly with sin2((p/2), where (p is the angle
between consecutive magnetic layers, only when there are no potential barriers between

adjacent materials. Alternatively, the linear variation of the conductivity with sin2((p/2) is

observed when kl = k;. Large deviations from the linear behavior in sin2((p/2) are

predicted by Vedyayev20 for ratios of the Fermi momentum different from one,

kit/k; 9t 1 .
A study2 lby Fert’s group using our samples showed that the variation in the sample’s
conductivity, 0, was proportional to sin2(cp/2), where q) is the angle between consecutive

magnetic layers. Similar experimental results have been observed in other systems such

as spin valves of Py/Cu/Py/Feanz, Py/Cu/Co trilayers23 and Fe/Cr/Fe sandwiches“.

I76

Measurement of Coupling Fields

Despite the effective decoupling of the Py layers from the Co layers, a small easily
measurable coupling ﬁeld does exist between Co and Py. It is calculated by comparing
major and minor hysteresis loops in either the resistance or the magnetization”. In each
case the sample is taken to saturation and then cycled through a minor loop which only
ﬂips the Py relative to the Co. In Figure 6.13 the half-width of the minor loop is just the
coercive ﬁeld of the Py, while the distance that the center of the minor loop is shifted
from zero represents the coupling ﬁeld. Note that the sample coercive ﬁeld and the Py

coercive ﬁeld are different.

Table 6.9 contains the calculated values of the coupling ﬁeld, H P y, and the coercive
ﬁeld, HC of Py. The coupling is shown in Figure 6.14 as a function of Co thickness for
both Ag and Cu based hybrid systems. The values in Figure 6.14 for the coupling ﬁeld
obtained from magnetization measurements (ﬁlled symbols) are in good agreement with
those based on the resistance measurements (open symbols). The coupling ﬁeld is
positive for almost every sample, indicative of ferromagnetic coupling between the Co
and Py. For both Cu and Ag based series the coupling ﬁeld increases with tCo. For
multilayers of Co/Cu and Py/Cu, a Cu thickness of 4.0nm lies within a weakly
ferromagnetically coupled region for these multilayers, so it is not surprising that the
Co/Cu/Py/Cu samples are slightly F-coupled. A smaller ferromagnetic coupling ﬁeld is
observed for the Ag based hybrids. The small coupling ﬁeld slightly complicates the

angular dependence analysis but is easily corrected”.

177

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

2’:
Tc
:3
E
3
2
Hcoupling .
0 Major loop
A Minor loop 9
-10 O 1 O 20 30
H (06)

Figure 6.13: Comparing major and minor hysteresis loops of the magnetization shows a
weak coupling ﬁeld between the Py layers and the Co clusters. The minor loop extends
zi450e from the Py coercive ﬁeld. The displacement of the minor loop from H=O
represents the coupling ﬁeld. Here the coupling is ferromagnetic. These hysteresis loops
are for [Co(0. 4nm)/Ag(4. 0nm)/Py(4. 0nm)/Ag(4. 0nm)]x10.

Also shown in Figure 6.14 is the Py coercive ﬁeld for each sample. The HC of the Py
layers is constant for both hybrid series which is expected since every sample has the
same nominal Py thickness. The Py of the Cu based hybrids has ch5.00e, more than
three times larger than the 1.SOe for the Py of the Ag based hybrids. The agreement
between the magnetization (ﬁlled symbols) and resistance (open symbols) measurements

in Figure 6.14 for the HC of Py is quite good.

I78

 

 

 
  

 

 

 

 

 

 

 

 

25
<3 in Co/Ag/Py/Ag
20 * 'f Co/Cu/Py/Cu
15 _ Hcoupling
’43 /
9 10-
:1:
A
A
5 — a 43 3 fl
A
0 g C O *— Py BC
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
tCo (nm)

Figure 6.14: The coupling ﬁelds for samples of [Co(tCJ/NM/PyM.0nm)/Nij10 plotted
as a function of tCo, where NM=Ag(4.0nm) or Cu(4.0nm). The open (ﬁlled) symbols are
measurements of the coupling taken from resistance (magnetization) hysteresis loops.
Nearly every sample shows ferromagnetic coupling. Plotted along with the coupling
ﬁelds is the Py coercive ﬁeld for each sample.

Table 6. 9: Measurements of the Py coercive ﬁeld, HC, and the coupling ﬁeld, Hg".
between the Co and Py layers for the [Co(tCJ/NM/PyM. 0nm)/NM]x10 series.

 

NM=Ag(4. 0nm)

NM =C u(4. 0nm)

 

 

 

 

 

 

 

tCo (nm) Hgy(0e)a HC (0e)a ta, (nm) H9708)“ HC (0e)a H:y(0e)b HC (0e)
0.4 4.90 6.3 0.4 2.05 -1.85 1.50 -2.10
0.6 4.30 14.0 0.6 0.50 1.80 0.83 3.65
0.8 6.20 15.3 0.7 1.15 10.85
1.0 5.20 18.0 0.85 0.50 4.85 0.48 5.00
1.3 5.15 20.8 1.0 0.75 6.85 1.60 6.40
1.6 5.10 20.5 1.15 0.80 8.14
2.0 5.08 20.2 1.3 1.15 10.85

 

 

 

 

 

 

 

 

 

 

a Measurement made using hysteresis loops in the resistance.

b Measurement made using hysteresis loops in the magnetization.

 

179
Raising the Blocking Temperature (b) Addition of Sm

To raise the blocking temperature of the Co islands, it is necessary to increase the
anisotropy energy. In the last section, this was done by making the Co layer thicker
thereby creating larger Co islands. However, giving the Co islands a stronger anisotropy
would also accomplish this task. Adding Sm to Co enhances the uniaxial anisotropy of
Co by up to two orders of magnitude25 in single crystals of CoSSm. Sputtered ﬁlms26 of
CoSm several pm thick have shown anisotropies of 5x107 erg/cm3, much larger than the
magnetocrystalline anisotropy of Co.

Sputtering from a composite target resulted in a 10 at.% Sm concentration. Results
for a [CoSm(tCOS,,,)/Cu(4.0nm)/Py(4.0nm)/Cu(4.0nm)]x10 series of samples are given in
Tables 6.10a and 6.1%. The ﬁeld dependence of the MR and magnetization, shown in
Figure 6.15, have similar forms to the Co/Ag/Py/Ag samples shown in Figure 6.7.

Comparing the CoSm/Cu/Py/Cu and Co/Cu/Py/Cu systems reveals several
differences between the two Cu based hybrid systems. The MR measured at both 4.2K
and 300K for the CoSm samples is roughly half of that measured in similar Co samples
as shown in Figure 6.16. This reduction in the MR also lowers the sensitivity by a factor
of two. Both the saturation and coercive ﬁelds measured for the CoSm hybrids are
nearly double those of the Co multilayers. This enhances the contrast between the Py and
the CoSm clusters, resulting in a broader and more easily deﬁned region in which the Py
moments are antiparallel to the CoSm cluster moments. Minor loop measurements

showed that the CoSm clusters exhibit a weaker coupling to the Py layers than the Co

180

clusters. Surprisingly, the blocking temperature for the CoSm clusters is not much
different from the Co clusters as shown in Figure 6.17.

The anisotropy of the CoSm clusters was not measured, however the CoSm blocking
temperatures indicate that the anisotropy energies for the CoSm/Cu/Py/Cu series and the
Co/Cu/Py/Cu series are approximately the same. There are two possibilities one can infer
from the TB measurements for CoSm and Co. (a) The CoSm clusters have nearly the
same volume as the Co clusters which means their values for K are nearly the same. (b)
The CoSm clusters are smaller than the Co clusters (VCoSm< V60) which means KC05m>KCO

SUCh that KCoSm VCoszKCo VCO'

Table 6.10a: Magnetic quantities for [CoSm(tCoS,,,)/Cu(4. 0nm)/Py(4. 0nm)/Cu(4. 0nm)]x10
attributed to the CoSm clusters.
’Cosm ("ml T3 (K) Ms (emu/cm )
0.4 115 1050
0.6 180 753

0.8 215 1010
1.0 250 1020
1.3 280 879

 

Table 6.10b: CIP Magnetoresistance and sensitivity measurements at both liquid He and
room temperatures for the [CoSm(tCoS,,,)/Cu(4. 0nm)/Py(4. 0nm)/Cu(4. 0nm)]x10 series.

 

 

 

 

 

 

10,5", (nm) MR (%)“ s (Va/0e)" MR (%)” S (Va/0e)”
0.4 14.9 1.25 1.30
0.6 15.5 . 2.00 1.64
0.8 13.3 0.97 2.80 0.22
1.0 10.5 1.93 3.67 0.73
1.3 14.3 3.45 0.71

 

 

 

 

 

 

 

a Measurements made at 4.2K.
b Measurements made at 300K.

I81

 

0.36
0.35’ 5 1

0.34

R (0)
\
_- i}
e/ /

0.33

 

 

 

 

 

 

 

 

0.32 -
________. \
0.31
-5 -4 -3 -2 -1 0 1 2 3 4 5
H (kOe)
3

M (x10-3 emu)
o

 

 

 

 

H (kOe)

Figure 6.15: The ﬁeld dependence of a) the CIP-MR and b) the magnetization at 4.2K for
a [CoSm(0. 6nm)/Cu(4. 0nm)/Py(4. 0nm)/Cu(4. 0nm)]x10 sample.

182

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30 t a) -
g8 20 * __
E + CoSm,4.2K
2 . ——e— CoSm,300K
—t-— Co,4.2K
—-e-— Co,300K
10 * _. _
”in (BM
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
tF (nm)
5
4 H + CoSm,4.2K
—-e— CoSm,300K
+ Co,4.2K
—-£r— Co,300K
3 3” i “
gt; 1
K
e 2*
"’ I
1 _ . a
‘ ‘ o A 5 .1
0 ~ -
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
tF (nm)

Figure 6.16: The a) CIP-MR and b) the maximum slope, S = AR / AH, of the CIP-MR are
plotted as a function of t; for samples of [F (tF)/Cu(4. 0nm)/Py(4. 0nm)/Cu(4. 0) ]x10 ,
where F =Co or CoSm. Lines are guides to the eye.

183

 

300 j
A

200 } I ,1
g .
a:
[—.

100f _.-_.__ _______._

i + CoSm
+ Co

 

 

 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
tCo & tCoSm (nm)

Figure 6.1 7: The blocking temperatures of [F (tF)/Cu(4. 0nm)/Py(4. 0nm)/Cu(4. 0) ]x1 0
samples plotted as function of t;, where F =Co or CoSm. Lines are guides to the eye.

27’28'29 have shown that the size of CoSm cystallites is related to the structure

Studies
of the underlying material. Typically, a grain size about Snm is observed for CoSm with
a 100nm underlayer of Cr27’28‘29. XTEM picturesn28 show that columns formed in the Cr
layer continue smoothly into the CoSm layer. However, no distinguishable columnar
structure was observed in CoSm for 100nm Cu underlayerszg. Furthermore, the absence
of a CoSm peak in x-ray diffraction measurements showed that CoSm was amorphous in

30,31

these samples. Although anisotropies can be large for amorphous CoSm, they are

about the same order of magnitude as the magnetocrystalline anisotropy of Co.

184

Columnar growth has been observed in multilayer systems made here at MSU. It
seems likely that columnar growth in the Co/Cu/Py/Cu samples would be similar to
columnar growth in the CoSm/Cu/Py/Cu samples which are sputtered under nearly
identical conditions. This would tend to make the volume of the Co clusters and the
CoSm clusters similar. This along with blocking temperature data from Tables 6.8a and
6.10a implies that KCozKCOSm and that adding the Sm did not increase the anisotropy of

the Co clusters signiﬁcantly.

Raising the Blocking Temperature (c) Growth in a Magnetic Field

Another way to change the anisotropy of the Co clusters is to grow the ﬁlms in the
presence of a strong magnetic ﬁeld. During growth the presence of a strong magnetic
ﬁeld induces a strong uniaxial anisotropy in the multilayer along the direction parallel to
the ﬁeld (see Figure 2.4c). Presented here are preliminary studies done on samples with
anisotropies induced during growth for multilayers with Py and for multilayers with Co.

In the same sputtering run, samples of [Py(4.0nm)/Ag(4.0)nm]x20 were deposited
with and without an induced easy axis. The samples with an induced easy axis were
subjected to a magnetic ﬁeld of approximately 2.6 kOe during growth. Figure 6.18
shows the magnetization of these samples with the measuring ﬁeld applied both
perpendicular and parallel to the induced easy axis in the plane of the ﬁlm. The
multilayer without the induced easy axis was rotated 90° with the applied ﬁeld in the

plane of the ﬁlm. This sample shows the same magnetization curve for both orientations

185

with respect to the ﬁlm, implying that the sample has no preferred direction in the plane
of the ﬁlm. The ﬁeld grown sample does show an easy axis along the direction of the
ﬁeld. The magnetization along the induced axis ﬂips rapidly near the HC for Py
(zO.SOe), reversing itself completely in just 1.0 Oe. The in-plane magnetization normal
to the easy axis shows very little hysteresis, passes through the origin and completely
reverses its direction in nearly 200e. These are indications that the Py layers are being
coherently rotated away from induced easy axis. The induced in-plane anisotr0py is
calculated by ﬁnding the area between the magnetization curves along and normal to the
easy axis. This gives K=2.08x103 emu/cm3, of the order of Py’s magnetocrystalline

anisotropy.

 

M/Msat

 

 

 

 

H (De)

Figure 6.18: The magnetization hysteresis curves along (squares) and normal (circles) to
the in-plane easy axis for a multilayer of [Py(4.0nm)/Ag(4.0nm)]x20 at T=5.0K. The
direction of the induced easy axis in the Py layers was deﬁned during growth by a 2.6kOe
magnetic ﬁeld (see Figure 2.40).

186

Samples of Co/Ag were also ﬁeld grown to induce an easy axis in the plane of the
ﬁlm. Results for samples of [Co(6.0nm)/Ag(6.0nm)]x20 are shown in Figure 6.19. The
large hysteresis present in the in-plane, normal curve implies that the reversal of the
magnetization is due to both coherent rotation and domain wall motion. There is a very
noticeable difference between both in-plane curves. The one along the easy axis is much
more square and reverses much faster than does the curve normal to the induced axis.
The induced anisotropy for this sample is K (:2. 0x104erg/cm3, an order of magnitude less

than the magnetocrystalline anisotropy of Co.

 

 

 

 

 

 

 

 

H (Oe)

Figure 6.19: The magnetization hysteresis curves along (circles) and normal (triangles) to
the in-plane easy axis for a multilayer of [Co(6.0nm)/Ag(6.0nm)]x20 at T=5.0K. The
direction of the induced easy axis in the Co layers was deﬁned during growth by a
2.6kOe magnetic ﬁeld (see Figure 2.4c). A similar sample without an induced anisotropy
is also shown for comparison (squares).

187

It was hoped that inducing an anisotropy during a sample’s growth would increase the
anisotropy energy of the Co clusters so that TB would be raised above room temperature.
However, several samples exhibited TB well below those samples made without an
induced axis. This suggested a reduced Co volume. Both high and low angle X-ray
diffraction measurements conﬁrmed this suspicion. The samples made with the induced
easy axis showed a smaller bilayer thickness. The magnets used to induce the easy axis
must be changing the sputtering conditions of the plasma, resulting in a slower than
expected rate of deposition. Careful monitoring of the target voltages and currents
revealed a 10% drop in each when the magnets rotated over the sputtering source. The
problem was dealt with by increasing the target voltages and currents 10% above that
required to produce the desired deposition rate in zero ﬁeld. However, it is unclear just
how fast the sputtering sources adjust to the presence of the magnets when they are
rotated over a source. X-ray diffraction measurements done on samples with this
correction showed a bilayer thickness closer to the nominal value.

Although evidence for an induced in-plane anisotropy was observed in Co/Ag
multilayers with thin discontinuous Co layers, it was unclear whether or not the
anisotropy energy has increased. The lower TB measurements indicate smaller Co cluster
volumes, so that even if the clusters are harder magnetically (via the induced anisotropy),
the reduced volume of the clusters could still shift TB to lower temperatures.

The goal of increasing the blocking temperature of the Co clusters by inducing an
anisotropy during growth was not realized. The inducing magnetic ﬁeld slowed the rate

of deposition producing smaller than expected Co clusters. The smaller cluster volumes

188

complicated our attempts to increase the anisotropy energy, KV, of the Co. However, the
ﬁeld does induce an anisotropy in magnetic multilayers. This should increase the
magnetic contrast between the Co and Py in two ways. (a) The induced easy axis
increased the remanent magnetization in the Co layers, as shown in Figure 6.19 for
Co/Ag samples. (b) The induced easy axis caused the Py magnetization to completely
reverse itself in just 1.0 Oe as shown in Figure 6.18 for Py/Ag samples. Combining these

characteristics in a hybrid sample should increase the sensitivity of these multilayers.

GMR in CPP hybrid Multilayers

Experiments with a series of Ag based hybrids in which the Py thickness was varied
were done to estimate the a for bulk Py. The samples were made in the usual CPP
fashion, section 2.6, with superconducting Nb leads on top and bottom. A series of
[Co(0.4nm)/Ag(4.0nm)/Py(th/Ag(4.0nm)]x20 multilayers was measured at 4.2K. A
2.0nm layer of Co was deposited between the multilayer and each Nb lead to eliminate
the proximity effect. The ﬁeld dependence of the CPP resistance of a typical hybrid
sample is shown in Figure 6.20. Comparing with Figure 6.7 one immediately sees that
the CPP-MR is double the CIP-MR for the hybrid system, similar to the simpler
Co/Agl’n, Co/Cu33 and Py/Cu34 systems. It was expected that the sensitivity of the
hybrids in the CPP direction would also be doubled. However, the slope (AR/AH) where
the Py ﬂips actually appeared to be greater for the CIP part of the sample, for the
following reason.

The ﬁeld necessary to saturate the Co layers in these samples is z3-5kOe, about 5
times larger than any ﬁeld applied to the Co/Cu, Co/CuX or Py/Cu systems studied
previously. At 4.2K the Nb leads stay superconducting until a ﬁeld of lOkOe is applied.
The Nb/Co boundary resistance increases slightly as the ﬁeld approaches 10kOe, after

189

which a rapid rise in the resistance is observed. However, before the transition from the
superconducting state to normal state, ﬂux penetration occurs for type II
superconductors” like Nb. Flux penetration in the Nb leads is thought to be a problem
only when the applied ﬁelds are much greater than 1.0kOe. Therefore the previous CPP
studies are unaffected. The high ﬁelds necessary to saturate the hybrid samples with thin
Co layers are well above this critical ﬁeld. Lowering the applied ﬁeld from 6-7kOe, traps
the penetrating ﬂux inside the sample. As the applied ﬁeld is reversed both the trapped
ﬁeld and the coercive ﬁeld of the Py must be overcome, to reorient the Py magnetization.
Since the CIP resistance is dominated by the two narrow strips well away from the CPP
sample (see Figure 1.5), the trapped ﬁeld only affects the CPP data resulting in a CIP
sensitivity which is apparently greater than the CPP sensitivity.

{Co(0.4nm)/Ag(4.0nm)/Py(1 0.0nm)/Ag(4.0nm)}x20

 

 

 

 

 

 

 

 

 

 

 

60
b) 1
155
~50
"E
a: 45
n:
<
. _ 440
CO —>
N1FC——-t>
35
-4 -2 o 2 4 -20 -10 0 10 20

H (kOe) H (06)

Figure 6. 20 : In a) AR(H) for [Co(0.4nm)/Ag(4.0nm)/Py(10.0nm)/Ag(4.0nm)]x20 is
plotted. The large saturation ﬁeld is indicative of island-like Co layers. Plotted in b) is
AR(H) in the vicinity of the ﬂipping Py moments after the trapped ﬂux has been released
(see text). The slope, AR/R, is a factor of 10 greater in b) than in a) the region where the

Py ﬂips.

190

Experiments to test this hypothesis were done. After the sample is taken through one

complete cycle and brought back to zero ﬁeld, the temperature of the multilayer is raised

to just above the TC of the superconductor, z8K in sputtered Nb ﬁlms. Above TC the Nb
is normal and the trapped ﬁeld is released. The T B of the Co islands is about 5 times
greater than the TC for Nb, so that the increased temperature will not thermally reorient a
signiﬁcant number of the Co clusters. After releasing the trapped ﬁeld, the sample is
cooled to 4.2K and resistance measurements are made over the range of :HS for Py. This
improved the slope of the CPP part to 10%/0e, nearly double that of the CIP part. This is
consistent with the doubling of the MR from the CIP to CPP geometries since the MR of
each occurs for the same change in ﬁeld. Figure 6.20b shows the ﬁeld dependence of the
resistance when cycled at low ﬁeld after the trapped ﬁeld is expelled.

The two channel model for electron transport in CPP multilayers is used to analyze
this system. The parameters, 8 and 'y, describing the scattering in the hybrid system are
much more difﬁcult to ascertain because AR+(AP)¢AR‘(AP). As a consequence
ART(AP) calculated from the equivalent resistance circuit, becomes a much more
complex quantity and the previous method of obtaining [3 and y no longer applies.
Therefore, the resistance measurements are compared with calculated ART values based

on the parallel combination of equations 4.73 for the AP state and 4.7b for the P state.
Figure 6.21 shows both measured and calculated values of AR(HP) and AR(HS) as the Py

thickness is varied. The HP resistance is chosen for comparison with the calculated AP

state because this resistance is the highest for each sample.

The model used for comparison purposes adds in series the resistivity of each metal: Ag,
Co and Py along with the interface resistances of Co/Ag and Py/Ag for each spin channel
in equations 4.7. The parameters used for the calculated resistances are given in Table
6.11. The parameters for Co and Co/Ag were derived from a detailed study of Co/Ag
multilayers done by SF. Lee36 . Those listed as Py/Ag parameters are estimates not

based on a detailed study of Py/Ag multilayers. They are based on the assumption that

191

the values ARM/Ag and ypymg are not very different from those of Py/Cu, which was
studied in detail in chapter 5. There is some justiﬁcation for this rather gross assumption

in that a comparison of the Co/Cu and Py/Cu parameters in Tables 5.6 and 5.10 reveals

36 Co/Ag interface

fairly similar interface values for both systems. In addition, Lee’s
values differ only slightly from those of Co/Cu in chapter 5. It would seem that the F/N
interface parameters are somewhat insensitive to which normal metal is used, Cu or Ag.
Therefore using the Py/Cu values in place of the Py/Ag ones may not be completely

without merit”.

Table 6.11: Parameters used in ﬁtting the CPP
[Co(0. 4nm)/Ag(4. 0nm)/Py(tPJ/Ag(4. 0nm)]x20 samples.

 

 

 

 

 

 

 

 

 

 

 

 

 

2ARS/F 6.1 ern1

p20 100 nﬂm

p Ag 10 nan
13cc 0.56
7C0 0.79

AREo/Ag 0.60 ern1

p'Py 164 nﬂm
[3,3, 0.46
7P}, 0.81

AR Bug 0.46 mez

 

 

 

150 . . - . 5

. AR(Hp) 0.4 nm N
A AR(HS) 0.6 nm

.AleQnﬂ)
(A 23
C> CD

 

 

i 0.4 nm

 

 

 

0.8 nm

AAR (f sz)
\\

 

 

 

007 i i 10 i ’ ’20 i A i 30

IPy (nm)

Figure 6.21: In a) AR(HP) and AR(HS) are plotted as a function of tpy. Plotted in b) as a
function of tpy is AAR=(HP)-AR(HS). In both a) and b) the lines represent the values

predicted by the two channel model assuming ’66 = 0.4, 0.6 and 0.8nm along with
(”=w.
J

193

More problematic to the analysis of this CPP hybrid system is the thin Co layer. A

2'3“”. This must affect the transport

0.4nm layer of Co is deﬁnitely not continuous
properties of the sample, since a thin discontinuous Co layer provides regions in which
the electrons may pass from one Py layer to the next Py layer without being scattered by
the Co layer. Since the Py magnetizations are pointing in the same direction, a portion of
the sample acts as if it is never in the AP state no matter what the relative orientation of
the Co and Py magnetizations. As a crude way of compensating for this, equations 4.7
have been modiﬁed in the following way. First it is assumed that the total volume of Co
in each Co layer is that of a nominally complete 0.4nm thick layer without clumping. To
allow for Co islands, the thickness of the Co layers is increased while at the same time

the area of these layers is reduced, keeping the total Co volume constant. These modiﬁed

equations are given below.

AR f5.) = 21111ng +2pAngg + p;,;,.,,(1-t3py)+2AR;y,Ag(1—y ”)1 6.7a
AR (A; = 2N[Rg;’ + 2p,,gt,,g + (5).);pr +8”) + 2AR ;,,,,g (1 + y ”)1 6.7b
where

RSI} = p}.t'c.(1+ 131+ 2ARE.,..g (1+ 114:. H'c.
R2? = p}.t;~.<1—B>+2AR2./.g (1 we. we.

Réio) represent the effective Co resistance due to the clusters. The Co/Ag interface

resistance is scaled by t'Co, the effective Co thickness. A in the last term is modiﬁed by

the factor lea/’60 < . A parallel combination of equations 6.7 models the resistance of
the AP state. Similarly the P state resistance is modeled by a parallel combination of

equations 6.8.

AR ﬁr) = 2N[Rg’ + 215,81“ + p1,); Py(1 — 1’19) + 2AR ;.,,/,,g (1 — 7 Pp] 6.8a

194

ARI?’ = 2N1Ré~2 ”mgr... + piano +9.,1+2ARP(1+1 p.11 6%

where

R4712) = pCotCo(l—B)+2ARCo/Ag(l —y)tCo /t6o
R2? = p}.t'c.(1+ B) HARE... (1 +0.. n...

This model for the hybrid CPP resistance assumes that [S] z 00 for all three

components, Ag, Co and Py. This is a valid assumption for the relatively thin Co and Ag
layers, but as the thickness of the Py increases one might expect to see ﬁnite SDL effects
occur in the Py layers. The Valet-Fert theory for ﬁnite SDL effects in magnetic
multilayers has not been completed for systems containing two different magnetic
components”, however, the extreme case of [if = 0 is easy to model. For this case the
series resistor model shown in Figure 4.3 is modiﬁed so that in each Py layer the two spin
currents mix together, resulting in the equivalent resistor network for a single unit cell
shown in Figure 6.22. Multiplying the equivalent resistance in Figure 6.22 by the
number of unit cells (N=20) and then adding on the Nb/Co boundary resistance gives the

total calculated resistance necessary for comparison with the measured values of ART.

The calculated values in ﬁgures 6.21 and 6.23 are based upon equations 6.7 and 6.8
for both iffy limits. The AR(HP) and AR(HS) data show some scatter but are generally

below the values predicted by both [if limits for complete 0.4nm Co layers. The data

seem most consistent with an effective Co thickness of 0.6nm for the average Co island.
Figures 6.21b and 6.23b plot AAR, the difference between AR(HP) and AR(HS), as a

function of tpy. This is done to eliminate errors common to both the AP and P states.

Although the AAR data was scattered, agreement appears to be better with the IQ” = 00

model since all the data fall below the ﬁt which assumed a continuous Co layer nominally

0.4nm thick. Whereas for the £3 = 0 model shown in Figure 6.23b, a signiﬁcant ﬁ'action

of the AAR data are well above the 0.4nm prediction. For the model to ﬁt these points

195

the interfacial scattering would have to be increased and the bulk scattering reduced (to
keep the Co volume constant). This seems to be contrary to the NMR structural studies

done on Co/Ag by van Alphen et al.4 which showed a signiﬁcant bulk signal down very

thin Co layers. Furthermore, the £9" = 00 model is more sensitive to small ﬂuctuations in

the Co thickness than is the 8:!" = 0 model. Only a ﬂuctuation of 0.4nm in the Co

thickness describes all the data in Figure 6.21b, whereas a number of points lie outside

this ﬂuctuation in the Co thickness in Figure 6.23b.

Spin Up Channel (+)

lllllllllllllllllllllll

llllllllllllllllll

g. ‘ .—

' ' Spin Down Channel (-)

Figure 6.22: Equivalent resistor model for I.” f} = 0.

196

 

150 .,

 

 

00
O
O

 

 

 

 

 

 

g? I o i
E . . g 0.4 nm .
c: . ,1 . .
“d 20 ” . . . o 9 0.6 nm 7
. .4
g ’ 0.8 nm 1
<1 * .
1 0 f O 7
. b) .
O n 1 1 . ' 1 1 1 A 1 1
0 10 20 30
th (nm)

Figure 6. 23: In a) AR(Hp) and AR(HS) are plotted as a function of tpy. Plotted in b) as a
ﬁtnction of tpy is AAR=AR(Hp)-AR(HS). In both a) and b) the lines represent the values

predicted by the two channel model assuming ’6‘0 :04, 0.6 and 0.8nm along with
62:0.
3f

197
Samples with extremely thick layers of Py were made to see if the SDL effects were

discernible on a larger scale. Figure 6.24 includes these two data points along with the

predictions for both models with an effective Co thickness of 0.6nm. Both these points
are lower than the 0.6nm prediction for the 8:} = 00 model. This suggests a slight ﬁnite

SDL effect but when the 0.8nm prediction is considered these two points are consistent
with an inﬁnite Py SDL. In Figure 6.24a the AR(HP) and AR(HS) data for the thick Py
samples deviates strongly from the linear behavior of the AR(HP) and AR(HS) data for
thinner Py samples. Neither SDL limit predicts such curvature as the Py becomes
thicker. Some other mechanism, possibly a structural change in the sample for larger Py

thickness must be causing the lower than expected resistances.

198

 

300 -
la)

..
‘1

. \ AR(HS), lsf =0

61‘
E
c: . \ .1 .
64.1 \
Z / A \ AR(Hs), lsf=oo
< /

200 j AR(HP), lsf=oo

 

  

 

 

100 I , ~
AR(HP), lsf=0 1. AR(HP)?
EA AR(Hs)J
Obeetete- 1" 13""-
i b)
301 o 1

. (sf= OO

 

AAR (fom2)
N
o. f . .
ﬂ
0
O

68f=0 j

p—r
O

 

 

 

005 A 25’ H 50 ’ 75‘ 100 i 125
th (nm)

Figure 6. 24: In a) AR(HP) and AR(HS) are plotted as a function of tp). Plotted in b) as a
function of tpy is AAR=AR(Hp)-AR(H5). In both a) and b) the lines represent the values

predicted by the two charmel model assuming ’60 = 0.6nm and either [if = 0 or £9" = oo.

I99

Table 6.12: CPP-AR values for the [Co(0.4nm)/Ag(4. 0nm)/Py(tpv)/Ag(4. 0nm)]x20 series.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample# 1,.v (nm) Area (mm‘) AR(HP) (152ml) AR(HSHme‘)
558‘” 2.0 1.194 56.95 36.32
558‘” 4.0 1.295 59.09 38.22
558‘” 9.0 1.545 70.50 49.00
5586‘ 16.0 1.459 87.12 56.98
558‘” 4.0 1.584 48.01 28.09
559‘” 20.0 1.429 87.12 65.50
559‘” 6.0 1.540 53.56 36.30
559“” 12.0 1.433 79.71 54.16
559‘” 3.0 1.590 51.58 30.96
559“ 4.0 1.514 50.85 31.04
571‘” 22.0 1.481 103.08 78.86
571‘” 5.0 1.254 65.59 38.85
571‘“ 17.0 1.584 75.32 53.33
571“ 14.0 1.375 63.73 53.90
605‘” 60.0 1.312 161.0 138.1
605‘” 5.0 1.326 56.30 36.89
605‘” 10.0 1.260 58.30 35.12
617‘n 120.0 1.431 235.0 212.7

 

 

200

6.3 Inverted Giant Magnetoresistancc

All previous studies presented here have been done on systems in which the
resistance drops with the application of a magnetic ﬁeld. This type of GMR is sometimes
referred to as Giant negative Magnetoresistancc since the resistance decreases as the ﬁeld
increases. Systems which exhibit an increase in resistance upon saturation have a
positive GMR. As a historical note, the term inverted or reversed is also used for positive
GMR systems since the effect was ﬁrst discovered in multilayers exhibiting negative
GMR. The reason why negative GMR is the most common can be seen from the crude
band pictures in Figure 4.1. For any of these band models DT>Di which means pT>pl
and a=p‘/pT<1. Clearly to obtain a positive GMR one needs detailed band structures with

Dl >DT or spin dependent scattering at the interface which gives a positive MR.

The inverted GMR systems differ from the normal GMR systems in that a is not the
same for all magnetic layers throughout the multilayer. Normal MR samples have all
magnetic layers with either 0t>1 or a<1, whereas an inverted sample has magnetic layers
which alternate a between 11>] and 0t<1. (See Figure 4.8.) The alternating a’s should
produce a short circuiting of the current for the AP state, leading to a lower resistance in

the AP state than in the P state.

CIP-MR measurements were performed at room temperature with the usual four point
probe technique on multilayers of [M,/Cu(tC,)/M,/Cu(tc,)]x5, where M, is itself a

sandwich of Fe(1.2nm)/Cr(0.4nm)/Fe(1.2nm) and M2 is a single Fe(1.5nm) layer as

201

illustrated in Figure 6.25. The Fe/Cu interfaces are believed to have 0t>1 from electronic
structure arguments39‘40. The trilayer of Fe and Cr that forms M , is believed to have 0t<1
by analogy with measurements made for Cr impurities in Fe41 and also by electronic
structure arguments“). The thin 0.4nm Cr thickness is chosen so that the two 1.2nm Fe
layers will be strongly ferromagnetically coupled together, essentially behaving as a

single magnetic entity.

 

Fe

1 Fe

Cu

 

 

 

 

Fe

 

Cu

 

 

 

Figure 6.25: Schematic representation of the structure of [M,/Cu(tCu)/M_a/Cu(t(~u)]x5
where M,=Fe(1.2nm)/Cr(0.4nm)/Fe(1.2nm) and M2=Fe(1.5nm).

202
The AP state of these multilayers is brought about by antiferromagnetic exchange

coupling through the Cu layer. Experimental results for sputtered F e/Cu multilayers”~13
indicate a maximum in the AF coupling at tCu=1.4nm. Samples with tCu ranging from

1.0nm to 2.0nm were made to ﬁnd the thickness of Cu which gives the maximum AF

coupling between M, and M,.

A positive MR was observed in several samples similar to the one shown in Figure
6.26. The maximum inverted MR is seen for tCu=1.6nm, close to the 1.4nm expected
from the Fe/Cu data42‘43. The MR curves in Figure 6.26a are similar for ﬁelds in the
plane of the ﬁlm, applied both parallel and perpendicular to the current direction. This
demonstrates that the observed MR is not attributable to the anisotropic
magnetoresistance, (AMR), resulting from the spontaneous resistivity anisotropy of

.45

ferromagnets44 . The AMR measured in these samples is less than 0.2%, an order of

magnitude below those shown in Figure 6.26a.

203

 

0.0
-0.1 b
-0.2 i
-0.3 .
-0.4
-05 L
-0.6 -
-0.7

-0.8 i
-0.9

CIP-MR (%)

 

 

 

 

1400 -300 -200 -100 0 100 200 300 400
H (06)

 

0.6
0.5
0.4
0.3
0.2 -
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6 F1
400 -300 -200 -100 o 100 200 300 400

H (G)

1))

'IYjﬁrT

M/MS
1’11'1

I

Y I r

 

I

 

 

 

 

Figure 6.26: The low ﬁeld behavior at 300K of a) the CIP-MR and b) the magnetization
for [M,/Cu(1. 6nm)/M/Cu(1. 6nm)]x5.

204

The magnetization curve for the tCu=1.6nm sample given in Figure 6.26b provides
indications that AF coupling is present in the sample. The remanent magnetization is
only 14% of the magnetization at saturation, typical of AF coupling in multilayers. The
low saturation ﬁeld z 1500c is also typical of relatively weak AF coupling in Fe/Cu42'43.
The usual correlations between the ﬁeld dependence of the resistivity and the
magnetization are noted. The saturation ﬁelds are both close to lSOOe and the minima
in the MR curve are close to the coercive ﬁelds of the multilayer. Further evidence
supporting AF coupling between the Fe/Cr/F e trilayers and the Fe layers through the Cu
spacer layer is found in the inverted MR’s dependence on the Cu thickness. In Figure
6.27b the inverted MR is plotted as a function of the Cu spacer thickness. Although the
inverted MR is much smaller than that of the F e/Cu system, Figure 6.27a, both systems
exhibit an oscillatory MR with the spacer thickness. Peaks in the MR are attributed to
strong AF exchange coupling through that particular thickness of the normal metal spacer

6’46. Both systems in Figure 6.27 couple Fe layers through a Cu spacer layer, so it is

layer
reasonable to expect that each system should have a maximum in the magnitude of the

MR at about the same Cu thickness, 1.4nm.

Careful examination of Figure 6.26 reveals that although the hysteresis of both the
MR and magnetization curves disappear by 1500c, both are slowly changing with ﬁeld.
Finally at lOkOe both the magnetization and the MR become completely saturated.
However, the MR curve of Figure 6.28a now shows that the small inverted effect seen at
low ﬁeld sits atop a very strongly coupled normal effect, which is double the inverted

MR. This slow increase in the magnetization was also observed in separate Fe/Cr/Fe

205

samples similar to M, in the inverted system. The magnetization data for both the simple
F e/Cr/F e samples and the more complex Ml/Cu/MZ/Cu systems suggest that the coupling
across the Cr layer is not perfectly ferromagnetic but a mixture of AF and F coupling
which is inducing a tilt47 between the Fe layer on either side of the Cr layer. A
straightforward calculation shows that an average tilt of 59° corresponds to the
intermediate saturation step of 70% of MS, derived by a linear extrapolation to zero ﬁeld

in Figure 6.28b.

206

 

,2 Fe/Cu .

MR (%)
\\
/

 

 

 

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

 

1 T 1 Y 1 ' 1 r T V f

0.0 . FeCrFe/Cu/F e

‘r—T

MR (%)

 

 

n I r r r J l 1

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
tCu (nm)

 

Figure 6.27: The variation of the MR with the Cu spacer thickness for a) Fe/Cu
multilayers from Petroff, et al.42‘43 and b) [M,/Cu(tc,,)/M/Cu(tcu)]x5 samples where M,
consists of an Fe(1.2nm)/Cr(0.4nm)/ Fe(l.2nm) trilayer and M2 is a single Fe(1.5nm)
layer.

207

 

 

MR (%)
2

 

 

 

 

-20 -10 0 10 20
H (kOe)

 

 

1.0 1
0.8 1 b)
0.6 L
0.4 l
0.2 l
0.0 L '5 A
.0.2 L ;
-0.4 l 4
-0.6 1 i
-0.8 1
-1.0 b

-20 -10 0 10 20

H (kOe)

M/Ms
<_ _.

 

 

 

 

 

Figure 6. 28: The high ﬁeld behavior of a) the CIP-MR and b) the magnetization of the
sample in Figure 6.28. The hysteresis is not seen on this scale.

..II! .+_

 

 

208

Applying a strong magnetic ﬁeld to improve the parallel alignment of the Fe moments
on either side of the Cr spacer layer is consistent with the observed high ﬁeld MR
behavior. The inset of Figure 6.28a shows the MR of a [Fe(1.2nm)/Cr(’0. 6nm)]x1()
multilayer exhibiting high ﬁeld behavior similar to that shown by the M,/Cu/M_./Cu

multilayers in both the magnitude of the MR and the magnitude of the saturation ﬁeld.

As a further test, samples were prepared in which M, =M2 so that 0., and or, would be
the same for every magnetic layer. Data previously published”43 for the Fe/Cu system
showed the normal negative MR. Similarly, multilayers with M, =M2=Fe/Cr/Fe also
exhibited the normal negative MR over the entire ﬁeld range. This test conﬁrms that the
on for the F e/Cr/F e trilayer must be different from the a for Fe/Cu, since the inverted MR
only appears when M , =F e/Cr/F e and M2=F e and vice versa. As yet it is not possible to

determine whether (1, >1 or (12 >1 from these MR measurements.

The magnitude of the inverted MR zl% is smaller than the few % predicted by the
Camley-Barnas free electron model“. This may be due to either or both of the
following”: Recently, non-free electron models have shown that channeling effects by
the periodic potential of multilayers can considerably change the magnitude of the MR
predicted by free electron modelss'so. The nature of M, necessitates that both F e/Cu and
F e/Cr interfaces exist for this magnetic layer. The small inverted MR’s may be a result of
the competition between the a’s at the Fe/Cu and F e/Cr interfaces in M, making the
overall a for M, just slightly less than one. An 01 close to one would tend make the

scattering in each spin channel about the same, severely reducing the MR.

209

Recently another type of multilayer system was shown to have an inverted MR.
Renard, et al.” showed that CIP multilayers of F eV/Au/Co/Au with V concentrations of
30 at.% in Fe produced an inverted MR. This system clearly demonstrated the inverted
effect without the complication of a large background normal MR seen for the system
mentioned above. Electrons near the Fermi level in the 3d band of the FeV alloy are
strongly scattered in the spin up band resulting in an or<1 for the F eV alloy. The Co/Au
interface provides 01>] necessary for the realization of the inverted MR. The inverted

MR’s reported by Renard51 are also quite small zl%.

The ﬁrst CPP measurements of an inverted MR were made at MSU by A.
Barthe'lémy52 on a similar FeV multilayer system, FeV/Cu/Co/Cu. This system combined
the principles used for the hybrid system, i.e., discontinuous Co layers for increased
magnetic contrast, with a<1 for F eV. Figure 6.29 shows a typical CPP inverted MR.
Currently, CPP resistance measurements of this system are being continued by S.Y. Hsu

at MSU.

210

 

144
143 ~ Me/
142 -

141 *-

R (n0)

140 F

 

0
1 3 9 "‘ 9:.0 a];

\" ‘0}

1 HP
-5-4-3-2-10123456
H (kOe)

Figure 6.29: The ﬁeld dependence of the CPP resistance is plotted for a multilayer of
[Co(0.4nm)/Cu(2.3nm)/Fe V(6.0nm)/Cu(2.3nm)]x20. The V concentration is 27%. Here
the HS resistance is the high resistance state. The MR of these samples are less than 3%.

 

 

 

138

211

 

' W.P. Pratt Jr., S.F. Lee, J.M. Slaughter, R. Loloee, P.A. Schroeder and J .Bass, Phys.
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2 R. Loloee, P.A. Schroeder, W.P. Pratt Jr., J. Bass and A. Fert, Physica B204, 274
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3 S. Araki, K. Yasui and Y. Narumiya, J. Phys. Soc. Jpn. 60, 2827 (1991).

‘ E.A.M. van Alphen, P.A.A. van der Heijden and W.J.M. de Jonge, J. Appl. Phys. 76,
6607(1994)

5 KO. Hood and L.M. Falicov, Phys. Rev. B46, 8287 (1992); J. Magn. Magn. Mater.,
121, 362 (1993); Phys. Rev. B49, 368 (1994).

6 Lithographic techniques have now been utilized to reduced the cross sectional area
enough so that standard (non-SQUID based) measuring techniques are possible. M.A.M.
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Gijs et al., Appl. Phys. Lett. 63, 111 (1993); S.K.J. Lenczowski et al., J. Appl. Phys. 75,
5154 (1992).

7 IBM hard drives now use GMR devices as read heads.

3 S.S.P. Parkin, Phys. Rev. Lett. 67, 493 (1991).

9 TL. Hylton, K.R. Coffey, M.A. Parker and J .K. Howard, Science 261, 1021 (1993).
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” P.A. Schroeder, P. Holody, R. Loloee, J.L. Duvail, A. , L.B. Steren, R. Morel and A.
Fert in Magnetic Ultrathin Films: Multilayers and Surfaces, edited by EB. Marinero, B.
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‘2 T. Shinjo and H. Yarnamoto, J. Phys. Soc. Jpn. 59, 3061 (1990).

'3 T. Valet, J .C. Jacquet, P. Galtier, J. M. Coutellier, L.G. Pereira. R. Morel, D. Lottis and
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” B. Dieny, V.S. Speriosu, S.S.P. Parkin and BA. Gurney, Phys. Rev. B43, 1293 (1991).

'5 P. Holody, L.B. Steren, R. Morel, A. Fert, R. Loloee and PA. Schroeder, Phys. Rev.
1350, 12999 (1994).

212

 

'6 B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading. MA
(1972) p.236.

‘7 Y. Cheng and MB. Stems, unpublished; P. Galtier, unpublished.
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2° A. Vedyayev, C. Cowache, N. Ryzhanova and B. Dieny, J. Phys. Condens. Matter 5,
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2' L.B. Steren, A. Barthélémy, J.L. Duvail, A. Fert, R. Morel, F. Petroff, P. Holody, R.
Loloee and PA. Schroeder, Phys. Rev. B51, 292 (1995).

22 B. Dieny, V.S. Speriosu, S.S.P. Parkin, A Gurney, D.R. Wilhoit and D. Mauri, Phys.
Rev. B43, 1297 (1991).

23 M. Patel, T. Fujimoto, E. Gu, C. Daboo and J.A.C. Bland, J. Appl. Phys. 75, 6528
(19941

2‘ A. Chaiken, G.A. Prinz and J .J. Krebs, J. Appl. Phys. 67, 4892 (1990).

2’ B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading, MA
(1972) p.585.

2" H. Hegde, S.U. Jen, K. Chen and F .J. Cadieu, J. Appl. Phys. 73, 5926 (1993).

27 Y. Liu, B.W. Robertson, Z.S. Shan, S. Malhorta, M.J. Yu, S.K. Renukunta, S.H. Lion
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2‘ Y. Okumura, H. Fujimori, 0. Suzuki, N. Hosoyo, X.B. Yang and H. Morita, IEEE
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2" E.M.T. Velu, D.N. Lambeth, J .T. Thornton and RE. Russell, J. Appl. Phys. 75, 6132,
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3° K. Chen, H. Hegde and F .J. Cadieu, Appl. Phys. Lett. 61, 1861 (1992).
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3’ P.A. Schroeder, J. Bass, P. Holody, S.F. Lee, R. Loloee, W.P. Pratt Jr. and Q. Yang,
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3“ P. Holody, to be published.

213

 

35 J.E.C. Williams, Superconductivity and its Applications, Pion Ltd.. London, England
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3" S.F. Lee, Ph.D. Dissertation, Michigan State University (1994).

37 For a proper analysis of Py/Ag multilayers, several series similar to those done by Lee
in Ref. 30 must be measured and globally ﬁt to obtain the parameters Aprmg, B and y.

3“ Attempts thus far have not been completed by WP. Pratt, Jr.. et a1.
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‘2 F. Petroff, A. Barthéle'my, D.H. Mosca, D.K. Lottis, A. Fert, P.A. Schroeder, W.P. Pratt
Jr., R. Loloee and S. Lequien, Phys. Rev. B44, 5355 (1991).

‘3 S. Pizzini, F. Baudelet, D. Chandesris, A. Fountaine, H. Magnan, J.M. George, F.
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4“ A. Fert and LA. Campbell, J. Phys. F 6, 849 (1976).

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‘9 J.M. George, L.G. Pereira, A. Barthe'lémy, F. Petroff, L.B. Steren, J .L. Duvail, A. Fert,
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5' J .P. Renard, P. Bruno, R. Mégy, B. Bartenlian, P. Beauvillain, C. Chappert, C. Dupas,
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’2 A. Barthéle'my, et al., to be published.

Chapter 7:

Summary and Conclusions

In this dissertation the transport properties of several magnetic multilayered systems
were studied in detail. Transport in these systems has been successfully described by the
two spin channel model. In the limit where spin ﬂipping is negligible, the current is
independently carried by parallel channels of spin up and spin down electrons. Large
negative MR’s arise from spin dependent scattering occurring in these channels.
Electrons with their spins parallel to the local magnetization undergo a different amount
of scattering from those with their spins antiparallel to the local magnetization.
Consequently, the sample’s resistance can be controlled through the relative orientation
of the F layer magnetizations. Usually multilayers with adjacent F moments aligned
antiparallel (parallel) have a high (low) resistance, so that changing from an antiparallel
to a parallel alignment produces a decrease in the resistance. Various methods of
producing GMR by changing from antiparallel to parallel alignment have been used in
the following projects studied in this thesis.

(1) Determination of Spin Dependent Scattering Parameters for Important Systems.

One of the ﬁrst objectives is to decide where the spin dependent scattering occurs, in the

214

215
bulk F metal or at the F/N interfaces. This separation is clearly made through CPP

measurements.
(2) Determination of Spin Diﬂusion Lengths. The analysis used in (1) above depends on
the spin diffusion length being much greater than the layer thickness of each constituent.
The CPP geometry provides a good method of determining spin diffusion lengths.
(3) Spin Engineering. Designing multilayers systems to have speciﬁc properties.

a) Systems with Two Ferromagnetic Components - CIP Hybrid Systems.

b) Systems with Two Ferromagnetic Components - CPP Hybrid Systems.

c) Systems having a Positive Magnetoresistance.
Conclusions from these projects are outlined below.

Magnetic multilayered systems were fabricated using a computer controlled Tri-mag
sputtering system. An in situ masking system gave samples a well deﬁned geometry
which allowed the measuring current to be applied in the directions parallel (CIP
geometry) and perpendicular (CPP geometry) to the layers. After fabrication, x-ray
diffraction at both high and low angles was used to check a sample’s crystal structure and
bilayer thickness. For several multilayer systems a metal alloy was sputtered. The alloy
concentration was measured using energy dispersive x-rays. Results from structural

studies performed by others on our sputtered samples were given in chapter 3.

(1) Determination of Spin Dependent Scattering Parameters for Important Systems.
The results for the study of the Co/Cu system are given in section 5.1. Three distinct

resistance states are observed in both the CIP and CPP samples. These are the H0 state

216

with the as-deposited resistance, the H5 the state with the saturation resistance and the Hp
the state with the highest resistance after the sample has been saturated.

For samples with negative MR’s the highest resistance state typically occurs for the
H0 resistance and is therefore chosen as the AP state. The H5 resistance has the lowest
resistance and is used for the P state.

Three separate series of Co/Cu multilayers were studied in which the total thickness
was held constant and the Co thickness was constrained to tCo=l.5nm, tCo=6.0nm or
tCu=tC0' To simplify the analysis all samples had tCu> 6. Onm which eliminated the
complication of exchange coupling. The spin asymmetry parameters for both bulk Co
and the Co/Cu interface were estimated by globally ﬁtting the three Co/Cu series to the
equations derived in chapter 4 based on the two channel model. It was found that the
Co/Cu interfaces contribute signiﬁcantly to the multilayer’s total resistance, with a Co/Cu
interface having a resistance the same as a C0 thickness of 7.0nm. In addition, the bulk
asymmetry parameter (ago/Cu=7.7) was found to be greater than the interface asymmetry
parameter (aCo=2.7). Therefore for a sample in which the total resistance of the
multilayer is equally divided between pCotCo and ARC,“ (this corresponds to tCo=7. 0nm),
the Co/Cu interface contribution to the spin dependent scattering will be nearly three
times larger than the contribution to the spin dependent scattering from bulk Co.

A similar study was done on Py/Cu multilayers in section 5.2. The low coercive ﬁeld
of the Py lead to some ambiguities in the H0 data. For thick Cu layers in the 1.5nm and
6.0nm Py data, the H0 data were generally the state with the highest resistance. In cases

where AR(H0)<AR(Hp), demagnetizing the sample resulted in AR(HD)>AR(H0). For

217
these particular samples the AR(HD) data were used as the AP state in the ﬁtting. The

data were analyzed in terms of the two channel model and global ﬁts were made to
equations derived in chapter 4. Fit A only considered the Py 1.5nm and 6.0nm sets of
data while Fit B included the HS data for the tpy=th (The H0 data for the 1,6,,=tCu series
were not included in either ﬁt because it was determined that the presence of a small ﬁeld
inside the sputtering system at the position of the substrate could be enough to alter the
H0 resistance of samples with very thick Py layers.) Overall the parameters from Fit B
describe the Py/Cu system better. Fit B reasonably describes all three sets of Py/Cu data
and is within the uncertainties of the independently determined Py resistivity. In contrast,
while Fit A agrees better with independent measurements of the Py resistivity and ﬁts the
1.5nm and 6.0nm Py data well, it does not represent the HS data for the tP),=tCu samples
well at all.

The apy values are somewhat smaller than one might have expected. The expectation
that a Ni-Fe alloy should produce more spin dependent scattering in the bulk F metal than
at the Py/Cu interfaces is not justiﬁed by our data. At best (Fit B) (lg/C309,, meaning
that for a Py thickness of 2.0nm, the interface and bulk spin dependent scattering
contributions are roughly equal.

The possibility of a ﬁnite spin diffusion length in Py was not considered in the
analysis done on the Py/Cu system. If if} 51,), then, to ﬁrst order, only the Py within a

spin diffusion length of the interface will contribute to the magnetoresistance. Since the

218

analysis done here assumes an inﬁnitetfj" = co , the value of up}. would be underestimated

if I if was indeed ﬁnite.

(2) Determination of Spin Diffusion Lengths.
Finite spin diffusion length (SDL) effects were studied in section 6.1 for Co/CuX
multilayers where X=Pt, Mn, Ge and Ni. The Valet-Fert theory predicted a rapid drop in

the MR as (sf approached the layer thickness of either the N or F metals. These

predictions showed that a ﬁnite SDL had a stronger effect in the N metal than in the F
metal. So impurities which ﬂipped spins were added to Cu to reduce the SDL of Cu.
The Pt, Ge and Ni impurities increased spin ﬂips by increasing the spin orbit scattering in

the Cu layers. The Mn impurities ﬂipped spins via an exchange scattering. The best ﬁt
parameters for [3“ agree well with estimates of the SDL based on ESR measurements

of spin orbit cross sections.

Finite SDL effects were also examined for the tCo=tCu data from section 5.1. The
slight curvature of the square root data for thick Co layers could be explained by
introducing a SDL in either the Cu or the Co. Plots comparing the tC0=tCu data and

predicted SDL in both Co and Cu are given at the end of section 6.1.

219

(3) Spin Engineering : a) Systems with Two Ferromagnetic Components - C [P
Measurements on a Hybrid System.

Ordinarily coupling between magnetic layers is used to align adjacent magnetic layers
antiparallel. However, an AP state may be formed if the adjacent magnetic layers have a
large difference in their coercive forces. Here Py with its very low coercive ﬁeld and Co
with its higher coercive ﬁeld are used to make an AP state. The contrast between the Py
and Co is further enhanced by the thickness of the F metals. The Py is thick enough to
form continuous layers but the Co is thin enough to be composed of discontinuous island-
like structures.

These hybrid samples show remarkable transport properties at low temperatures. The
MR changes rapidly in the vicinity of the Py coercive ﬁeld, over 5%/Oe for CIP samples
with a Ag spacer layer. However, superparamagnetism in the island-like Co clusters
reduces the coercivity of these clusters to zero above the blocking temperature which
severely reduces the MR in these samples at room temperature.

To raise the blocking temperature, the anisotropy energy, K V, of the Co clusters must
be increased. This is done by increasing either the size of the particles or the strength of
the anisotropy. Although the blocking temperature did increase with the thickness of the
Co layer, it never reached room temperature. Adding Sm 10 at.% to the Co also failed to
increase the strength of the anisotropy enough to bring the blocking above room
temperature. Samples of Co/Ag and Py/Ag deposited in a magnetic ﬁeld showed that an

easy axis could be induced in sputtered samples. However. a blocking temperature above

220

room temperature was not seen. It is believed that inducing an easy axis in the

Co/Ag/Py/Ag system should increase AR/AH beyond 5%/Oe.

(3) Spin Engineering : b) Systems with Two Ferromagnetic Components - CPP
Measurements on Hybrid System.

The Co/Ag/Py/Ag system (with a nominal Co thickness of 0.4nm) was studied as
function of the Py thickness in the CPP geometry in section 6.2. Fields of 5.0kOe were
required to saturate the discontinuous Co layers. The high saturation ﬁeld caused ﬂux
trapping by the Nb leads. After expelling this trapped ﬁeld the AR/AH near the Py
coercive ﬁeld for the CPP geometry was found to be le%/Oe, two times larger than for
the CIP geometry. The MR was also 2 times larger in the CPP direction. The data for
AR, was compared to a two spin channel model which simultaneously varied the area of
the Co/Ag interface and thickness of the Co layers such that the total volume of Co was
held constant. The best ﬁt was obtained for an effective Co thickness of 0.6nm. In
addition the AAR-, data was compared with the two spin channel model in the limits of
inﬁnite and zero spin diffusion length. The AAR, data seems to remain independent of
the Py thickness beyond 20.0nm. The samples with very thick Py layers do not ﬁt either
limit of the model very well. The ART of these samples are much lower than the model

predicts, suggesting this model is too simplistic to represent the thick Py samples.

221

(3) Spin Engineering : c) Systems Having a Positive Magnetoresistance.

A system designed to produce a positive MR was examined. The ﬁrst observations of
positive MR were made on CIP samples of M,/Cu/M2/Cu, where M,=Fe/Cr/Fe and
M2=F e. Measurements showed a small positive MR whose magnitude was dependent
upon the Cu spacer thickness. The ﬁeld dependent features of the MR and magnetization
correlate well. Coupling through the Cr layer in M, complicated the analysis of the
results. In addition, the ﬁrst positive CPP-MR observations were made on the
Co/Cu/FeV/Cu system. These samples also exhibit MR’s of only a few percent.

All analyses in this study were done in the context of the two spin channel model,
considering only the AP and P states. All of these results hinge on our choice of the H0
resistance as the best approximation for the AP state. Experimentally the H0 resistance
seems to be unique and‘after saturation of the sample it can never be restored. Some
experimental evidence was presented in chapter 5 which indicated that the H0 resistance
at least behaves like an AP state. Experiments using CPP hybrid samples of
Co/Ag/Py/Ag and CPP spin valves with Py and Cu are currently underway in the
department that will conﬁrm (or otherwise) this assumption. However, it is unclear why

the H0 resistance should act like the AP resistance.

New Directions:
(1) Measurements of a series of F/N multilayers in which either the interface spin
dependent scattering or the bulk spin dependent scattering is varied would provide useful

information about how these parameters depend on the character of the PM interface and

222
the bulk F metal. Some CoFe/Cu multilayersl have exhibited an enhanced MR (relative

to Co/Cu multilayers) near 10 at.% Fe concentrations. A series of Co(,_x,Fex/Cu CPP
multilayers which vary the Fe concentration should reveal a maximum in the bulk F
metal spin asymmetry parameter. Also it has been reported that a magnetically dead
layer of Py exists at the Py/Cu interfacez. Depositing a thin layer of Co at the interface
should increase the interface spin dependent scattering. This has already been done for
CIP multilayers by others.

(2) Measurements of the dependence of the MR on the angle between the F layers for a
CPP spin valve should provide insight on the question of scattering from potential steps
at the F /N interfaces.

(3) Extending the work started here on depositing magnetic multilayers in a magnetic
ﬁeld should prove interesting. Hybrid samples with induced easy axes in both the Co and
Py layers should improve AR/AH. Hybrid samples using CoSm which is deposited in a
field may prove to have TB above room temperature. Interesting initial magnetic
conﬁgurations of multilayers could be studied by applying a ﬁeld during deposition at
particular angles with each magnetic layer. For example inducing easy axes at 90° from
one F layer to the next could be used to study biquadratic coupling in magnetic

multilayers.

 

' K. Inomata, Y. Saito and S. Hashimoto, J. Magn. Magn. Mater. 121, 350 (1993).

2 J .P. Nozieres, V.S. Speriosu, B.A. Gurney, B. Dieny, H. Lefakis and TC. Huang, J.
Magn. Magn. Mater. 121, 386 (1993).

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