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Perpendicular Giant Magnetoresistance
Studies of Spin-Dependent Scattering
in Magnetic Multilayers

By

Qing Yang

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

1995

ABSTRACT

Perpendicular Giant Magnetoresistance
Studies of Spin—Dependent Scattering
in Magnetic Multilayers

By

Qing Yang

We present new measurements of Giant (negative) Magnetoresistance (GMR) in

Ferromagnetic/Non—magnetic (F/N) metal multilayers in the Current Perpendicular to the
layer Plane (CPP) geometry. At low temperature, when the spin difl’usion lengths £13} and
81:, in the N and F metals are longer than the layer thicknesses, tN and tF, and the elastic
mean-free-paths 1:1, and if, a simple two current, series resistor model should describe
CPP data. Prior work in our group showed that this model describes well data on Co/Ag,
Co/Cu, and Pennalloy (Py)/Cu. The present thesis both tests this model further, and first
tests an extension of the model by Valet and Fert to shorter spin-diffusion lengths.

The intrinsic CPP quantity is the area A times total resistance Rt of the multilayer.

The first study in this thesis extends work by Lee in testing the model's prediction that a

 

plot of a certain square root quantity J[ART(Ho)-ART(HS )]ART(H0) versus the

bilayer number N should give the same straight line for a given F/N pair and for the same

pair upon alloying the N-metal with impurities (e. g., Sn) that don't flip spins. Importantly,

the prediction is independent of the specific values of the parameters of the multilayer. We
show that samples of Co/Ag and Co/AgSn with fixed tCo = tN obey the prediction.

In the previous test, the experimental quantities ARt(Ho) and ARt(HS)--H0 is the
state of the sample as initially prepared and HS is the state after taking the sample to above
the saturation field Hs where the resistance stops decreasing--were taken to closely
represent, respectively, AR,” and ARI), the states of anti-parallel (AP) and parallel (P)
alignment of the magnetizations of adjacent F layers that are assumed in the models. In our
second study, we test this assumption quantitatively. We made a set of [Co/Cu/Py/Cu]N
quadrilayers, measured AR in the well defined P state above HS states and in the also well
defined AP state near H=O, and examined how well these values of AR are predicted with
no adjustable parameters from independent data on Co/Cu and Py/Cu multilayers for the
Ho and HS states. The data and the no-free-parameter predictions agree rather well.

Thirdly, we made the first tests of effects on AR of reducing the spin-diflhsion
length 8% by adding impurities to N that flip spins (Mn, by exchange scattering, and Pt,
via spin-orbit interactions). Using a theory by Valet and Fert to fit deviations of the
square root quantity listed above from a straight line passing through the origin, we isolate
effects due to reduced 3;. Our values of (I; are close to independent estimates.

We also measured the first CPP-MRS with the F metal, Ni, finding that the CPP-
MRs in Ni/Ag are several times larger than the MRS with Current flow In the layer Planes
(CIP-MR), but the CPP-MRS for Ni/Ag are much smaller than those for Co/Ag or Co/Cu.

Lastly, we describe preliminary results on some exploratory projects.

To my parents

iv

ACKNOWLEDGMENTS

I would like to thank to my thesis advisor Professor Jack Bass for his insightful
guidance, support, and encouragement to me. I especially thank him for his patience
during the writing of this thesis. I would also thank Professor Peter A. Schroeder and
Professor William P. Pratt Jr. for their invaluable advises and discussions during these
years.

I would like to express my gratitude to Professor Jerry Cowen, Professor S.D.
Mahanti, Reza Loloee and Vivion Shull for their help and instructions.

My greatest thanks must be due to my parents for their support and inspiration.
Uncle Chen, aunt Wu and their daughter Katie also deserve great recognition for all their
help and kindness.

I would like to extend special thanks to Dr. R. Fan, Dr. L. Zhao, Dr. J. Song, Dr.
W. Zhong, Dr. Y. Cai, Dr. N. In, Dr. X. Yu, Dr. Y. Wang, Dr. SE Lee, Dr. Henry, Dr.
W. Chiang, P. Holody and L. Su for their many valuable discussions throughout my
graduate study.

I would also like to express my great appreciation to the following fiiends: B.
Zhang, Dr. J. Wang, Dr. T. Lan, F. Tian, B. Ren, J. Sheng, R. Huang, and B. Lian. Their
fi'iendship enriches my life at MSU.

The support of the US. National Science Foundation, the Michigan State University
Center for Fundamental Materials Research, and the Ford Motor Co. is gratefirlly
acknowledged.

TABLE OF CONTENTS

LIST OF TABLES ..................................... viii

LIST OF FIGURES .................................... xii

1 Introduction

1.1 Brief Summary of Important Advances in Magnetic Multilayers ...... 2
1.1.1 CIP-MR ......................................... 2
1.1.2 GMR in Grannular System ............................... 6
1.1.3 CPP-Magnetoresistance ................................ 7
1.2 Our Studies of CPP Magnetoresistance ....................... 10
2 Sample Preparation, Characterization and Experiments Techniques
2.1 Introduction ....................................... 22
2.2 Samples and Sample Preparation .......................... 23
2.3 Measurements of Resistivity and Sample Geometry ............... 26
2.3. 1 Resisitivity ........................................ 26
2.3.2 Film Thickness and CPP Area ............................ 28
2.4 Sample Characterization ................................ 30
2.4.1 X-ray Diffraction .................................... 30
2.4.2 Other structural Analysis Methods .......................... 36
2.5 Experimental Setup ................................... 36
2.5.1 CPP and CIP Measurements ............................. 36
2.5.2 Sample Magnetizations ................................. 39
3 Theory
3.1 Introduction ....................................... 43
3.2 Electron Transport in Multilayers .......................... 43
3.3 The CIP and CPP Magnetoresistance ....................... 45
3.3.1 CIP Magnetoresistance ................................ 45
3.3.2 CPP Magnetoresistance ................................ 47
3.3.2.1 Historical Review .................................. 47
3.3.2.2 Phenomenological Two-current, Series Resistor Model .......... 52
3.3.2.3 Theory of CPP MR with Spin-flip Scattering ................. 57
4 Data Analysis
4.1 Introduction ....................................... 65
4.2 Giant CPP-Magnetoresistance of Co/AgSn Multilayers ............ 66
4.3 Spin Flip Diffusion Length and GMR at Low Temperature .......... 73

VI

4.3.1 Effects of Finite Spin Flip Diffusion Length .................... 74

4.3.2 Experimental Results .................................. 94
4.4 Prediction and Measurement of Perpendicular Giant
Magnetoresistances of Co/Cu34Fe16/Cu Multilayers .............. 103
4.4.1 Perpendicular and CPP MR Measurements of
Co/Cu/Py/Cu Multilayers .......................... 104
4.4.2 Experimental Results .................................. 1 17
4.5 Giant CPP-Magnetoresistance of Ni/Ag Multilayers ............... 123
4.5.1 Giant CPP-Magnetoresistance of Ni/Ag Multilayers ............... 123
4.5.2 Experimental Results .................................. 131
5 Exploratory Studies
5.1 Effects of Spin-Dependent Scattering at interfaces ................ 135
5.2 Dependence of Sample quality on Sputtering Conditions ............ 140
5.3 Further Studies of Spin-Valve Structure ...................... 150
5.3. 1 Measurements of Co(t1)/Cu/Co(t2)/Cu,
Co(t1)/Ag/Co(t2)/Ag Multilayers ..................... 150
5.3.2 Dependence of GMR on the order of Ferromagnetic Layer .......... 157
6 Summary and Conclusions ................................ 166
Appendix A Extra Data for Co/AgAu ......................... 170
BIBLIOGRAPHY ....................................... 173

vii

LIST OF TABLES

3.1 Two-current model parameters for Ho (column 3) and Hp
(column 4). Column 2 contains the three parameters
that can be independently measured ........................

4.2.1 CPP ART and CIP values at Ho, Hp and Hs of [Co(t)/AgSn(4%)(t)]xN
samples. Total sample thicknesses are as close as possible to 720nm.
(* Si substrate, without Co cap layer, # Si substrate with Co cap layer).
4.2.2 CPP MK CIP NIR and [(ro-rs)ro]1/2 values at Ho, and Hp of
[Co(6nm)/AgSn(4%)(t)]xN samples. ro and rS are ART at Ho
and Hs- Total sample thicknesses are as close as possible to
720nm.(* Si substrate, without Co cap layer, # Si substrate,
with Co cap layer) ...................................

4.3.1 Estimated parameters for Co/Ag, Co/AgSn, Co/AgMn and Co/AgPt . .
4.3.2 CPP ART and CIP values at H0, H and Hs of
[Co(6nm)/AgMn(6%)(t)]xN, and [Co(ans)/AgMn(6%)(t)]xN
(*) samples. Total sample thicknesses are as close as possible to 720nm
4.3.3 Measured parameters for Co/AgMn(6%), Co/AgMn(9%) and Co/AgPt
4.3.4 CPP ART and CIP values at Ho, Hp and HS of
[Co(6nm)/AgMn(6%)(t)]xN samples. Total sample thicknesses

..... 56

..... 71

..... 72

..... 75

are as close as possible to 720nm .............................. 95

4.3.5 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at Ho, and Hp of
[Co(6nm)/AgMn(6%)(t)]xN samples. r0 and rS are ART at Ho
and HS. Total sample thicknesses are as close as possible to 720nm . . .
4.3.6 CPP ART and CIP values at H0,H and HS of
[Co(t)/AgMn(6%)(t)]xN samples otal sample thicknesses

..... 95

are as close as possible to 720nm .............................. 96

4. 3. 7 CPP MR, CIP MR and [(rO-rs)ro]1’2 values at Ho, andH
[Co(t)/AgMn(6%)(t)]xN samples r0 and rS are ART at Hfizf and
HS. Total sample thicknesses are as close as possible to 720nm ......
4.3.8 CPP ART and CIP values at H0, Hp and HS of
[Co(6nm)/AgMn(9%)(t)]xN samples. Total sample thicknesses

..... 96

are as close as possible to 720nm .............................. 97

4.3.9 CPP MR, CIP MR and [(ro-rs)r0]1/2 values at Ho, and Hp of
[Co(6nm)/AgMn(9%)(t)]xN samples. r() and rS are ART at H0
and HS. Total sample thicknesses are as close as possible to 720nm . . .
4.3.10CPP ART and CIP values at H0,H and HS of
[Co(t)/AgMn(9%)(t)]xN samples. 'IPo tal sample thicknesses
are as close as possible to 720nm .........................

viii

..... 98

..... 99

4.3.11CPP MR, CIP MR and [(ro-rs)ro]1/ 2 values at Ho, and Hp of

[Co(6nm)/AgMn(9°/o)(t)]xN samples. r0 and r8 are ART at Ho and

H3. Total sample thicknesses are as close as possible to 720nm .......... 99
4.3.12CPP ART and CIP values at Ho, Hp and HS of

[Co(2nm)/AgMn(6%)(t)]xN samples. Total sample thicknesses

are as close as possible to 720nm .............................. 100
4.3.13 CPP MR, CIP MR and [(ro-rsyojl/2 values at H0, and HI) of

[Co(2nm)/AgMn(6%)(t)]xN samples. ro and rS are ART at Ho and

HS. Total sample thicknesses are as close as possible to 720nm .......... 100
4.3.14CPP ART and CIP values at H0, Hp and HS of

[Co(6nm)/AgPt(6%)(t)]xN samples. Total sample thicknesses

are as close as possible to 720nm.(large target) ..................... 101
4.3.15 CPP MR, CIP MR and [(ro-r'_.~,)r0]1/2 values at HO, and Hp of

[Co(6nm)/AgPt(6%)(t)]xN samples. ro and rS are ART at H0

and H5. Total sample thicknesses are as close as possible to

720nm (large target) ...................................... 101
4.3.16CPP ART and CIP values at H0, Hp and Hs of

[Co(t)/AgPt(6%)(t)]xN samples. Total sample thicknesses are

as close as possible to 720nm.(large target) ....................... 102
4.3.17CPP MR, CIP MR and [(ro-rs)r0]l/2 values at H0, and H of

[Co(t)/AgPt(6%)(t)]xN samples. ro and r8 are ART at PI; and H3.

Total sample thicknesses are as close as possible to

720nm (large target) ...................................... 102

4.4.1 Fit parameters and independent measurements. (Column 1)
Constrained fit to Co/Cu and Py/Cu. (Column 2) Independent
measurements of 2ARNMCO [40] and ZARNb/Py

and of PC.» Pa» and pp), from films sputtered with the Co/Cu

and Py/Cu multilayers. ( Column 3) Independent Measurements
of PC.» pCO, and ppy from films sputtered with Co/Cu/Py/Cu

multilayers ............................................. 107
4.4.2 CPP ART and CIP values at Ho, Hp and Hs of
[Co(3)/Cu(t)/Py(8)/Cu(t)]xN ................................. l 18

4.4.3 CPP MR, CIP MR at H0, and H and ratio of the measured
and predicted MR values of [Co(3)/Cu(t)/Py(8)/Cu(t)]xN.

r kandrsareARTathanst .............................. 119
4.4.4 PP ART and CIP values at Ho, Hp and HS of

[Co(6)/Cu(t)/Py(16)/Cu(t)]xN ................................ 120
4.4.5 CPP MR, CIP MR at H0, H and ratio of the measured and

predicted MR values of [Co&)/Cu(t)/Py(l6)/Cu(t)]xN.

r k and rS are ART at H() and HS .............................. 120
4.4.6 PP ART and CIP values at Ho, Hp and HS of

[Co(6)/Cu(t)/Py(10)/Cu(t)]xN samples .......................... 121

4.4.7 CPP MR, CIP MR at HO, HI) and ratio of the measured and

1X

predicted MR values of [Co(6)/Cu(t)/Py(10)/Cu(t)]xN samples.

rok and rs are ART at H0 and HS .............................. 121
4.4.8 CPP ART and CIP values at H0, H1) and HS of
[Co(3)/Cu(t)/Py(5)/Cu(t)]xN samples ............................ 122

4.4.9 CPP MR, CIP MR at Ho, HI) and ratio of the measured and
predicted MR values of [Co(3)/Cu(t)/Py(5)/Cu(t)]xN samples.
rok and r8 are ART at H0 and HS ............................. 122

4.5.1 CPP ART and CIP values at Ho, HI) and HS of

[Ni(6nm)/Ag(t)]xN samples. Total sample thicknesses

are as close as possible to 720nm .............................. 131
4.5.2 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at Ho, and Hp of

[Ni(6nm)/Ag(t)]xN samples. ro and rS are ART at H() and H3.

Total sample thicknesses are as close as possible to 720nm ............. 132
4.5.3 CPP ART and CIP values at H0, Hp and HS of

[Ni(t)/Ag(t)]xN samples. Total sample thicknesses are

as close as possible to 720nm ................................. 132
4.5.4 CPP MR, CIP MR and [(ro-rsgrofl’2 values at Ho, and H of

[Ni(t)/Ag(t)]xN samples. r0 and rS are ART at HO and HS.

Total sample thicknesses are as close as possible to 720nm .............. 133

5.1.1 CPP AR and CIP values at HO, H and Hs of
[Cu(9nm)/(Ni)/Co(6nm)/(Ni)/Cu( nm)]4g samples ................... 138
5.1.2 CPP MR and CIP MR values at H0 and Hp of
[Cu(9nm)/(Ni)/Co(6nm)/(Ni)/Cu(9nm)]43 samples.

r() and rS are ART at Ho and HS, respectively ....................... 138
5.1.3 CPP AR and CIP values at Ho, H and HS of
[Cu(9nm)/(Co)/Ni(6nm)/(Co)/Cu( nm)]43 samples ................... 139

5.1.4 CPP MR and CIP MR values at HO and Hp of
[Cu(9nm)/(Co)/Ni(6nm)/(Co)/Cu(9nm)]43 samples.
r() and r8 are ART at Ho and H3, respectively ....................... 139

5.2.1 CPP AR and CIP values at Ho, Hp and Hs of [Co(6nm)/Ag(t)] N

samples with reduced sputtering rates by means of reducing the

target voltages and target currents .............................. 147
5.2.2 CPP MR and CIP MR values at H() and Hp of [Co(6nm)/Ag(t)] N

samples with reduced sputtering rates by means of reducing the

target voltages and target currents. r0 and rS are ART at H0

and HS, respectively ....................................... 147
5.2.3 CPP AR and CIP values at Ho, Hp and HS of [Co(6nm)/Ag(t)] N

samples with reduced sputtering rates by means of increasing

the sputtering pressure .................................... 148
5.2.4 CPP MR and CIP MR values at H0 and Hp of [Co(6nm)/Ag(t)] N

samples with reduced sputtering rates by means of increasing the

X

sputtering pressure. ro and rs are ART at H() and HS, respectively ......... 148
5.2.5 CPP AR and CIP values at H0, Hp and HS of [Co(6nm)/Ag(t)] N

samples with standard sputtering rates ........................... 149
5.2.6 CPP MR and CIP MR values at H0 and HI) of [Co(6nm)/Ag(t)] N

samples with standard sputtering rates. r0 and rS are ART at Ho

and HS, respectively ....................................... 149

5.3.1 CPP AR and CIP values at H0, Hp and HS of

Co(t1)/Ag/Co(t2)/Ag samples ................................. 154
5.3.2 CPP MR and CIP MR values at H0 and HI) of

Co(tl)/Ag/Co(t2)/Ag samples with standard sputtering rates.

To and rs are ART at Hp and HS, respectively ....................... 154
5.3.3 CPP AR and CIP values at Ho, Hp and HS of
Co(t1)/Cu/Co(t2)/Cu samples ................................. 155

5.3.4 CPP MR and CIP MR values at H0 and HI) of
Co(tl)/Cu/Co(t2)/Cu samples with standard sputtering rates.

ro and rs are ART at Hp and HS, respectively ....................... 156
5.3.5 CPP AR and CIP values at H0, Hp and HS of
Co(3nm)/Cu/Py(8nm)/Cu samples. (* : type II multilayers.) ............. 162

5.3.6 CPP MR and CIP MR values at H0 and Hp of
Co(t1)/Cu/Co(t2)/Cu samples. ro and r8 are ART at Hp and H3,

respectively.(* : typeII multilayers.) ............................. 163
5.3.7 CPP AR and CIP values at H0, HI) and HS of Co/Cu/Py/Cu samples ....... 164
5.3.8 CPP MR and CIP MR values at Ho and Hp of Co/Cu/Py/Cu

samples. ro and rS are ART at Hp and HS, respectively ................ 164
5.3.9 CPP AR and CIP values at Ho, Hp and HS of Co/Ag/Py/Ag samples ....... 165
5.3.10 CPP MR and CIP MR values at HO and Hp of Co/Ag/Py/Ag

samples. r() and rS are ART at Hp and HS, respectively ............... 165

Al CPP ART and CIP values at Ho, HI) and Hs of
[Co(6nm)/AgAu(6%)(t)]xN samples. Total sample
thicknesses are as close as possible to 720nm ..................... 172
5.3.10 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at HO, and Hp of
[Co(6nm)/AgPt(6°/o)(t)]xN samples. ro and rS are ART at H0 and HS.
Total sample thicknesses are as close as possible to 720nm ............ 172

LIST OF FIGURES

 

1.1 Schematic picture of mechanism of spin-dependent scattering

in magnetic multilayer at (a) AP state; (b) P state ..................... 5
1.2 (a) CPP resistance, (b) CIP resistance, and (c) magnetic moment

versus field for a [Co(6nm)/Ag(6nm)]X 60 sample .................... 13
1.3 MR(%) CPP and MR(%) CIP vs ICU for [Co(1.5nm)/Cu(tcu)]

multilayers with tT=3 60nm ................................... 15
1.4 AR(HO) vs bilayer number N for [Co(l .5nm)/Cu(tcu)]

multilayers with tT=3 60nm ................................... 15
1.5 J[AR,(HO) — AR,(H,)]AR,(HO) vs bilayer Nfor Co/Ag, and Co/AgSn.

The line is calculated from Eq.1.2, using Co/Ag parameters .............. 19
2.1 Sample geometry for CPP and CIP measurements .................... 23
2.2 Dektak profile of a Nb strip. The vertical scale is in - and horizontal one

in um ................................................. 29
2.3 9-29 spectrum for A =120A, tCo=tAg= 60A ........................ 32
2.4 Determination of bilayer thicknesss A for Bragg' Law for A =120A,

tCo=TAg= 60A. The slope of the straight line is the bilayer thickness ........ 32
2.5 9-29 spectrum for A =120A, tCo=tAgSn= 60A ..................... 33
2.6 Determination of bilayer thicknesss A for Bragg' Law for A =120A,

tCo=1AgSn= 60A The slope of the straight line is the bilayer thickness ....... 33
2.7 9-29 spectrum for A =120A, tCo=tAgMn= 60A ..................... 34
2.8 Determination of bilayer thicknesss A for Bragg' Law for A =120A,

tCo=tAgMn= 60A. The slope of the straight line is the bilayer thickness ...... 34
2.9 9-29 spectrum for A =120A, tCo=tAgPt= 60A ...................... 35
2.10 Determination of bilayer thicknesss A for Bragg' Law for A =120A,

tCo=tAgPt= 60A. The slope of the straight line is the bilayer thickness ....... 35
2.1 1 Experiment setup for CPP geometry resistance measurements ............ 37
2.12Magnetization measurement for tCo=tAgSn= 60A .................... 41
2.13 Magnetization measurement for tCo=tAgMn= 60A ................... 41
2.14Magnetization measurement for tCo=tAgPt= 60A .................... 42

3.1

(a) Schematic representation of densities of states in the s and (1 bands
of a noble metal at 0K. (b) Schematic representation of densities of states
in the s and (1 bands of a magnetic metal at 0K. The bands are filled up to

xii

the Fermi level EF.[82] ..................................... 44
3.2 J[AR,(HO) — AR,(HS )]AR,(H0) vs N. The solid line is calculated

for €§=£Ef :00. The dash curves are calculated from VF theory for

the indicated values of (”sq/g , with (Sf =00 .......................... 60

3.3 J[AR,(HO) - AR,(H_, )]AR,(H0) vs N. The solid line is calculated
for (ff =83)" =00. The broken lines are calculated from VF theory for
values of eff=3nm (top), lnm (middle), and Onm (bottom), with
6?} =00 ................................................ 61
3.4 J[AR,(HO) — AR,(H, )]AR,(H0) vs N. The solid line is calculated

for (ff =€Ef° =00. The dash curves are calculated from VF theory for

 

 

 

the indicated values of Eff, with 3E; =00 .......................... 62

3 .5 J[AR,(HO) - AR,(H_, )]AR,(H0) vs N. The solid line is calculated

for eff =6?!" =00. The broken lines are calculated from VF theory for

 

(top to bottom) €E}’=12nm , 6nm ,3nm, and 0m, with (ff =00 ........... 63

4.2.1 Global fit of [Co(t)/AgSn(t)]XN samples for Area times CPP

 

resistances at Ho, and Hs- All samples have total thickness 720nm ......... 69
4.2.2 II = CPP-MR(Ho)/CPP-MR(Hp) versus bilayer number N for Co/Ag
and Co/AgSn samples ...................................... 69
4.2.3 ART(Ho)-ART(HS), versus N for [Co(t)/AgSn(t)]XN samples.All
samples have total thickness 720nm ............................. 70
4.2.4 J[ART(HO) — ART(H,)ART(HO) versus N for [Co(t)/AgSn(t)]XN
samples.A11 samples have total thickness 720nm ..................... 70

 

4.3.1 ,/[ART(H,) - ART(H, )]ART(HO) vs bilayer number N calculated

fi'om VFequations in Ref. [133] for samples with tCo=6nm. The line
labeled no is a fit with parameters for Co/Ag. The solid curves for the

indicated values of efi} are calculated with these same parameters

and pN=150an. The dashed curves for ۤ=7nm show the effect

of varying pN from 80 to 300 nm .............................. 77
4.3.2 ART(H)-ART(HS) versus H for Co/Ag, Co/AgSn(4%),

Co/AgMn(9%), (6nm/6nm)60 multilayers. The curves through the

data are simply computer drawn guides to the eye .................... 79
4.3.3 ART-(Ho) (solid symbols) and ART(HS) (open symbols) vs bilayer

number N for Co/Ag (circles), Co/AgSn (square), and Co/AgMn

(diamonds) multilayers with fixed tCo=6nm and tT=720nm. The colid

Co/Ag curves and solid Co/AgSn curves are fits to Rq. 4.3.2; the

downward curvature at small N for Co/Ag comes from corrections

xrll

because these samples did not have a covering Co layer under the top

Nb strip. The dashes Co/AgMn curves are fits to Eqs. (3.6)-(3.9) of

chapter 3. We do not expect the Co/AgMn fits to be as good as

those for Co/Ag and Co/AgSn ................................ 80
4.3.4 ART(HO) (solid symbols) and ART(HS) (open symbols) vs bilayer

number N for Co/Ag (circles), Co/AgSn (square), and Co/AgPt

(diamonds) multilayers with fixed tCo=6nm and tT=720nm. The colid

Co/Ag curves and solid Co/AgSn curves are fits to Rq. 4.3.2; the

downward curvature at small N for Co/Ag comes from corrections

because these samples did not have a covering Co layer under the

top Nb strip. The dashes Co/AgPt curves are fits to Eqs. (3.6)-(3.9)

of Ref. chapter 3. We do not expect the Co/AgPt fits to be as good as

those for Co/Ag and Co/AgSn ................................ 81

4.3.5 J[ART(HO) — ART(H, )]ART(HO) vs N for Co/Ag, Co/AgSn(4%),
Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with
fixed tco=6nm. The dashed lines is for ۤ=oo[l3]. The curves (solid
for Co/AgMn and dashed for Co/AgPt) correspond to the indicated
best fit values of 6?}. Some measuring uncertainties are also shown.

 

Those not shown are smaller than the symbols or 55%, whichever
is larger ............................................... 83

4.3.6 ,[rART(H,) — ART(H, )]ART(HO) vs N for Co/Ag, and
Co/AgMn(6%) multilayers with fixed tCo=2nm. The dashed
lines is for 8’}; =00[13]. The solid curve for Co/AgMn correspond

to the indicated best fit values of Elsi/f. Measuring uncertainties are

 

smaller than the symbols or 55%, whichever is larger ................. 84
4.3.7 ART(H) vs field H for a Co/AgMn(6%) multilayer (6nm/9nm)48
in low field system then in high field system ....................... 87

 

4.3.3 ,fiARTwo) — ART(H, )]ART (Ho) vs bilayer number N calculated

from VF equations in Ref. [133] for samples with tCo=tN The line
labeled 00 is a fit with parameters for Co/Ag. The solid curves for

the indicated values of Eff are calculated with these same parameters

and pN=150n£2m. The dashed curves for €Q}=7nm show the effect

of varying pN from 80 to 300 nm .............................. 89
4.3.9 J[ART(H0) — ART(HS )]ART(HO) vs N for Co/Ag, Co/AgSn(4%),

Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with

fixed tCo=tN- The dashed lines is for Zfilf=oo[13]. The solid curves

for Co/AgMn Co/AgPt) correspond to the indicated best fit value

of (2}. Because of the scattering of our data, it iis hard to derive best

 

fit value of 8?} for AgPt. Measuring uncertainties are smaller than

xiv

the symbols or 35%, whichever is larger .......................... 90
4.3.10 J[ART(H, ) — ART(H,)]ART(H,,) vs N for Co/Ag, Co/AgSn(4%),
Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with
fixed tCo=6nm. The dashed lines is for £13} =oo[13]. The curves (solid
for Co/AgMn and dashed for Co/AgPt) correspond to the indicated
best fit values of (2}. Measuring uncertainties are smaller than the

 

symbols or 35%, whichever is larger ........................... 91
4.3.11 fiARfiHp ) — ART(HS )]ART(HP) vs N for Co/Ag, Co/AgSn(4%),

Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with

fixed tCo=tN. The dashed lines is for 31;} =oo[l3 ]. The curves (solid

for Co/AgMn and dashed for Co/AgPt) correspond to the indicated

best fit values of [1!]. Measuring uncertainties are smaller than the

 

symbols or 35%, whichever is larger ........................... 92

4.4.1 (a) Sample geometry for simultaneous measurements for CPP(V/I)

and CIP (V/l) resistances. The CPP current I flows through the

overlap area Azl .25 mm2 of the Nb strips. (b) Schematic of the

antiparallel (AP) state of Eq. 4.4.] .............................. 105
4.4.2 (a) Magnetoresistance and (b) magnetization M of a

[Co(3)/Cu(20)/Py(8)/Cu(20)]3 multilayer vs magnetic field H.

Sample dimensions are in run ................................. 1 10
4.4.3 (a) Magnetoresistance and (b) magnetization M of a

[Co(6)/Cu(20)/Py(16)/Cu(20)]8 multilayer vs magnetic field H.

Sample dimensions are in run ................................. 11 1
4.4.4 ARt(HAp) and ARt(I-IS) for [Co(3)/Cu(20)/Py(8)/Cu(20)]3

multilayers for N= 2,4,6,8. For tCu=20nm, the solid lines are for

the parameters in column 1, Table 4.4. 1. Open and filled symbols

for N=4 and N=8 are for samples from different sputtering runs;

their differences show our reproducibility. The crosses are for

samples with tCu= 40nm and the pluses for tCu=20nm. With

pcquan, the changes in ARt from tCu=20nm to 10nm or 40nm

are z—O. le'Qm2 and +0.2Nme2, respectively. Even for N=8,

these are only z-0.8 and +1 .otan, about our reproducibilities ........... 112
4.4.5 ARt(I-IAp) and ARt(Hs) for [Co(6)/Cu(20)/Py(16)/Cu(20)]3

multilayers for N= 2,4,6,8. For tCu=20nm, the solid lines are for

the parameters in column 1, Table 4.4. 1. Open and filled symbols

for N=4 and N=8 are for samples from different sputtering runs;

their differences show our reproducibility. The crosses are for

samples with tCu= 40nm. With pcquan, the changes in ARt

from tCu=20nm to 40nm are z+0.2Nme2. Even for N=8, these

are only z +1.6fnm2tabout our reproducibilities ..................... 113

XV

4.4.6 ARt(HAp) and ARt(HS) for [Co(3)/Cu(20)/Py(5)/Cu(20)]3 and
[Co(6)/Cu(20)/Py(10)/Cu(20)]8 multilayers for N= 2,4,6,8. For
tcu=20nm, the solid lines are for the parameters in column 1,
Table 4.4.1. Open and filled symbols for N=4 and N=8 are for
samples from different sputtering runs; their differences show

our reproducibility ........................................ l 14
4.4.7 The ratios of the measured and predicted magnetoresistance,

[AR,(HAP ) - AR,(H_, )]/ [ARf‘P — ARf’ 1 for four sets of samples ......... 115
4.4.8 The improved ratios of the measured and predicted magnetoresistance,

[AR,(HAP ) — AR,(H, )]/ [.4pr — ARf’ ] for four sets of samples ......... 1 16
4.5.1 CPP and CIP magnetoresistances vs field H for a Ni/Ag (6nm/6nm)

multilayer .............................................. 126
4.5.2 CPP-MR and CIP-MR vs t Ag for Ni/Ag (6nm/tAg) mutilayers ........... 127
4.5.3 CPP-MR and CIP-MR vs t Ag for Ni/Ag (tCoqu) mutilayers ........... 128
4.5.4 CPP-MR(HO) vs tN for Ni/Ag, Co/Ag, and Co/Cu (6nm/tN)

multilayers, where N=non-magnetic metal, Ag or Cu .................. 129
4.5.5 CPP-MR(HO) vs t Ag for Ni/Ag, and Co/Ag multilayers (tCoqu) ........ 130
5.1.1 ART(H) versus tNit the thickness of thin Ni layer, for

[Cu(9nm)/(Ni)/Co(6nm)/(Ni)/Cu(9nm)]43 samples ................... 136
5.1.2 ART(H) versus tCo’ the thickness of thin Ni layer, for

[Cu(9nm)/(Co)/Ni(6nm)/(Co)/Cu(9nm)]4g samples .................. 136

5.2.1 ART versus bilayer number N for samples with reduced sputtering

rates by means of reducing the target voltages and target currents,

and samples grown under the standard conditions ................... 142
5.2.2 ART versus bilayer number N for samples with reduced sputtering

rates by means of increasing the sputtering pressure, and samples

grown under the standard conditions ............................ 142
5.2.3 MR at Ho versus bilayer number N for samples with reduced sputtering

rates by means of reducing the target voltages and target currents,

and samples grown under the standard conditions .................... 143
5.2.4 MR at Ho versus bilayer number N for samples with reduced sputtering

rates by means of increasing the sputtering pressure, and samples

grown under the standard conditions ............................ 143
5.2.5 9-29 spectrum for sample tCo=1Ag=6nm grown with reduced

sputtering rates by means of reducrng the target voltages and

target currents ........................................... 144
5.2.6 9-29 spectrum for sample tC0=tAg=6nm grown with reduced

sputtering rates by means of increasing the sputtering pressure ........... 144
5.2.7 9-29 spectrum for sample tCO=tAg=6nm grown under standard

sputtering conditions ....................................... 145

xvi

5.2.8 Magnetization measurement for sample tC0=t A =6nm grown
with reduced sputtering rates by means of reducrng the target

voltages and target currents ...............................

5.2.9 Magnetization measurement for sample tC0=tAg=6nm grown
with reduced sputtering rates by means of increasing the

sputtering pressure .....................................

5.2.10 Magnetization measurement for sample tCo=tAg=6nm grown

under standard sputtering conditions ........................

5.3.1 (a) Magnetoresistance and (b) magnetization M of a
[Co(6)/Ag(20)/Co(2)/Ag(20)]4 multilayer. The sample

dimensions are in run ....................................

5.3.2 (a) Magnetoresistance and (b) magnetization M of a
[Co(6)/Cu(40)/Co(2)/Cu(40)]2 multilayer. The sample

dimensions are in nm ....................................
5.3.3 Schematic of the antiparallel (AP) state of type II multilayers .........

5.3.4 (a) Magnetoresistance of a [Co(3)/Cu(10)/Py(8)/Cu(10)]2
multilayer (type I).and (b) Magnetoresistance of a
[Co(3)/Cu(10)]2[Py(8)/Cu(10)]2 multilayer (type H). The sample

dimensions are in nm ....................................

5.3.5 (a) Magnetoresistance and (b) magnetization M of a
[Co(3)/Cu(10)]6[Py(8)/Cu(10)]6 multilayer (type II).

The sample dimensions are in run ............................

 

A.1 J[ART(HO) — ART(HS )]ART(HO) vs N for Co/Ag, Co/AgSn(4%),
and Co/AgAu(6%) multilayers with fixed tco=6nm. The dashed lines

is for eff, =oo[13] .......................................

xvii

145

146

146

...152

153

157

160

161

.. 171

CHAPTER 1

Introduction

We define Magnetoresistance (MR) as the fractional change in electrical resistance
of a conducting material in response to an applied external magnetic field H. The change
can be defined either with respect to the initial or final resistance. In pure metals it is
usual to define the MR with respect to the initial resistance at H = 0, because the MR can
continue to change monotonically with increasing field. For the ferromagnetic/non-
magnetic (F /N) multilayers described in this thesis, it is generally more convenient to use

the final state resistance and define

MR = [R(H) ‘ R(Hs)l/R(I‘Is)t (1)

because the R(H) saturates to a constant value above a saturation field HS, and it is this
saturation state that is usually best characterized.

In pure metals and alloys, the MR can be readily explained in terms of the Lorentz
force that the magnetic field exerts on the moving electrons. The effect of the field on the
trajectory of the electrons increases the electrical resistivity (positive MR).[78] At room
temperature, the MR in pure metals or alloys is small.

In 1988, a most exciting and surprising phenomenon--Giant Magnetoresistance
(GMR)-~was discovered in magnetic multilayers composed of alternating layers of
ferromagnetic (F) and non-magnetic (N) metals.[8][10][20][104] Application of a
magnetic field greatly reduces their electrical resistance (negative MR), even at room

temperature. This discovery has stimulated great interest in understanding the

1

2

fundamental science underlying the phenomenon and in developing applications.
Promising applications of GMR in magnetic multilayers include heads for tape drives that
can read more densely packed information, increases in information storage densities,
and position and motion detectors.[86] Present MR devices are based on thin films of
permalloy (N igOFezo), where the film resistance drops by about 2% upon application of a
field of 10 Oe.[12] GMR sensors with sensitivities of more than 2% below 10 Oe
already exist. [29][[30]

In this chapter, I will briefly outline the historical development of GMR. More
complete discussions of related phenomena in magnetic multilayers such as magnetic
coupling between the F layers, are given in the Ph.D. thesis of SF. Lee[71] and in
reviews.[32][78] I begin with the standard MR measured with Current in the Layer
Planes (CIP-MR), where GMR was first discovered. As the research on this topic is now
voluminous,[78] I concentrate on studies of direct relevance to the present thesis. After
brief mention, for completeness, of studies of MR in granular magnetic alloys(g-
MR),[143], I then turn to the less usual MR measured with Current Perpendicular to the
layer Planes (CPP-MR) which is the main subject of this thesis.

1.1 Brief Summary of Important Advances and Issues
in Magnetic Multilayers

1.1.1. CIP-MR

In 1986, P. Grunberg's group[55] in Julich, Germany made a three-layer Fe/Cr/Fe
sandwich structure to investigate exchange coupling between Fe layers and found

antiferromagnetic (af) coupling between the Fe layers for a particular Cr thickness (10A).

3

This discovery led Albert F ert of the University of Paris Sud in Orsay, France to
ask if such coupling could give rise to a large change in resistance when a magnetic field
is used to reorient the order of the magnetizations Mi of neighboring layers in the
structure from antiparallel (AP) at zero field to parallel (P) at high fields. In 1988, F ert
and his colleagues[8][10] reported that such an effect existed, and christened it "Giant
Magnetoresistance" (GMR). At 4.2K, they found that a field of 2 T could decrease the
resistance of molecular-beam-epitaxy (MBE) fabricated af-coupled Fe/Cr multilayers by
50%. A similar, but smaller, effect was reported nearly simultaneously by P. Grunberg
and his group[20][103] for an MBE-grown Fe/Cr/Fe sandwich structure; at room
temperature they observed an MR of 1.5%. In Fe/Cr trilayers they obtained an MR of 3%,
which increased to above 10% with a saturation field H5 = 0.15T upon cooling the
sample to 5K. In both cases, the resistance was maximum in the zero-field af state, and
decreased monotonically with increasing field.

F ert and colleagues proposed that the decrease in resistance resulted from spin-
dependent scattering of the conduction electrons at the interfaces between the F and N
metals and in the bulk F layers. The basic idea is as follows. In the F metal, the
conduction electrons can be divided into two classes, spin up and spin down, with respect
to the local magnetization Mi.[8][10] Spin-dependent scattering means that there is a
different scattering probability for spin up and spin down electrons. Such a difference
could result from: (a) a difference in the density of empty states at the Fermi level into
which the conduction electrons can be scattered; or (b) different scattering rates from
impurities in the F metal. The schematic of Fig. 1.1 illustrates the mechanism of spin-
dependent scattering for two magnetic states: (a) anti-parallel (AP) state with layer
magnetizations Mi anti-parallel to each other; (b) parallel state (P) with layer

magnetizations Mi parallel to each other. For simplicity, the figure is drawn with only

4

scattering at the interfaces, but there is also scattering within the layers. Lets assume that
one kind of electron (say spin down) is strongly scattered either in bulk F or at the F/N
interface and the other (spin up) is weakly scattered. In an F/N multilayer, electrons
travel from one F layer to another, so spin up electrons in one F layer will be either spin
up or spin down electrons in the next F layer, depending on whether the layer
magnetizations Mi are parallel (P) or anti-parallel (AP) to each other. At low
temperatures, spin flip scattering should be rare.[138] In this case, it is better to define
the, direction of electron spin (up or down) relative to a fixed direction (such as the
direction of the applied magnetic field). Up or down electrons then keep their spin
directions fixed and carry current in parallel through the multilayer. In Fig. 1.1(a), when
the Mi in the F layers are aligned AP to each other, both spin down and spin up electrons
will be strongly scattered at alternate F layers. The total resistance for each will be the
same, and will involve an average of weak and strong scattering. In contrast, in Fig.
1.1(b), when the Mi are aligned P to each other, spin down electrons will be strongly
scattered at each F layer, but spin up electrons will be only weakly scattered. The P state
thus opens up a low resistance channel (the spin up electrons), leading to a lower total
resistance. The largest GMRs are found when applying an external field reorients the Mi
from an AP state at low fields to a P state at fields above HS. However GMRs can be
seen in F/N multilayer or sandwiches whenever a field changes the relative orientation of

the Mi of adjacent F layers.

 

 

(a) F N F ( b ) F N F
l l l l
t /\ \ /‘_flf——~ / / ” I I k ___,_rl./J”””” rigid-TH”
+ | + I
— l e m I“ s """"" s/ __ l" “ l \r’

 

 

 

 

 

 

 

Figure 1.1 Schematic picture of mechanism of spin-dependent scattering in
magnetic multilayer at (a) AP state; (b) P state.

This spin-dependent scattering model has formed the basis of most theoretical and
experimental analyses of GMR in magnetic multilayers.[27] [33][[8][10] [20][104] [61][62]
[63][113][114][34][76] Clearly a fundamental question arising from it is the relative
importance of spin-dependent scattering at F/N interfaces and in the bulk of the F -metal.
While there is now broad agreement that spin-dependent scattering at F/N interfaces
usually plays an important role in GMR.[56][18][57][91][92][3l][45][58] there remain
disagreements concerning the relative importances of bulk and interface scattering for
particular F -N metal pairs.[65]

In 1990, S. Parkin and colleagues[87][88] at the IBM Almaden reproduced the
GMR results of Fert on sputtered samples, thereby demonstrating that the more complex
and slower MBE procedure is not essential for finding GMR. They also discovered that
the magnetic coupling in Fe/Cr oscillated from af to f and back again, with decreasing
strength as the thickness of the Cr layers increased. Parkin[87][88][89] and others[84]
subsequently showed that similar oscillations in both coupling and GMR occurred in a
number of different ferromagnetic (F)/non-magnetic (N) multilayers. One important
consequence of oscillatory coupling is that one can't simply study systematic variations of
parameters at H = 0 with the thickness tN of the N metal in the range where the

oscillations occur, because the magnetic order is changing with W.

«\u s

6

Further studies showed that GMR could normally be produced either by MBE or by
sputtering. Sometimes one technique gave larger MR5 and sometimes the other[87][88].
Although theory suggests that interface roughness should normally increase the GMR,
[8][10][61][62][63][113] experimentally, inferred increases in interface roughness
sometimes seem to enhance the GMR effect[45] and sometimes to reduce it [58]. The
effect of interface roughness might be different in different F /N systems.[45][5 8]

For a given F/N pair, the largest MRs are usually found when the F layers are af
coupled, since such coupling guarantees an AP state at H = 0. But this situation has the
disadvantage that a large HS is required to overcome this coupling and reach an f state. It
was, thus, of interest to find ways to produce an AP state without the need for af
coupling. V. Speriosu and colleagues[129] showed how to do this using a more complex
multilayer "spin-valve" structure in which the HS of one F layer was increased by
exchange coupling to an antiferromagnet. If the F layers are far enough apart so that
exchange coupling is weak, an AP state should be obtained by reducing the field from
saturation in one direction to beyond zero by just enough to flip the Mi of the unpinned
layer while leaving that of the pinned layer unchanged. We call this a spin-valve of type
(a). An AP state can also be (at least approximately) obtained by using two different F
metals with different saturation fields (e.g. Co with H3 ~ 100-200 Oe and Permalloy (Py)
with H3 3 10 Oe) (spin valve of type b),[111] or the same metal with thicknesses different
enough to give significantly different values of Hs(spin-valve of type
c).[120][147][121][l48] We will use a spin-valve type (b) structure composed of
Co/Cu/Py/Cu in one part of the present thesis in an attempt to obtain a good

approximation to an AP state.

1.1.2 GMR in Granular Systems

GMR is not restricted to multilayer structures. In 1992, Chien's group[l43] at
Johns Hopkins University and Berkowitz's group[19] at the University of California, San
Diego, reported GMR in granular materials, alloys containing nanometer-sized grains of
cobalt in copper or silver ("g-MR"). For most granular systems, large magnetic fields are
required to obtain large GMR. However, Hylton et a1. [66] find MR ratios of order of 4%
to 6% in fields of 5 to 10 Oe at room temperature in hybrid systems of NiFe/Ag, prepared
by annealing multilayers with very thin NiFe layers to break up the NiFe layers into

islands.

1.1.3 CPP-Magnetoresistance

All the GMR measurements discussed above were made in the conventional
Current In the layer Plane (CIP) geometry. Measurements of GMR with Current
Perpendicular to the layer Plane (CPP) were pioneered by our group at MSU. At 4.2K we
combine superconducting contacts with a Superconducting QUantum Interference Device
(SQUID) null-detector to measure the resulting very small resistances.[95] Progress in
CPP MR made by our group will be described in section 1.2.

Both CIP-MR and g-MR are easier to measure than the CPP-MR because CIP
multilayers or g-films have resistances z 0.1-1 ohm. These large resistances also make
the CIP-MR and g-MR more suitable for technological applications. In contrast, the CPP-
MR is hard to measure because the CPP resistance of a typical sample used for CIP
studies is z 10'7Q.[95] Either superconducting leads and precision devices such as
SQUID are needed to measure the CPP MR, or complex lithography technique is used to

make small samples with resistancesz10'20.[46]

(A) CPP MR studies by others.

Following our work, Gijs et al. [46] measured the CPP MR on samples with small
areas (~10-100 umz) prepared by lithography. The big advantage of their technique is
that measurements can be extended to above room temperature. But with wider than long
samples, the technique has two main disadvantages. (l) The cm'rents are non-uniform,
necessitating corrections. (2) It is difficult to correct for, or eliminate, unwanted lead
resistances.[47][50] They made the first measurements of the CPP MR on Fe/Cr
multilayer and found that CPP-MR > CIP-MR[48] as we had for Co/Cu and
Co/Ag.[72][73][97] Their most important contribution was to first measure the
temperature dependence of the CPP MR which in agreement with prior studies of the
CIP-MR,[49][48] they found to be larger in Fe/Cr[48] than in Co/Cu.[51] That is, the
CIP- and CPP-MRS of Fe/Cr decrease more strongly with temperature then do those of
Co/Cu.

Recently, Prinz's group[140] measured the CPP MR of three component
(Co/Cu/Py/Cu) lithographically patterned microstructures. They studied MR
dependencies on device size, magnetic layer thickness, and temperature. As had Gij s,[48]
they found that their current distributions were nonuniform. But they found the MR ratio
AR/R to be independent of contact diameter for diameters up to 5pm, from which they
inferred that the nonuniform current density affects AR and R equally. They also
discovered that changes in the resistance of the metal contacts with temperature can cause
the current distribution through the multilayer to vary strongly with temperature, leading
to a spurious apparent temperature dependence of the MR. Lastly, they discovered that

the magnetic fields at the center of their 2.5 pm wide sample produced by the "poles" at

9

the ends of the F layers are not negligible, ranging from 10-240 Oe for F layer
thicknesses of 10-60A.

Assisted by Dr. Pratt from our group, D. Greig's group in University of Leeds is
working on the CPP-MR of MBE-grown Co/Cu multilayers and is close to publishing
their results. They apparently find large differences between CIP results on samples
made by sputtering and those grown by MBE, while CPP results are very much alike.[54]

Recently, Gijs et a]. [52] proposed a novel technique for measuring a partial-CPP-
MR in magnetic multilayers that is technologically simpler than the usual 'pillar'
microfabrication technique[48]. Using holographic laser interference lithography and
anisotropic etching, they fabricated a V-groove pattern into a substrate, and then
evaporated a multilayer at an angle with the substrate normal. The result was a sample on
which the CIP-MR could be measured by sending current in one direction, and a partial-
CPP-MR could be obtained for current in another direction. With Co/Cu multilayers,
they obtained a partial-CPP-MR of about 37% at low temperature and 17% at room
temperature.

Very recently, another technique, electrodeposition, has been used to fabricate
multilayers for CPP measurements in channels with diameters of 105 of nm.[2] Chien et
al [141] first showed how to fabricate arrays of ferromagnetic nickel and cobalt
nanowires by electrodeposition into 30nm-200nm diameter holes that had been made in
dielectric template by nuclear track etching with a basic process that the rapid passage of
heavy ions through a dielectric material creates latent nuclear damage track. Piraux et
al.,[94] subsequently extended such studies to Co/Cu multilayers. Electrodeposition of
Co and Cu from a single solution gives Cu layers that are relatively pure (3 1 % Co), but
Co layers that contain subtantial Cu (~15%). Piraux et a1. achieved CPP-MRS in Co/Cu

at room temperature of about 15%. However, the saturation fields are quite high (~ 1T).

10

They found little temperature dependence of the CPP-MR; the CPP-MR fell from only
about 19% to 15% in going from 4.2K to room temperature. At almost at the same time,
A. Blondel et al. [21] reported similar results on electrodeposited Co/Cu (CPP-MR about
14%) and (N i,Fe)/Cu (about 10%). The resistance values in their samples ranged from 1
to 500 ohms. Recently, Chien's group[80] also fabricated Co/Cu nanowires and studied
their structural characteristics. The found a large CPP-MR, of up to 11% at room
temperature and 22% at 5K. From the Cu layer thickness at which the GMR disappeared,
they estimated the spin-flip diffusion length (see next section) in their Cu (3 1 % Co) to

be about 20 nm.

1.2 Our Studies of CPP MR.

Intensive theoretical studies have been done to explain the differences between the
CPP- and CIP-MRS. We will examine these in chapter 3. Here we only make a few
essential points to place our studies in context.

Zhang and Levy[149] first predicted that the CPP MR should be much larger than
the CIP MR. We first confirmed this prediction in Co/Ag multilayers[95] and
subsequently in Co/Cu and Py/Cu.[72][73][97][109] In the present thesis we show that it
is also true in Ni/Ag multilayers.

It is now clear[138][25][23] that there are three characteristic lengths in GMR : (1)
the elastic mean free paths in the N and F metals, 9,: and 15,, which dominate the CIP-
MR; (2) the spin diffusion lengths in the N and F metals 13:} and A; --which play a role in
the CPP-MR; and (3) the spin—mixing length in the F metal, 13m, which at low
temperatures is normally long enough that it can be taken as "infmite" and neglected for

both the CIP- and CPP-MRS. Details of these lengths will be discussed in chapter 3. In

11
the CIP-MR, the ratios IN / Ag and IF / kgutN and II: are the thicknesses of N and F

layers--play an essential role, making it difficult to isolate the fundamental physical
parameters underlying GMR from simple two-component F/N multilayers. In contrast, in
the CPP-MR, lsf is expected to be long at low temperatures,[138] and Valet, Fert and
Camblong et al.[23] have shown that when lsf >> [712' ,1; ], there are really no
characteristic lengths in the CPP geometry. Rather, scattering in the system becomes
"self-averaging"[l38][23][25] and the data should be describable in terms of a simple two
current, series resistor model. One of the main foci of the Ph.D. thesis of SF. Lee,[7l]
and a significant part of the focus of the present thesis, has been to test how well this very
simple model can describe CPP data at low temperatures.

The intrinsic quantity in the CPP geometry is the conductance per unit area (G/A).
For reasons discussed in Chapters 3 and 4, we normally measure its inverse, ARt, where
A is the cross-sectional area of the CPP sample through which the current passes. We
call ARt the "specific resistance" and use ARt from here on.

Theorists usually focus upon two magnetic states for GMR: (l) The Parallel (P)
state with adjacent F layers oriented parallel to each other, which occurs above a
saturation field HS. (2) The Anti-Parallel (AP) state with adjacent F layers, usually taken
to be single domain, oriented antiparallel to each other. This state gives total
magnetization = zero. As discussed in the last section, exchange coupling between F
layers oscillates between af and f with increasing tN, with decreasing strength as 1N
increases.[87][[88][89] Similar oscillations also happen in GMR, but a true AP state
probably occurs only at the first af oscillation peak. It is thus hard to systematically
analyze GMR as a function of tN in the oscillatory regime. To avoid having to deal with
these oscillations, we usually limit our measurements to samples with tN large enough

(typically 2 6 nm) to make exchange coupling weak and oscillations disappear. In two-

12

component F/N multilayers it is then not clear whether a truly AP state can be achieved.
In this circumstance, we have to determine the state that has an ARt as close as possible
to that for the AP state.

From our typical ARt and magnetization measurements on uncoupled multilayers
(see Fig. 1.2), three different states must be considered, R(Ho), R(Hp), and R(Hs). R(HS)
is the state with the sample taken to above the saturation field H3, which is the P state.
The other two states, (1) H0, the as-prepared state at H = 0; and (2) Hp, the state of
maximum resistance after cycling to above HS, have locally maximal MRS. Now the
question is: which state behaves most like the AP state? Substantial effort has been made
by our group to answer this question. We now focus on Ho as our best estimate of the
AP state for uncoupled samples for three reasons: (1) R(Ho) is almost always larger than
R(Hp)--one expects the AP state to have the highest resistance; (2) R(Ho) fits better a
data analysis on Cu/Cu[107][109][108], involving extrapolation from the af state to the
completely uncoupled regime, which will be described just below. (3) We have shown
that we can usually increase R(H) to above R(Hp) (but still have it 3 R(Ho)) by dc.

demagnetization of uncoupled samples.[108]

 

 

 

 

 

 

90— . .
A (a) \ \ ‘1
g 80 ~ 1 I
>— I
:33 f l \ A i
m GOr— \ -1
i 1*” “-\.}.IL.“ 1
50 f‘ ‘> < A
L.._LLL..;..LJ-3.1...1...1
{*vflflWi—r‘fi—
1.8[' l H0 H
E 1.7m 11,, N H
a l j
u r 1.x l
a: toe ‘~ —
l -\\ a.
r ___, :3" / \““ '35:)“
1.5 LML # 44 #1 J ‘ p 1 1 g L + ’7
{fl """" l r 'T . fi+*“'—j
A 60 1— m, ,, ._._._._.~i.
g ml (9) {V 1
5 20 »— 4 ff —{
C? i i NI -1
o or t" / 3
x—‘i —20F 'y H
v i f 1
_40 J 7.4
E? —60 i—‘M‘ “1'" €
L143.I.L.1..ul...l..11.u.j
—0.6 —0.4 -0.2 0.0 0.2 0.4 0.6
H (kOe)

Figure 1.2 (a) CPP resistance, (b) CIP resistance, and (c) magnetic moment versus
field for a [Co(6nm)/Ag(6nm)]X 60 sample

14

Zhang and Levy[151] have argued that the condition 2 Mi = 0 should uniquely
determine the CPP AR,” , with the assumption that each Co layer is a single magnetic
domain, and an Mi can point only along or opposite to the applied magnetic field. For
our uncoupled multilayers, ARt is systematically larger at H0 than at Hp, whereas the
magnetizations of both states are z 0. We must thus conclude that the condition 2 Mi z 0
does not uniquely specify ARt in our samples. Further checks on the use of the H0 state
as an approximation to the AP state are a part of the present thesis, including use of a
more complex three-component "spin-valve" structure to achieve better control over the
AP state.

In addition to being first to show that CPP-MR > CIP-MR in Co/Ag, Co/Cu, and
Py/Cu,[95][72][73][97][109] we also were the first to show the presence of oscillations in
the CPP-MR, finding a CPP-MR 5: 170% at the af peak in Co/Cu multilayers with tCo =
1.5 nm (Fig.1.3).[107][109]

Following up on work by Zhang and Levy[149] (see also Mathon et al. [82]) we
also developed the first detailed two current, series resistor model for the CPP-MR,
described in chapter 3. This model led to two equations that we write here because we
need them to explain what we have learned. We use the forms appropriate to a set of
samples with fixed t1: and fixed total thickness, tT = MN + NtF, where N is the number of
bilayers. The quantities in the equations are as follows. 2ARs/F is the interface
resistance between our superconducting current leads and the F-metal outer layers of our
multilayer; for Nb/Co its independently measured value is 6 me2.[4l] pN is the
resistivity of the sputtered normal metal, independently measured to be z 10 nflm for Ag
and z 6 an for Cu.[72][73][107][96][97] The specific values of the remaining
quantities, [3F and P; for the F-metal and yp/N and AR Ir,” for the F/N interfaces, are not

needed for our present purposes.

15

 

200

a

p—s
()1
O

O : CPP(H°)
Cl : ClF(HP)

 

 

Fe(5nm)[Co(l.5nm)/Cu(t)] Cu(5nm) j
l
l
l
l
l
l

 

Magnetoresistance %
p—a
o
o

 

" “IF—T ‘T_T_]'—T—T AT'W-r r—T—T—j T—I'F'm" T—I"'

 

l
i
I
EL Q
U
L l

 

 

 

50
0 A . l . . . if .
0.0 7.5 10.0
tCu (nm)

Figute 1.3 MR(%) CPP and MR(%) CIP vs tCu for [Co(l .5nm)/Cu(tCu)]
multilayers with t1=360nm

 

    
  
   

 

 

tCu(nm)
5.7 2.1 0.9
"wort *l‘ii' 1 ‘ ‘3 Ilrpi
,— Fe(5nm)[co(1.5nm)/Cu(t)luCu(5nm) 1‘
A P i‘ 32Ho "
N IUO_ 03H3 “7
E t l
c: _ l
i"; r- o 1‘
Aloo— F -l
I? : "Uncoupled" i
v . <>
5— 3) .
1:1: _ t- 8> 1
<1: 00.: <>F<si><p ‘j
0 * . _ * * ‘ ' ‘ ‘ ‘ r?“
0 30 100 1:30

Bilayer No. N

Figure 1.4 AR(HO) vs bilayer number N for [Co(l.5nm)/Cu(tcu)]
multilayers with tT=360nm

16

The essential features of the first equation, Eq. 1.1,
ARI“) = ZARS/F + PN’T + N[( Pl} " PN )tF + ZARF/N]

(1.1)

are that AR I”) should fall on a straight line as a function of N, and that the intercept
ZARS/F + PCutT = 10 me2 (i.e., tT = 720 nm) is both independent of the magnetic
properties of the multilayer and can be determined independently.[72][73][l07] [96] [97]

The essential features of the second equation, Eq. 1.2,

 

AJRT(AP)[RT(AP) - RT(P)l = BpitrN + 2tARi-mN (1.2)

are that a plot of the experimentally determined left hand side (LHS) versus N should
produce a straight line passing through the origin, and that the slope of this line (RHS)
should be independent of the resistivity of the non-magnetic metal, pN. When Eq. 1.2
applies (i.e. in the long 13f limit), it predicts a universal straight line for multilayers of a
given F-metal with a given N-metal or its alloys. That is, so long as alloying doesn't
affect the properties of the F metal (9}? and 9;) or the F/N interface (VF/N and AR 3.711;),
data for the given N-metal and all of its alloys should fall on exactly the same line.

We were able to examine how well ARt(Ho) approximates AR 3“" by combining
Eq. 1.1 with data for two well defined states, the AP (af) state = AR {”3 at the first
oscillation peak of Fig. 1.3 and the independently determined limit of 10 me2 for Eq.
1.1 as N —>0 (i.e., no —> tT ). The solid line in Fig. 1.4 experimentally defines the AP
state for all values of tN. We find that AR(HO) for our uncoupled samples with tCu 2 6

17

nm falls closely along this line, thus proving that ARt(Ho) for this sample set is close to
AR {”9 for this series of samples.

Using ARt(H0) as our best approximation for AP state, we have derived bulk spin-
asymmetry parameters [3, interface parameters 7, and interface resistances 2AR}, N from
CPP-MR data for Co/Ag,[73] Co/Cu,[97] and Py/Cu.[109] In all three cases we found 7
z 0.8 to be significantly larger than [1 z 0.5, demonstrating that interface scattering
dominates over bulk scattering until the F layers become very thick (2 20
nm).[73][97][109]

We also used Eq. 1.2 to make a parameter free test of the applicability of the two-
current, series resistor model and to show that the CPP resistance is independent of the

electron mean-free-paths, except as they enter through the resistivities pN and Pp.

[23][151][137][138] Fig. 1.5 shows that a plot of J[ART(H0)—ART(HS)]ART(H0)

 

versus N for Co/Ag and for Co/AgSn with fixed tCo = 6 nm yields data for both that fall
closely on the same line passing through the origin, even though the electron mean-free-
path in the AgSn is about 20 times smaller than in Ag (i.e., p AgSn z 20 p Ag)- This result
provides important support for the two current model. To further study effects of finite
mean free path, in the present thesis we made a series of samples with equal but varying
Co and AgSn thicknesses. I will present and analyze these data in Chapter 4.

It is fundamental to scientific research that models must be subjected to ever more
stringent tests. As part of this thesis, we thus devised a new, quantitative test both of the
two current, series resistor model, and of our use of H0 as the AP state. If the two
current model is correct for multilayers PIN and Fz/N, then the parameters obtained
from measurements on F1/N and F2/N can be used to predict the ARs for the three
component system F 1/N/Fz/N. If, moreover, the values of HS for F1 and F2 are very

different, and N is thick enough to minimize coupling between F1 and F 2, then P} and F2

18

represent a spin-valve system of type (b) as described above, where reducing the applied
field H from above the larger HS (say H51) through zero to just beyond -H32 should
produce a true AP state. The test is then to correctly predict ARt in both the P and AP
states for F l/N/FZ/N using only independently determined parameters for F1/N and
FZ/N. In Chapter 4 of this thesis we describe the results of such a test with F1 = C0 (H52
100 Oe), F2 = Nig4Fe16 (H5310 Oe), and N = Cu.[l46] Under preliminary studies, in
chapter 5, we also present data for a modified type (c) spin-valve, where the F layers are

both Co, but with different thicknesses to obtain different values of HS.

l9

 

 

 

 

 

 

 

 

 

l [ ff l f* 1 i 1 l l
(‘1 g
o?“ 90 - g: _-
E /
E / O
v “ 1C0: 6mm 1: /
N g /
\ /
2': 60 ._ 0 ~
/“ / O O
3:”) i /
L—t .
(is 0/0
:3 [.7
l ./
.2 40 —— a -~
5" L O/ J
,_._.
V /
D: o / s
<r. .. / -
X L_ go 0 Co/Ag
O / /_,J *1 (TV, ~—
I {3.0 / 1 :3 C.o/Agbr1(/l%)
\_:/ k L
Di l /§
.( ‘ - a
._:. / i
L / I
/ l l ! 1
O l {j l l g: 14 _1 l l l l l

0 2.0 40 60 80
Bllayei“ No. N

 

Figure 1.5 J[AR,(H0) — AR,(HS )]AR,(H0) vs bilayer N for Co/Ag, and Co/AgSn.
The line is calculated from Eq. 1 .2, using Co/Ag parameters

 

mode
shoul
lengtl
Eq. 1
can b
dlllllS
exam;
heaxi'
data 1'
fcn[l

indept

SCallC:

Histor

hme I
the C1

SUQSES

20

As discussed in the beginning of this section, the simple two current, series resistor
model should apply only when lsf >> the other lengths in the multilayer. This limit
should be valid for Co/Ag, Co/Cu and Co/AgSn.[l38] If we can reduce the spin diffusion
lengths, however, we should be able to see deviations from the straight line behavior of
Eq. 1.2. Because this behavior is independent of the mean-free-path in the N-metal, we
can be sure that deviations must result from spin-flips. To isolate effects of finite spin
diffusion length, we try to reduce 15f by adding impurities to Ag that flip spins, for
example, a magnetic impurity such as Mn which produces exchange scattering, or a very
heavy impurity such as Pt which has a strong spin-orbit interaction. By combining the
data with a theory extending the two current model to the case of finite lsf by Valet and
Fert[138] discussed in Ch. 3, we can derive values of lsf and compare them with
independent estimates.

As indicated above, understanding the relative importance of spin-dependent
scattering at F/N interfaces and in the bulk of F metal is key to understanding GMR.
Historically, the most convincing evidence in the CIP geometry for the importance of
such scattering has come from studies where a few monolayers of a third metal
(magnetic--F2--or non-magnetic--N2) have been deposited ("dusted") at the interfaces of
a given F1 and N1 metal[1 14] to produce N/(F2)/Fl/(F2)/N multilayers. For dusting
with F2, the clearest results will result when F1 and F 2 give very different MRS with the
given N1 metal, since then the "dusting" should either greatly increase or decrease the
MR, depending on which metal is host and which the "cluster".

As preparatory work for the first "dusting" experiments in the CPP geometry, we
have measured the CPP- and CIP-MRS of Ni/Ag multilayers. Ni/Ag was chosen because
the CIP MRs for Ni/Ag appeared to be much smaller than those for Co/Ag,[144] thereby

suggesting that the Co, Ni, Ag system should be ideal for "dusting". The results of our

21

measurements on Ni/Ag are presented in chapter 4, and those of preliminary dusting
studies are given in chapter 5.

Lastly, in all of our prior CPP studies, and most of those in this thesis, the
sputtering conditions (sputtering rates, Ar pressure, etc) were held as nearly constant as
possible, to obtain stable sample quality and reproducible data over extended periods of
time. In this thesis we also made some preliminary tests of effects on sample quality of

varying the sputtering conditions. The data are presented and discussed in chapter 5.

CHAPTER 2

SAMPLE PREPARATION, CHARACTERIZATION

AND EXPERIMENTAL TECHNIQUES

2.1 Introduction

The samples studied in this thesis are sputtered in-situ in the form shown in Fig. 2.1
to allow simultaneous CPP and CIP measurements. The CPP portion of the sample
consists of a Nb layer 300 nm thick, on top of which is sputtered the multilayer of
interest, over which is sputtered a second Nb layer, also 300 nm thick, oriented
perpendicular to the first one. Current I is injected into one Nb lead and removed form
the other, giving rise to a voltage V between the two leads. The Nb leads are about 1.1
mm wide, giving a total area A z 1.25 mm2 through which the CPP current passes. For
CIP measurements, a current i is injected into the pad on one side of the sample and taken
out of the pad on the opposite side. Here the voltage drop v occurs primarily over the two
narrow strips of the sample between the current-voltage pads and the wider central
portion.

The samples shown in Fig. 2.1 are made in an Ultra-High-Vacuum compatible,
four-gun dc magnetron sputtering system designed primarily by Dr. William Pratt Jr. and
built by Simard Inc.[123] As most of the facilities and procedures for sample fabrication
and analysis were described in the Ph.D. thesis of SF. Lee, we limit ourselves here to
describing only essential features of the system and procedures that differed from those

used by him. The most important single difference was that all of our multilayers, except
22

23

where specified otherwise, are capped with a final magnetic layer (usually Co) to
eliminate the proximity effect whereby contact of a thin non-magnetic (N) layer with a

superconductor (S) turns the N metal superconducting.[95]

 

 

 

 

 

 

 

 

 

i V Sample
V Top Nb
\
\ \ \ s Area A
\
I Bottom Nb
1 V — Substrate

 

 

 

 

 

 

Figure 2.1 Sample geometry for CPP and CIP measurements

The chapter is organized as follows. We first briefly describe the system and
procedures for sample preparation. We then introduce the measurements of resistivity
and sample geometry. X-ray diffraction analyses were made to check the bilayer
thickness and to compare the behaviors of multilayers with pure metals and alloys
structure of the samples. Magnetizations of some multilayers were measured to

investigate magnetic properties of our samples.

2.2 Samples and Sample Preparation.

The sputtering system is described in detail in the dissertations of J. Slaughter[124]
and S-F. Lee.[71] To achieve high vacuum in the sputtering chamber, UHV conflate
flanges are used everywhere except for the main flange and the flange to the main rotary
seal, which are viton. A cryopump (CTI Cryo-Torr 8[28]) provides high pumping speeds

(1500 Us air, 4000 Us water) without oil vapor contamination. After the cleaning

24

procedure described below, and light baking to ~ 65°C, the system pumps down
overnight to a few times 10'8 Torr. After 24 hours of pumping and filling of a Meissner
cold trap, the vacuum reaches 3 1-2 x 10'8 Torr, after which sputtering is begun. A
Hydrox[81] gas purifier is used to remove residual impurities from the initially ultra-
high-purity Ar gas. The chamber contains four L. M. Simard[l22] "Tri-Mag" sputtering
sources. The beams of sputtered materials are collimated and shielded from each other by
chimneys placed above the sources. The chimneys can be closed or opened to shield the
particle beams or let them through. A rotary sample positioning plate (SPP) holds the
substrates and two quartz crystal film thickness monitors ( FTMs ) above the desired
sources. A computer controlled stepping motor coupled to the SPP shaft, positions the
substrates and FTMs over the desired sources. An in-situ mask changing system[74]
allows fabrication of the samples shape shown in Fig. 2.1. A wobble stick is used to
rotate the three different masks and a blank in and out of place under the substrates
without breaking vacuum.

Nb, Co, Ni, and Ni34Fe16 targets were purchased from commercial
companies[l36]. The purities of the bulk materials were specified as 99.95% for Nb,
99.95% for Co, 99.99% for Ni and 99.999% for Nig4Fe16. The Ag and Ag-based alloy
targets were made using an rf-induction furnace. The alloy targets were made from pure
Ag, pure Mn, pure Pt and pure Au. The purity of the starting materials was 99.999% for
Ag, 99.999% for Cu, 99.999% for Pt, 99.999% for Au and 99.9% for Mn. Before
alloying, the raw materials were cleaned in dilute nitric acid, rinsed in de-ionized water
and then in alcohol, weighed, and then put into a cylindrical graphite crucible painted
with boron nitride to eliminate possible carbon contamination of the alloy. The crucible
was placed inside a quartz tube encircled by an RF coil. The tube was evacuated to 5x10'
6 Torr and then back filled with a 90% Ar and 10% Hz to about 250 Torr. The H2 helped

to remove 02 from the chamber. The alloy was heated and kept molten for about 15

25

minutes, and then cooled slowly enough to minimize formation of bubbles. The
temperature of the crucible was measured with an optical pyrometer. Upon cooling, we
obtained a slightly oversized disc that was cut to its final cylindrical shape of diameter =
5.72 cm and thickness = 0.64 cm with a traveling wire electrical discharge machine.

Before the system is assembled, most of the Nb deposits from the previous runs are
scraped away using razor blades, and the rest is removed with 5% HF in 25% water and
75% HNO3. The sputtering guns, SPP, and mask components are then cleaned using the
25% water-75% HNO3 mixture. After this acid etch, the components are cleaned with
acetone and alcohol. Rubber gloves are used during this etching for protection, and
plastic gloves are used during assembly to minimize contaminants that could degrade the
vacuum.

Most of the multilayers were deposited onto substrates of polished, 0.5" square, c-
axis oriented, single crystal sapphire, cleaned in acetone and then given a final ultrasonic
rinse in alcohol. A few multilayers were sputtered onto (100) single crystal silicon to
check that the substrate material is not crucial to our results. In each run we also made
300 nm or 500 nm thick simple thin films of the Nb and the multilayer constituents to
check their resistivities, for reasons described below. These films were sputtered onto
(100) single crystal silicon substrates.

For making a CPP/CIP sample, each substrate is located in the center of a circular
holder that is mounted in one of eight holes in the SPP[123], which is located 12cm
above the guns. The SPP is oscillated under computer control to bring a given substrate
sequentially over the desired targets for chosen amounts of time. The substrates are
thermally anchored to the actively cooled SPP. Alternatively, each of the eight holes in
the plate can hold two substrates for making thin films or simple CIP multilayers. Two
other holes contain the quartz crystal thickness monitors used to determine deposition

rates.

26

During sputtering, the Ar pressure in the chamber is normally held at 2.5 mTorr,
and the voltage and current of each sputtering target are kept fixed. The deposition rates
of different materials are measured with two F TMs, with appropriate corrections for the
different densities and acoustic impedances of different material. The monitor readings
for the deposition rates were found to be in good agreement with high angle x-ray
diffraction results for bilayer thicknesses, as described below. The deposition rates for
different materials were within the following ranges: z1.1~1.4 nm/s for Cu, z1.1~l.4
nm/s for Ag, z0.9~l.1nm/s for AgSn(4%), z0.5nm/s for AgMn(9%), z0.8nm/s for
AgMn(6%), zO.7nm/s for AgPt(6%), zO.9~l.lnm/s for AgAu(6%), zO.7~O.8nm/s for Ni,
z0.7nm/s for Ni34Fe16, z0.8~1 .Onm/s for Co, and z0.9~1.0 nm/s for Nb.

The procedure for making the sample shown in Fig. 2.1 is as follows
(1) Measure the deposition rates of all materials with the blank mask in place.

(2) Change to the first strip mask and deposit the bottom 300 nm thick Nb strip.

(3) Change to the sample mask and deposit the multilayer.

(4) Change to the second strip mask and deposit the top 300 nm thick Nb strip.
(5) Change to the blank mask.

To obtain good crystal structures and minimize interdiffusion at interfaces, the
substrates are held at temperatures between -30°C and +30°C using a substrate cooling

system.[98] If the temperature reached 30°C, we shut off the guns to let the system cool.

2.3 Measurements of Resistivity and Sample Geometry

2.3.1 Resistivity

27

The resistivities of the separate films of the multilayer constituents and Nb were
measured using the van der Pauw method.[93] For the multilayer components, we
wished to check stability, and to determine their resistivities for use in fitting procedures
that will be described in Chapter 3. For the Nb we also wished to check stability, since
the interface resistance between the Nb and the ferromagnetic (F) component of the
multilayer depends on the resistivity of the Nb.[40]

The Van der Pauw method allows the determination of the resistivity of flat
samples of arbitrary shape. The method is based on a theorem that holds for such a
sample if the following conditions are fulfilled: (l) The contacts are located at the
circumference of the sample. (2) The contacts are sufficiently small. (3) The sample is
homogeneous in thickness. (4) The sample must be simply connected, i.e., it should not

have isolated holes. When these conditions are satisfied, this method gives:

 

= 1rd (RAB,CD + RBC,DA) f( RAB,CD
ln 2 2 RBC, DA

p )

Here f is a function of the ratio RAB,CD/RBC,DA’ where R AB,CD is the potential
difference VD-VC between the contacts D and C per unit current through the contacts A
and B, and d is the film thickness. A table of f is given in Ref [40]. Small solder joints
were made to the thin films using In and cerralloy 117 or just In (depending on the
material of the film). After the contacts were checked, the sample holder was lowered
into a liquid helium Dewar slowly to avoid breaking the contacts. With a lmA current
provided by a current source through contacts A and B, we measure the potential
difference between C and D using a DVM and calculate R AB,CD- The same procedure
is used to measure RBC,DA- The film thickness d is then measured using a Dektak I'IA
surface profiler,[127] and the resistivity is calculated. The resistivity of each Nb film is

28

measured similarly at 12K, above the Nb superconducting transition temperature (about
9K), in a Quantum Design MPMS.[99]

The thicknesses of these thin films are not easy to measure due to substrate
imperfections such as curvature and discontinuities of slope. The film edges are also not
perfect sharp due to the small gap between the mask and the substrate. The combination

of these difficulties leads to uncertainties of several percent in the derived resistivities.

2.3.2 Film Thickness and CPP Area

As noted in the section I, the intrinsic quantity in the CPP geometry is the
conductance per unit area (G/A) or its inverse, AR, the sample area A times total sample
resistance R. The effective sample area is the overlap area between the crossed Nb strips.
To determine this area, the widths of both Nb strips must be measured. These widths are
measured using a Dektak II A surface profiler[127] that has a vertical resolution of 5A
and a horizontal resolution of 500A. Figure 2.2 shows a Dektak profile of a Nb strip.

The measuring procedures and uncertainties are described in detail in the
dissertation of SF. Lee.[7l] We note here only that each 1 mm wide Nb strip is
measured three times and the average taken, and that the uncertainty for each strip is

typically 1-3%, giving uncertainties for the effective CPP sample areas of 2-5%.

29

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 2.2 Dektak profile of a Nb strip. The vertical scale is in A and horizontal one
hrtumh

30

2.4 Sample Characterization

2.4.1 X-ray Diffraction

Details of the structure of the individual components of the multilayer and of the
interfaces can be important in determining the magnetic and transport properties of
multilayers. Among various methods of characterizing multilayers, x-ray diffraction
techniques are most widely used because of their relative ease of use. In our
measurements, both the bilayer thickness, A, and the sample structure, are checked with
low angle and high angle scans.

We use x-ray diffraction to determine the spacings of the atomic planes and the

bilayer thicknesses of our multilayers. The diffraction condition, know as Bragg's law, is:

nk=2dsin9 or nk=2Asin9 (2.1)

Here the integer n is the order of the corresponding reflection, is is the wavelength of the
incident x-ray, 29 is the angle between incident and reflected rays, (1 is the spacing
between two lattice planes in a crystal, and A is the bilayer thickness.

Our x-ray data are taken on a Rigaku x-ray diffractometer.[100] The selected
wavelength of Cu-Ka is 0.1542 nm. At high angles, values of d and A can be obtained
direction from Eq. 2.1. At low angles, however, corrections must be made for the
difference between the x-ray index of refraction in air and in a metal, to properly obtain A
. [124] The low angle diffraction peaks were seldom seen for our Co/Ag samples made
on sapphire substrates, probably because of a combination of substrate curvature and

columnar growth of the multilayers.

31

A fairly detailed discussion of x-ray analysis of sample structures is given in the
Ph.D. thesis of J. M. Slaughter[124] From his work and our own measurements we
learn the following. Our sputtered multilayers are polycrystalline structures. The Nb has a
bcc structure with (110) planes parallel to the surface of the substrate. Ag has an fcc
(111) structure, and Co can have either fcc (111) or hcp (0001) structures, depending
upon the Co layer thickness.

In this thesis I also describe studies involving several different dilute alloys,
especially AgSn, AgMn, and AgPt. We added these impurities to the host metal to test
for mean free path effects (Sn) on the CPP-MR, or to introduce strong spin-flip scattering
(Mn and Pt) in order to isolate spin-flip scattering effects on GMR . We used x-ray
analysis to check that the presence of impurities does not significantly change the lattice
structure of host metal.

Figure 2.3[71] shows a typical high angle diffraction scan on a simple square
Co(6OA)/Ag(60A) sample (bilayer thickness A=120 A). It shows peaks for bulk close
packed lattice planes of Ag, Co and Nb, and satellites for multilayer thickness around the
bulk peak. The bulk peaks for Ag and Co are at detector angle 29 roughly 38 and 44
degrees, the peak for Nb is also around 38 degrees. These angles are consistent with the
crystal orientations given above: Co(l 1 1), Ag(111) and Nb(110). We can calculate the
bilayer thickness from the Bragg condition using these satellites' positions. Figure 2.4[71]
shows that the slope of the best fit line for A falls within 4% of the nominal thickness.
Our data confirm that our samples are highly textured. Similar plots for
(Co(60A)/Ag4%Sn(60A)), (Co(60A)/Ag9%Mn(60A)) and (Co(6OA)/Ag6%Pt(60A)) are
presented in Figures 2.5-Fig. 2.10. We see that the forms of the 9-29 spectrum are quite
similar and the derived bilayer thicknesses are all within 5% of the desired thicknesses.
From this x-ray analysis we conclude that the presence of impurities does not change the

lattice structure of the host metal enough to strongly affect our analysis.

32

 

l
, ~~ 1
8000:“ A ll
. l
_ 1 ll
5 1500»~ l M
$0 i l .
. . ll 1
2? loooi— l' '
U : l i ,1 /
a 1'.
500 :_ / if V
: 1'; “will
5.1 aapfhri..fhflumjkgi.l11i4333314.

 

0
34 36 38 40 42 44 46 48 50

2 THETA (DEGREE)

Figure 2.3 9-29 spectrum for A =120A, tCoqu= 60A.

f
6 ._
4 is /
L ,2,“
E: 2—— A :116391 04 A /////
is —— .1.
L4 /
f: O T /g
"O » .rif/
t... 1/
E 2 3 H”
C. * /
~4~— /4
r ..X/
_ 6 L /../
I. 0/
__8 - l l 4 l l J__L l 1 Mil . 1_Ml l 1 4 Md__.l l I l r l l l

 

 

0.40 0.42 0.44 0.46 0.48 0.50

casu19)/’x (A‘U

Figure 2.4 Determination of bilayer thickness A for Bragg' Law for A =120A,
tCo=TAg= 60A. The slope of the straight line is the bilayer thickness.

33
ZSOOE
2000*—

1500”“ k

 

CNTS/SEC

; .
10001" /

L.

 

500?— l l .
: 11’ K V)
: , j W ‘W

0 .133334111..:Hmwsgb«:.1.1¥dzz.l.

34 36 38 40 42 44 46 48 50

23THETA(DEGREE)
Figure 2.5 9-29 spectrum for A =120A, tCo=tAgSn= 60A.

2e— A : tyre 1 04.A ,///

n (arbitrary)
o
l
\

6
__ L.—
,—

 

___8 LMLlMMlLLlu ll 1 l 1 ll 1 ;I_LLIM11 1 l1 1
(I40 (I42 (I44 (I46 (148 (ISO

(2 mo 0)//A (A‘U

Figure 2.6 Determination of bilayer thickness A for Bragg' Law for A =120A,
tCo=tAgSn= 60A. The slope of the straight line is the bilayer thickness.

2000

CNTS/SEC

500

l 000 "

 

34

 

I
V
36 38

34

l l
A 111!
4

/

L.

'1 ‘fiLfikJAL A J. .1
4 46 48 50

40 42

2 Tl-IETA (DEGREE)

Figure 2.7 9-29 spectrum for A =120A tCo-fiAgMIfi 60A

 

 

4F— /2>
r ,3“
is 2 *‘“ A ' 115.3 3: 0.7 A .//6
m /,1dr
2 0L /,;7/
.Q r ra//
:6 r) //I
v “a. i“ //V
C 9
-4h— //€/
" (5/,
_6 ——
L
“8 llLLIMllaMILLIIlIIIAllIIIlIL
0.40 0.42 0.44 0.46 0.48 0.50
(2 mn.0)//A (A‘U

Figure 2.8 Determination of bilayer thickness A for Bragg' Law for A =120A,
tCoztAgMn= 60A. The slope of the straight line is the bilayer thickness.

35

CNTS/SEC

l
l
\
1,11
‘ \W'W l I
l 1 L J— ;1 14 1

JMLAJE-J I L LA) I

34 36 38 40 42 44 46 48 50

  

2 THETA(DEGREE)
Figure 2.9 9-29 spectrum for A =120A, tCoztAgPt= 60A.

 

 

,1
i
4 33 0
/
A b n /O/
3 2b— A::llotia 04-A //6/
is - a9"
/.
:4: O 1“ //£’/
FD L Lit/r
S—t //'
.9 ~2b— v/
1: L ,x’J/
//
— 4 1._. /,<’J’
L (33/
-6 ~—
i"
HBiIli¥llglglMlllLlJllLlllllIlllJ

0.40 0.42 0.44 0.46 0.48 0.50

(2 mh.e)/’A (A‘U

Figure 2.10 Determination of bilayer thickness A for Bragg' Law for A =120A,
tCoztAgPt= 60A. The slope of the straight line is the bilayer thickness.

36

2.4.2 Other structural analysis methods

Cross-sectional transmission electron microscopy (XTEM) and nuclear Magnetic
Resonance (NMR) have also been used to study the structure of thin film multilayers
made by our sputtering system. From XTEM Studies performed by D. Howell et al. [64],
we learn the following: (1) the first few layers have rather uniform layering, but
thereafter dark-field micrographs clearly show the existence of columnar growth leading
to a more complicated structure. The columns largely determine crystal grain-sizes in the
layer planes (a few hundred A). (2) the presence of the Nb strips has little effect on the
smoothness of the layering or the column sizes.

NMR studies on multilayers made in our sputtering system were carried out by
van Alphen et a1, [3] as discussed in the thesis of SF. Lee.[71] These studies[3] found
that the Co layers were continuous for tC021.5nm, which will be the case for all of the
studies in the present thesis. Analysis comparing the strain in the Co layers measured by

NMR with a model prediction indicates that our Co/Ag interfaces are incoherent.

2.5 Experimental Setup

2.5.1 CPP and CIP Measurements

The sample structure shown in Fig. 2.1 permits simultaneous measurements of
CPP and CIP resistances at 4.2K, where the Nb cross-strips are superconducting.

The CPP measuring setup consists of a SQUID null detector and a high precision
current comparator. A schematic diagram of the circuit is presented in Fig.2.] 1. The

SQUID, based on London's concept of fluxoid quantization in a superconductor and on

37

Josephson tunneling through a "weak link" between two superconductors, permits high
sensitivity measurements of magnetic flux and, thereby, of electrical current. The high
precision current comparator puts out two currents, the reference current Iref and the
current through the sample 13. For the measurements, IS is usually set to 50mA and the
ratio Irep’ls is adjusted to null the current through the SQUID. The system contains a
small inductor (z 50 pH) and a small resistor (z 170110) in series with the SQUID input
as a high frequency noise filter. In followed by cerralloy 117 is used to make solder
joints to the Nb strips. The finite resistance of these joints should be small compared
with the resistance added as part of noise filter. When the circuit is balanced, the ratio of

the sample resistance RS to the known reference resistance Rref (l.84:I:0.01uQ[43]) can

 

 

  
 

be obtained from
R I,
s = e’ , (2.2)
Rref Is
thereby giving RS.
SQUID
] rat I 3
reference sample

 

j L

F i g 2.11 Experiment setup for CPP geometry resistance measurements

38

For CIP measurements we use a simpler four-terminal technique. A pair of Cu
wires is soldered to each of the two sample pads as current and voltage leads. Either a
SHE model PCB potentiometric conductance bridge is used to measure the conductance
of the sample, or a Fluke 8502A multimeter is used to measure its resistance. Due to
Joule heating produced by the current of the multimeter, the conductance bridge is the
first choice for CIP measurements if the readings are within its range.

The magnetic field on the sample is produced by a hand wound superconducting
magnet that can produce 1 kOe (kilo-oersted) with 20 amperes of current. The magnet's
supporting rods are fixed at one end of the cryostat built by V.O. Heinen and WP Pratt
Jr. A small piece of thick Cu wire is added as a resistor between the magnet leads to
increase the time constant, and thereby reduce field fluctuations due to the high frequency
noise produced by the power supply. Two layers of pure lead are wrapped around the
magnet to reduce the flinging field at the SQUID. The cryostat is inserted into a glass
liquid helium Dewar with an outer liquid Nitrogen jacket. A u-metal shield is wrapped
outside the Dewar and the whole setup is placed in a screened room to minimize
electromagnetic noise.

A Hall probe was used to calibrate the magnetic field at the center of the magnet,
and the calibration was also compared against a Quantum Design MPMS. The magnetic

field is given by:

H = 0.431

where H is in Oersted and the magnet current is in Amperes.[71] The handwound magnet
gives a field that is uniform over the small CPP part of the sample in the center of the
magnet, but is slightly different at the CIP portion further out. The differences are

discussed elsewhere.[75]

39

2.5.2 Sample Magnetizations.

Sample magnetizations and the CIP MRs of some independent test thin fihns are
measured on a Quantum Design Magnetic Property Measurement System (MPMS).
There are several sources of potential residual fields in the MPMS system-«trapped fields
in the superconducting magnet, any portion of the Earth's field that is not completely
eliminated by the MPMS Environmental Shield, and fields from remnant magnetization
in the shield itself. To obtain the lowest possible residual field, one must degauss the
permalloy shield, and then set zero residual field in the magnet. The residual field which
can be obtained following this procedure is 2.7 mG. There are two fundamentally
different temperature control mechanisms used in the system. The normal one is used for
temperatures above 4.4K, while below this temperature, control is achieved by
controlling the pressure on a small reservoir of liquid He. To save time and liquid He, we
usually chose 5K as our measuring temperature. When the sample is made with Nb as a
buffer layer, we have to choose 12K as a temperature above the Nb superconducting
transition temperature so as not to allow any magnetic flux expelled by the
superconducting Nb to disturb the magnetic field applied to the sample. Both the CPP-
CIP and thin fihn CIP samples made in our sputtering system are too large to put directly
into the MPMS sample chamber. The substrates are thus scribed on the back with a
diamond scribe and then broken. Simple films on Si substrates are usually broken into as
nearly equal halves as feasible. CPP-CIP multilayers on sapphire have both sides of the
square broken off so as to leave as much of the multilayer intact as possible.

The resulting smaller sample is then put into a straw that is tied at one end using
threads. Figures 2.12-2.14 show hysteresis plots for the same samples of
(Co(6OA)/Ag4%Sn(60A)), (Co(60A)/Ag9%Mn(60A)) and (Co(60A)/Ag6%Pt(60A)) as

those in Figs. 2. These plots show that the values of He are all around 50-80 Oe, and that

4O

Mr/MS (Mr is the remnant magnetization at zero field and MS is the saturation
magnetization) is about 80%. The variations in saturation magnetizations are presumably
due to differences in sample volumes remaining after the samples are broken. All these
results fall within the ranges found for Co/Ag samples.[7l] We thus conclude that the
presence of these impurities in the Ag is not substantially changing the weak interaction

between the Co layers 60 A apart. .

41

 

{\J
O
l
3
1
1

 

1 ' ' 1
1 5 »
l . -l

3100 ‘T

E t

(D L

a“ 1

:2 01

\__J +

E

 

O

 

~r—T‘fi—r—9' f—‘T—T—fi’
I
l
I
R
l

. ' . 1.1.1..
000.75 0.500 5000 .350 500 /5100
[K081

L

l
:L

1

L
L_.
fit
L

r

|
r—4 O
C

Figure 2.12 Magnetization measurement for tCoztAgSn= 60A.

 

 

 

 

 

 

20{””'thlr’*“ trmr
l -
r 4
l i
r? WOL_ - 41>
E i “
(1) t ,
(7‘ t .
O L
:3 0t 3
'1 i
:- i 1
\“ l
1 ‘ - -
10L ' l
t 1
l l
[ , . . 1
205.1...ng ..l .1.A....A.l....
1.000.750.5300. 250000321050 .75l.00

H 1 km U G J
Figure 2.13 Magnetization measurement for tCo=tAgMn=6OA.

42

 

 

 

 

 

1 T I 15*?
. ‘1
1 *‘fi ‘ 7 “5
”3101L
E L
(D 1 1
9')
.. 1
1:? O1“ 2
1
E L
101 1
L. _
1
7,101. ..3....i.-..l-...
1.0 5 0.50 0.751.00

. , 5 . .
H [ k 0 e J
Figure 2.14 Magnetization measurement for tCo=tAgPt= 60A.

CHAPTER 3

Theory

3.1 Introduction

In this chapter I will first briefly review properties of ferromagnets and those
features of the development of classical and quantum models for the transport properties
of magnetic multilayers in the CIP geometry that are essential for understanding the more
detailed analysis of the CPP geometry which is the focus of this thesis. More details
about ferromagnets and CIP thory are given in the dissertation of S.F. Lee[71] and a
recent review by Levy.[78] I will then review in more detail the development of the
theory of the perpendicular (CPP) magnetoresistance in magnetic multilayers, ending

with the analysis by Valet and F ert that takes into account effects of spin-flip scattering.

3.2 Electron Transport in Multilayers

The following properties of ferromagnetism are essential to better understand
magnetic and associated transport properties of magnetic multilayers. In ferromagnetic,
transition metals such as Fe, Co and Ni, the magnetic moment is associated with the spin

of electrons which occupy partially filled d atomic orbitals. The electrons are standardly

43

44

separated into two orientations, spin up and spin down with respect to the direction of the
local magnetization. For a bulk crystal, since the d-band is able to contain five times as
many electrons as the s-band, and is also narrow, we expect to have Dd(E) >> DS(E),
where Dd(E) and DS(E) are densities of states for d- and s-bands. As illustrated in Fig.

3.1, the up and down spin d-electrons split into two sub-bands.[82]

(a) E (b)

 

4s 3d 43
Figure 3.1 (a) Schematic representation of densities of states in the s and d bands of
a noble metal at OK. (b) Schematic representation of densities of states in the s and
d bands of a magnetic metal at OK. The bands are filled up to the Fermi level
EF.[82]

At low temperature, electrons in metals within kBT of the Fermi level are scattered
mainly elastically from impurities. Such scattering normally conserves spin: spin up —)
spin up and spin down —) spin down. The scattering probability is proportional to the
empty density of states at EF, D(EF). In noble metals, such as Ag or Cu, the Fermi level
mainly intersects an s-p band, with small density of states. In the magnetic metals Co,
Ni, and F, in contrast, the Fermi level intersects both 5 and (1 bands, and the density of
states in one d spin-subband is much higher than in the other. This difference in density
of empty d-states at the Fermi level for different spin directions, can lead the predominant
current carrying spin up and spin down s-electrons to have quite different scattering rates
in these metals, and thus different resistivities.[6]

Some electron scattering--e.g. spin-orbit scattering, spin-spin scattering, or electron
magnon scattering in ferromagnetic metals--can change the orientation of the spin. At low

temperature, electron-magnon scattering is frozen out. The likelihood of spin-orbit

45

scattering or spin-spin scattering is very small in pure metals.[85][7] When no strong
spin-flip scattering is present, the spin up electrons and spin down electrons carry current
independently. As described in section I, the MR in magnetic multilayers is believed to
come from differences in the scattering of spin up and spin down electrons as they pass

through the multilayer.

3.3 CIP and CPP Magnetoresistances

3.3.1 CIP Magnetoresistance

Since the theory of the CIP MR has been extensively described in a recent review
by Levy,[78] we limit ourselves here to briefly outlining the development of ideas
essential to our later analysis of the CPP-MR.

The original discovery of large MR in magnetic multilayers of Fe/Cr, for which
they coined the name Giant MR (GMR), was made by Baibich et al., in the geometry
with current flow in the layer planes (CIP-MR).[8] They argued that the GMR is due to
reorientation of the magnetizations of the F layers under the influence of the external
magnetic field, and ascribed this GMR to spin dependent scattering of the conduction
electrons in the bulk F layers and at the F/N interfaces, with no spin flip scattering. To
understand GMR in multilayers, one has to know how to describe electron transport in a
layered structure and how to include electron spin in the theory. Two basic approaches
are adopted to describe electron transport in magnetic multilayers. One starts from the
semiclassical Boltzman equation and the other from the quantum Kubo linear response
formalism.

The semiclassical approach of the giant MR effect was first formulated by Camley
and Barnas.[27], as an extension of the F uchs-Sondheimer theory for treating transport

where the scattering is inhomogeneous in space.[44][128] They describe what happens at

46

the interfaces in terms of transmission coefficients T0, with the total probability of either
transmission or diffuse scattering taken to be unity. Here electrons of spin 0 (up or
down) were assumed to carry current independently through the superlattice. Additional
parameters, the mean free paths for spin up and spin down conduction electrons, were
taken to characterize scattering in the F layers. Other charactersistics of the two metals
were taken to be the same. Camley and Barnas obtained expressions for the unknown
parameters by matching boundary conditions at the interfaces of the layers. They found
that they could qualitatively describe the experimental data in terms of their coefficients.
However, when Barthelemy and Fert[IO] used the model of Camley and Barnas to derive
analytic expressions for the MR in limiting cases under some approximations, they found
that a single set of parameters could not simultaneously fit both the MR and the
resistivity for the magnetic layer. They ascribed this failure to the restriction T0 .<_ l in
the Camley-Barnas model. Subsequently, Hood and Falicov[6l] improved the Camley
and Barnas model by introducing spin-dependent reflection, and Johnson and Camley[69]
showed how one could account for bulk and interfacial scattering in a unified way by
representing the interfacial region as a mixed interdiffusion layer.

Because changes in the scattering potential in multilayers occur over distances
comparable to the lattice constant, one cannot use a unique scattering rate in a local
region to describe the electron scattering in the metal; thus, the local relaxation time
approximation in the semiclassical Boltzmann equation is not strictly valid. To get
around this problem, Levy and co-workers were the first to use the Kubo formula to
develop a fully quantum model of GMR. Starting from a Hamiltonian which included
only spin-dependent impurity scattering, [77][150] they developed an analysis in
momentum space that allowed them to solve for the Green's function and thereby obtain

the conductivity of the multilayer. [75][l 50][[24][1 53] The term in the Hamiltonian due to

47

impurity scattering contained two parts, one for bulk and one for interface scattering. The
key to this quantum analysis in k-space is a random impurity average, in which the actual
impurity distribution is replaced by a random distribution of scatters, and a single average
mean-free-path (arising from the average scattering) is defined for the system, and then
serves as the characteristic length scale for the system. They found that when there is no
spin-dependent scattering in the bulk F layers, the MR decreases with increasing F and N
layer thicknesses; when there is no spin-dependent scattering at the interfaces, the MR is
a more complex function of the layer thicknesses. They found that the CIP-MR
decreased exponentially with increasing thickness of the N spacer layer, with the average
mean-free-path described above as the characteristic length. We will see below that the
mfps in the F and N metal layers do not play the same fundamental role in the CPP-MR,
which has the property described below of being "self-averaging". We note in passing
that Zhang et al. have argued that the mfp does not play a fundamental role in the MR of
granular alloys either; the MR in these alloys is "self-averaging" in a somewhat more

complex fashion than the CPP-MR. [25]

3.3.2 CPP Magnetoresistance

3.3.2.1. Historical Review

The first analysis of the CPP-MR was made by Zhang and Levy, who adopted to
this geometry the quantum Kubo model that they had developed for the CIP MR.[151]
They assuming no-spin flip scattering and analyzed data in two magnetic states, one with
the magnetizations of adjacent layers parallel (P) and the other anti-parallel (AP). They
found the CPP-MR to be "self-averaging"--i.e., the averaging of the position dependent
resistance removes the length scales set by the mean free paths, and, unlike the CIP-MR,

48

the elastic mean free paths are no longer characteristic lengths in the CPP geometry. This
self-averaging leads to a simple, two current, series resistor model in which the layer and
interface resistances for a given spin direction are added in series and then the resistances
for the two spin directions are added in parallel. They predicted that the CPP MR should
be systematically larger than CIP MR.

Our group next combined the ideas from Zhang and Levy's analysis with our own
first CPP-MR experimental results described in chapter 1, to develop a phenomenological
model of the CPP-MR which we describe in section 3.3.2.2 below.

When Zhang and Levy tried to fit our first Co/Ag CPP- and CIP-MR data
simultaneously, they found that they obtained ratios of the CPP-MR to the CIP-MR that
were too small. To try to remove the discrepancy, they introduced a third magnetic state,
a superposition of statistically uncorrelated (SU) magnetic configurations that satisfy the
condition 2 M ,- = 0. (Mi is the magnetization of the individual F layers).[138] Since the
thicknesses of our Ag layers were so large that exchange coupling between the F layers
should be weak, they argued that the M = 0 states of our samples were more likely to lie
closer to SU than to AP. They also argued that, because it is independent of the
electronic mean-free-paths, the CPP MR should be same for the AP and SU states. In
contrast, the dependence of the CIP-MR on the electronic mean-free-paths should make it
smaller in the SU state than in the AP state. Ratios of the CPP-MR to the CIP-MR for the
SU state should thus be larger than those for the AP state, improving the agreement of
their predictions with our data. Camblong, Zhang and Levy0 subsequently argued that the
condition of Z M ,- = 0 should uniquely determine the CPP-ARffi’. We will see below
that our data do not seem to confirm such a simple result.

Up this time, all CPP analyses had assumed that the spin directions of the electrons

were conserved as they crossed the multilayer (i.e. that there was no spin-flip scattering).

49

Valet and Fert (V F)[138] first examined the effects of such scattering on the CPP-MR,
making two important contributions. First, they showed how the two current series
resistor model arises from the Boltzman transport theory when spin-flip scattering is
absent. Second, they extended the two current model to the case where spin-flip
scattering is present, but still does not mix currents. Because of its importance for the
analysis of some of our data, we describe the VF results below in some detail. Here I just
briefly discuss the important concept of the spin-diffusion length that is essential to the
theory of CPP-MR with spin-flip scattering. Assume an isolated interface separating two
semi-infinite domains with opposite magnetizations, and a current flowing perpendicular
to the interface. With spin dependent resistivity, the currents of spin up and spin down
channels are not the same. To make the chemical potentials continuous at the interface
for each spin channel, net spin accumulation for each spin channel occurs at the interface.
The spin accumulation is relaxed by spin flip processes over a length called the spin
diffusion length. This effect gives rise to an extra potential drop "at the interface" and
thus to a boundary resistance.

Soon thereafter, Camblong, Zhang and Levy[23][25] also examined effects of finite
spin-flip scattering in terms of the spin mixing length lsma the distance over spin-flips
mix the two currents. When lsm is much longer than the elastic mean free path, he], the
simple two current, series resistor model applies. If, however, lsm z A ( thickness of
bilayer) and the condition of lsm >> 161 is not satisfied, then the two currents will mix
and the CPP-MR will be reduced.

Next, following Hood and Falicov's analysis of the CIP-MR, Levy et al. [79]
studied the role of spin-dependent potentials in both the CIP- and CPP-MR. They showed
that spin-dependent potentials can change the GMR from its value due just to spin-

dependent impurity scattering. When they neglect spin-dependent impurity scattering,

50

the CIP-MR due solely to spin-dependent potentials is zero, but the CPP-MR is non-zero.
More generally, the effect of spin-dependent potentials can be significant on the CPP-MR
geometry, but usually only gives small corrections to the CIP MR. Barnas and Fert[9]
also studied effects of spin-dependent potentials, concluding that the available CPP
measurements of the interface resistances for Co/Ag and Co/Cu suggested that effects of
spin-dependent scattering and spin-dependent potential steps might well be comparable.

The systematically larger value of ARt for our uncoupled samples (t Ag 26nm) at
Ho than at Hp described in section I is difficult to understand if each Co layer is a single
domain. Zhang and Levy[152] recently examined possible effects of magnetic domains
on GMR, and concluded that the presence of finite domains in a given F-layer can
produce spin diffiision that affects the spin-accumulation in the CPP geometry and
reduces the MR. In the simplest case, the AR of a multilayer in the AP state with infinite
lsf and finite in-plane domain size D is equivalent to that for a multilayer with single
domain F -layers and a spin-diffusion lsf = D/fi. Of possible significance for the issue
of R(Ho) vs R(Hp), they found that finite magnetic domains can make the CPP-MR of
the SU state smaller than that of AP state.

Some theoretical studies have also been made by other groups from different points
of view to try to better understand the differences between the CPP-MR and CIP-MR.
Maekawa's group[5][68] used a single-band-tight-binding model with a periodic potential
along one dimension, and the Kubo formalism, to examine effects of interface roughness,
layered structure, and spin-dependent potentials on the CIP and CPP conductances. In
agreement with previous work, they found the CPP MR to be larger than the CIP MR.
Their most important result relevant to experiments is that they predict that the CIP MR
should increase with increasing interface roughness (assumed to generate spin dependent

scattering), but the CPP-MR should decrease with increasing interfacial roughness.

quaurur
number
mimau
formula
interfac
superb
Subseq
approx:

be com

derclo}
multila
luterfar
bull; a1
regions
lal‘rSlng
aflllysi
5‘93] Cl.
gained
‘0 bra
underlr

lu‘lmm

Usual“

51

Based on the Landauer-Buttiker formalism, E.W. Bauer et al.,[ 17] made another
quantum approach to CPP transport. In their work, the conductance is proportional to the
number of the conducting channels in the structure, and the number of the channels were
estimated for different magnetic states. In their first paper, they derived a simple looking
formula in the absence of spin-flip scattering that included effects of contact potential,
interface roughness and bulk impurity scattering in its parameters. In the large
superlattice limit, their results agreed with those from the Kubo formalism.
Subsequently, using parameter-free calculations based on the local-spin-density
approximation, they found in the ballistic limit[105] that their calculated CPP-MR5 could
be comparable to experimental values, even without defect scattering.

Lastly, we note that H. Camblong[26] has used the real-space Kubo formula to
develop a "non-local" quantum theoretical framework for studing treansport in magnetic
multilayers in the limit of infinite spin-diffusion length. In the Hamiltonian, bulk and
interface scattering are both treated in terms of spin-dependent local potentials. To handle
bulk and interface scattering together in a consistent way, the interfaces are treated as
regions of interdiffusion (alloying). Instead of using a single average mean free path
(arising from the average scattering) as was done in the previous k-space
analysis[77][150] [24], he was able to use separate mean-free-paths in each layer for each
spin channel. Important results of his analysis include the following: (1) some insight is
gained into the regimes where quantum corrections to the Boltzmann equation are likely
to become significant; (2) for the CIP-MR, some new insight is gained into the physics
underlying the parameters used in the previous classical analysis; in particular, the
quantum transmission coefficients analagous to the classical ones used by Camley and
Barnas (ref) are inherently angular dependent; (3) for the CPP-MR, the analysis yields the

usual two-current, series resistor model.

52

3.3.2.2. Phenomenological two-current, series resistor model.

To allow information about spin-dependent scattering in the bulk F-metal and at
F/N interfaces to be extracted from CPP data, Prof. Pratt of our group developed a set of
parameters and formulae based upon the two-current, series resistance model.[73] The
electrons are divided into two channels, up(+) and down(-) relative to the direction of the
applied field H. Spin-flip scattering is assumed to be negligible, so that (+) and (-)
electrons carry current independently.[132] The series resistor model is applied to each

electron channel separately, using the following definitions:

 

 

 

T_2PF
pF—1+B
l_2PF
PF-1_B
RT =2RF/N
F/N 1+y
L 2RF/N
R .—
F/N l—y
911v=P1lI=ZPN

T Jr
RS/F = RS/F = 2RS/F

Here p; is the resistivity of an F layer when the electron spin and the local Mi are parallel
to each other, p; is the resistivity when they are antiparallel to each other, and RIM,
and Rim are the equivalent resistances at the PIN interfaces. p F and p N correspond to
the F- and N-metal resistivities measured on independent thin films.
RE”: = Rém = 2R5”: where assume that the transmission of electrons from the

superconducting Nb to the multilayer and vice-versa is independent of electron spin

orientation. 2R5, F is independently measured on S/F/S sandwiches.[40][41][42][125]

\llre

channels. r

( 4

ARI

Beca'

mill ART

ARfl
“tel? p; :
.the relatio

“her

fifieremtly,

AR"

AR“

53

When the samples are in the AP state, with equation(3.2) applied to (+) and (-)

channels, we have:

1- N T N N
AR(T+)(AP)= ZARS/F+_ 2 PF’F‘f; Pra’rvr‘gprttrv

N N
+‘2—‘2AR2/N +32ARF/N JV

2 2
=4ARS/F+'1—_- [32 2_MthF+2NpNtN+1 ZNZARF/N
‘72

=AR¥RAP)

Because the resistances of these channels add in parallel, ART is just half of the
equal ART values for (+) and (-) channels:

ART(AP)=2ARS,F+Np;rF+NerN +N2AR;,N (3.1)

where p}.- = pF /(1— B 2) and R},N = Rpm /(1—y 2). Thus, for either fixed tF or t1: =tN
, the relation of ART versus N still give the same straight lines predicted by equation
(3.1), with the parameters p F and RF, N simply replaced by p].— and KEN.

When the samples are in the P state, spin up and spin down electrons behave

differently. Here, adding their resistances in parallel and rearranging yields:

AR(+)(P) = 2.419;, F + NplrF + prvtN + N2ARI~W

2 2
=4ARS/F+2NpNtN+1 NthF+1+y NZARF/N

+ B
= 4.4125,,r + 2NpNtN + 2(1— [5 )Np;tp + 4(1—r )NARir/N
AR“)(P) = 4ARS,F + zrvat,V + 2(1+ r3 )Np;tF + 4(1+y)NARj.—,N

ARA

lhe quantir
right side c
the other ;
ARgpequaIi

The :
multilayers
lllllllllayers
amuoh Sm
Hu- past 2
given Simr
dour], POI
themuoua

F or 2

Spin direcri

Are-4

54

[BNPFIF +Y 2NAN/and2
ART(AP)

 

ART(P) = ART(AP)— (3.2)

Rearranging terms we get the important relationship:

 

AJRrAlezAP " RtP] = BPF’FN + ZYARF/NN (3-3)

The quantities in the left side of equation 3.3 can be measured in our CPP samples. The
right side of the equation is independent of the resistivity of the normal metal p N, and
the other parameters [3, y, p} and R2”, can be found from fitting to the AR,” and
AR,P equations. These parameters will be described below.

The simple two current model can also be applied to three-component F1/N/F2/N
multilayers. Here an AP state can be produced more easily than in two-component
multilayers by choosing F l to have a relatively large saturation field, H31, and F2 to have
a much smaller saturation field, H52. With such a sample, reducing the applied field from
H31, past zero, to a negative value just beyond -H32, should give an AP state. ARt is then
given simply by a parallel combination of the AR's for electrons with spin up and spin
down. For CPP data, AR is, in turn, a series sum of the AR's for each of the interfaces in
the multilayer plus the resistivities times layer thicknesses.

For a multilayer with N layers of Co/Cu/Py/Cu (Py = Ni34Fe16), AR for the up (+)

spin direction and the AP state is :

ARAPH) = 4ARNb/Co + 4NPCu’ Cu + (N +1)pg‘otCo
+2NAR§0,C,, + Np ,iyr P}, + 2NARfiy,Cu (3.4)

55

ARAPH = 4ARNb/Co + 4N pCutCu + (N +1)pé‘otCo
+2NAR$NCu + Nplyrpy + 2NARI.,,C, (3.5)

Substituting in the definitions above gives ARAP(+) as a function of B and y. ARAP(') is
found by replacing T by t and vice versa in equation (3.4). Similar expressions can be
written for ARP(+) and ARP(') , and AR,” and AR,P are then parallel combinations of
the appropriate (+) and (-) components. It is important to notice that, unlike the case for a
two-component system, ARAP(+) is not equal to ARAPH.

In our analyses below, we will need parameters for Co/Ag, Co/Cu. and Co/Py
multilayers. The parameters we use for Co/Ag were derived by S.F. Lee using a global
fit procedure describe elsewhere.[71] The best values for Ho and Hp are given in

columns 3 and 4 of Table 3.1. One should notice that the values of ZARNb/Co and p Ag

derived for both Ho and HI) agree with the independently measured ones in column 2 to
within mutual uncertainties, and the new values of p50 and AREO, Ag for H1) are only
about 20% less than those for Ho.

The parameters we use for Co/Cu and Co/Py were derived by me from data of P.

Holody (unpublished). They are listed in Table.4.4.1 in chapter 4.

56

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Independent Ho(4 sets) Hp(4 sets)
Measurements
ZARNb/COU‘QmZ) 6:1 69:06 73:06
pAg(an) 10:1 73:19 10.9:1.9
pC0(an) 68:10 77:12 77:34
p5,,(an) 100:6 84:6
[3 C0 0.48:0.06 0.29:0.06
(1C0 2.9:04 1.8:04
AREO/ Ag (mmz) 0.60:0.02 0.45:0.02
ARCo/Ag(mm2) 0.18:0.02 0.15:0.02
Y Co/Ag 0.84:0.04 0.32:0.05
aeo/ Ag 115:; 10‘:4

 

Table 3.1 Two-current model parameters for Ho (column 3) and Hp(column 4).
Column 2 contains the three parameters that can be independently measured.

 

57

To summarize our present understanding of characteristic lengths in GMR, there
are three such lengths. EF (1) The first is the elastic mean free path, he], for momentum
transfer that appears in the electrical resistivity for a metal or alloy. We define one of
these for each F or N constituent of a multilayer. )5 and A5 are the primary
characteristic lengths in the CIP-MR; (2) The second is the spin diffusion length, 13f ,
which specifies the distance over which spins flip, but no momentum is transferred, and
therefore currents do not mix. We also define one of these for each F and N metal layer,
3:} and {1;}, and they are the characteristic length for the CPP-MR. If 8:} and (2} are
much longer than he"; and 19A,, , then there is no characteristic length in the CPP-MR, and
the 2-current, series resistance model is applicable. (3) The last is the spin-mixing length,
lsm, over which the two currents are mixed by scattering that both flips spin and
simultaneiously transfers momentum. At the low temperatures at which we make
measurements, lsm is expected to be so long that it can be neglected for both the CIP— and
CPP-MR3.

As this discussion indicates, the basic limitation of the simple two current, series
resistor model is that the spin diffusion lengths must be long. We conclude our

discussion of CPP theory by examining the VF model with finite spin diffusion length.

3.3.3.2. Theory of CPP MR with spin-flip scattering

The generalization of the two-current, series resistor model to the situation where
the spin diffusion lengths are finite was made by Valet and Fert.[138][137] To simplify
their analysis they assumed that both metals had: (1) simple parabolic conduction bands,
(2) the same effective mass m, and (3) the same Fermi velocity VF, but it is believed that
their conclusions are not limited by these assumptions. Their analysis takes into account

both volume and interface spin dependent scattering, but is limited to low temperature,

where ele
spin-orbit
Boltzman
to *he spi
of the mf
at sucees
potential.
each lay:
accumul:
thickness
lWO cum
diffusion
Change t
bWeen

He

58

where electron-magnon spin-flip scattering is frozen out and spins are flipped only by
spin-orbit or exchange scattering on defects and impurities. They first showed that the
Boltzmann equation for a multilayer reduces to macroscopic transport equations so long
as the spin diffusion length is much longer than the elastic mfp, independent of the ratio
of the mfp to the layer thicknesses. Then, matching solutions to these transport equations
at successive interfaces, they solved for the steady state spin dependent electrochemical
potential, the spin-dependent electric field, and the spin dependent current densities in
each layer. Requiring the currents to be continuous across the interfaces leads to spin
accumulations at the interfaces. In the long spin diffusion length limit, where the layer
thicknesses are much smaller than the spin diffusion length, the equations reduce to the
two current, series resistor model discussed in the previous section. However, if the spin
diffusion lengths are comparable to the layer thicknesses, the conduction electrons will
change their spin directions as they pass through a given layer, reducing the difference
between ARt(Ho) and ARt(HS) for their values for infinite spin-diffusion lengths
Here, the VF model gives the generalized equations: [137][138][133}

(P, AP)

 

 

R(P 4”) — ..N(rO +2rS, ) (3.6)
Here ro = (1— B )p; + pm +2rl—y 2m; (r; = ARM). (3.7)
2 2
93 -3-7) —co th[—— N ]+ Y F coth[——— F ]+ p—
(P): pN€SIth21fo1pFKSf 2(sf rb
’51 1_1'1‘1

 

 

 

 

(3.8)

(AP)
’51

131‘
.(._4

Been
predictions
use too se
other with
shoon in |
and [9

more sensi

gellifiC'ctrrr

 

2 2
I
(B Y—————)——N ~——~———tanh[tN ~1+ Z F coth[—-——-—FF]
(AP) 194/st 2‘ f PF sf 23.;

 

’SI=1

 

 

 

anh—IL[ N] co oth[—— F]+—[ —t%—]+—l——coth[—£f— F]]
pNelt/fst 263/ pFlsgf ZKSf rb legSf 2165/ p ngf 26f

(3.9)

Because of the complexity of these equations, it is most instructive to examine their

predictions graphically for a range values of (N sf, (F f. To illustrate what one expects, I
use two set of samples (1) one with t}: = 6nm, total thickness tT = 720nm, and (2) the
other with tF= tN, tT= 720nm. The results for samples ( 1) with varying (N sf and [F sf are
shown in Figs. 3.1 and 3.2, respectively. The results for samples (2) with varying 3N sf
and [1} are shown in Figs. 3.3 and 3.4. We note that the predictions are much

more sensitive to (N f than to [F Sf. That rs, it takes much smaller values of [F f to produce

significant deviations from the two-current, series resistor straight lines.

.33.:

\114

N .

__ I: :...:<

7; :9: /.. 2 ca \ 5:: 3,;

Figllrr

..ig
"sf :1.

s

Val Uec

60

 

 

 

 

l

 

 

 

4.0 60 80
Bila‘yer' N0. N

F igure3.2 J[AR,(HO)—AR,(HS )]AR,(H0) vs N. The solid line is calculated for
3 fig =€Sf°=oo. The dash curves are calculated from VF theory for the indicated

values of 3:}, with (Sf: .

 

61

 

 

 

 

   

 

 

.L 1

4O 6 O 8 O
lillayer NO. N

 

Figure3.3 J[AR,(H0)-AR,(HS)]AR,(H0) vs N. The solid line is calculated for

€3f=13$=om The broken lines are calculated from VF theory for values of

3 $=3nm (top), lnm (middle), and Onm (bottom), with Eff =00.

62

 

“2 80 , 4
o o 4

4

N

 

C:
Lo—r
v
(\2
\
r——'t
A
Ur
p—T—q
P—‘-"l
v
E—*
G:
<2
1 ,
A -
o 40 3
l—r—i
P-‘-'l
V
E-1
D:
<
/"‘\
O
p_.__4
4L4
V
C—
9:;
<3
L—_.J

 

" LL __: :1: l l 1 i 4 l i

 

 

O 4o so so
Bilalyel“ No. N

Figure 3.4 J[AR,(H0)— AR,(HS )]AR,(H0) vs N. The solid line is calculated for

e§=eff=oq The dash curves are calculated from VF theory for the indicated

 

values of ff)? , with ($200.

63

 

 

 

 

 

 

,4- 74* l l
A T
or ,

E 80 7‘ F
A; F _ . I) . ,- ‘1 l q
t. . 1,,CO4tAg 71:,Ollllr

V

1

Q? r l
:1: 60 1" F
:3) t a
1.1.4 r

V _ J

E_.

cc;- 1
< t

I .
”540+— 7
1'7"" 4
C

E—‘ F '1
'14 t

<13 1

if: t

O

: Z10 [ —q
j l ////

Q: l ////

4: L//// 4
1__—J '

h
0 L1 , . 1 . : L.

F“)
x.)

2o 4o (n) so
jlsya oo>;N

Figure3. 5 J[AR, (Ho )-AR, (HS )]AR, (H0 ) vs N. The solid line is calculated for

(Ag f— =€Co f=oo. The broken lines are calculated from VF theory for (top to bottom)

8S;=12nm , 6nm ,3nm, and Onm, with 8:33 =66.

 

64

As we noted above, Equations 3.6-3.9 are strictly only valid for (1le >> kel-
.[137][138] Valet[139] has extended the analysis to second order in >43 M5,, and found

a correction terszZSKQIIOQ,’ miff). Further analysis must show if such a simple

correction holds to all orders.

4.1

funk

ate:

Stud

and

‘v‘alit

Pair

CHAPTER 4

DATA ANALYSIS

4.1 Introduction

This chapter consists of four subtopics of CPP MR research. Three are intended to
further test the two-current model described in the previous chapter and the fourth
extends CPP measurements to a new metal pair.

(1) We further test effects of a finite mean free path in the normal (N) metal by
studying a series of samples with equal but varying Co and AgSn thicknesses.

(2) We combine data on Co/AgMn and Co/AgPt multilayers with the theory of Fert
and Valet to, for the first time, isolate effects of finite spin diffusion lengths on GMR.

(3) We use three component multilayers: (a) to make a new quantitative test of the
validity of the two current model; and (b) to provide an additional check on using the Ho
state as the AP state.

(4) We measure the CPP- and CIP-MRs of Ni/Ag multilayers to explore a new MR

pair and as preparation for "interface dusting" studies.

65

66

4.2 Giant CPP-Magnetoresistance of Co/AgSn
Multilayers

S.F. Lee[7l] tested the effect of reducing the elastic mean-free-path xel in the
normal (N) metal layers by adding 4 at.% Sn to Ag to make AgSn alloy spacer layers and

studying multilayers with fixed tCo = 6 nm and fixed tT = 720 nm. Most importantly, he
found that the quantity J[AR,(H,) — ART(H_,)]ART(H0) is independent of the

 

resistivity of the spacer layer, as expected from Eq. 3.3.

In this thesis I make fiirther such tests, using samples with tCo = t AgSn and fixed
t1 = 720 nm. Because of the lingering uncertainty over the use of ARt(I-Io) as an estimate
of A114“), as well as modest deviations from expectation for the form of data with tCo =
t Ag found by S.F. Lee,[7l] we felt that it was important to check that data for samples
with tCo = t AgSn also fall along a common curve with data for tCo = t Ag as predicted by
the two-channel, series resistor model. In this section, we examine four different sets of
data: (1) We compare our AR, data for Co/AgSn with predictions from the two-current
model using parameters previously derived by S.F. Lee.[71] (2) We compare the ratio H =
LJRGIO)/I\'IR(HP) for Co/Ag and Co/AgSn to check that it isn't much changed by adding
Sn impurities. (3) We compare data for samples grown on sapphire and on Si to check
that a different substrate doesn't significantly change the behaviors we see. (4) We test

whether the Co/AgSn data follow the prediction of Eq. 3.3 and fall on the same curve as
for Co/Ag when we plot the square root quantity, J[ART(H0) — ART(H, )]ART(HO) , as

 

a function of N. The detailed data underlying these studies are listed in Tables 4.2.1 and
4.2.2.

To avoid proximity effects in the N layers, the first and last layers are Co at least 3
nm thick.[125] Most samples thus consist of two Nb strips, the multilayer starting with

Co, and a "cap" Co layer just below the top Nb strip. To check if different substrates or

67

absence of a cap layer made any significant difference, one set of samples was deposited
on Si substrates without a cap layer.

We use the following two current model equations Eq. 4.2.1 and Eq. 4.2.2 to
analyze our data at Ho and HS, respectively. For our specific set of samples with

tF=tN=tT/2N, the general two channel model equations 3.1 and 3.3 reduce to:

1 t 1 t It
ART(H0) : ZARNb/Co +§(pCo + pAgSn )IT +fi pCotT + NZARCo/AgSn (4-2-1)

 

tT(N+1)

JIART(H.)— Mama/1mm.) = ape. 2N

+ N7 2ARE'o/AgSn (4-2-2)

 

Since the quantity J[ART(Ho)—ART(HS )]ART(H0) does not depend on the

resistivity of the spacer layer, the two channel model predicts exactly the same behavior
for pure Ag and AgSn samples.

Fig.4.2.1 compares the AR, data for the samples made on sapphire substrates with
the predictions of the two current model using the parameters determined for Co/Ag from
a global fit by S.F. Lee, except that the resistivity of pure Ag is replaced by that of
p A85" = 185i 1 Inflm for AgSn. The data are consistent with the predictions of the two
current model. The AR, data for samples made on Si substrates are also reasonably
consistent with those on sapphire substrates (see Tables 4.1.1 and Table 4.1.2), but it is

more convenient to consider these data in detail below in the forms of AR,(H0) - AR,(HS)

and J[ART(HO) — ART(H, )]ART(H0). We shall see there that the substrate material is

 

not crucial to our results.
Figure 4.2.2 compares the ratio II for Co/Ag (open symbols) and Co/AgSn (filled
symbols). We see that H for Co/AgSn fluctuates mostly around 2, which agrees with the

behavior of IT for Co/Ag. The similar behaviors for Co/AgSn and Co/Ag suggest that

with a
both 5
model
pure .1
and or
two c1
that th

have It

applies

TfSlStix

68

adding impurities does not significantly change the relationship between AR,(HO) and
AR,(Hp). We thus focus our attention in the following to the behavior at Ho.

Fig.4.2.3 shows ART(Ho)-ART(HS) versus N for AgSn deposited onto sapphire
with a cap layer (filled circles) and onto Si without a cap layer (crosses). We see that

both sets of data agree well with each other and with the prediction from the two-current

model (solid curve. Fig.4.2.4 compares J[ART(HO)— ART(HS )]ART(H0) versus N for

 

pure Ag (open circles) with AgSn deposited onto sapphire with a cap layer (filled circles)
and onto Si with (+) or without (x) a cap layer. The solid line is again the best fit from the
two current model using parameters determined with global fit by S.F. Lee. Here we see
that the data for both Co/Ag and Co/AgSn fall on the same curve, although Ag and AgSn
have resistivities that differ by a factor of 20.

We conclude that our new Co/AgSn data provide fiirther support for the
applicability of a simple two-current model to CPP data on samples with a wide range of

resistivities in the N metal.

69

 

 

 

 

 

250 _ .
A 200 ;
E :
g 150 .
E 100 :— *1
E-‘ , J
as : <
50 f T.
L -<
O l nil a .l l i i
0 2o 40 6O 80 100

Figure 4.2.] Global fit of [Co(t)/AgSn(t)]XN samples for Area times CPP
resistances at Ho, and HS. All samples have total thickness 720nm.

 

l ' l ' l

B? I

2 O O 5

\ 2* 0 ° 0 . ‘
O o 0

r3 8 o

E O o

o:

E O

H .

C

tCOZtN Co/Ag <> : tT:720nm
Co/Ag O : tCo=tAg=6nm
Co/AgSn 0 : th720nm
O _L l m l t l
O 20 4O 60

N

Figure 4.2.2 II = CPP-MR(Ho)/CPP-MR(HP) versus bilayer number N for Co/Ag
and Co/AgSn samples.

 

 

 

Figure

53mph

A..._~.~..uhy

A

2...:.<<:.....CZ< AleeEt
”\—

sample

7O

t’Co-——tAgSn(nrn)

£92942,8,2§..,,

 

 

 

 

(\f—\ 4

E t X on Si, without Co "cap" .

E 60 *- /

’33 [ff/

:2 » / .

\g 40 f ‘ fl.

Of.

<3 + O

| . ‘

A %_ fl

3:3 20, ‘

QE— '\/. /<

<3 0* . . . l . . . l . . . 1 . .4 l .4 .
0 20 4O 60 80 100

N

Figure 4.2.3 ART(Ho)-ART(HS), versus N for [Co(t)/AgSn(t)]XN samples. All
samples have total thickness 720nm.

tCoztAgSn(nrn)
50 20 12 8

 

 

 

 

 

a? 150 . . , . , . , . . . I . . . , .

g E O: go/Ag .
t: 125 E 0: CEO/AgSn 7
a : >< : on Si, without Co "cap" /1
:2; 100 — + : on Si / 4.
E '75 A
e? E 3
of: 50: fl
E 25: 7
BE i
:5. ~ 1 J
v O 1 1 i 1 1 1 l ‘ 1 1 l l 1 L 1

o 20 40 so 80 100

 

Figure 4.2.4 J[ART(H0) — ART(H,. )]ART(H0) versus N for [Co(t)/AgSn(t)]XN
samples. All samples have total thickness 720nm.

Here, 1

 

 

 

 

 

 

 

 

 

.1»: I‘m l1. “‘5 I4. — ll~_ I1x~ l1._ ‘~hi .‘.l~ Q‘sg

mu gnu. m." m m. m ML (no; i 3. N in.
A}. an... 8 fire 1;. oh. al....

6f 6 n._ 9 ll ill I“ 6 at. l 1 71

Table 4'

Sample

Withou

Here, I will present CPP and CIP data for Co/AgSn(6%).

71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t N sample CPP AR (me2) CIP(Q'1) 11
nm .no. H0 Hp 11. Hn H9 Hi

6 60 353-01 187.2 166.9 151.4 0.2347 0.2394 0.2423 2.31
6 60 369-01 208.3 185.0 167.9 0.2033 0.2062 0.2082 2.36
7.2 50 369-07 170.7 158.7 144.4 0.2583 0.2589 0.2610 1.84
9 40 353-07 148.9 139.3 127.9 0.2628 0.2652 0.2675 1.84
12 30 353-05 140.5 133.5 125.1 0.3018 0.3031 0.3050 1.67
18 20 353-06 120.8 116.8 112.8 0.3062 0.3068 0.3082 2.03
4 90 32907“ 203.3 174.1 149.7 0.2189 0.2200 0.2260 2.20
6 60 32901* 202.9 180.0 165.9 0.1783 0.1791 0.1804 2.62
7.2 50 329-04” 167.8 158.4 141.1 0.1527 0.1533 0.1546 1.54
12 30 32903" 134.4 134.3 126.6 0.2869 0.2870 0.2883 1.02
15 24 32902“ 135.9 131.1 125.5 0.2938 0.2941 0.2951 1.84
7.2 50 36605# 180.8 166.2 149.7 0.2230 0.2261 0.2298 1.89

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.2.1_CPP ART and CIP values at H0, HD and HS of [Co(t)/AgSn(4%)(t)]xN
samples. Total sample thicknesses are as close as possible to 720nm.(* Si substrate,
without Co cap layer, # Si substrate with Co cap layer)

72

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t N sample CPP MR% CIPMR% error [(ro-rs)ro]l/2
nm . no. H0 H9 H,l H9 %
6 60 353-01 23.6 10.2 3.2 1.2 3.4 81.86
6 60 369-01 24.1 10.2 2.4 1.0 2.9 91.7
7.2 50 369-07 18.2 9.9 1.0 0.8 3.7 67.0
9 40 35307 16.4 8.9 1.8 0.9 1.4 55.9
12 30 35305 11.2 6.7 1.1 0.6 3.2 46.5
18 20 35306 7.1 3.5 0.7 0.46 4.7 31.1
4 90 32907‘ 35.8 16.3 3.2 2.7 2.8 104.4
6 60 329-01* 223 8.5 1.2 0.7 2.3 86.64
7.2 50 329-04“ 18.9 12.3 1.2 0.8 2.6 66.9
12 30 32903“ 6.2 6.1 0.5 0.5 2.2 32.2
15 24 329-02" 8.3 4.5 0.4 0.3 2.7 36.9
7.2 50 366-05# 20.8 11.0 3.0 1.6 3.9 75.0

 

 

 

Table 4.2.2 CPP MIL CIP MR and [(ro-rs)ro]l/2 values at H0, and H of
[Co(6nm)/AgSn(4%)(t)]xN samples. r0 and r8 are ART at H0 and 11:.

Total sample

thicknesses are as close as possible to 720nm.(* Si substrate, without Co cap layer,

# Si substrate, with Co cap layer)

4.3 5
Tem

C0141
length
(MM
and E
11106

the f1

cs;

73

4.3 Spin Flip Diffusion Length and GMR at Low
Temperature

In this section we describe measurements of the CPP-MR of Co/AgMn, and
Co/AgPt multilayers designed to see if we can isolate the effects of reduced spin diflirsion
lengths due to alloying of the nonmagnetic metal with impurities that produce spin-spin
(Mn) or spin-orbit (Pt) scattering. If so, then combining the data with a theory by Valet
and Fert should give the spin difiirsion lengths in alloys. Such measurements not only
provide a test of our qualitative understanding of the CPP-MR, but would also represent
the first direct determinations of spin-diffusion lengths.

The basis of our analysis is Eq.3.5, in particular, the fact that for samples with fixed
t1: the Right-Hand-Side (RHS) of this equation is independent of the resistivity of the N
metal (pN). That is, a plot of the experimental square root on the LHS of Eq.3.5 versus N
should give a straight line passing through the origin with slope independent of pN. In
such a case, alloying a host metal (such as Ag) with impurities that simply scatter electrons
elastically should not give any deviation from this universal line, as has been previously
shown to be true for AgSn.[73] If, however, the added impurities flip the spins of the
electrons, then the LHS should decrease more rapidly with decreasing N than the universal
straight line, and the deviation from the line should provide a measure of the spin-
difl‘usion length, 6:}. It is these deviations that we search for, and that we compare with
the theory of Valet and Fert (VF) described in chapter 3. To fully test our method of
analysis, we apply it to Ag with both a magnetic impurity (Mn) that reduces 81;} by spin-
spin scattering, and a nonmagnetic impurity (Pt) that reduces 8);} by spin-orbit scattering.
We also examine two different concentrations of Mn in Ag

The organization of this section is as follows. (1) We compare values of AR,(H) for

Co/Ag, Co/AgSn, Co/AgMn multilayers with fixed tCo = 6 nm to see if there are any

74

qualitative differences in behavior that might cause us problems. We'll see that the
behaviors are similar in all three cases. (2) We compare ART(HO) and ART(HS) versus N
for Co/Ag, and Co/AgSn, Co/AgMn, and Co/AgPt to again look for any qualitative

differences. Again, we find none. (3) We use plots of the Square Root
‘[[ART(Ho)—ART(H,)]ART(HO) versus N to derive values of rig} for AgMn(6%),

 

AgMn(9%), and AgPt(6%) fiom data on samples with fixed tco=6nm. We will see that
the results obtained are surprisingly similar to independent estimates. (4) As a first
independent check on this analysis, we similarly analyze Co/AgMn(6%) samples with fixed
tCo=2nm. (5) As a second independent check, we similarly analyze samples with tCo=tN-
(6) Lastly, to evaluate the sensitivity of our values of (N ,f to alternative choices of the AP-
state we use AR(Hp) instead of AR(HO) in the square root and perform the same analyses
as in (3) and (5). In section 4.3. 1, we concentrate on graphical analyses. The complete

data for all samples are given in Tables in section 4.3.2.

4.3.1 Effects of Finite Spin Flip Diffusion length

In chapter 3, we described the Valet and F ert theory that can be used to analyze
deviations from the universal straight line of Eq 3 6- 3 9 when [N f is finite, and thereby

derive values of (Nf.[137][138] We show VF predictions m Figure 3 1 for a range of

values of KN f. For convenience we reproduce those equations here.

 

R(P AP) -_—N(rO +2rS “’ ,A”)) (4.3.1)
Here r0 = (1‘ '52 )PF + PN’N + 2(1—7 2)’1:-(r1:= ARF/N) (4.3-2)
2 2
(’3 7)or111t[——’N—]+———7Footh[——’;—]+fl
(p) Pngrf 2[sf lPF‘rf zgsf ’b (4 3 3)
r8] = l ' '

 

 

 

 

l
coth[— N] co—tE—th[ F]+ -—[ coth[N N ]+ . coth[i— F]]
pNZN Sfco 2£3f pplgsf 26F 3f V), pN 1612.} 26 sf pp [©- 2651'

indept

the id]

75

 

 

 

(_______fl- -7)2 72
—————tanht’” 1+ . cotht— 1
rgfph 1 1”ng ”if, ”ff if); 1 I (4.3.4)
tanht—L— 1— cotht—‘f— 1+ —.1 t N 1+ . .- coth[—F711

pNgsf 2€sf ngcho zgsf Vb roll/(sf 2(sf ngsf 2(sf

Table 4. 3. 1 contains the parameters that we will use in this analysis, along with

independently estimated values of 65/ to compare with those we derive. The captions to

the table explain how the estimates were obtained.

 

 

 

 

 

 

 

 

 

 

 

 

Metal or Pf] P67 32A; 33/, 81:}
alloya (numb (mm)c (mod 01m)e (um)f
AL 9il 85 zl7000 2:500
AgSn(4%) 190 200120 4.4 4950 ~26
AgMn(6%) 100 1102125 8 leO ~12
AgMn(9%) 150 155220 5.6 490 a9
_AgPt(6%) 90 110:1 9 ~32 4.7

 

Table 4.3.1 Estimated parameters for Co/Ag, Co/AgSn, Co/AgMn and Co/AgPt.

a Impurity concentrations are in atomic %.

b Calculated from intended impurity concentrations and known resistivities per atomic percent

impurity.[l4]

c Measured on sputtered 300-500nm thick films. The uncertainties are the largest deviations from the

average values.

d Calculated from p X; ( pg} for Ag ) and free-electron equations.[6]

 

76

e it; for AgPt was calculated from a free-electron conversion of ESR cross sections.[85][53] The AgMn

estimates were made by Fert[38] from available information about exchange coupling in these alloys. The
AgSn value assumes a cross section (3/4)2 of that for Ang in Ref.21 of Ref. [85]. The sputtered Ag value

assume defect contents zl% and spin-orbit cross sections z lxlO'18 cm2.

WC} = ,l(1§,’2§,’)/6.[137][138]

To avoid complications of changing magnetic coupling between neighboring Co
layers as tN varies,[107][96][97][87][90][84] we limit ourselves in the present study to tN
2 6nm, where any coupling should be weak. From the x-ray analysis and magnetization
measurements presented in Chapter 2, we conclude that the presence of impurities does
not change either the lattice structure or the magnetic structure of the host metal enough
to invalidate our analysis of these alloy-based multilayers. If coupling is indeed weak as
we expect, then we should find similar behaviors of ART(H)-ART(HS) for both Co/Ag
and all of our alloy-based multilayers. Figure 4.3.2 compares this quantity for selected
Co/Ag(6nm/6nm), Co/AgSn(4%) (6nm/6nm) and Co/AgMn(9%) (6nm/6nm) multilayers.
The forms and magnitudes are quite similar, suggesting that the magnetic impurities do not
strongly modify the weak interaction between the F layers. As a further test involving all
of the samples, we compare the ratio IT for Co/Ag, Co/AgSn, Co/AgMn, and AgPt as
listed in Tables 4.3.4-4.3.17. We see that II for all of the different data sets fluctuates
mostly around. 2. The similar behaviors of IT for all of our samples shows that adding
impurities does not significantly change the relationship between AR,(I-Io) and AR,(Hp).
Thus we first focus our attention on data at H0. We will show later that an analysis of

data at Hp yields similar spin-diffusion lengths.

Fim
fror
fit v

Cale

77

 

  

[AthHo>tARr<Ho>—ART<Hs>i1“2 (111mg)

 

 

 

l
4o~ -
,
20”— ‘l
" l
,
:1/
. //
O / Jill 114

 

O 20 4O 6O 80
Bilayer No. N

Figure 4.3.1 flARflHO) — ART( H S )]ART(H 0) vs bilayer number N calculated
fi'om VF equations in Ref. [133] for samples with tCo=6nm. The line labeled 00 is a
fit with parameters for Co/Ag. The solid curves for the indicated values of 8’2], are

 

calculated with these same parameters and pN=150an. The dashed curves for
(a; =7nm show the effect of varying PN from 80 to 300 nm.

TF6“
(Eq. 3.
1.1111 th
predicti
below.
expect:
Cos’Agl
eqi3.6-
consist
EAR“
difficul
12,1.
root fu
b‘.’ Silo
l
S'SIem
tattle l
ARm
1'81 un.
not 8&1

be fOu

78

Fig. 4.3.3 shows ART(H0) and ART(HS) versus N for Co/Ag, Co/AgSn, and
Co/AgMn(9%) multilayers with fixed tCO=6nm, and Fig. 4.3.4 shows ART(H0) and
ART(HS) versus N for Co/Ag, Co/AgSn, and Co/AgPt(4%) multilayers with fixed
tCo=6nm. The solid lines in these two figures are predictions from two current model
(Eq. 3.1-3.2) using the Co/Ag parameters previously derived by S.F. Lee[71] combined
with the independently measured values of PN for each alloy. The dashed lines are
predictions from the VF Eqs.(3.6-3.9) for the finite values of €13} given in Table 4.3.3
below. The ART(HO) data for Co/Ag and Co/AgSn fall close to straight lines, as
expected by Eq.3.1. Within their 210% scatter, the ART(H0) data for Co/AgMn and
Co/AgPt are consistent either with straight lines or with the curvature predicted by
Eq(3.6-3.9). With either form, the ordinate intercepts for all of the multilayers are
consistent to within experimental uncertainties with independently measured values of
ZARNb/Co'l'PNTT- Simply from examining figures Fig. 4.3.3 and Fig.4.3.4, it would be
diflicult to conclude which, if any, of the data sets are associated with reduced values of

3);}. To isolate effects of reduced 6?, we must turn to an analysis based on the square

root function of Eq.3.6-3.9. As indicated above, we begin with data for H0 and conclude
by showing that very similar results are obtained if we use Hp instead.

For AR,P, we take ART(H) at H=1kG, the maximum field of our usual measuring
system. A higher field system showed that ART(H) has reached the desired minimum
value by l kG for multilayers of all of our metals and alloys except AgMn. For AgMn,
ART(H) continues to decrease slowly with H above 1 kG, nearly linearly, a behavior not
yet understand.[67] Otherwise, the AgMn data look like the rest of our data. As we have
not seen similar behavior in CuMn, we presume that this anomaly in AgMn will eventually

be found to be irrelevant to our present purpose.

79

 

 

 

 

 

 

 

 

 

 

 

 

 

 

80 I r 7 V Y I r r r r I r r r 1 I r r f r I _,
6‘ 60 :— HO _4
g : CO/Ag :
C; l- u
3’40 T l i
Y— »- P1P a
m —4
<1: 20 l— —:
E5: : / \. \ :
OE— _ HS :i_// -.‘r-L‘ 4
<: O — = __'_, ._ _ = ~

*- 1 i i #1 l l l I l L l l 1 l 1

40 r I I I I I I I TifI I T I I I I I I I I _‘
NE 30 :_ ‘
E : Co/AgSn(4%) :
V I- _4
22m 20 :— t F:
:- ,_ .1
m - -1
<2 - 4
,L 10 f- _:
35; : / \ \ :
03 T ,____.__4___—_/—// \‘ it "
<1 0 r" '— _. ‘.:‘ = i

P L L 1 1 1 l 1 1 1 1 l 1 1_ 1 1 l 1 1 1 l "

F I I I I I I I I T T I r r I I .4

67‘ 30 —- —
E : , g

E . Co/AgMn(9‘.’/Z) .1
V __ \ _,
I j i
\1: u a
as . ~
I 10 ”" —“

:35: ‘ / \\\ .
01“ : ,/ \.\ :
<1: 0 — F '4 ‘\ , - A
'— l 1 1 1 1 l 1 1 1 _m l 1 1 1 1 l 1 1 1 1 l “l

-1.0 —0.5 0.0 0.5 1.0

H (ROG)

Figure 4.3.2 ART(H)-ART(HS) versus H for Co/Ag, Co/AgSn(4°/o),
Co/AgMn(9%), (6nm/6nm)60 multilayers. The curves through the data are simply
computer drawn guides to the eye.

")
'\/l'()111

7 {II

I .

0.

Fig
rllll
ml;
C0
C0
la,
W1
C0

80

 

ZOO —* —7

 

100

50

ART<HO> a AthHsttmm2>

 

 

 

 

O 20 4O 6O
Bilayer No. N

Figure 4.3.3 ART(HO) (solid symbols) and ART(HS) (open symbols) vs bilayer
number N for Co/Ag (circles), Co/AgSn (square), and Co/AgMn (diamonds)
multilayers with fixed tCo=6nm and tT=720nm. The solid Co/Ag curves and solid
Co/AgSn curves are fits to Eq. 3.1-3.2; the downward curvature at small N for
Co/Ag comes from corrections because these samples did not have a covering Co
layer under the top Nb strip. The dashes Co/AgMn curves are fits to Eqs. 3.6-3.9.
We do not expect the Co/AgMn fits to be as good as those for Co/Ag and
Co/AgSn.

81

 

ZOO *- ‘—

100

50

ART(Ho) a AthHsttmm2>

 

 

 

 

O 20 4O 6O
Bilayer No. N

Figure 4.3.4 ART(HO) (solid symbols) and ARTCHS) (open symbols) vs bilayer
number N for Co/Ag (circles), Co/AgSn (square), and Co/AgPt (diamonds)
multilayers with fixed tCo=6nm and tT=720nm. The solid Co/Ag curves and solid
Co/AgSn curves are fits to Eq. 3.1-3.2; the downward curvature at small N for
Co/Ag comes from corrections because these samples did not have a covering Co
layer under the top Nb strip. The dashes Co/AgPt curves are fits to Eqs.3.6-3.9. We
do not expect the Co/AgPt fits to be as good as those for Co/Ag and Co/AgSn.

Plot
Within ex
111115. the
origin. Tl
the lines.
Curt'es tl
\tlues oi
The \T
supereor
found th
make fu:

evaluate

82

Plots of the LHS of Eq.(3.5) vs N are shown for our Ag-based data in Figure 4.3.5.
Within experimental uncertainties and variations among samples from different sputtering
runs, the Co/Ag and Co/AgSn data are consistent with a single straight line through the
origin. The Co/AgMn(9%), Co/AgMn(6%), and Co/AgPt(6%), in contrast, fall well below
the lines, and display the expected larger fractional deviations from the line as N —-)O. The
Curves thougth the Co/AgMn and Co/AgPt are calculated using the VP equations with the
values of 3);} indicated on the graphs (also listed in the second column of Table 4.3.3).
The VF eqations have not yet been rigorously generalized to samples with
superconducting Nb contacts, thus we just simply add ZARFWb z 6.1 film2 to AR,. We
found that the results obtained are surprisingly similar to independent estimates. We will
make fiirther independent check on samples with tCo=tN later in this section, and lastly, to
evaluate the sensitivity of our values of £2} to alternative choices of the AP-state we use
AR(I-Ip) instead of AR(H0) in the square root.

To analyze the other alloy data, we use the values of pN or our sputtered alloys

given in Table 4.3.1 The VF theory then gives the best fits for BC} shown in the figures. In
Figure 4.3.6, we also show the data for Co/AgMn(6%) with fixed tCo=2nm. We found
out that the value for Q} derived from this set of samples is within 10% of the previous
result derived from samples with fixed tCo= 6nm.

For AgPt[53], we can compare our values of (a; with ones derived from published
ESR values for the spin-flip mean free path, 2g (see Table 4.3.1). Differences in ESR
values among investigators[l30] suggest uncertainties in A]; of at least a factor of 2,

giving more than a 50% uncertainty in 6’2}. The values of 8’3} for Pt in Table 4.3.1 lie

within 50% of ours.

A...

A

.~__~MCV

41.n\. u

_M1A./H_ _v._.W_ (4..

A-.__C.r~_/\w»..._\

A; <

~

83

 

     

 

 

av 80 *— —
E _ -
C3
:3 2 2
N -_ 2
it
C: 60 — -
”3, - -
m
\; _ __
a: - -
<E
Ado— —
O
a: _ _
E _ .
<2 - -
;: Co/Ag
f 20 -— Co/AgSn(4%)
\I: . Co/AgMn(67 o) 7
33' / :é Co/AgMn(9%) -
“’ 1 i Co/AgPt(6‘7o) -
/
O u 32.3 , 1 1 1 l 1 1 1

 

O 20 4O 60 80
Bilayer No. N

Figure 4.3.5 ,[[AR7(H0) — AR,(HS )]ART(H0) vs N for Co/Ag, Co/AgSn(4%),
Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with fixed tCo=6nm.
The dashed lines is for eg— =oo[l3] The curves (solid for Co/AgMn and dashed for

Co/AgPt) correspond to the indicated best fit values of (N f Some measuring

 

uncertainties are also shown. Those not shown are smaller than the symbols or 35%,
whichever is larger.

lOl

72mm:o..>_I.r_:._.z< A3:._..:<....to::z<,\

A

84

 

10011

80—

1/2 (me2)

)1]

”60*

H

 

OMAR-11111941211
O
l

20 ”— / —
— / V Co/AgMn(6%) 7
OCo/Ag —

(H

[ART

 

 

 

O 25 50 75 100
Bilayer No. N

Figure 4.3.6 ,[[ART(HO) — AR,(H, )]ART(H,,) vs Nfor Co/Ag, and
Co/AgMn(6%) multilayers with fixed tCO=2nm. The dashed lines is for 81;} =oo[l3].
The solid curve for Co/AgMn correspond to the indicated best fit values of 62}.

Measuring uncertainties are smaller than the symbols or 35%, whichever is larger.

 

For
1;: 2611
outrepro
hounds, 1
thiekll3}
5114.35

We
113 equat
examine‘

On
with spin
we woul
diiferent
and the

magnetiz

85

For the other alloys, we use the estimates of [21" described in Table 4.3. 1. The value

(fail/z 26nm for AgSn is large enough that we cannot distinguish it from éfiz 00 to within

our reproducibility. The estimates for paramagnetic Mn in Ag and Cu may be only lower

bounds, since these alloys are in a spin-glass state at 4.2 K- even in layers only 6nm

thick[13]- where coherent interactions between Mn ions could increase 81;}. Our fits in

Fig.4.3.5 agree with the unmodified estimates for AgMn in Table 4.3.1.

We conclude that the data in Fig 4.3.5 are consistent with the predictions from the
VF equations with reasonable values for 13?}. Before concluding this section, we briefly
examine whether these behaviors could be due to other causes.

One possibility is that the couplings between F layers might be more ferromagnetic
with spin glass interlayers, leading to reduced values of the square root in Eq.(4.3. 1) If so,
we would expect to see differences in the hysteresis curves for multilayers with the
difl‘erent N metals. To check this possibility, we measured the saturation magnetization
and the coercive fields He for Co/AgPt, Co/AgSn, and Co/AgMn. The results of
magnetization measurements shown in Chapter 2 are very similar to each other.

Another possibility is that the magnetic character of the spin glass layers causes the
saturation field Hs for the CPP MR to be larger than the maximum field of 1 k6 in our
standard CPP measuring system. To check this possibility, we measured selected samples
in a higher field system, up to 10 KG, limited by the ch of our Nb strips. No evidence of
a higher saturation field was found for Co/Ag, Co/AgSn, Co/CuMn. However, the values
of ARTGD for Co/AgMn(9%) samples continued to decrease approximately linearly with
increasing field up to 10 kG. In Table 4.4.2, I show comparison of low field and high field
measurements for some Co/AgMn samples. Figure 4.3.7 show ART(H) for a
Co/AgMn(6%) multilayer (6O/90)4g in low field system then in high field system.
Assuming Hs to be 10 k6 would cause the data points for AgMn in Fig 4.3.5 to rise only

86

part of the way toward the straight line for no spin-flip scattering; however, it is possible
that the data continue to decrease to still higher fields. Since it is known that SGs alone
can have substantial negative linear MRs at high magnetic fields,[115] we made some
S/SG/S sandwiches of AgMn and measured their CPP MRS. For Nb/AgMn(9%)(t)/Nb
samples (750AStSIOOOOA), we first measured them in the low field system, and ARs are
the same at H0 and HS within our uncertainties. I measured one of them in high field
system and even found that the ARs slightly increase with increasing field. I also measured
AgMn(SOOA)/Co(1OOA)/AgMn(500A) and
AgMn(lOOOA)/Co(200A)/AgMn(l000A), (AgMn 6%) in low field system, and observed

two CPP samples,

slight positive MR5 in these two samples. We did not find negative MRs large enough to
explain the high-field behaviors of the Co/AgMn multilayers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgMn N sample CPP AR(low field) (mm?) CPPAR(high field) Hs field
nm .no. Hn H}; H.: 11,, H8 (3G)
9 48 421-02 115.5 103.0 93.19 99.34 91.98 8.75
18 30 42106 94.44 92.74 89.74 92.11 90.26 6.0

6 90 44404“ 183.84 171.36 148.07 155.60 142.94 7.6

6 90 444-07* 159.51 149.56 120.0

12 51 444-06* 125.54 121.72 114.03 113.55 108.53 7.3
58 12 444-05* 95.00 95.00 94.90 88.95 88.91 1.7

 

Table 4.3.2 CPP ART and CIP values at Ho, Hp and HS of

[Co(6nm)/AgMn(6%)(t)]xN, and [Co(2nm)/AgMn(6%)(t)]xN(*) samples. Total

sample thicknesses are as close as possible to 720nm.

 

87

 

130 VTfW'YfriT'YV'TV'V'IVVY—fiTVVYVIVYfiV‘ITVYfIVYVVITYTVIVfiYT‘f
p

 

 

 

 

 

 

 

 

A ’ <
N C i
E 110 - -
C: .
{1_1 .
V l
2.. 105~ ~
.11 , l
9‘ d
m 100.,
<3 I ,0
“l / a
95 Iowafl\ /
> \D‘T‘MH -~D~L
1 “F”fl*fi"’w
90 ....1,..LL1 11.211.+.Lt 1-11L11LLLJ...

0123416789101112
H(kOe)

Figure 4.3.7 ART(H) vs field H for a Co/AgMn(6%) multilayer (6nm/9nm)43 in low
field system then in high field system.

To conclude this part of the analysis, we note that these studies do not close the
books on the VF equations. There are some questions that still need to be resolved. First,
these equations were initially shown to be valid only for lsf>>/l,,,, a criterion not met by
our Mn or Pt alloys, for which Table 4.3.1 and Fig 4.3.6 give [{2} == 25. This problem has
been discussed in Chapter 3. Second, the VF equations have not yet been rigorously
generalized to samples with superconducting Nb contacts. Third, as noted above, the high
field negative linear MR in AgMn must also still be understood.

To check that the values of lsf just obtained are not unique to samples with fixed tF,

we also made sets of samples with equal but varying t1: and tN thicknesses. The total

88

sample thicknesses are kept as close as possible to 720nm, consistent with integer bilayer
numbers. To minimize coupling between the Co layers, we limit our analysis to
multilayers with ma 6nm, and to avoid situations where the hysteresis curves have shown
additional structure beyond that in a simple multilayer, we also limit the analysis to tFS

18nm.RR If Eq. 3.5 applies, data for alloys with a long 8?} must fall on the same line as

the host metal, with no adjustable parameters. In Figure 4.3.9, we find that the data for

Co/Ag, Co/AgSn fall on the same curve and close to the prediction for 8?} = 00. In

contrast, the data for Co/AgMn and Co/AgPt fall well below this line, and the values of
61;} derived from a fit to the Valet and Fert equations (listed on the figure) agree rather
well with those derived from data for fixed tCo = 6 nm (see Table 4.3.3).

Lastly, we try similar fits for samples with fixed tCo = 6 nm using data for Hp
instead of H0, as shown-in Figs. 4.3.10 and 4.3.11. We might expect similar results to
those obtained with Ho, since we showed above that the ratio H for Co/Ag,Co/AgSn,
Co/AgMn, and AgPt fluctuates mostly around 2. Indeed, the qualitative behaviors of the

data are the same as for Ho, and the values for 8’3} change by less than 50% (see Table

4.3.3).

mun \.. —

.~./~/\~
. . C_gv a

it v

0..

.. .<

AATQ—v_a/_

A

from '

with l

89

 

[ART(HO)EART(Ho)—ART(HS) i] 1/2

 

 

 

 

O 20 4O 60 80
Bilayer No. N

Figure 4.3.8 J[ART(HO) — AR,(H S )]ART (H 0) vs bilayer number N calculated
from VF equations in Ref. [133] for samples with tCo=tN- The line labeled 00 is a fit
with parameters for Co/Ag. The solid curves for the indicated values of 81:, are

 

calculated with these same parameters and pN=150nflm The dashed curves for

[gr =7nm show the effect of varying pN from 80 to 300 nm.

...v_/\‘
A3. _v._.v_<:.o:v

. .r _<-

.f__v v

:A

n

Figu

C01,:

The

COfl'

data

Sill'cl

 

   

 

 

 

100 l l I T l l l l I I I lj I l I l l
N _ _
> ~ 1
E 80 _ em 1,, 6 .
m e— _.
EB . O -
Er _ _.
an: 7 10nm 7
| 2 a

A '7

E 5 0 “
m9. ” _
5, Z ’ 1
’33 40 e O Co/As ~
SE- B Co/AgSn 2
3 V Co/AgMn67o :
20 A Co/AgMno‘J/zz’j
0 Co/AgPt 7

O 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1

O 25 50 75 100
Bilayer‘ No. N

Figure 4.3.9 $412,010) — AR,(H, )]ART(HO) vs Nfor Co/Ag, Co/AgSn(4%),
Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with fixed tCo=tN-
The dashed lines is for (If, =00[13]. The solid curves for Co/AgMn Co/AgPt)

correspond to the indicated best fit value of 61;}. Because of the scattering of our

 

data, it is hard to derive best fit value of 6?} for AgPt. Measuring uncertainties are
smaller than the symbols or 55%, whichever is larger

9l

 

   
   

I l l I I I I I I I l I l T I
60 —0 Co/Ag —
§ _ D Co/AgSri(4%) .
:2 V Co/Ang1(6%)
:01 A Co/AgMn(9%) 11211111
05‘ o Co/AgPt(6%) 9m“ *
<f.
| 6nm —~
2
:1: 1
ft:
C11 4
:5.
a _I
U:
\E: A
Of.
.3. -
tC :6nm 7

 

 

 

O 20 4O 6O 80
Bilayer’ No. N

Figure 4.3. 10 J[ART(H,, ) - AR,(H,)]ART(H,,) vs N for Co/Ag, Co/AgSn(4%),
Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with fixed tC0=6nm.
The dashed lines is for ۤ=oo[l3]. The curves (solid for Co/AgMn and dashed for

Co/AgPt) correspond to the indicated best fit values of 6?}. Measuring uncertainties
are smaller than the symbols or 55%, whichever is larger.

 

Jr)
‘\4

HI"

-A l\’...(il l._.

)

)§/\l€...(ll_

(ll

I A I\)

FigUre
CO/Ag'
The da
Co/Ag-
are 8m:

92

 

 

 

 

 

l T T I l T l 1 fi 1 1 T
6 O b O C o ,ng —~
g p D Co/AgSnMCZ) .
x V Co/AgMn(6%)
Cf) '— _
E A Co/Aghln(9%)
a: o Co/’”AgPt(6‘?/Z) 1
<1:
1 4O 1— D —
A /
.1
E D / / / -1
a? 1 j -
<1 ‘10 /
r: _ 9 At. .
£1. / // /
I g /
v __ /1_1 // /” . _
o? 20 / O /,./ 17
< L ” '/ V/
L—" / / 7
/
. //
I“ (”X tCo_tN i
A
._ ’2/ .4
/
O 4&1 1 l 1 1 1 l Ll 1 l 1 1 L

O 20 4O . 6O 80
Bilayer No. N

 

Figure 4.3. 1 1 J[ART(H,, ) — AR,(H, )]ART(H,,) vs N for Co/Ag, Co/AgSn(4%),
Co/AgMn(6%), Co/AgMn(9%), and Co/AgPt(6%) multilayers with fixed tCo=tN-
The dashed lines is for €g=oo[l3]. The curves (solid for Co/AgMn and dashed for
Co/AgPt) correspond to the indicated best fit values of £12.}. Measuring uncertainties
are smaller than the symbols or 55%, whichever is larger.

Our de
HP or data f1
12, are thus ‘

I‘—

Alloys

. AEMlllt”

. Adlnt‘,

 

a Meats
b Meats
c Meas
dhlfias

6 Meg

93
Our derived values of £2} are clearly not sensitive to whether we use data for H0 or
Hp or data for fixed tCo = 6 nm or variable tCo = tN. We conclude that these values of

(32} are thus likely to be reliable.

 

 

 

 

 

 

 

 

 

 

 

 

Ahoy, af, [2} 8;“, 8f, egtesp)
(an (um)b (nm)° (nm1d tum)e
AgMn(6°@ ~1 1 ~ 10 ~ 10 ~9 ~8
whom ~7 ~7 ~6 ~5.5
AgPt(6%) ~10 ~12 ~7.5

 

Table 4.3.3 Measured parameters for Co/AgMn(6%), Co/AgMn(9%) and Co/AgPt.

a Measured parameters from samples with fixed tC0=6nm using H0 state as AP state.
b Measured parameters from samples with {Co-4N using l-lo state as AP state.

c Measured parameters from samples with fixed tCo=2nm using H0 state as AP state.
d Measured parameters from samples with fixed tCo=6nm using Hp state as AP state.

e Measured parameters from samples with fixed tCo=1N using Hp state as AP state.

94

4.3.2 Experimental results
In Tables 4.3.4-4.3.17, I present CPP and CIP data for Co/AgMn(6%),
Co/AgMn(9%), Co/AgPt(6%)

95

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgMn N sample CPP AR (@112 CIP (0'1)

(11m) .no. Hn Hp 1g Hfl H,L H,:

60 11 42104 77.36 77.32 77.25 0.4061 0.4061 0.4066
18 30 421-06 94.44 92.74 89.74 0.4131 0.4142 0.4174
12 40 42108 98.52 93.90 86.85 0.3954 0.4005 0.4123
9 48 321-02 115.5 103.0 93.19 0.3192 0.3316 0.3466
6 60 421.07 131.9 115.1 97.40 0.3727 0.3854 0.4058
6 60 42103 133.5 116.9 100.7 0.3457 0.3744 0.3937

 

 

 

Table 4.3.4 CPP ART and CIP values at Ho, Hp and HS of
[Co(6nm)/AgMn(6%)(t)]xN samples. Total sample thicknesses are as close as
possible to 720nm.

 

 

 

 

 

 

 

 

 

 

 

t AgMn N sample CPP MR % CIP MR % II error [(ro-rs)ro]1/2
(nm) . no. Hn 11,, 11,1 11,, %

60 11 421-04 0.14 0.09 0.12 0.12 1.56 3.0 2.92

18 30 421-06 5.24 3.34 1.04 0.77 1.57 4.4 21.07

12 40 421-08 13.4 8.12 4.3 2.95 1.66 3.7 33.91

9 48 321-02 23.9 10.5 8.6 4.52 2.27 2.6 50.76

6 60 421-07 35.4 18.3 8.9 5.29 1.95 1.35 67.46

6 60 421-03 32.6 16.1 13.9 5.15 2.02 4.47 66.17

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.3.5 CPP MR, CIP MR and [(ro-rs)ro]l/2 values at Ho, and Hp of
[Co(6nm)/AgMn(6%)(t)]xN samples. rO and rS are ART at HO and HS. Total sample
thicknesses are as close as possible to 720nm.

96

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgMn N sample CPP AR(me2) own-1)

(nm) .no. Hn H;1 m Hn Hp H.:
18 20 420.04 77.18 74.85 73.84 0.4775 0.4829 0.4880
12 30 421.05 90.02 85.62 82.38 0.3232 0.3247 0.3283
9 40 421-06 96.71 80.57 75.63 0.3426 0.3548 0.3693
6 60 42107 131.9 115.1 97.40 0.3727 0.3854 0.4058
6 60 421.03 133.5 116.9 100.7 0.3457 0.3744 0.3937

 

 

 

Table 4.3.6 CPP ART and CIP values at Ho, Hp and HS of [Co(t)/AgMn(6%)(t)]xN

samples. Total sample thicknesses are as close as possible to 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgMn N sample CPP MR% CIPMR% 11 error [(ro-rs)ro]1/2
(nm) .no. l-In H9 H0 H£1 %

18 20 42004 4.52 1.37 2.20 1.06 3.3 1.14 16.06
12 30 421.05 9.27 3.93 1.58 1.11 2.36 3.06 26.23
9 40 421-06 27.9 6.53 7.79 4.09 4.27 4.08 45.15
6 60 421.07 35.4 18.2 8.88 5.29 1.94 1.35 67.46
6 60 42103 32.6 16.1 13.9 5.15 2.02 4.47 66.17

 

 

 

Table 4.3.7 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at Ho, and H of
[Co(t)/AgMn(6%)(t)]xN samples. r0 and r8 are ART at HO and HS. Total sample
thicknesses are as close as possible to 720nm.

97

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘AgMn N sample CPP AR(fnm2) CIP (0’1)
(um) .no. 11., 11% 11. H9 H.
60 11 373-02 111.2 111.2 111.2
30 20 388-02 134.2 134.2 134.0
30 20 373-06 123.8 123.8 123.6
18 30 388-03 136.4 136.0 135.0
12 40 388-05 149.5 147.2 144.2
9 48 373-04 152.5 148.5 141.5
6 60 37307 167.4 153.7 143.1
6 60 37301 162.6 148.8 138.7
6 60 388-01 158.9 146.5 134.7

 

 

 

 

 

 

 

Table 4.3.8 CPP ART and CIP values at Ho, HD and HS of

[Co(6nm)/AgMn(9%)(t)]xN samples. Total sample thicknesses are as close as

possible to 720nm.

 

 

98

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgMn N sample CPP MR% CIPMR% 11 error [(ro-rs)ro]1/2
(11111) .no. Hfl H9 H0 H9 %

60 11 37302 0.0 0.0 0.0
30 20 38802 0.15 0.15 1.0 5.2
30 20 37306 0.16 0.16 1.0 5.0
18 30 38803 1.04 0.74 1.41 13.8
12 40 2388-05 3.68 2.08 1.77 28.1
9 48 37304 7.77 4.95 1.57 41.0
6 60 37307 17.0 7.41 2.29 63.8
6 60 37301 17.2 7.28 2.37 62.3
6 60 38801 18.0 8.76 2.05 62.0

 

 

 

 

 

Table 4.3.9 CPP MR, CIP MR and [(ro-rs)r011/2 values at Ho, and Hp of
[Co(6nm)/AgMn(9%)(t)]xN samples. re and rs are ART at HO and HS. Total sample
thicknesses are as close as possible to 720nm.

99

 

 

 

 

 

 

 

[AgMn N sample CPP AR (me2) CIP (Q'l)
(nm) . no. Hn Hp HL Hn Hp HQ
18 20 373-03 120.7 119.5 119.0
9 40 373-05 129.2 123.1 117.8
6 60 373-07 167.4 153.7 143.1
6 60 373-01 162.6 148.8 138.7
6 60 388-01 158.9 146.5 134.7

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.3. 10 CPP ART and CIP values at H0, H and Hs of
[Co(t)/AgMn(9%)(t)]xN samples. Total sample t 'cknesses are as close as possible
to 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgMn N sample CPP MR% CIPMR% r1 error [(ro-rs)ro]l/2
(11111) .no. H(L HIrL 11L Hnfi %

18 20 37303 1.43 0.42 3.4 3.5 14.32
9 40 37305 9.68 4.50 2.15 0.8 38.38
6 60 37307 17.0 7.41 2.29 2.0 63.8
6 60 37301 17.2 7.28 2.37 3.4 62.3
6 60 388-01 18.0 8.76 2.05 3.4 62.0

 

 

Table 4.3.11 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at Ho, and H of
[Co(6nm)/AgMn(9%)(t)]xN samples. r0 and rS are ART at H0 and Hs- Total sample
thicknesses are as close as possible to 720nm.

100

 

 

 

 

 

 

 

 

t AgMn N sample CPP AR (me2) CIP (Q'l)

(11m) . no. Hn Hp Hg Hr1 Hp H.;
6 90 444-04 183.84 171.36 148.07 0.4205 0.4236 0.4262
6 90 444—07 159.51 149.56 120.0 0.2341 0.2347 0.2522
12 51 444-06 125.54 121.72 114.03 0.2985 0.3008 0.3050
58 12 444-05 9500 95.00 94.90

 

 

 

 

 

 

 

 

 

Table 4.3.12 CPP ART and CIP values at H0, Hp and HS of
[Co(2nm)/AgMn(6%)(t)]xN samples. Total sample thicknesses are as close as
possible to 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgMn N sample CPP MR% CIPMR% 11 error [(rQ-rgrdl/z
(nm) .no. Hn Hp 1-1n i, %

6 90 44404 24.2 15.7 1.36 0.61 1.54 3.9 81.09
6 90 44407 32.9 24.4 7.73 7.46 1.35 1.5 79.39
12 51 44406 10.1 6.74 2.18 1.40 1.50 5.0 38.01
58 12 44405 0.11 0.11 1.0 2.44 3.08

 

 

Table 4.3.13 CPP MR, CIP MR and [(ro'TQToJI/z values at Ho, and Hp of
[Co(2nm)/AgMn(6%)(t)]xN samples. to and 1S are ART at H0 and H5. Total sample
thicknesses are as close as possible to 720nm.

101

 

 

 

 

 

 

 

 

 

 

 

tAgpt N sample CPP AR Q‘sz) CIP (o-l)

(nm) .no. Hfl Hp H.i Hn Hp HL
6 60 49505 114.42 110.22 94.48 0.9044 0.9080 0.9202
6 60 49605 118.98 93.95 0.7659 0.7872
9 48 49506 112.53 107.45 96.84 0.3334 0.3354 0.3416
9 48 49608 118.38 115.02 102.34 0.4895 0.4846 0.4916
18 30 49604 100.95 100.45 95.97 0.3615 0.3616 0.3639
30 20 49508 94.56 94.27 92.93 0.3638 0.3639 0.3648
30 20 49503 96.56 96.32 95.03 0.3473 0.3469 0.3476
60 11 49602 94.50 94.44 0.2906 0.2907 0.2908

 

 

 

 

 

 

 

 

 

 

Table 4.3.14 CPP ART and CIP values at Ho, Hp and HS of
[Co(6nm)/AgPt(6%)(t)]xN samples. Total sample thicknesses are as close as
possible to 720nm.(large target)

 

 

 

 

 

 

 

 

 

 

 

tAgpt N sample CPP MR% CIPMR% 11 error [(ro-rs)ro]1/2
11m) .no. Hn Hp Hn 11% %

6 60 49505 21.1 16.7 2.15 1.34 1.27 3.3 47.77
6 60 496-05 26.6 2.78 3.0 54.57
9 48 495-06 16.2 11.0 2.46 1.85 1.45 1.7 42.02
9 48 49608 15.7 12.4 0.43 1.44 1.26 2.5 43.58
18 30 49604 5.19 4.67 0.66 0.64 1.11 1.5 22.42
30 20 495-08 1.75 1.44 0.27 0.25 1.22 4.9 12.42
30 20 49503 1.61 1.36 0.09 0.20 1.18 3.4 12.15
60 11 49602 0.06 0.07 0.03 3.3 2.38

 

 

 

 

 

 

 

 

 

 

Table 4.3.15 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at Ho, and Hp of

[Co(6nm)/AgPt(6%)(t)]xN samples. 10 and 1S are ART at H0 and HS. Total sample

thicknesses are as close as possible to 720nm(large target)

 

 

102

 

 

 

 

 

tAgpt N sample CPP AR(me2) CIP go")

.no. Hn Hp 11L H0 H9 HL
6 60 49505 114.4 110.2 94.48 0.9044 0.9080 0.9202
6 60 496-05 119.0 93.95 0.7659 0.7872
9 40 49507 98.35 94.31 86.99

 

12 30 496-03 93.32 89.29 85.39

 

18 20 495-04 76.30 75.47 74.36 0.5849 0.5847

 

 

 

 

 

 

 

 

 

 

 

 

18 20 496-07 75.30 74.32 73.18 0.7434 0.7450 0.7512

 

Table 4.3.16 CPP ART and CIP values at H0, HI) and HS of [Co(t)/AgPt(6%)(t)]xN
samples. Total sample thicknesses are as close as possible to 720nm.(large target)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t AgPt N sample CPP MR % CIP MR % 1'] error [(ro-rS)ro]1/2
(11m) . no. H6 H9 Ha Hp %

6 60 495-05 21.1 16.7 2.15 1.34 1.27 3.3 47.77

6 60 496-05 26.6 2.78 3.0 54.57

9 40 495-07 13.1 8.41 1.55 0.9 33.43

12 30 496-03 9.29 4.57 2.03 3.9 27.20

18 20 495-04 2.61 1.49 1.75 4.0 12.17

18 20 496-07 2.90 1.56 1.05 0.83 1.86 1.4 12.63

 

 

 

 

Table 4.3.17 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at Ho, and Hp of
[Co(t)/AgPt(6%)(t)]xN samples. ro and rS are ART at H0 and H5. Total sample
thicknesses are as close as possible to 720nm(large target)

103

4.4 Prediction and Measurement of Perpendicular Giant
Magnetoresistances 0f C0/Cu34Fe16/Cu Multilayers

The ability to tailor GMR systems for specific uses requires understanding the
physics underlying GMR. Demonstrating the ability to predict new data from old is an
important step along the path of understanding. In this section we describe the results of
an attempt to test the predictive ability of the simple two current, series resistor model.

As a quantitative test of the validity of the two current model, and our use of the
virgin state for ARfP, we made sputtered Co/Cu/Py/Cu (Py=Ni34Fe16zPermalloy)
multilayers with neighboring Co and Py layers in well-defined parallel (P) or antiparallel
(AP) magnetic states to compare the data with predictions of the two current model using
only parameters derived without adjustment from prior measurements on Co/Cu and
Py/Cu multilayers. We have argued above that the H0 state, when the sample is first
prepared and before any field is applied, seems to give a good approximation to the AP
state. We take this H0 state as the AP state for Co/Cu and Py/Cu in our present analysis.
Alternatively, the data and analysis that we present can be viewed as a test of
approximating the AP state by the H0 state.

As noted in Chapter 1, one ought to be able to produce an AP state in F1/N/FZ/N
multilayers by choosing F 1 to have a relatively large saturation field, H51, F2 to have a
much smaller saturation field, H82, and tN to be large enough so that exchange coupling
between the F l and F2 layers is weak. With such a sample, reducing the applied field fi'om
+Hsl, past zero, to a negative value just beyond -H52, should give an AP state. The
samples here contain Co layers with H81“ 100-200 0e and Py layers with H525 lOOe.

We present our results in the following order. (1) First, we compare total
magnetization Mt versus H to ARt versus H for Co/Cu/Py/Cu (3/20/8/20)3 and
(6/20/16/20)8 multilayers to show that Mt does indeed decrease rapidly at low fields as

the Py layer magnetizations reorient, and that ARt increases rapidly over the same small

104

field range. (2) We then compare data on Co/Cu/Py/Cu (3/20/8/20)N multilayers with
with no-adjustable-parameter predictions from the Co/Cu and Py/Cu parameters. Using a
global fit from S.F. Lee, I derived the parameters based on data of Co/Cu and Py/Cu fiom
P. Holody. The parameters are listed in Table 4.4.1. To check the sensitivity of results to
tCu: a few samples are made with tCu = 40 nm or tCu = 10 nm. The layer thicknesses of
Py and Co were chosen: (a) to give nearly equal magnetizations for the Co and Py, so that
the total magnetization will be near zero when only the Py layer magnetizations flip, and
(b) to lie within (for Co) or close to (for Py) the thicknesses actually used in determining
the parameters for the no-parameter fit. We will see that the fits are reasonably good, but
not perfect. (3) To test how sensitive the predicitions are to the Co and Py thicknesses,
we then compare the predictions with additional multilayers where the conditions set
above are relaxed: (6/20/16/20)N, (3/20/5/20)N, and (5/20/10/20)N. To look for
systematic effects, we also check the ratios of measured and predicted magnetoresistances
for the four sets of samples. (4) Lastly, we test whether we can improve the ratios by
adjusting the parameters within their uncertainties. Detailed data for all of the samples are

given in tables in 4.4.2.

4.4.1 Prediction and CPP MR measurements of Co/Cu/Py/Cu multilayers

To avoid proximity effects in the N layers, the first and last layers are always Co at
least 3nm thick.[125] Each sample thus consists of two Nb strips, the quadrilayers of

interest, and a "cap" Co layer just below the top Nb strip.

105

Nb Co Cu Py Cu Co Cu Py Cu Co Nb

 

 

1 1 m1 1 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.4.1 (a) Sample geometry for simultaneous measurements for CPP(V/I) and
CIP (v/i) resistances. The CPP current I flows through the overlap area Az1.25
mm2 of the Nb strips. (b) Schematic of the antiparallel (AP) state of Eq. 4.4. 1.

Following the two-current equations in chapter 3, for a multilayer with N layers of

Co/Cu/Py/Cu, AR for the up (+) and (-) spin directions and the AP state are:

ARAP(+) = 4ARNb/Co + 4NPCu’Cu + (N +1)pgoICo
T J- i
+2NARC0/Cu + NpPyth + ZNARPy/Cu (4.4.1)

_ l
ARAP( ) : 4ARNb/Co + 4NpCutCu + (N +1)pCotCo
+2NARéo/C, + ijlyrpy + 2NAR,E, m, (4.4.2)

It is important to notice that, unlike the case for a two-component system, ARAP(+) is not
equal to ARAP(')- Each quantity must thus be calculated separately. Substituting in the
definitions given in Chapter 3 gives ARAP(+) and ARAP(') as functions of B and 7.
Similar expressions can be written for ARP(+) and ARP(') , and AR,” and AR,1D are then
parallel combinations of the appropriate (+) and (-) components. For comparison with our
data, these calculations are carried out numerically.

The bilayer number N, and the layer thicknesses tCu, tCo, tpy, are chosen for a

given sample, and the parameters ZARNb,C0, pCu, pCo, ppy, can all be measured

a.

w‘.-

‘A-h

106

independently of the ARt's of Co/Cu, Py/Cu, and Co/Cu/Py/Cu.[97][106][40] Thus, in
principle, to calculate ARt for our Co/Cu/Py/Cu samples, only three "unknowns" each--
pCo’ 7Co/Cw ARCo/Cua and flPya 7Py/Cu: ARPy/Cu"mUSt be determined from ARt
measurements on Co/Cu and Py/Cu multilayers. The prior measurements on Co/Cu and
Py/Cu were made by P. Holody, and the parameters are determined using global fits
described in S.F. Lee's thesis.

In practice, however, sputtered samples do not give precise values for all three
parameters. The data scatter, and independently measured values of ZARNb,C0, pCu, pCO,
ppy vary among sputtering runs--e.g., columns 2 and 3 of Table 4.4.9 show that the
average resistivities of 300-nm-thick films of Co, Cu, and Py sputtered with Co/Cu/Py/Cu
are lower than those previously sputtered with Co/Cu and Py/Cu, although they agree
within mutual uncertainties.

Here we want to see how well we do with no adjustability. We thus fix the Nb/F

interface resistances at independently measured values ZARNb,C0=6.1me2,[1 l6][40] and

ZARmey=7£Qm23191 and require all common parameters for Co/Cu, Py/Cu, and

Co/Cu/Py/Cu to be the same. With these constraints, the remaining parameters are fixed

by fits oqus.4.4.1 and 4.4.2 to the Co/Cu and Py/Cu data.[131]

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Best Fit Indep. Meas. Indep. Meas.
parameters Co/Cu; Py/Cu Co/Cu/PyCu
2ARNb/Co (mmZ) 61:03 61:03
ZARNb/Py (191112) 711.5 57-85
1050 (nflm) 7615
Pco = P500 - fl 2) 6019 60110 5113
p}. (mm) 164126
pPy = 1013(1- 16 2) 123140 137130 11118
pCAan) 4.5105 611 5.511
flea 0.461008
7Co/QuL 0.751005
flpy 05010.16
7Py/Cu 08110.12
ZARE‘o/g (£01112) 1.051005
ZARCo/Cg = ZARCo/Cua ‘7 2) 04610.10
2(4131150631(mmz) 10010.08
2ARPy/Cu = ZARA/6'41 -7 2) 03410.22

 

 

 

 

Table 4.4.1 Fit parameters and independent measurements. (Column 1) Constrained
fit to Co/Cu and Py/Cu. (Column 2) Independent measurements of ZARNb/Co [Ref

40] and ZARNb,py. and of PC.“ pCo, and ppy from films sputtered with the Co/Cu
and Py/Cu multilayers. ( Column 3) Independent Measurements of pCu, pCO, and

pp), from films sputtered with Co/Cu/Py/Cu multilayers.

 

108

To justify applying the two—current model for simple AP and P states to our data,
we must show that the magnetizations of Co and Py layers reorient at very different fields,
and that ARt and the total magnetization change together. Figure 4.4.2 compares
magnetization M versus H [Fig 4.4.2(b)] to ARt versus H [Fig 4.4.2(a)] for a
Co/Cu/Py/Cu (3/20/8/20)3 multilayers. The lower HS (Py) layer reorients over a narrow
field range near H=0, and ARt increases rapidly over the same range. This narrow range
for the Py layers gives a well-defined rise and maximum for ARt. We designate this
maximum as ARt(HAp). The higher Hs (Co) layer, in contrast, reorients over a much
wider field range, giving a near plateau in M and a nearly flat region in ARs, followed by a
much slower return to saturation. Similar behavior has been seen in CIP measurements on
such systems.[117] Figure 4.4.3 show compression between magnetization and ARt for
Co/Cu/Py/Cu (6/20/16/20)8 multilayer.

Fig. 4.4.4 shows the data for the samples with nearly equal Co and Py layer
magnetizations and with Co and Py thicknesses comparable to those used in the fits.[13 1]
The open symbols are for Cu layers with tCu= 20nm, which should be thick enough to
make exchange coupling between Co and Py layers weak. A few points with tCu= 10nm
(+8) and tCu= 40nm (xs) show that the results are not sensitive to tCu.

Figs 4.4.4-4.4.7 compare Co/Cu/Py/Cu (3/20/8/20)N, (6/2016/20)N, (3/20/5/20)N
and (5/20/10/20)N data with no-adjustable-parameter predictions (solid lines) from the
Co/Cu and Py/Cu parameters (column 1 of Table 4.4.9) obtained as described above. The
measuring uncertainties for individual data points are usually dominated by i2-5%
uncertainties in the areas A. Reproducibility is indicated by the difi‘erences between open
and filled symbols, which were sputtered in both HAP and Hs- If, instead of the Co/Cu
parameters in column 1 of the Table 4.4.1, we start with previously published

ones, [97][106] the agreement is almost as good.[73]

109

A more stringent test of out prediction involves the ratio of the measured and
predicted magnetoresistance, [AR,(HAP)— AR,(HS )]/ [AR,"UD — AR}D ]. The ratios shown
in Figure 4.4.8 for four sets of data range from 1.1-1.3 and average about 1.2 instead of 1.
Given the constraints placed on the fits, this agreement is rather good. The fit in Figure

4.4.4- Figure4.4.7 can be improved, giving a ratio average of about 1.1, by increasing the

values of pfiy, ,pr and ,BCO, within their uncertainties. Figure 4.4.8 shows the improved
ratios. (ppy=0.67, 75:0.90, p;y=l9.0)

We conclude that the rather good agreement between the no-free-parameter
predictions and our data provides important new evidence that low-temperature CPP data
for magnetic multilayers can be described by a simple, independent two-current model that
contains no lengths other than the thicknesses of the constituent layers. The agreement
also provides filrther support for our argument that the H0 state resistances of our Co/Cu,
and Py/Cu multilayers lies near those for AP F -layer alignment.[73][110]

Besides the Co/Cu/Py/Cu multilayers described above, we also tried measurements
of another spin-valve structure, Co(tl)/N/Co(t2)/N, with different thicknesses of Co to
obtain different coercivities. To investigate the magnetic coupling across the spacer layer
and the magnetic ordering between the F layers in our samples, we also developed a new
type of spin-valve stmcture (Co/Cu)N(Py/Cu)N from Co/Cu/Py/Cu multilayers. The

results of preliminary studies on these systems are described in the next chapter.

 

 

110

 

 

 

 

 

 

 

4 0, -1 I. 2
A15— | r
m a
E <> I
E ” r’ ‘
:10r i 7
U) -4
33 / 111 \
E‘-
O: 5 l
in 5* l “
E
E— .
<2 O =1 J’if/: .1 \1
l l l
4 l 1 l

 

m (IO—3emu)

 

 

 

 

_4 1 1 1 i #141 1 1 1 1

——0.4 —0.2 0.0 0.2 0.4
H (kOe)

Figure 4.4.2 (a) Magnetoresistance and (b) magnetization M of a
[Co(3)/Cu(20)/Py(8)/Cu(20)]3 multilayer vs magnetic field H. Sample dimensions
are in run.

 

 

 

 

 

 

 

 

 

 

1
—0.3 —0.2 —0.1 0.0 0.1 0.2 0.3
H (kOe)

 

p.
4 1 1 1 1 i 1 1 1 1 i 1 1 1 1 1 1 A 1 i 1 1 1 i 4 1 1 1

Figure 4.4.3 (8) Magnetoresistance and (b) magnetization M of a
[Co(6)/Cu(20)/Py(l6)/Cu(20)]3 multilayer vs magnetic field H. Sample dimensions
are in run.

112

 

(CO(3)/CU(20)/PY(8)/CU(20))N

ART(HAP)AND AR,(HS) (meZ)

 

 

 

 

Figure 4.4.4 ARt(HAp) and ARt(HS) for [Co(3)/Cu(20)/Py(8)/Cu(20)]3 multilayers
for N: 2,4,6,8. For tCu=20nm, the solid lines are for the parameters in column 1,
Table 4.4.1. Open and filled symbols for N=4 and N=8 are for samples from
different sputtering runs; their differences show our reproducibility. The crosses are
for samples with tCu‘ 40nm and the pluses for tcu=20nm. With pCUzSan, the
changes in ARt from tCu=20nm to 10nm or 40nm are z-0.1anm2 and +0.2NfQ
m2, respectively. Even for N=8, these are only z—0.8 and +1.61!)er about our
reproducibilities.

113

 

03
O

(CO(6)/CU(20)/PY(16)/CU(20))N

(\3 CO ab- 01
O Q Q Q

ART(HAP)AND AR,(HS) (10mg)
0

 

 

 

CD
I

p—
>—
—
.___..._
p——
p—
1__

 

Figure 4.4.5 ARt(HAp) and ARt(HS) for [Co(6)/Cu(20)/Py(l6)/Cu(20)]3
multilayers for N= 2,4,6,8. For tCu=20nm, the solid lines are for the parameters in
column 1, Table 4.4. 1. Open and filled symbols for N=4 and N=8 are for samples
from different sputtering runs; their differences show our reproducibility. The
crosses are for samples with tCu= 40nm. With pCqunflm, the changes in ARt
from tcu=20nm to 40nm are z+0.2NfI2m2. Even for N=8, these are only z +1 .6fQ
mzrabout our reproducibilities.

114

 

6'0

50

40

30

 

TTl—llllll[lllllllllIlTlTIIIII

 

 

 

40

30

AR,(HP) AND AR,(HS) (meZ)

20

10

lTllllTTl]lTlT[lllj]llll

 

 

 

 

Figure 4.4.6 ARt(I-1Ap) and ARt(HS) for [Co(3)/Cu(20)/Py(5)/Cu(20)]3 and
[Co(6)/Cu(20)/Py(l0)/Cu(20)]8 multilayers for N= 2,4,6,8. For tcu=20nm, the solid
lines are for the parameters in column 1, Table 4.4. 1. Open and filled symbols for
N=4 and N=8 are for samples from different sputtering runs; their differences show
our reproducibility.

115

 

 

 

 

(Co(6)/Cu(20)/’Py(10)/Cu(20))N
_ O D 5 Cl
1: 1 f
DC 22;; p ‘ . 7 2:3
<|E ” (CO(3)/CU(20)/PY(5)/CU(20))N
% a
O; O [3 Cl
:5. 1 7
\ 22:; P:
'73) (Co(6)/C11(20)/Py(16)/Cu(20))N
z
a? * [3 D 6}
<1: 1 7‘
KL 2:: 2:
:0 “ (C0(3)/CU(20>//PY(8)/CU(20))N
35
[2:3 -
fl. " 1:1 0 :1
1 _
f 1 2 + CuélO;
. O [:1 >< Cu 40
O . . L . 11 11 R . l .
0 2 4 6 8 10

Figure 4.4.7 The ratios of the measured and predicted magnetoresistance,

[AR,(HAP)— AR,(H, )]/ [AR,AP - ARf’ ] for four sets of samples.

116

 

 

 

 

Q
t (Co(6)/C11(‘2.0)/P)«"(10)/CL1(20))N
r—1 1 _ O D S [1
[L
E" be r\.2
Q: 2... ,. 8..
<5 ~ (Co(31/Cu<29)/Py<5>/Cu<2o>>s
0...
<2
m9
,3, 1 *— 0 D E]
\ 22:. a:
”:2 * (Co(6)/C11(20)/Py(16)/Cu(20))N
:1: i
E" 1
<3 1 7 D El [:1 13
A 22;. 2:
:0 . <00<3>/Cu<29>/Py<8>/Cu<2o>>..
: :
DC
:3 L .
1 7 13 g [:1 Q
1 2 + C11 10
_ O [:1 X C11 40
O..M1.111...1...1.11
0 2 4 0 8 10

Figure 4.4.8 The improved ratios of the measured and predicted magnetoresistance,
[AR,(HAP ) — AR,(H, )]/ [AR,AP — AR,P ] for four sets of samples.

117

4.4.2 Experimental results

In Tables 4.4.2-4.4.9 I present four sets of data for Co/Cu/Py/Cu multilayers for
different relative thicknesses of Co and Py: Co(3nm)/Py(8nm), Co(6nm)/Py(l6nm),
Co(3nm)/Py(5nm), and Co(6nm)/Py(10nm). There are some data are "bad" because of a
few reasons listed below: (a) Sample is current dependent (c.d.), (b) The resistivity of the

Nb is so large that ZARS/p is much bigger than usual value of 6.1 me2.

118

 

 

 

 

 

 

 

 

 

 

 

 

 

tCu sample CPP AR (mmZ) CIP (0'1)

(11m) . no. Hn Hp HS H0 H9 H.:
20 53303 35.78 39.20 27.25 0.7286 0.7151 0.7686
20 55104 32.55 36.72 25.09 0.8344 0.8133 0.8897
20 55103 26.57 28.52 21.02 0.6985 0.6835 0.7401
20 53302 22.03 23.20 18.62 0.3527 0.3492 0.3666
20 55106 19.45 21.36 16.06 0.4076 0.3970 0.4317
20 55105 13.71 14.63 12.77 0.2113 0.2083 0.2193 (a).
10 53306 18.71 20.88 15.33 0.1084 0.1026 0.1159
40 55107 34.34 38.09 27.63 2.012 1.975 2.093
40 53307 20.82 22.56 17.26 1.2330 1.2049 1.3007
40 55108 22.26 23.93 18.84 1.2199 1.2003 1.2760

 

 

 

 

 

 

 

 

 

 

Table 4.4.2 CPP ART and CIP values at H0, Hp and Hs of
[Co(3)/Cu(t)/Py(8)/Cu(t)]xN.

 

 

ll9

 

 

 

 

 

 

 

 

 

 

tCu N sample CPP MR % CIP MR % error r pk T r 3
(nm) . no. H,L Hnfi H0 H9 % rap - r p
20 8 533-03 31.3 43.9 5.49 7.48 4.3 1.26
20 8 551-04 29.7 46.4 6.63 9.37 2.5 1.23
20 6 551-03 26.4 35.7 5.96 8.28 4.6 1.11
20 4 53302 18.3 24.5 3.94 4.98 3.6 1.11
20 4 551-06 21.1 33.0 5.91 8.74 4.0 1.28

 

20 2 55105 7.36 14.6 3.79 5.28 (a). 1.2 1.11

 

 

 

 

 

 

10 4 533-06 22.1 36.2 6.92 13.0 2.8 1.32
40 8 551-07 24.3 37.9 4.03 5.97 2.6 1.15
40 4 533-07 20.6 30.7 5.49 7.95 5.2 1.33
40 4 551-08 18.2 27.0 4.60 6.31 3.4 1.27

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.4.3 CPP MR, CIP MR at H0, and H and ratio of the measured and
predicted MR values of [Co(3)/Cu(t)/Py(8)}Cu(t)]xN. rpk and rS are ART at Hp
and HS.

120

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tCu N sample CPP AR CIP

(nm) . no. Hn Hnfi Hg Hn Hp HS

20 8 533-05 41.77 46.82 32.23 0.7344 0.7169 0.7745

20 8 550-04 42.23 46.87 32.46 0.9334 0.9134 0.9855

20 6 550-03 30.66 35.56 25.68

20 4 533-04 25.27 27.77 20.81 0.4126 0.4047 0.4311

20 4 550-06 22.87 24.87 18.87 0.4034 0.3961 0.4276

20 2 550-05 15.68 17.12 14.12 0.2347 0.2292 0.2439

40 8 550-07 43.57 48.80 34.15 0.2829 0.2763 0.3018

40 4 550-08 24.95 27.80 20.84 0.9145 0.9046 0.9471

Table 4.4.4 CPP ART and CIP values at H0, Hp and HS of
[Co(6)/Cu(t)/Py(1 6)/Cu(t)]xN.

tCu N sample CPP MR % CIP MR % error r pk “ r 5
(nm) . no. Hn Hp 11,, Hnfi % r ap " r p
20 8 533-05 29.6 45.3 5.46 8.03 1.3 1.28
20 8 550-04 30.1 44.4 5.58 7.89 1.2 1.28
20 6 550-03 19.4 38.5 3.7 1.195
20 4 53304 21.4 33.4 4.48 6.52 2.8 1.346
20 4 550-06 21.2 31.8 6.00 7.95 2.0 1.16
20 2 550-05 11.1 21.3 3.92 6.41 4.1 1.367
40 8 550-07 27.6 42.9 6.68 9.23 4.1 1.32
40 4 550-08 19.7 33.4 3.56 4.70 2.1 1.38

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.4.5 CPP MR, CIP MR at Ho, H and ratio of the measured and predicted
MR values of [Co(6)/Cu(t)/Py(16)/Cu(t) xN. Tpk and r8 are ART at HO and H5.

121

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tCu N sample CPP AR11nm2) CIP (03
(nm) . no. Hn H,i Hn Hp H.i
20 8 591-03 54.76 59.16 42.46 0.8055 0.7978 0.8415 (b)
20 8 602-03 38.7 43.67 30.07 0.8193 0.8055 0.8631
20 6 602-07 34.04 35.96 25.60 0.5681 0.5668 0.6207
20 6 528-04 28.85 32.37 22.20 0.4930 0.5029 0.5165 Si
20 6 591-05 52.77 59.16 46.27 0.7062 0.6898 0.7512 (b)
20 4 591-07 40.38 44.26 34.47 0.3847 0.3786 0.4087 (b)
20 4 602-05 24.26 27.02 20.81 0.3611 0.3534 0.3704
20 2 528-03 15.47 16.24 13.74 Si
Table 4.4.6 CPP ART and CIP values at H0, Hp and HS of
[Co(6)/Cu(t)/Py( 1 0)/Cu(t)]xN samples.
tCu N sample CPP MR % CIP MR % error r pk _ r s
(11m) . no. I-Ifl Hp Hn Hp % r 0}) - r p
20 8 59103 29.0 39.3 4.47 5.48 (b) 2.8
20 8 602-03 28.7 45.2 5.35 7.15 4.1 1.30
20 6 602-07 33.0 40.5 9.26 9.51 3.1 1.38
20 6 528—04 30.0 45.8 4.77 2.70 Si 2.3 1.355
20 6 59105 14.1 27.9 6.37 8.90 (b) 2.9
20 4 591-07 17.2 28.4 6.24 7.95 (b) 4.5
20 4 602-05 16.6 29.8 2.58 4.81 1.6 1.34
20 2 528-03 12.6 18.2 12.6 18.2 Si 2.0 1.31

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.4.7 CPP MR, CIP MR at Ho, H and ratio of the measured and predicted
MR values of [Co(6)/Cu(t)/Py(10)/Cu(t ]xN samples. rok and r8 are ART at Ho

and Hs-

 

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:0, N sample CPP AR (me2) CIP (01)
(nm) . no. Hn H? H.: Hn H;1 H.;
20 8 602-04 33.66 34.49 24.41 0.6973 0.6935 0.7424
20 6 528-06 23.31 24.77 17.13 Si
20 6 602-08 27.85 28.78 20.65 0.4836 0.4785 0.5155
20 4 602-06 21.44 22.00 16.90 0.2302 0.2302 0.2386
20 2 528-05 12.38 12.73 10.83 0.1283 0.1277 0.1307 Si
Table 4.4.8 CPP ART and CIP values at Ho, Hp and HS of
[Co(3)/Cu(t)/Py(5)/Cu(t)]xN samples.
‘Cu N sample CPP MR % CIP MR % error r pk " r 3
(nm) . no. Hn H9 {-10 H9 % r ap r p
20 8 602-04 37.9 41.3 6.47 7.05 5.0 1.14
20 6 528-06 36.1 44.6 Si 3.0 1.22
20 6 602-08 34.9 39.4 6.60 7.73 3.1 1.30
20 4 602-06 26.9 30.2 3.65 3.65 6.2 1.35
20 2 528-05 14.3 17.5 1.87 2.35 Si 5.0 1.27

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.4.9 CPP NHL CIP MR at H0, Hp and ratio of the measured and predicted MR
values of [Co(3)/Cu(t)/Py(5)/Cu(t)]xN samples. rpk and rS are ART at H0 and HS.

123
4.5 Giant CPP-Magnetoresistance of N i/Ag Multilayers

These first measurements of CPP-MR on Ni/Ag multilayers had two goals. (1) To
extend CPP measurements to a new F metal to begin to establish the systematic data
needed to look for trends in MR. (2) As preparatory work on F UN and F 2/N multilayers
needed for studies of three component N/(Fz)/F 1/(F2)/N multilayers, in which very thin
(1-2 monolayersnML) F2 intermediate layers are inserted between F1 and N to
systematically change interface scattering.[114]

The results are presented as follows. (1) First we compare CPP MR(HO), CPP
MR(HP), CIP MR(HO) and CIP MR(Hp) for Ni/Ag multilayers with fixed tNi= 6nm and
with tNi=t Ag to see the differences of MR effects between Co/Ag and Ni/Ag. (2) We
compare the CPP MR at Ho for Ni/Ag with those for Co/Ag and Co/Cu to show how
much smaller are the values for Ni/Ag. We compare first samples with fixed t1: = 6 nm

and then samples with t1: = t Ag- Complete results are listed in tables in 4.5.2.
4.5.1 Giant CPP-Magnetoresistance of Ni/Ag Multilayers

We chose Ni/Ag for these measurements for two reasons. (1) Like Co/Ag and
Co/Cu, Ni and Ag have very small equilibrium mutual solubilities, thereby minimizing
interdiffusion. (2) The few published measurements suggest that the CIP-MR8 of Ni/Ag
are smaller than those of Co/Ag and Co/Cu, but still sizable.[103][102] We limit
ourselves to multilayers with Ag thickness t Ag26n1n, which we expect to be large enough
for the Ni layers to be magnetically uncoupled.

Figure 4.5.1 compares CPP-MR(H) with CIP-MR(H) for a Ni/Ag (6nm/6nm)

multilayer. Starting from the as-sputtered sample at magnetic field H=0 (designated Ho),

124

the MR first increases slightly, and then decreases monotonically up to the saturation field
H3, after which it cycles reproducibly, with maximum values at Hp, slightly above the
coercive field, no This behavior is similar to that in (6nm/6nm) Co/Ag[95] and Co/Cu
multilayers except that, for those pairs, the MRS at Ho were always larger than those at
Hp when the F and N metal layer thicknesses were 2 6 nm. As shown in Fig.4.5.2, in
Ni/Ag we had to go to t Ag > 9nm and Ni = 6nm to find CPP-NR(HO)>CPP-MR(Hp).
The reasons why Ni/Ag requires a larger t Ag to achieve this behavior need more study;
one possibility is that the Ni layers are still weakly coupled at t Ag=9nm. A similar plot to
Fig. 4.5.2 is shown in Fig.4.5.3 for samples with equal but varying Ni and Ag thicknesses,
and total thickness still fixed at 720nm.

We first compare the CPP-MRS with the CIP-MRS for Ni/Ag multilayers. This
comparison is shown in Fig. 4.5.2 for multilayers with fixed tNi=6nm and variable t A82
6nm and in Fig. 4.5.3 for multilayers with tNi=tAg- We see that the CPP-MR is
systematically several times larger than the CIP-MR for this range of Ag thicknesses.

The CIP-MR of Ni/Ag has also been measured by B. Rodmacq et al.[lOl], who
found that a peak in the MR at t Ag=1 1A (about 30%) for tNi=8A, and MRs around 6%
for Ni 2 30A. Our CIP-MR values are compatible with theirs. H.Sato, et al.[103] also did
some magnetoresistivity anisotropy on Ni/Ag in CIP geometry, but did not show MR
results.

We next, compare the CPP-MR at H() for Ni/Ag multilayers (filled symbols) with
the same quantities for Co/Ag multilayers. Fig. 4.5.4 and Fig. 4.5.5 shows that the CPP-
MR8 for Ni/Ag are systematically much smaller than those for Co/Ag. Further study is
needed to determine if this difference is due primarily to the magnetic properties of Ni and

NiAg alloys or if sample structure play a role.

125

These large differences in GMR for Co/Ag and Ni/Ag make them a very promising
pair for studies of three component N/(F2)/F1/(F2)/N multilayers, in which very thin (1-2
monolayers--ML) F2 intermediate layers are inserted between F1 and N metals to
systematically change interfaces scattering. In section 5.1 of chapter 5, exploratory

studies, I will show and discuss some data on Ag/(Ni)Co(Ni)/Ag and Ag/(Co)/Ni(Co)/Ag

multilayers.

126

 

:7 1 l r l I l l T l I l 1 l l l—rfir 1'14

10;— HP i

o ;_ c l J
E : v“ :
V 6___ ___4
D: : :
2 4: :
0.. i 2
0.. Z i
U 27 i
: \ ‘ HS;

0'- ‘ -t

" 1 1 g 1 1 1 1 l 1 1 1 1 1 1 l ‘

 

 

 

 

 

 

 

-1.0 —0.5 0.0 0.5 1.0
H (kOe)

Figure 4.5.1 CPP and CIP magentoresistances vs field H for a Ni/Ag (6nm/6nm)
multilayer.

127

 

 

 

83 _
Q110.0 — 0: CPP—MR(HO)
_ - . .
E : El 0: CPP—MR(HES)
t O . ‘ __ ,
$3 7.5 f .0 O :1: CIP I131201,
S”. g . . . CIP— {R(Hp)
’m i 0
Q) 5 O — 1:1
S i i
E : 0
ED 2'5 :— [:1 0
CU : i 0 i a I
z 0 O 1 1 1 1 l 1 1 1 1 l 1 1 1 1
0 20 40 00
tN (nm)

Figure 4.5.2 CPP-MR and CIP-MR vs t Ag for Ni/Ag (6nm/tAg) multilayers.

 

128

 

 

 

 

83 t

(1)10'0 :— 0; CPP—MR(HO)

i5 ; 6 0: CPP—MR(HP)

CD .75 ;_ e I; CIP—MR(HO)

7,; ; . o a; CIP—MR(HP)

.g i; . O .

L. 5.0 :— 11

O ._

*5 i

C 25 :— :1

CD 2

CU L i i I E

E O O 1 1 1 1 J 1 1 1 1 l 1 1 1 1 l
0 230 40 60

t N ( n m )
Figure 4.5.3 CPP-MR and CIP-MR vs t Ag for Ni/Ag (tCo=tAg) multilayers.

129

 

 

 

 

2)\(3100

Q) h

0 : V : CPP(HO) Co/Cu

g 7,. —_ 3V A : CPP(HO) Co/Ag

7, Q ; $913 . : CPP(HO) Ni/Ag

% i A A A A

8 50 j“ v v A

B : V Vv A A

Q.) 7 V

c 35 :— 1 A

OD _ V

g 0; "° '1 ° 1 11
0 20 40 60

1N (nm)

Figure 4.5.4 CPP-MR(HO) vs W for Ni/Ag, Co/Ag, and Co/Cu (6nm/m)
multilayers, where N=non-magnetic metal, Ag or Cu.

130

 

 

 

 

B€100”

8 :

g '75 E_ 8 A I CPP(HO) Clo/Ag

773 : M 0 : CPP(HO) Ni/Ag

§ 50?— A A

8 2

a 25k— A

8” : A

2 011.1.71.l11.,111111
O 20 4o 60

tN (mm)

Figure 4.5.5 CPP-MR(HO) vs t Ag for Ni/Ag, and Co/Ag multilayers (tC0=tAg).

131

4.5.2 Experimental results

In Tables 4.5.1-4.5.2 I present CPP MR and CIP MR data for Ni/Ag multilayers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t Ag N sample CPP AR (glmzL CIP (0'1) error

nm . no. I-In H? H; I-In H£L HQ %

6 60 400-01 69.1 71.2 65.4 0.03222 0.03318 0.03047 3.1

6 60 400-07 59.8 61.0 56.0 0.02774 0.02833 0.02600 3.9
9 48 400-001 57.5 57.9 53.6 0.02820 0.02839 0.02626 3.8
12 40 400-006 48.6 47.6 44.5 0.02295 0.02247 0.02100 1.9
18 30 402-02 43.7 42.8 39.9 0.01713 0.01681 0.01566 1.7
30 20 400-003 32.0 31.5 30.1 0.01543 0.01522 0.01451 2.7
60 11 400-02 25.5 25.3 24.8 0.01076 0.01067 0.01045 2.8

 

 

 

 

 

Table 4.5.1 CPP ART and CIP values at H0, Hp and HS of [Ni(6nm)/Ag(t)]xN

samples. Total sample thicknesses are as close as possible to 720nm.

 

132

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1Ag N sample CPP MR% CIPMR% [(ro-rs)ro]1/2
nm .no. H0 H9 H0 Hp

6 60 40001 5.72 8.82 1.48 2.09 16.0

6 60 400-07 6.69 8.96 1.30 1.59 14.95
9 48 400-001 7.39 8.11 1.13 1.40 15.09
12 40 400-006 9.29 7.0 1.02 1.21 14.17
18 30 402-02 9.39 7.34 4.13 4.24 12.80
30 20 400.003 6.34 4.89 0.60 0.47 7.8

60 11 40002 2.97 2.11 0.85 0.80 4.3

 

 

Table 4.5.2 CPP MR, CIP MR and [(ro-rs)r0]1/2 values at Ho, and Hp of

[Ni(6nm)/Ag(t)]xN samples. rO and r8 are ART at H0 and HS.Total sample

thicknesses are as close as possible to 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t N sample CPP AR (mefi CIP (0'1 error
nm . no. H0 H9 Hq H0 H9 HS %
6 60 40001 69.1 71.2 65.4 0.03222 0.03318 0.03047 3.1
6 60 400-07 59.8 61.0 56.0 0.02774 0.02833 0.02600 3.9
9 40 400-002 54.4 50.5 54.4 0.02196 0.02198 0.02040 5.1
12 30 402-01 49.5 48.9 46.3 0.02256 0.02229 0.02112 2.0
18 20 400-03 38.1 37.5 36.0 0.01865 0.01836 0.01759

 

 

 

 

 

Table 4.5.2 CPP ART and CIP values at Ho, Hp and H5 of [Ni(t)/Ag(t)]xN samples.
Total sample thicknesses are as close as possible to 720nm.

 

133

 

1 N sample CPP MR% CIPMR% [(fo'rs)roll/2

 

. no. Ho Hn 1-1n Hn

r

 

6 60 400-01 5.72 8.82 1.48 2.09 16.0

 

6 60 400-07 6.69 8.96 1.30 1.59 14.95

 

9 40 400-002 7.65 7.75 1.35 1.59

 

12 30 402-01 6.82 5.54 1.01 0.96 12.50

 

 

 

 

 

 

 

 

 

 

 

18 20 400-03 6.03 4.38 0.84 0.67 9.10

 

Table 4.5.4 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at HO, and Hp of
[Ni(t)/Ag(t)]xN samples. r0 and rS are ART at Ho and HSTotal sample thicknesses
are as close as possible to 720nm.

CHAPTER 5

Exploratory Studies

To probe additional physics underlying GMR, a variety of exploratory studies have

been done.

5.1 Effects of spin-dependent scattering at interfaces

Understanding scattering of electrons at interfaces and relative importance of the
scattering from bulk and from interface is key to understanding GMR. As indicated in
introduction chapter 1, historically, attention has focused mostly on the CIP
geometry.[l 14] We are interested in getting at the essence of interface scattering in CPP
geometry. In order to investigate the importance of spin-dependent scattering at interfaces
in CPP geometry, we fabricated three component N/(F2)/F1/(F2)/N multilayers, in which
very thin (1-2 monolayers--ML) F2 intermediate layers are inserted between F1 and N to
try to systematically change interface scattering. As we found[144] that the CPP MRS for
Ni/Ag are much smaller than those for Co/Ag, Co/Ag and Ni/Ag make a very promising
pair for evaluating the importance of interface scattering by introducing a few MLs of
each at interfaces of the other. If spin-dependent interface scattering is the dominant
mechanism of GMR, thin layers of Co added to Ni/Ag interfaces should produce a large
increase in MR. In contrast, if bulk scattering is dominant, much thicker layers of Co will

be required to substantially alter the MR. Similar case is also for Ni on Co/Ag interfaces.

134

135

From the data shown in the Figure 5.1.1-5.1.2, we can not find a simple clear way
in which CPP MR varies with the ultrathin layer thickness, thus further investigation

needs to be done.

 

 

 

1 T 1 l 7 f 1 T l 1 l l l l l

2001— 9 :HO

U :11

6x 1 o :H:
E 1501 -%
E? 1001~ 9 —j
\: L13 0 ‘71 Q 1
0: <1 9 <> ;
<1 501 —fi
()1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d

01) 0.1 012 0:3 021 015

1 Ni 1 n m 1
Figure 5.1.1 ART(H) versus tNi: the thickness of thin Ni layer, for
[Cu(9nm)/(Ni)/Co(6nm)/(Ni)/Cu(9nm)]43 samples

 

 

 

-‘T—V—1’ l 1— 1 1 l l Tfi 1 1 l 1

200Er 0 ll “7

_ 13 H 1

/\ 1 0 HS 1
NE 1501‘ '1
E 1 a i
. <> -

E 100} i1
a: — .9. .
D: - C} _
z: [— 1 O —:

00 O

1

1

O1 1 1 . 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1
0.0 0.1 0.2 0.3 0.4 0.5

tCO (mm)

Figure 5.1.2 ART(H) versus 1C0, the thickness of thin Ni layer, for
[Cu(9nm)/(Co)/Ni(6nm)/(Co)/Cu(9nm)]43 samples

137

Table 5.1.1-5.1.4 show CPP and CIP data for two sets of samples : (1)
[Cu(9nm)/(Ni)/Co(6nm)/(Ni)/Cu(9nm)]48. (2)
[Cu(9nm)/(Co)/Ni(6nm)/(Co)/Cu(9nm)]4g.

138

 

11.“ N sample CPP AR (fflmz) CIP (0-1) error

 

A . no. H0 13, Hs HQ Hr) H5 %

 

0 48 483-05 97.91 89.57 64.58 0.6663 0.6675 0.7430 3.1

 

1 48 483-01 105.7 103.2 81.8 0.6793 0.6781 0.7225 3.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 48 483-08 72.23 72.93 70.16 2.1
2 48 483-02 0.7239 0.7323 0.81 19
3 48 483-07 79.2 81.87 66.59 3.5

 

Table 5.1.1 CPP AR and CIP values at Ho, Hp and HS of
[Cu(9nm)/<Ni)/Co(6nm)/(Ni>/Cu<9nm>14s samples.

 

 

 

 

 

 

 

 

tNi N sample CPP MR % CIP MR % error [(ro-rs)ro]1/2
A . no. H1, H9 H0 H9 %

0 48 483-05 51.6 38.7 11.5 11.3 3.1 57.13

1 48 483-01 29.2 26.1 6.36 6.55 3.0 50.26

2 48 483-08 2.95 3.95 2.1 12.23

2 48 483-02 12.2 10.9

3 48 483-07 18.9 23.0 3.5 31.60

 

 

 

 

 

 

 

 

 

 

 

Table 5.1.2 CPP MR and CIP MR values at Ho and Hp of
[Cu(9nm)/(Ni)/Co(6nm)/(Ni)/Cu(9nm)]43 samples. r0 and rS are ART at H0 and
HS, respectively.

 

139

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1C0 N sample CPP AR (me2) CIP (9'1) error
A . no. 110 Hp HS ”11 HP 115 %
0 48 482-03 0.6898 0.6840 0.7154
1 48 482-06 70.54 70.34 60.84 0.6318 0.6359 0.6805 2.9
2 48 482-08 82.75 80.98 73.10 6.83
2 48 48202 132.2 122.6 114.0 0.6301 0.6417 0.6710 3.5
4 48 482-01 42.41 42.41 42.05 0.5689 0.5697 0.5908 1.6

Table 5.1.3 CPP AR and CIP values at Ho, Hp and HS of

[Cu(9nm)/(Co)/Ni(6nm)/(Co)/Cu(9nm)]43 samples.

1C0 N sample CPP MR % CIP MR % error [(ro-rs)ro] 1’2

A . no. H0 H9 H0 H9 %

0 48 482-03 3.71 4.59

l 48 482-06 15.9 15.6 7.71 7.01 2.9 26.16

2 48 482-08 13.2 10.8 6.83 28.26

2 48 482-02 16.0 7.55 6.49 4.57 3.5 49.05

4 48 482-01 0.86 0.21 3.85 3.70 1.6 3.91

 

 

 

 

 

 

 

 

 

 

 

Table 5.1.4 CPP MR and CIP MR values at 110 and HI) of
[Cu(9nm)/(Co)/Ni(6nm)/(Co)/Cu(9nm)]43 samples. r0 and rS are ART at Ho and
H3, respectively.

140

5.2 Dependence of sample quality on sputtering
conditions

In the studies detailed earlier, it was essential to hold the sputtering conditions as
constant as possible to obtain comparable sample quality and reproducible data. For
example, the pressure of the high purify Ar sputtering gas was held at 2.5 mTorr to make
the mean free path of the ejected atoms in the order of the distance between target and
substrate, and the sputtering voltages and currents were also held within narrow ranges.
To investigate the dependence of sample quality on sputtering conditions, we decided to
reduce the sputtering rates by a factor of 2 using two means: (1) reducing the target
voltages and target currents( type 1); (2) increasing the sputtering pressure (type 2), and
then compare the data of these samples with those sputtered under standard sputtering
conditions.

In Table 5.2.1-5.2.4 , I present data for samples with reduced sputtering rates. In
Table 5.2.5-5.2.6, I present data for samples with standard sputtering rates made in the
same sputtering run, which are reasonably consistent with the old Co/Ag data from S.F.
Lee.

We show the comparison of the data with those grown under standard conditions in
Figures 5.2.1, 5.2.2, and compare of the MRS with those grown under standard conditions
in Figures 5.2.3. and 5.2.4. (1) The data of the samples made with reduced sputtering
rates by means of reducing the target voltages and target currents are generally similar to
the data of the samples made under standard sputtering conditions; (2) the data of the
samples made with reduced sputtering rates by means of increasing the sputtering
pressure are mostly quite different.

In Figures 5.2.5, 5.2.6, and 5.2.7, we show typical high angle diffraction scans on

samples made under type 1, type 2 and standard conditions. In all three scans, we found

141

that constructive interferences from bulk Ag and bulk Co respectively give the expected
peaks at detector angle 20 roughly 38 and 44 degrees. Scans of samples made under type
1 and standard conditions show clear multilayer satellites around the bulk peaks, while
those under type 2 conditions do not. In Figures 5.2.8, 5.2.9, and 5.2.10, we show the
magnetization measurements on the same samples. The Hcs are all between 50—80 0e,
and MO/MS (M0 is magnetization at zero field, MS is saturation magnetization) is about
80%. Taking into account uncertainties in samples area, the saturation magnetizations are
close to each other. We found the magnetization measurements for samples made under
different sputtering conditions to be roughly similar.

When the sputtering pressure is increased, the mean free path of the sputtered atoms
is reduced, thus increasing the sputtering pressure may substantially change the structures
of the N and F metal layers, and the roughness at the interfaces. Further studies need to

been done to better understand behaviors uncovered here.

 

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0 2 0 4 0 6 0 8 0

Bilayer No. N

Figure 5.2.1 ART versus bilayer number N for samples with reduced sputtering
rates by means of reducing the target voltages and target currents, and samples
grown under the standard conditions.

 

 

 

 

:-—- 1 1 l T 1 [1 f 1 l 1 T f 1
200 e . :l-lo l) 9 110 N j
- - llp P 9 .l-lp N .
NA ; . 113 P 9 113 N ~
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0 20 40 60 80

Bllayer No. N

Figure 5.2.2 ART versus bilayer number N for samples with reduced sputtering
rates by means of increasing the sputtering pressure, and samples grown under the
standard conditions.

143

 

 

 

N i
1001~
Cl)
0 1 0
C3 1 O
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(Vt) —
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£1 1 9 MR(A)
,2. ()1_1 I 1 1 1 1 1 1 1 L11 1 1 1 1
20 4O 60 80
N

Figure 5.2.3 MR at H0 versus bilayer number N for samples with reduced
sputtering rates by means of reducing the target voltages and target currents, and
samples grown under the standard conditions.

 

O

 

 

1. 1;“

81001?“ 0

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g 7: P O

1/1 .1

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g 1 o : MR(N) °

2—1 0 f 1 1 1 1 1 1 1 1 1 1 1 1 1 1
20 4O 60 80

N

Figure 5.2.4 MR at H() versus bilayer number N for samples with reduced
sputtering rates by means of increasing the sputtering pressure, and samples grown
under the standard conditions.

144

4000
3000 — 1

‘DOOOL 1 1

1000 1

’1
1 11,11,141

34 36 38 4O 42 44 46 48 50

CNTS/SEC
r

 

2 THETA (DEGREE)

Figure 5.2.5 9-29 spectrum for sample tCO=tAg=6nm grown with reduced
sputtering rates by means of reducing the target voltages and target currents.

2000 F“

 

 

1500L
1
£73 1 11
.9 ~ 11
l 1.
D F 1 ‘1 fl
1 f“ 1 j
r ‘1
000 1‘ 1, J11! \‘4
0*-11 1.11...{mf‘*~:‘~1..1..mm1
34 36 88 4O 42 44 46 48 50

2 THETA(DEGRBE)

Figure 5.2.6 9-29 spectrum for sample tCo=tAg=6nm grown with reduced
sputtering rates by means of increasing the sputtering pressure.

145

5000
11
1 1
4000;w 111
'1 11 1!
B 3000 11 *1
ED 1‘ 1 1‘
\ 1
m 1111 1
F - ' 1
5 2000 f 11, 1
t 1 1 1. ,
1 / v 1 11V
1000 1 1

1 1 19 11 ‘ 1
0 1 1 191.99" 11111 \3/ ’\Y—’/\\.I'. 1 1 ,\-1-11. 1 . .1

34 (if) 38 4O 42 44 46 48 50

2 'I‘HETA (DEG REE)

Figure 5.2.7 6-29 spectrum for sample tC0=tAg=6nm grown under standard
sputtering conditions.

 

 

 

 

 

 

FT/"\111 , .
.11117717771”*17*1”“7*7717‘1‘TW
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_l/:1 1L11l l 11111111 111111111 1 11111 1 111 11111441
-1.00-0.7§0.500.250.00 025 0.500.751.00
11 {54001

Figure 5.2.8 Magnetization measurement for sample tCo=tAg=6nm grown with
reduced sputtering rates by means of reducing the target voltages and target
currents.

146

[C7 O r Y'_" — 1 . ‘_T"Y_*|' ’T ffifi—fi—j'j—TTT“ , 1
‘ fi1 T 1 W

 

 

 

 

1 1

1 1 ‘

1 1 :

3101‘ 1 1M 3 A 3 -

E 1 .4
0) 1 / -

(j) 1 .

O 1 111 .

:3 01 -~

1 1 .

E3 1 1 4

101*‘*‘ 3' , i

1 1 A

1 _

1 1 “
113111.422 2241....12...‘“221.2..Lu2rl...

“'"0.00 0.25 0.50 0.751.00

Figure 5.2.9 Magnetization measurement for sample tCo=tAg=6nm grown with
reduced sputtering rates by means of increasing the sputtering pressure.

 

2 1 Y 7‘7 Y r1 f7 r I T T T TV T ffT fT Y Y T Y T T T l l l l I Yfi
O 1 1 1 1 1 1

0

1 1

 

 

 

 

1 1
2-:.fi._fi - - - 4- «‘1
3101 r/ —1
E} 1 1 / 1
(p 1 11 1
:. .11 11 1
.4 U1 11 —
_\ 11 z
%— 1
1 A
—1OL: - ‘4‘.._1‘::- 1 1
1 1 +
1 1 ~
{101333313 u-..1....1.--21 .12 120.21
“1.00 0 71:30 500.251.0010 2 \0 51 0./i3100
h ”K38

Figure 5.2.10 Magnetization measurement for sample tCo=tAg=6nm grown under
standard sputtering conditions.

147

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t Ag N sample CPP AR (mez) CIP (9‘1) error
nm . no. H0 H9 H5 H0 H9 l-lS %

6 60 608-02 89.10 85.38 58.73 0.6837 0.7261 0.8040 Si 3.0

9 48 608-06 85.38 73.88 49.21 0.9880 1.0440 1.1757 Si 3.7
18 30 607-03 70.8 63.82 44.63 1.2615 1.2882 1.3936 Si 11

6 60 594-05 102.0 84.70 60.00 0.6658 0.7082 0.7846 6.3

 

 

 

 

Table 5.2.1 CPP AR and CIP values at H0, Hp and HS of [Co(6nm)/Ag(t)] N
samples with reduced sputtering rates by means of reducing the target voltages and
target currents.

 

 

 

 

 

 

t Ag N sample CPP MR % CIP MR % error [(ro-r$)ro]1/2
(nm) . no. H0 H9 H0 :19 %

6 60 608-02 51.7 45.4 17.6 10.7 Si 3.0 52.02

9 48 608-06 73.5 50.1 19.0 12.6 Si 3.7 55.57

18 30 607-03 58.6 43.0 10.5 8.18 Si 11 43.04

6 60 594-05 54.6 41.2 17.8 10.8 6.3 65.45

 

 

 

 

 

 

 

 

 

 

 

Table 5.2.2 CPP MR and CIP MR values at H0 and H of [Co(6nm)/Ag(t)] N
samples with reduced sputtering rates by means of re ucing the target voltages and
target currents. r0 and r8 are ART at Ho and HS, respectively.

148

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAg N sample CPP AR (mm?) CIP (9") error
(11m) . no. H0 H9 H5 H0 H9 H5 %
18 30 608-05 56.52 45.93 37.29 1.2212 1.2677 1.3696 Si 2

6 60 608-04 79.71 83.50 71.45 1.4416 1.4695 1.5450 Si 6.3
9 48 608-07 60.76 61.01 45.77 1.0388 1.0397 1.1627 9.3
18 30 594-06 60.45 49.69 37.72 1.3903 1.4970 1.6525 2.30

 

Table 5.2.3 CPP AR and CIP values at H0, Hp and HS of [Co(6nm)/Ag(t)] N
samples with reduced sputtering rates by means of increasing the sputtering

 

 

 

 

 

 

 

pressure.

tAg N sample CPP MR% CIP MR% error% [(ro-rs)ro]1/2
(nm) .no. H0 H9 11‘L Hg

18 30 608-05 51.6 23.2 12.2 8.04 Si 2.0 32.97
6 60 608-04 11.6 16.9 7.17 5.14 Si 6.3 25.66
9 48 608-07 32.8 33.3 11.9 11.8 9.3 30.18
18 30 594-06 60.3 31.7 18.9 10.4 2.3 37.07

 

 

 

 

 

 

 

 

 

 

 

Table 5.2.4 CPP MR and CIP MR values at HO and HI) of [Co(6nm)/Ag(t)] N
samples with reduced sputtering rates by means of increasing the sputtering
pressure. rO and rS are ART at HO and HS, respectively.

 

149

 

 

 

 

 

 

 

 

 

 

t Ag N sample CPP AR CIP error
(nm) . no. HL “9 Hi 1-1o 1-15L HS %
9 48 594-03 87.14 69.50 47.60 0.9900 1.0726 1.1861 2.2

6 60 594-02 1 16.7 91.63 65.9 0.651 1 0.7360 0.8049 8.9

6 60 608-03 97.9 74.14 50.67 0.8468 0.9139 1.0559 Si 3.9

 

 

 

 

 

 

 

 

 

 

 

Table 5.2.5 CPP AR and CIP values at Ho, Hp and Hs of [Co(6nm)/Ag(t)] N
samples with standard sputtering rates.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t Ag N sample CPP MR % CIP MR % error [(ro-rs)r0]1/2
(nm) . no. H0 H9 H0 Hp %

9 48 594-03 83.1 46.0 19.8 10.6 2.2 58.70

6 60 594-02 77.1 39.0 23.6 9.36 8.9 77.0

6 60 608-03 93.2 46.3 24.7 15.5 3.9 68.0

 

 

 

Table 5.2.6 CPP MR and CIP MR values at H0 and 12%“ [Co(6nm)/Ag(t)] N

samples with standard sputtering rates. r0 and rS are

respectively.

T at Ho and H5,

 

150
5.3 Further studies of Spin-Valve Structure

5.3.1 Measurements of Co(t1)/Cu/Co(t2)/Cu, Co(t1)/Ag/Co(t2)/Ag Multilayers

In section 4.4 of chapter 4, we described a kind of spin valve structure, three
component Co/Cu/Py/Cu multilayer. We also made some additional simple two
component Co(t1)/Cu/Co(t2)/Cu multilayer with different thicknesses of Co layers to
obtain different Hc(tco). If the difference between the two saturation fields is large
enough, an AP state can be produced in Co(t1)/N/Co(t2)/N multilayers, and 1}} to be large
enough so that exchange coupling between the Co(tl) and Co(t2) layers is weak. Earlier
studies of two component systems, Co/Cu and Co/Ag, yielded that Co(3nm) has a
saturation field of 100-200 Oe and Co(6nm) has a saturation field around 1000c. At low
temperature, the characteristic lengths in the CPP geometry, spin diffusion lengths in the
F and N metal layers, are normally long enough to be assumed infinite.[137][138] We
should then be able to predict the resistances of any Co(t1)/N/Co(t20/N multilayers in the
P and AP states, using only parameters from in dependent measurements on the Co/Cu or
Cu/Ag multilayers.

Table 5.3.1-5.3.4 show CPP and CIP data for two sets of samples : (1)
Co(t1)/Ag/Co(t2)/Ag multilayers. (2) Co(t1)/Ag/Co(t2)/ Ag multilayers. There are some
data are "bad" because of a few reasons listed below: (a) Sample is current dependent
(c.d.), (b) The resistivity of the Nb is so large that ZARS/F is much bigger than usual
value of 6.1 fnmz.

Figure 5.3.1 compares magnetization M versus H [Fig. 5.3.1(b)] to ARt versus H
[Fig. 5.3.1(a)] for a Co(tl)/Ag/Co(t2)/Ag (6/20/2/20)4 multilayer. Figure 5.3.2 compares
magnetization M versus H [Fig.5.3.2(b)] to ARt versus H [Fig. S.3.2(a)] for a

151

Co(t1)/Cu/Co(t2)/Cu (6/40/2/40)2 multilayer. In Fig. 5.3.1(a) and S.3.2(a), near zero, the
ARts all increase and reach the peak values between sz100-200 0e, not as fast as in
Co/Cu/Py/Cu multilayer. The Filled circles are the predictions from two current model,
we found that the predicted values are all higher than the actual measured peak values.
Then the AR for Co(t1)/Cu/Co(t2)/Cu has a small flat region around peak value, while
the AR for Co(t1)/Ag/Co(t2)/Ag has a pretty sharp peak. In Fig. 5.3.1(b) and S.3.2(b),
near zero, the magnetizations decreases until 100-200 Oe which is around Hp, then go to
saturation values relative slower. So in Figure 5.3.1 and 5.3.2 we do not see the same
phenomena as we observed in the Co/Cu/Py/Cu multilayers that the lower HS (thicker
Co) layer reorients over a narrow field range near H=0, thus ARt increases and M
decreases rapidly over the same range. As discussed above, an AP state is not easily
produced in the Co(t1)/Ag/Co(t2)/Ag, Co(t1)/Cu/Co(t2)/Cu multilayer system. This
behavior could be due to the fact that the difference between saturation fields of two Co
layers with different thicknesses is not large enough to produce an AP state. For further
work, we should increase the difference between the saturation fields of two Co layers
with different thicknesses under the conditions: (1) the thickness of Co layer should be
thick enough (above 2nm) to have complete Co layer structure; (2) the thickness of Co
layer shouldn't be too thick (above 18nm) to give rise to internal magnetic structure
changes. For further studies, we should try the Co thicknesses which are 2nm and 12nm,

or 2nm and 16nm.

 

 

 

. l
_ // \.~ -\_\
_ A 2 I» _ __ F.— [J14 T T“‘”~O—*—~_ K 7‘ x
O .22 ——- Rq-—-2:—
|
g 4 i4 i J; 1 #i 4_ l 1 i i u 1_Lr 1

 

 

 

 

 

 

 

E?
E I 4
Q) r l ‘4
IO 0 H I _—4
v—l >_ I T
v . I f a
I
E: ~1.L x/ 1/ j
1— - ”*3,” ~ - ,
r ----- ~ -25.-.. 1
i .
_2-441 1 l lki‘HILLhklillllJ‘ll
“0-8 —O.6 —0.4 —0.2 0.0 0.2 0.4 0.6 0.8
H (kOe)

Figure 5.3.1 (a) Magnetoresistance and (b) magnetization M of a
[Co(6)/Ag(20)/Co(2)/Ag(20)]4 multilayer. The sample dimensions are in nm.

 

 

i.eBFT‘II‘F T1 fiji firlf l j—
I
.(Ei) . 1
1.0 | ~
_ |
|
|

 

O O

C CD

. r —.—T—

l

k

l

i H.

[K\\\\j

//
r . 1 A A

 

 

 

 

 

 

 

1 ¥ 4 ......... 13,-sz, I, ,4
F 1 4
A 0 5 i< b) .2 "'"KA ”I g
3 l -
E ‘ -
no 0
EC) 0.0 f A
5 l 1
g 0 . 5 ..-f/ , —
3.1.5 57:---~«/ ”J 7 1 +
l 1 .
_1_Ol,.. .L....1....1....1....L.-.-1.-..1.-..
~08 ~06 —-0.4 —0.2 0.0 0.2 0.4 0.6 0.8
11 (kOe)

Figure 5.3.2 (a) Magnetoresistance and (b) magnetization M of a
[Co(6)/Cu(40)/Co(2)/Cu(40)]2 multilayer. The sample dimensions are in nm.

' 2 a Lats...’

154

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

description N sample CPP AR (me2) CIP (0‘1) error
(11111) . no. H0 Hp H5 H0 Hp HS %
6/20/2/20 8 $38-04 26.41 25.34 18.09 3.6
6/20/2/20 6 538-03 24.71 23.36 17.97 0.5467 0.5507 0.6072 2.9
6/20/2/20 4 538-05 18.1 1 17.96 14.06 0.4083 0.4073 0.4520 4.9
6/20/2/20 2 53 8-06 12.96 12.74 11.44 0.1754 0.1764 0.1835 2.5
6/8/2/8 4 515-04 18.01 17.64 13.80 0.0919 0.0895 0.1006 5.8
6/8/2/8 2 515-03 13 .75 13 .82 12.27 0.0451 0.0438 0.0462 1.6
6/8/1.5/8 8 51506 27.47 29.83 19.42 4.5
6/8/1.5/8 2 515-05 12.94 12.70 11.23 0.0477 0.0472 0.0508 2.5
Table 5.3.1 CPP AR and CIP values at H0, H1) and Hs of Co(t1)/Ag/Co(t2)/Ag
samples.

description N sample CPP MR % CIP MR % error

nm . no. H0 H9 H0 H9 %

6/20/2/20 8 538-04 46.0 40.1 3.6

6/20/2/20 6 538-03 37.5 30.0 11.1 10.3 2.9

6/20/2/20 4 53 8-05 28.8 27.7 10.7 1 1.0 4.9

6/20/2/20 2 538-06 13.3 1 1.4 4.62 4.00 2.5

6/8/2/8 4 515-04 30.5 27.8 9.47 12.4 5.8

6/8/2/8 2 515-03 12.1 12.7 2.44 5.48 1.6

6/8/1.5/8 8 51506 41.5 53.6 4.5

6/8/1.5/8 2 515-05 15.2 13.1 6.50 7.63 2.5

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.3.2 CPP MR and CIP MR values at H0 and H of Co(tl)/Ag/Co(t2)/Ag
samples with standard sputtering rates. r0 and rS are AIRT at HI) and HS,
respectively.

155

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

description N sample CPP AR (me2) CIP (0")

nm . no. HQ Hp 119 H0 H9 HS

6/8/2/8 10 514-08 28.91 27.93 19.35 0.1873 0.1895 0.2330
6/8/2/8 4 514-03 16.49 16.27 13.45

6/8/2/8 2 514-02 13.60 13.45 12.33 0.0381 0.0383 0.0412
6/20/2/20 8 534-04 22.10 22.10 16.55

6/20/2/20 2 527-02 16.36 16.46 15 .45 (b)
6/10/2/10 2 514-06 12.44 12.39 11.17 0.0723 0.0721 0.0763
6/40/2/40 8 534-02 24.37 24.95 19.96 2.827 2.791 2.934
6/40/2/40 2 527-03 16.31 16.40 15.44 6.017 6.016 5.994 (b)
6/8/1.5/8 8 514-05 25.55 25.69 18.77 0.2443 0.2421 0.2820
6/10/1.5/10 2 514-07 12.14 12.23 11.01 0.0481 0.0475 0.0509

 

 

 

 

 

 

 

 

 

 

Table 5.3.3 CPP AR and CIP values at Ho, Hp and HS of Co(t1)/Cu/Co(t2)/Cu

samples

 

156

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

description N sample CPP MR % CIP MR % error

nm . no. H0 H9 H0 1-1p %
6/8/2/8 10 514-08 49.4 44.3 24.4 23.0 2.6

6/8/2/8 4 514-03 22.6 21.0 2.5
6/8/2/8 2 514-02 10.3 9.08 8.14 7.57 3.2
6/20/2/20 8 534-04 26.9 26.9 2.0
6/20/2/20 2 $27-02 5.92 6.52 (b) 2.3 Si
6/10/2/10 2 514-06 11.3 11.0 5.53 5.83 2.6
6/40/2/40 8 534-02 22.1 25.0 3 .78 5.12 5.2
6/40/2/40 2 527-03 5.58 6.19 (b) 2.0 Si
6/8/1.5/8 8 514-05 36.1 36.9 15.4 16.5 3.4
6/10/1.5/10 2 514-07 10.3 11.1 5.82 7.16 2.0

 

Table 5.3.4 CPP MR and CIP MR values at Ho and Hp of Co(t1)/Cu/Co(t2)/Cu
samples with standard sputtering rates. ro and r8 are ART at Hp and HS,
respectively.

157

5.3.2 Dependence of GMR on the order of Ferromagnetic layers

As we have discussed above, at low temperatures, in the limit where the spin-
diffusion lengths in the F and N metals are much longer than the mean-free-paths and
layer thicknesses (i.e., lsf effectively infinite),[l37][l38] the total resistance of a
multilayer can be calculated by the two channel series resistor model, and all that matters
is the scatterings of Spin up and spin down electrons in the bulk layers and at the
interfaces. There is then nothing in Eq. 4.4.1 that depends upon the order of the
ferromagnetic layers. To test whether this order matters, we designed a new type of
[F1/Cu]N[F2/Cu]N multilayer (type 11), shown in Figure 5.3.3. From the two current
model, this type II multilayer should have the same ARS for the AP and P states as the
standard spin-valve [F 1/Cu/F2/Cu]N multilayer (type I) (see Chapter 4). To avoid
proximity effects in the N layers, we deposited a 6nm Co "cap" layer just below the top

Nb strip for all the samples.

Nb Co Cu Co Cu Py Cu Py Cu Co Nb

Figure 5.3.3 Schematic of the antiparallel (AP) state of type II multilayers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

When, however, lsf becomes comparable to the multilayer thickness tT, then we
might expect to see one of the following deviations from behaviors for infinite 13f. (#1)
The shapes of the CPP ARS vs H for the two kinds of multilayers might remain similar,
but the maximum ARt for the type II multilayer could be smaller than that for the type I
multilayer due to the finite value of 15f. (#2) The behaviors of the Co and Py layers in the

158

type II multilayer might decouple to where the total MR becomes approximately the sum
of the separate contributions from Co/Cu and Py/Cu.

We first compare type I and type II magnetizations M to see if any significant
differences occur. Fig. 4.4.2b shows M vs H for a [Co(3)/Cu(20)/Py(8)/Cu(20)]3
multilayer and Fig. 5.3.5b shows the practically indistinguishable behavior of M vs H for
a [Co(3)Cu(lO]6[Py(8)/Cu(10)]6 multilayer. We conclude that there are no significant
differences in magnetizations of our type I and type II multilayers

Fig. 5.3.4 compares AR(H) - AR(HS) for a [Co(3)/Cu(l0)/Py(8)/Cu(10)]2 type I
multilayer and a [Co(3)/Cu(l 0)]2[Py(8)/Cu(10)]2 type II multilayer. The forms are rather
Similar, except that there is some evidence of additional structure in the type II multilayer,
and the virgin state value (black dots) is lower than the maximum after HS in both type I
(as required if the maximum is the AP state) and type 11. Moreover, the maximum value
of AR(H) -AR(HS) for the type II multilayer is only about 68% of that for the type I.
These behaviors are all consistent with deviation #1 above.

For larger N, we compare Fig. 4.4.2 for a [Co(3)/Cu(20)/Py(8)/Cu(20)]3 type I
multilayer with Fig. 5.3.5a for a [Co(3)/Cu(10)]6[Py(8)/Cu(10)]6 type II multilayer.
Here we find that ARt for the type II multilayer increases more rapidly just beyond H=0,
and decreases more quickly from its peak. This is the qualitative behavior we would
expect for a Py/Cu multilayer alone, since the maximum would then occur near the
coercive field Hc rather than at HS. We also find that the value of ARt for the virgin
sample is larger (black dot) for the type II multilayer in Fig. 5.3.5a than at any subsequent
value, whereas for the type I multilayer the value of ARt for the virgin sample is less than
that for ARt(AP) (not shown in Fig. 4.4.2). Comparing ART(H) - ART(HS) for the type

I and type II cases (reducing the values of Fig. 4.4.2 by 3/4 to approximately convert N=

159

8 to N = 6) Shows that the type 11 maximum is only about half that of the type I. These
behaviors look intermediate between cases #1 and #2 above.

If we take a simple exponential model: (””4 = MR” / MRI, to describe the
effect of finite spin-diffusion length on the multilayers with N=2, then the measured MR1

1/MR1 z68% gives tT/lsfz 0.38, suggesting that lsf is comparable to t'r. If we simply use
tT/lsf z 0.38x2 for multilayer with N=4, we would predict MRII/MRI z 0.46, and for a
multilayer with N=6, MRII/MRI z0.32. The latter result is smaller than what we see in

Fig. 5.3.5a, suggesting that we must take account of case #2.
To check whether 15f comparable to tT is reasonable, we make the following rough

. t t - . . . .
estimate. We assume that f = 217“, where 15 1 is the index for each layer. We use
Sf 1' sf

[Ef‘z 450nm[refj, and assume that the values of If; and (5} are reduced from that for Cu
solely due to reduction of Xe]. Since PCu/PCo/PPy z 1/10/26, we use 13 Sf =

(Asfle,)/6.[137][138] to estimate [ff z 150nm and if} z50nm. For the multilayer
with N=2, we thus estimate tT/lsfz 0.49 and MRn/MRI z 63%. This theoretical estimate
is comparable to the experimental one made above. The simplest interpretation of our
data is thus that the total spin diffusion length is comparable to the total thickness of the
N = 2 multilayer. More complete studies of type I and type II multilayers must be made to

firrther test this very simple picture.

 

.l l i

 

 

 

 

 

ART(H)—ART(HS) (meZ)

 

 

 

“0.4 --0.2 0.0 0.2 0.4
H ( k 0 e )
Figure 5.3.4 (a) Magnetoresistance of a [Co(3)/Cu(10)/Py(8)/Cu(10)]2 multilayer

(type I).and (b) Magnetoresistance of a [Co(3)/Cu(l0)]2[Py(8)/Cu(10)]2 multilayer
(type II). The sample dimensions are in nm.

161

 

 

 

 

 

 

 

 

 

 

6 1__4 1 y 7 j? T .
..C 1 .
E; I‘ (a) 1 fl
5 1 11
a? L ' ‘
<1 2 ’ / lll \ J
- ‘1 it
33 O 1__.5 Wrij” I “if-
1 1
1 . . 1 1 1 M
2 1 1 t 1 1 1 T
l (b) 1 .... -
1 --.. ’1
A 1 1:— /r; i
:5 r 1 1
E 1
mm 0
0 OP : r
v I 1 :
1
1
g: __ 1 fl
LLLLZ'éAw—«r* | 4
1
_2i 1 5 1 l . 1 1 l . . . l h .
—0.4 —0.2 0.0 0.2 0.4

H (kOe)

Figure 5.3.5 (a) Magnetoresistance and (b) magnetization M of a

[Co(3)/Cu(10)]6[Py(8)/Cu(10)]6 multilayer (type II). The sample dimensions are

innm.

162

Table 5.3.5 Show CPP and CIP data for two types of F l/Cu/FZ/Cu samples.
There are some data are "bad" because of a few reasons listed below: (a) Sample is

current dependent (c.d.), (b) The resistivity of the Nb is so large that 2ARS/F is much

bigger than usual value of 6.1 fnmz.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tcu N sample CPP AR (mm?) CIP (1)-1)

nm .no. H0 H9 H5 H0 H9 HS
10 6* 603-07 25.22 23.80 19.74 0.2203 0.2282 0.2377
10 6 603-08 26.89 29.41 19.31 0.2028 0.1921 0.2238
10 5* 606-06 24.60 23.80 20.66 0.1530 0.1589 0.1666
10 5 606-07 24.27 26.42 18.75 0.1836 0.1751 0.2005
10 4* 603-05 15.07 15.05 13.02 0.1725 0.1742 0.1824
10 4 603-06 18.79 20.91 14.66 0.1320 0.1322 0.1400
10 4* 606-05 19.73 19.39 17.21 0.1594 0.1630 0.1712
10 3* 606-04 18.73 18.55 16.21 0.1024 0.1043 0.1093
10 3 606-03 (a)
10 2* 603-04 13.24 13.49 11.85 0.0670 0.0656 0.0686
10 2 603-03 14.38 15.04 12.63 0.0721 0.0708 0.0749

 

Table 5.3.5 CPP AR and CIP values at H0, Hp and HS of Co(3nm)/Cu/Py(8nm)/Cu

samples. (* : type II multilayers.)

 

163

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cu N sample CPP MR % CIP MR % error
nm . no. Ho 11L H0 H3) %
10 6" 603-07 27.8 20.6 7.90 4.16 3.5
10 6 603-08 39.3 52.3 10.4 17.1 4.5
10 5“ 606-06 19.1 15.2 8.89 4.85 6.1
10 5 606-07 29.4 40.9 9.20 14.5 1.5
10 4" 603-05 15.8 15.6 5.74 4.71 2.1
10 4 603-06 28.2 42.6 6.06 5.90 2.7
10 4* 606-05 14.6 12.7 7.40 5.03 3.9
10 3* 606-04 15.6 14.4 6.74 4.79 1.8
10 3 606-03 (a

10 2* 603-04 11.7 13.8 2.39 4.57 0.96
10 2 603-03 13.9 19.1 3.88 5.79 5

 

 

 

Table 5.3.6 CPP MR and CIP MR values at HO and Hp of Co(t1)/Cu/Co(t2)/Cu
samples. to and rs are ART at Hp and HS, respectively.("‘ : typeII multilayers.)

164

Lastly, I list data for a few samples that don't belong to the sets listed above.

 

description N sample CPP AR (fflmz) CIP (9'1)

 

. no. HO Hp H5 H0 H9 HS

 

600/800 2 527-05 18.88 19.57 17.06 0.0936 0.0932 0.0947 (b)

 

6/20/8/20 2 527-07 18.31 19.68 16.91 0.3692 0.3686 0.3869 (b)

 

 

 

 

 

 

 

 

 

 

3/20/16/20 4 $34-07 21.96 24.16 17.94 0.3574 0.3496 0.3762

 

 

 

Table 5.3.7 CPP AR and CIP values at Ho, HD and Hs of Co/Cu/Py/Cu samples.

 

description N sample CPP MR % CIP MR % error

 

.no. 110 HIL H1, 11,, %

 

6/20/8/20 2 527-05 10.7 14.5 1.18 1.61 (b) 5.5 Si

 

 

6/20/8/20 2 527-07 8.28 16.4 4.79 4.96 (b) 3.0 Si

 

 

 

 

 

 

 

 

 

 

 

 

3/20/16/20 4 534-07 22.4 34.7 5.26 7.61 1.9
Table 5.3.8 CPP MR and CIP MR values at H0 and HI) of Co/Cu/Py/Cu samples.
r0 and rs are ART at HI) and HS, respectively.

 

165

 

 

 

 

 

description N sample CPP AR(mez) CIP (0")

. no. HQ Hp HS HO Hp HS
3/20/8/20 8 538-07 41.34 47.16 30.07 0.8366 0.8109 0.9044
3/20/8/20 4 538-08 23.41 26.19 18.39

 

 

 

 

 

 

 

 

 

 

 

Table 5.3.9 CPP AR and CIP values at Ho, HI) and Hs of Co/Ag/Py/Ag samples.

 

 

 

 

 

description N sample CPP MR % CIP MR % error
. no. H0 H9 H0 H9 %

3/20/8/20 8 538-07 37.5 56.8 8.10 11.5 2.3

3/20/8/20 4 538-08 27.3 42.4 1.7

 

 

 

 

 

 

 

 

 

 

 

Table 5.3.10 CPP MR and CIP MR values at Ho and Hp of Co/Ag/Py/Ag samples.

to and rs are ART at HI) and HS, respectively.

CHAPTER 6

Summary and Conclusions

In my thesis, I briefly described the first measurements of the Giant
Magnetoresistance (MR) with Current flowing Perpendicular to the layer Plane (CPP) at
MSU. As our basic technique for making multilayers for simultaneous CPP-MR and
CIP-MR measurements has been detailed in S.F. Lee's thesis, I focus mainly on essential
features of the system procedures that differed from him. I showed how to measure small
CPP magnetoresistance using a combination of a SQUID and a high precision current
compactor. Using a UHV dc magnetron sputtering system, multilayers consisting of
alternating layers of a ferromagnetic (F) metal and a non-magnetic (N) metal were
fabricated to permit simultaneous CPP and CIP MRS measurements. The most important
difference was that all our samples are capped with a final F layer (usually Co) to
eliminate the proximity effect. X-rays diffraction analysis were made to check the bilayer
thickness and to characterize the structure of the samples. Sample magnetization is
measured with a MPMS system. The surface profiles were taken by a Dektak IIA surface
profilometer to determine the CPP area.

We further studied elastic mean free path effect using the two-current model given
as Eqs.4.2.1 and 4.2.2 in Chapter 4 developed by our group. The quantity
@RfiHo) — ART(HS )]ART(H0) does not depend on the resistivity of the spacer layer.

 

Thus the two current model predicts the same dependence on N for pure Ag and AgSn
166

167

samples and the data must fall on exactly the same curve. The validity of this prediction
is shown in Fig. ‘2? for samples with equal but varying Co and Ag thicknesses, and total
sample thickness fixed at 720nm.

We devised a new, quantitative test both of two current model, and of our use
ARt(Ho) for AR,"“D . We examine how well the two current model, using the parameters
found for the simple two-component Co/Cu and Py/Cu multilayers, predict the values of
ARt for [Co/Cu/Py/Cu]N spin-valve multilayers in the P and AP states. Because the
values of HS are very different for Co (HslzIOO-ZOO Oe), and Py (H52z10 0e), such
multilayer structures have well-defined parallel (P) or antiparallel (AP) magnetic states.
We found that the rather good agreement between the no-free-parameter predictions and
our data provides important new evidence that low-temperature CPP data for magnetic
multilayers can be described by a simple, independent two-current model. The agreement
also supports that the Ho state resistances of our Co/Cu and Py/Cu multilayers lies near
those for AP F -layer alignment.

We have used the CPP geometry first to see deviations from Eqs. of this model due
to reductions in the spin diffusion length. As noted in Chapter 1, the two-current model
apply only in the limit lsf.>_other lengths. This limit should be valid for Co/Ag, Co/Cu and
Co/AgSn. But We are able to Show effects of reduced lsf by adding impurities to Ag that
flip spins-- either a magnetic impurity such as Mn which produces exchange scattering, or
a very heavy impurity such as Pt which has a strong spin-orbit interactions. Valet and
F ert recently extended the two-current model to the case of finite lsf. Combing the data
with their theory, we found that the more rapid falloffs with decreasing N for Co/AgMn
and Co/AgPt are exactly as predicted by Valet and Fert, and the resulting values of spin
diffusion lengths agree well with independent measurements or estimates detailed in

Chapter 4.

168

As preparatory work for the first "dusting" in the CPP geometry, we also first
measured GMR of Ni/Ag multilayers with CPP geometry. As previously seen in Co/Ag
and Co/Cu multilayers, at 4.2 K the CPP-MR is typically much larger than the more usual
CIP MR. Both the CPP-MR and CIP-MR for Ni/Ag and smaller than those for equivalent
Co/Ag and Co/Cu multilayers, which suggests that the Co, Ni, Ag system should be ideal
for "dusting". From our studies of spin-dependent scattering at interfaces, we found that
inserting a very thin 3rd metal layers at interfaces will significantly change interface
scattering, and thus substantially change magnetoresistance as well. Systematical studies
needs to be done to understand spin-dependent scattering at interfaces.

To understand the physics underlying GMR, it is very important to investigate the
magnetic ordering between the ferromagnetic layers in our samples. From the two-current
model, we predict that CPP ARS should be independent of the order of ferromagnetic
layers. To test this prediction, we designed a new type of F1/Cu/F2/Cu multilayers (type I
I) which is described in Chapter 5. We found differences of ARS and MRS between type I
and type II spin-valves. There may be a few possible causes which are responsible for
these discrepancies. One possibility is that the Cu layers for type II multilayers are not
thick enough so that the couplings between F layers might be more ferromagnetic,
leading to reduced values of CPP ARS and MRS of type II spin-valves. Another
possibility is that the spin-flip scattering lengths in F layers are not infinite, which also
might reduce the CPP ARS and MRS for type II multilayers. Further tests and analysis
must be done to clarify the discrepancies between type I and type II multilayers and to
have better understanding of magnetic coupling and magnetic ordering in our samples

To obtain comparable sample quality and reproducible data, We investigate the
dependence of sample quality on sputtering conditions. We found that the data of the

samples made by reduced target voltages and currents are comparable with those made

169

under standard conditions, while the data of samples made by increased sputtering
pressure are quite different. It shows that sputtering conditions are really important to
control sample quality and to effect CPP ARS. To study the effects of changing interface
roughness on CPP ARF/N, Further studies should be done to test this effect by changing
sputtering conditions.

As we have shown that "spin-valve" structure has a better control over the magnetic
states, we can extend our CPP studies of Co/Cu/Py/Cu to more layer thicknesses to fully
explore this system, and also to other spin valve structures.

It has been shown that inserting a monolayer (ML) or two of a 3rd metal at
interfaces can significantly change the CIP-MR, and also the CPP MR from our
exploratory studies. For future work, in the CPP geometry, where resistances add in
series, it is important to know that at what thickness an "interface layer" becomes a
"separate layer". It is known that insertion of thin layers can change the physical

structures of the original layers, and we will be careful to watch out for such effects.

Appendix A

Extra Data For Co/AgAu

We also alloy of Ag with another nonmagnetic impurity (Au) reduces (2} by spin-
orbit scattering. The data in Fig 4.10 obviously fall below the straight line, but much

more scattered than other data.

170

 

 

 

 

f? l l T l 1 fl 17 1 fil—
1 1 1 1
0? 80 F0 CO/Ag i __
g; 1 U Co/AgSifi/lk) //O -
:3 1 9 Co/AgAu(4%) D / 2
.6 1 / .
‘\ 1 /
T41 3 i /r . fl
7‘}; ()0 #— //6 O 4
:1: B 0
F4 O/ 0
Q: 0
<4 1 f1 7
I m
A 4.0 ‘7’ 1:1 ‘1
1__.0 /9
1+4 i 9 T
a; ” / t
Z}: /
W 1 43 7
A I) L_ A. __
ID 450 / -- tCO—6nm *1
{—- 7 A) 7
D: 1 /% 0 fl
.- /1 1
O Ling} 1 1 1 1 1 1 1 1 1 1 1 1 1 1

O 20 4O 60 80
Bilayer‘ No. N

 

Figure A.1 J[ART(HO) — ART(HS )]ART(H0) vs N for Co/Ag, Co/AgSn(4%), and
Co/AgAu(6%) multilayers with fixed tCO=6nm. The dashed lines is for I 1;} =oo[1 3].

172

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgAu N sample CPP AR (fflmz) C1P(Q‘1)
(nm) . no. Ho Hp HS H0 H9 HS
60 11 460-03 61.46 60.42 59.34 0.6939 0.6941 0.6945
30 20 42707 50.34 47.72 41.02 0.9695 0.9762 0.9899
18 30 460-05 86.34 82.68 70.87 0.5146 0.5141 0.5294
9 48 427-05 92.57 76.31 54.39

9 48 460—01 64.41 63.32 62.19 0.3727 0.3854 0.4058
6 60 427-02 103.7 87.45 66.92 0.6119 0.6180 0.6280
6 60 460-02 113.2 108.8 88.28 0.5123 0.5141 0.5263

 

 

 

 

 

 

 

Table A.l CPP ART and CIP values at HO, Hp and HS of
[Co(6nm)/AgAu(6%)(t)]xN samples. Total sample thicknesses are as close as
possible to 720nm.

 

 

 

 

 

 

 

 

 

 

 

 

 

tAgAu N sample CPP MR% CIPMR% r1 error [(ro-rs)ro]1/2
(nm) .no. H0 H9 H0 H9 %

60 11 460-03 3.57 1.82 0.09 0.06 1.96 3.57 11.41

30 20 427-07 22.7 16.3 2.10 1.40 1.39 5.1 21.66

18 30 460-05 21.8 16.7 2.88 2.98 1.31 2.9 36.55

9 48 427-05 70.4 40.3 1.75 3.5 59.45

9 48 460-01 3.57 1.82 8.88 5.29 1.96 2.51 11.96

6 60 427-02 55.0 30.7 2.63 1.62 1.79 6.6 61.76

6 60 460-02 28.2 23.2 2.73 2.37 1.21 1.83 53.11

 

 

 

 

 

 

 

 

 

 

 

Table A2 CPP MR, CIP MR and [(ro-rs)ro]1/2 values at H0, and H of
[Co(6nm)/AgPt(6%)(t)]xN samples. re and rS are ART at Ho and s- Total sample
thicknesses are as close as possible to 720nm.

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181
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