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This is to certify that the
dissertation entitled

NEW METHOD FOR DETECTING DOMAIN WALL
TRAPPING AND MOTION AT A CONSTRICTION IN
NARROW FERROMAGNETIC WIRES USING
PERPENDICULAR-CURRENT GIANT
MAGNETORESISTANCE

presented by

Antonio Javier Zambano

has been accepted towards fulﬁllment
of the requirements for the

PhD. degree in Physics

 

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Date

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIRC/DateDuopss-sz

 

 

NEW METHOD FOR DETECTING DOMAIN WALL TRAPPING AND MOTION AT
A CONSTRICTION 1N NARROW FERROMAGNETIC WIRES USING
PERPENDICULAR-CURRENT GIANT MAGNETORESISTANCE
By

Antonio Javier Zambano

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

2004

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EE.E.E$I I‘m. Sir Errt‘lllu'r-PEKIF’. It: .7. Inn-INNS .aI Iii. I .

ABSTRACT
NEW METHOD FOR DETECTING DOMAIN WALL TRAPPING AND MOTION AT
A CONSTRICTION IN NARROW FERROMAGNETIC WIRES USING
PERPENDICULAR-CURRENT GIANT MAGNETORESISTANCE
By

Antonio Javier Zambano

We present a versatile, new method for detecting the presence and small motions
of a trapped domain wall in a narrow ferromagnetic wire using current-perpendicular-to-
plane, CPP, giant magnetoresistance, GMR. We have adapted the Ono et al. "2 method for
trapping domain walls to CPP GMR measurements. We shaped a spin valve multilayer
Cu(lOnm)/Py(20nm)/Cu(10nm)/Py(5nm)/Cu(5nm)/Au(lSnm), where Py = Ni34F616, into
a long ~ SOO-nm-wide wire with a U-shaped or V-shaped constriction (notch) near its
middle that acts as a trapping site for a head-to-head (or tail-to-tail) domain wall. A
sweeping external magnetic ﬁeld, H, is applied along the wire axis. The magnetization is
restricted to be parallel to the wire axis due to the shape anisotropy. Magnetization
reversal in the wire takes place by propagation Of a magnetic domain wall, which initially
nucleates in a diamond-shaped reservoir and is injected from there into the nanowire at a
particular value of H. As a wall in either Py layer moves past the measuring contact, the
CPP GMR detects the change of the relative magnetizations of the two Py layers, from
parallel to antiparallel. The CPP GMR response to small motions of the trapped domain

wall is enhanced because the CPP current is restricted to the region of wall trapping; but

 

' T. Ono , H. Miyajima, K.Shigeto and T. Shinjo, App]. Phy. Lett. 72, l 116(1998).

2 T. Ono, Y. Ooka, S. Kasai, H. Miyajima, N, Nakatani, N. Hayashi, K. Shigcto, K. Mibu and T.
Shinjo, Mater. Sci. Eng. B 84, 126 (2001).

in addition, the CPP current can be also localized to a measuring region outside the
constriction. Superconducting 150-nm-thick (top) and IOO-nm-thick (bottom) Nb contacts
are used to obtain a uniform CPP current density in the wall trapping region at 4.2 K; but
measurements at 295K, including ZOO-nm-Au top contacts, have also been successful
with non-uniform CPP currents. Data for the two different types of constrictions show
that for U-shape notches, several pinning sites were seen as the wall in the thinner Py
layer remained trapped in the constriction, while in V-shaped notches one trapping site
occurred. Successful pinning of a wall at the constriction in the thicker Py layer was more
improbable. With this technique, the position of the wall inside the notch region can be
precisely determined. While H is swept, a wall trapped in a constriction moves between
different points in the notch seeking a lower energy state, and it does not have to leave the
constriction when the system is relaxed by sweeping the ﬁeld to 0 0e. When H is kept
ﬁxed, time dependence of wall position inside a U-shaped constriction in the thinner
Py layer appears to be thermally activated at 4.2 K. No wall motion was observed in a V-
shaped notch under the same circumstances. Along with these results, data from other
studies, such as domain wall stability and effects of a high-density CPP current, are

presented in this thesis to conﬁrm the success and effectiveness of our technique.

FOR MY FATHER

iv

ACKNOWLEDGEMENTS

I am professionally indebted to many people who have helped me in the course of
my work. I am most grateful to Dr. William P. Pratt Jr., for his assistance and invaluable
teaching in the ﬁeld of experimental physics. My gratitude to him is for being not only an
excellent adviser but also a patient and supportive person. I am also enormously thankful
to Dr. Jack Bass for his guidance during the ﬁrst stage of my research in this group, and
for his exemplary professionalism.

I would like to thank Dr. Reza Loloee for his assistance and technical support. His
knowledge and “consistently positive attitude”, greatly contributed to make our work be
efﬁcient and pleasant. My deep thanks go to my co-workers and friends: Mustafa Al-haj
Darwish, Huseyin Kurt, Ion Muraru, and Mike Crosser for their inestimable suggestions
and constructive criticism during the development of this thesis. Each of them made our
laboratory a great and friendly environment to work.

I also acknowledge the preliminary work by Robert Slater, the useful advice of
Sergei Urahzdin, the assistance Of Dr. Baokang Bi, the support by the Keck
Microfabrication Facility and NSF grant DMR-02-02476.

Finally, I would like to express gratitude for their patience and support to my
family: my mother Nené, my brother Luis, my sister Liliana, and my niece Lucia; also to
my friends: Guillermo Quinteiro, Julian Mickelson, Severine Collignon, and especially

Bryan Fink.

TABLE OF CONTENT

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

LIST OF FIGURES ................................................................................... ix

CHAPTER 1 THEORY: CURRENT PERPENDICULAR TO THE PLANE
GIANT MAGNETO-RESISTANCE, MAGNETIC DOMAIN STRUCTURES

 

 

AND DOMAIN WALLS - l

1.1 INTRODUCTION ........................................................................................................... 1
1.2 CURRENT PERPENDICULAR To THE PLANE GIANT MAGNETO-RESISTANCE ................. 5
1.2.1 Giant Magneto-resistance. Semiclassic Analysis .............................................. 9
1.2.2 Total Resistance of an asymmetric F/N/F Trilayer using the Two-current
Series-resistor Model (2CSR) ................................................................................... 12
1.2.3 Inclusion of Spin Diffusion Length in a F/N/F Trilayer Resistance Calculation
................................................................................................................................... 17
1.3 MAGNETIC DOMAIN STRUCTURES AND DOMAIN WALLS .......................................... 22
1.3.1 Magnetic Domain Structures - Total Free Energy ........................................... 22
1.3.2 Type of Domain Walls in Unconstrained Thin Films ...................................... 28
1.3.3 Domain Walls in Magnetic Fields and Shape Effects ..................................... 32
1.3.4 Domain Wall Structure in a Ferromagnetic Wire and at a Constriction in
Presence of an External Magnetic Field ................................................................... 34
1.3.5 Double F Films ................................................................................................ 38
1.3.6 Wall Displacement Calculation using a Simple Model of a Trapped Head-to-
Head Domain Wall ................................................................................................... 40
REFERENCES .............................................................................................................. 45
CHAPTER 2 EXPERIMENTAL METHODS 49
2.1 INTRODUCTION ......................................................................................................... 49
2.2 SAMPLE PREPARATION ............................................................................................. 49
2.2.1 Design of a Mask for Photolithographic Patterning of Au Electrical Leads 51
2.2.2 Multilayer Thin Film Preparation via Sputtering ............................................. 55
2.2.3 E-beam Lithography to Deﬁne the Required Geometry (i.e., Wire with Central
Notch) for Domain Wall Trapping ........................................................................... 58
2.2.4 Ion Milling and Planar Insulation of the Patterned Wire ................................. 62
2.2.5 E-beam Lithography and Sputtering to Obtain the Final Top Contact Strip 67
2.3 EQUIPMENT AND MEASUREMENTS ............................................................................ 70
2.3.1 Nanovolt Measurements .................................................................................. 71
2.3.2 Lock-in Ampliﬁer ............................................................................................ 71
REFERENCES .............................................................................................................. 75

vi

CHAPTER 3 RESULTS AND DISCUSSION 76

 

 

 

3.1 INTRODUCTION ......................................................................................................... 76
3.2 CPP RESISTANCE DATA ........................................................................................... 77
3.3 CPP RESISTANCE vs. MAGNETIC FIELD ................................................................... 81
3.4 MULTIPLE RUNS ....................................................................................................... 85
3.5 SAMPLE WITH CPP CURRENT OUTSIDE CONSTRICTION ............................................ 87
3.6 ESTIMATION OF THE DISPLACEMENT OF A DOMAIN WALL WITHIN THE CONSTRICTION
.................................................................................................................................. 90

3.7 STABILITY OF A WALL WITHIN THE CONSTRICTION .................................................. 92
3.8 TIME STUDIES ........................................................................................................... 96
3.9 CURRENT DRIVEN STUDIES ....................................................................................... 99
REFERENCES ............................................................................................................ 103
CHAPTER 4: SUMMARY AND CONCLUSIONS 104
REFERENCES ............................................................................................................ 107
APPENDIX UNIFORMITY OF THE CCP CURRENT DENSITY 108
REFERENCES ............................................................................................................ 112

vii

1.1

1.2

2.1

3.1

3.2

LIST OF TABLES

Values of average bulk resistivities, p*, thicknesses, t, average speciﬁc interface
resistances, AR“ and spin diffusion lengths 15;. Values obtained from Refs. 48, 49
and 50 ........................................................................................... 21

Low temperature values of ARM» and AAR calculated with Eqs. 1.17 and 1.18, for S
= Nb, F = Py, and N= Cu in Fig 1.5, Nb top contact; and S = Nb, F = Py, N= Cu,
N1= Cu and N2= Au in Fig 1.6, Au top contact. RAP and AR», for the same s stems
with estimated area of A~ 1.5 x 10'” m2 for U notches and A~ 2.2 x 10'13 m for V
notches. GMR percentage obtained with Eq. 1 .1 ......................................... 21

Ratio ion milling rate / Au ion milling rate for Nb, Cu, and Py. Ion mill rates
(including Au) were obtained from Refs. 3 and 9 ........................................ 63

Experimental data of samples showing trapping. RAP and Rp are resistances of the
antiparallel and parallel states, respectively. GMR = RAP - Rp / Rp. * means samples
remeasured with extra Nb strip over the original Au top contact strip. ** indicates
that the width of the top contacts was increased by a factor of 1.5 .................... 78

Average values of the experimental data presented in Table 3.1. The uncertainties
were estimated by o/(n)”2, where o is the data standard deviation and n the number
of measurements. *** sample 1563-7B-a was not considered in the average ........ 80

viii

1.1

1.2

1.3

1.4

1.5

1.6

LIST OF FIGURES

Domain walls move in both ferromagnetic layers at different times because of the
different switching ﬁelds. As the wall moves in the thin F layer, past the top
measuring contact, the resistance changes in proportion to the location of the wall.
Antiparallel magnetizations of the F layers give higher value of resistance, and
parallel magnetizations give a lower resistance. Superconducting contacts guarantee
uniform CPP current ........................................................................... 4

Simpliﬁed diagram of the 4s and 3d energy, 8, bands vs. density of states, (1X8), of:
a) a normal metal, no net magnetic moment, and b) a ferromagnetic metal, there is a
net magnetic moment ......................................................................... 10

Schematic explanation of the basic GMR effect for a particular magnetic
conﬁguration. a) When the magnetizations (arrows) of the magnetic layers are
antiparallel, both moment-up and moment-down electrons have equal resistance
path. b) When the magnetizations of the F layers are parallel, the moment-up
electrons have a lower resistance path compared with moment-down electrons,
leading to a lower overall resistance ....................................................... 11

Diagram of the 2CSR model for the AP state of an asymmetric F/N/F trilayer with
superconducting contacts. Big arrows indicate orientation of local magnetization. F
layers have different thicknesses. The current is divided into two channels: moment
up channel and moment down channel. There is one resistance per channel that is
the sum of each resistance in series. The total resistance is the combination of the
resistance of each channel in parallel ..................................................... l3

Diagram of the 2CSR model for the AP state of a tri—layer F/N/F with
superconducting contacts. F layers have different thicknesses. The inclusion of the
spin diffusion length in the ﬁrst F layer, tn >> IFS; , shortens the two channels. The
current is divided into two channels: moment up channel and moment down
channels. There is one resistance per channel that is the sum of each resistances in
series. The total resistance is the combination of the resistance of each channel in
parallel plus the contributions of that part of P; not in the two-channel region and
the S/F boundary resistance on the left .................................................... 18

Diagram of the 2CSR model for the AP state of N2 right contact. The right Nb layer
in Fig. 1.5 is replaced by a N 1+ N2 layer. The inclusion of the spin diffusion length
in the N2 layer, tN2 >> [ms/r, shortens the two channels ................................. 19

ix

1.7

1.8

1.9

1.10

1.11

1.12

1.13

Sketch of the demagnetization ﬁeld for an uniaxial-like shape anisotropy in a plate
of thickness t and inﬁnite extension in x-z plane that is uniformly magnetized
perpendicular to its plane .................................................................... 25

a) Thin ﬁlm domain conﬁguration after saturation, with the subsequent reduction to
approximately zero ﬁeld. b) and c) Adding oppositely magnetized domains reduces
the magnetostatic energy. d) Formation of triangular closure domains at the edges
of the ﬁlm with magnetization at 90° to the original domains reduces the
magnetostatic

energy ........................................................................................... 27

Two domain wall conﬁgurations in a ﬁlm of thickness t, inﬁnite extent in x-z plane,
and easy axis along 2: a) Bloch wall b) Néel wall ........................................ 29

Results presented by Trunk et. al.57 for a Py ﬁlm. a) Wall energy per unit area as
function of ﬁlm thickness. b) Wall widths in the center of the material, as a
function Of ﬁlm thickness .................................................................... 31

Top view of a sample used to trap a DW. A constriction placed in the middle traps
the wall while it is traveling from one end to the other. A reservoir creates closure
domains which nucleate the wall, and a sharp tip on the other side prevents wall
nucleation ....................................................................................... 33

Results presented by Mo Michael er al. a) “Traverse” domain structure for a head-
to-head wall calculated for a 2-nm-thick, 250-nm-wide Py strip. b) “Vortex”
domain structure calculated for a 32 nm thick, 250m nm wide Py strip. c) Phase
diagram of head-to-head domain structures. A and B points represent our samples,
500-nm-width Py ﬁlms of two different thicknesses, tA~5nm and t3~20 nm. C
represents the constriction region, width ~100nm, for the thicker Py layer .......... 35

Geometry used by Mo Michael er al. to simulate domain wall motion in a 5m thick
Py layer ......................................................................................... 36

1.14

1.15

1.16

1.17

1.18

2.1

2.2

Calculations by Mo Michael et al. for spin conﬁgurations at zero applied ﬁeld. a)
Unstable state after application of H in the —y direction. b) and c) Stable
conﬁgurations after application of H in the +x and —x directions, respectively. d) A
hysteresis loop for a domain wall trapped in the constriction. The switching ﬁeld
for moving the domain wall from one end of the notch the other is 1.1 mT, and the
domain wall is pushed out of the constriction at H = 3.2mT. Note the linear
behavior of the magnetization vs. H while the wall is trapped ......................... 37

a) Orange peel effect may lead to ferromagnetic coupling. It occurs if the interlayer
is thin compared to the corrugations in the magnetic ﬁlms. b) Free poles at the edge
of the F layers may alter the stray ﬁeld and induce antiferromagnetic coupling
between F layers when the thickness of the F layers are comparable to their lateral
dimensions .................................................................................... 39

As a wall moves past the top measuring contact, the resistance changes in
proportion to the location of the wall. Antiparallel-state resistance > parallel-state
resistance ....................................................................................... 41

Conﬁguration of our model to calculate the wall displacement, Ax, of a head-to-
head wall within a V shaped constriction. Arrows mean magnetization direction.
AAp, Ap, and Aw are the areas of the antiparallel region, the parallel region and the
wall, respectively, where the CPP current ﬂows ......................................... 41

Maximum wall displacement within the constriction as a function of the initial wall
width D. Curves for a ﬁxed D and for a ﬁxed wall area Aw do not exhibit large
differences ..................................................................................... 44

Perspective view of a sample, illustrating the actual geometry. The superconducting
top and bottom Nb contacts, at 4.2 K, ensure a uniform CPP current density through
the sample. For some samples Au top contacts were used instead. Note that the
vertical is exaggerated ....................................................................... 50

a) Picture of the shadow mask used to make the Au leads prior to the deposition of
the multilayer onto the Si substrates. This shadow mask provided 24 (1.27 cm x
1.27 cm) individual substrates from each Si wafer. b) Sketch of a Si wafer, which is
positioned under the shadow mask during exposure to ultraviolet light .............. 51

xi

2.3

2.4

2.5

2.6

2.7

2.8

2.9

2.10

Cartoon of the Au leads deposition procedure. This technique can be used for any
process involving evaporation or sputtering. i) Photoresist over a Si substrate. ii)
Developed patterned photoresist after exposure to light. iii) Evaporated Au on a Si
substrate and on the photoresist. iv) Au leads on a Si substrate after lifting-
off ............................................................................................... 53

a) Top view of the patterned Au leads on a single Si substrate of 1.27 cm by 1.27
cm. Note that the Au contact pads are shorted to prohibit burning out of the samples
due to static charges. b) Magniﬁcation of the central region of the Si substrates;
there is an empty area of size 40 pm by 60 um, surrounded by the Au leads ........ 54

Sputtered multilayer. a) Sketch of the exposed area with different e—bearn doses
(different size rectangles), to create a bigger undercut. b) Top view of patterned e-
beam resist. c) Top view of the actual sputtered multilayer. The upper cartoons
Show side views of the lithographic process ............................................... 56

a) Sketch of a multilayer nanowire showing its typical shape and dimensions. The
reservoir helps nucleate the domain wall. b) Top view of the center of a substrate,
showing the wires drawn in the e-beam resist ............................................ 58

SEM pictures showing 300 nm thick nanowire Al masks on the multilayer. The two
typical geometries of the notch are displayed: a) V-shaped notch, and c) U-shaped
notch. b) and d) are magniﬁed views of the constriction regions ...................... 60

a) Sample preparation sequence prior to Ar+ ion etching. b) Top view of Al masks
on multilayer that select the area to be exposed to ion-beam etching, and of the e-
beam resist layer, that protects Au leads outside of the central open rectangular
area .............................................................................................. 61

a) Sketch of the magnetic arm used to load the samples into the ion milling chamber
and to hold and rotate them during SiO deposition. b) Holders for top ion milling.
The sample is localized under a metallic mask with a hole in its center to select the
area to be ion milled. c) Cylindrical holders for side ion milling ....................... 62

a) Typical proﬁle of a multilayer nanowire after the Al mask was removed. SiO was
evaporated leaving a ~13 nrn high protrusion of Au. b) Top view of the patterned
and planar insulation of SiO ................................................................ 64

xii

2.11

2.12

2.13

2.14

2.15

2.16

2.17

Cartoon showing the sequence followed to ion mill the substrates and deposit a
planar SiO insulation. i) Etching from the top. ii) Particle wall build up on the sides
of the Al mask. iii) SiO deposition. iv) and v) Ion milling from the sides to remove
build up. vi) SiO lift Off via Al removal ................................................... 65

a) SEM image of a nanowire after SiO deposition and A1 removal was ﬁnalized. b)
Magniﬁcation of a U-shaped notch. c) Magniﬁcation of a V-shaped notch ......... 66

a) Top view of patterned resist mask to create the ﬁnal top strip. The strips are
designed to avoid contact with the SiO-coated edges of the bottom Nb layer that
could be damaged by Ar+ milling. U type strips allow tracking of wall motion in
two different regions of the wire. b) Top view of ﬁnal top Nb S-shaped strips.
Extra Nb rectangles assure good connection between the bottom Nb layer and the
Au leads ........................................................................................ 68

SEM image of three nanowires (V -shaped notch) on the central area of a substrate
and S-shaped Au top contacts deposited over the SiO insulating layer. Au top
contacts were used for 295-K-measurements mainly .................................... 69

Diagram of the measuring system. The Lock-in ampliﬁer is connected to the
Voltage-Current Box via two co-axial cables and from there a triaxal cable goes to
an adapter. The adapter is used to change the current triaxal cable into a Fisher
seven-pin connector, which goes to the sample probe. The adaptor is also used to
change the Cu Omega-Engineering thermocouple connectors into a triaxal cable
which brings back the voltage to the preampliﬁer. The adapter selects the channels
to be used as well. The preampliﬁer is connected via a coaxial cable to the Lock-in
ampliﬁer ....................................................................................... 72

a) Photo of the room temperature magnet with the probe not yet inserted. b) The
substrate is placed at one end of the long probe, and the samples are connected via
indium contacts to the probe Cu wires. c) The probe is inserted into the sheath that
contains a superconducting solenoid, and the whole system is dipped into a He
dewar .......................................................................................... 73

Sample connections. a) The external Cu leads are connected with indium to the
sample via the external contacts at the outer edges of the substrate. V and I external
contacts are shown for connection to the central nanowire. b) Magniﬁcation of the
central part of the substrate ................................................................. 73

xiii

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

AR= (RAP-Rp) vs. RAP. Two least-squares ﬁts were performed: at 295 K (all the
points were considered); and at 4.2 K (Au-U and Nb-V were excluded). Lines were
forced to go through the origin ............................................................. 79

CPP resistance R vs. magnetic ﬁeld, H, at 4.2 K for a V shaped notch. Curved
dashed arrows indicate change in H. Sample1470-6B-a, Nb top contact ............. 82

AR (=R-Rp) vs. magnetic ﬁeld, H, for a U shaped notch. R is resistance, AP means
antiparallel state and P means parallel state. Arrows indicate different H sweeps.
Sample l470-1B-a, at 4.2 K, Au top contact ............................................. 83

AR(=R-Rp) vs. magnetic ﬁeld, H, for a NC notch. R is resistance, AP means
antiparallel state and P means parallel state. This curve has two reproducible wall-
trapping substeps for the thin Py layer. Arrows indicate different H sweep. Sample
1470- lA-a at 295 K, Au top contact ...................................................... 84

Multiple CPP resistance, R vs. magnetic ﬁeld, H, curves. H sweeps move back and
forward between —500 Oe and 500 Oe. Samples a) 1470-5B-a at 4.2 K, U-shaped
notch, Nb top contact, and b) 1470-6B-a at 4.2 K, V- shaped notch, Nb top contact.
Stable and reproducible conﬁgurations. U-shaped notches only: samples 0) 1470-
lB-a at 4.2 K, Au top contact, and d) l470-lB-b at 295 K Nb top contact. More
unstable conﬁgurations ...................................................................... 86

AR (= R— Rp) vs. H for a sample with one Nb top contact placed to the left of a U-
shaped notch and the other contact over the notch. Solid and dashed arrows show
direction of ﬁeld sweep at 4. 2 K. Sample 1470- lB-b, Nb top contact ............... 88

AR (= R— Rp) vs. H for a sample with one Nb top contact placed to the left of a U-
shaped notch and the other contact over the notch. Solid and dashed arrows show
direction of ﬁeld sweep at 295 K. Sample 1470- lB-b, Nb top contact .............. 89

AR= (R-Rp) vs. magnetic ﬁeld, H, data showing the displacement of the wall
trapped in the thin Py layer within the constriction. 8R value from the V shaped
notch puts a constraint on the relationship between the width of the domain wall
and the distance the trapped wall moves as the ﬁeld changes. Sample1470-6B-a,
Nb top contact, Fig. 3.1 ..................................................................... 91

xiv

3.9

3.10

3.11

3.12

3.13

3.14

AR (= R — Rp) vs. magnetic ﬁeld, H. Head-to-head wall motion in a U-shaped notch
of a Au top contact sample at 295 K. a) Overall major ﬁeld sweep. b) Detail of
minor ﬁeld sweep. Sample 1470-3B-c at 295 K, Nb top contact ....................... 93

AR (= R-Rp) vs. H, a head-to-head wall motion in a NC-shaped notch of a Au top
contact sample at 295 K. a) Reproducible cycles of AR vs. H between 0 0e and 40
Oe occurs, after wall-trapping. The wall moves back and forth inside the
constriction following the same path. b) AR depicts stability of the AP state, once
the wall has leﬁ the notch. c) A wall in the thicker Py layer is trapped in the
constriction, and even when H is reduced to 0 0e, the wall has not left the notch.
Sample 1470-1A-a ........................................................................... 94

AR (= R — Rp) vs. magnetic ﬁeld, H. Sweeping H back and forth between 150 Oe
and 0 0e shifts the wall between the same two points within the notch. Back and
forward motions follow different paths. Sample 1470-5B-a at 4.2 K, U-shaped
notch and Nb top contact .................................................................... 95

a) AR(= R - Rp) vs. magnetic ﬁeld, H, at 4.2 K for a sample with a V-shaped
notch. H sweeps start at —500 Oe and then stopped for about 1000 s at a given H
represented by A and B. Then the ﬁeld sweep is started again at 500 Oe and then
stopped for about 1000 s at a given H represented by C. b) Resistance, R, vs. time,
commencing 10 s after magnetic ﬁeld sweep is stopped at A-C. Sample 1470-6B-a,
Nb top contact ................................................................................ 97

a) AR (= R — Rp) vs. H, at 4.2 K for a sample with a U-shaped notch. Open circles:
H sweeps start at -500 Oe and then stop for over 1000 s at a given H represented
by A—F. Then the ﬁeld sweep is started again at —500 Oe. b) AR vs. time,
commencing 10 s after magnetic ﬁeld sweep is stopped. A—F correspond to values
of H shown in (a). The ordinate values of these curves have been shifted somewhat
for clarity, but they share the same incremental resistance scale. Sample 1470-1B-
a, Au top contact ............................................................................. 98

Wall motion by applying a CPP DC current density of 3 x 1010 Almz. a) AR(= R —
Rp) vs. magnetic ﬁeld, H. H sweeps start at —500 Oe, stop at a given H represented
by A and C, and ﬁnally go to 0 0e. A and C indicate wall trapping in the thinner
and thicker Py layers, respectively. B represents relocation of wall trapped in the
notch of thinner Py layer. D represents P state after the wall has left the notch in
the thicker Py layer. b) AR vs. DC current. Sample1492-1A-b at 4.2 K, Nb top
contact and U-shaped notch ............................................................... 101

XV

A.1 Sketch of the current density in the nanopillar Ohmic model studied by
Lenczowski .................................................................................. 108

A2 Simulation of the current density through a multilayer pillar using Lenczowski and
et al. method.1 a) L was taken to be equal to notch width at the center ~ 0.1 pm. b) L

was taken to be equal to 0.5 pm, the maximum width of the notch area, which is the
worst-case scenario .......................................................................... 110

xvi

CHAPTER 1

Theory

Current Perpendicular to the Plane Giant
Magneto-resistance, Magnetic Domain Structures

and Domain Walls

1.1 Introduction

In ordinary ferromagnets, F, the parallel alignment of their magnetic moments due
to their strong interaction produces a large local magnetization within the F, even in
absence of an external applied magnetic ﬁeld, H. Yet, a F sample of macroscopic extent
can exhibit zero average magnetization. Such a demagnetized state is due to the presence
of magnetic domains with randomly oriented close-tO-uniform magnetizations. When
exposed to a varying H, the magnetic domain structure will change so that the sample
becomes magnetized. This redistribution of the magnetic domains is established by the
reduction of the overall energy of the sample. In general the minimum-energy structure of
a bulk ferromagnet is a three-dimensional multi-domain state, within each of which the
magnetic moments are aligned. For thin ﬁlms of large lateral extent, such multi-domain

states can exist, but with the constraint that the domain magnetizations are usually

parallel to the surface Of the ﬁlm. It is energetically more favorable for the magnetic
moments to change their direction gradually rather than abruptly at the interface between
adjacent domains. Between any two domains, this means there is always a transition
region of ﬁnite extent within which the magnetic moments vary in direction. These
regions are called domain walls, DW, whose widths and magnetic moment conﬁgurations
are determined by the relative magnetic moment orientation of the adjacent domains, the
anisotTOpies, and the exchange stiffness constant, Acx, as well as local imperfections and
the geometry of the ferromagnet. There are two main processes by which domains change
their structure under an applied H: one is the coherent rotation of the magnetic moments
of an entire domain to a more favorable orientation; the other one is the growth of
favorably oriented domains, during which DWs move to incorporate more moments that
have switched to a favorable orientation. DW propagation is strongly inﬂuenced by the
sample shape and anisotropiesl’z.

Control and detection of geometrically conﬁned DWs are of intense interest both
for physics and device applications. One of the most important areas of magnetic
technology nowadays is the study of small features where the size of the F thin-ﬁlm
elements used in a device is comparable to the domain size. As the size of those elements
gets smaller, DW propagation mechanisms are strongly affected, and the physics
involved in that process is of great interest. In this work we present an alternative
scheme for detecting the presence and motion of trapped DWs that also provides
enhanced sensitivity to small wall motions.

Among the different techniques that are utilized to characterize DW motions, we

focus on magnetoresistance, MR, which is historically associated with the fractional

change in resistance Of a sample upon the application Of H. We use the giant
magnetoresistance, GMR, of a magnetic multilayer, consisting of alternating thin ﬁlms of
F metals and non-ferromagnetic metals, N. Until now, most of the GMR studies of DW
motions have used the so called current-in-plane geometry, CIP, in which the measuring
current is along the plane of the multilayer. Unfortunately, in the CIP geometry, there is
no control over the region Of the current ﬂow and the sample geometry independently.
Thus, the sensitivity of the method is signiﬁcantly reduced because there is a CIP MR
contribution from regions that are not of interest. What is needed is a way to localized the
measuring current to a region of interest that is somewhat independent of the sample
geometry which is controlling the domain structure. We utilized a current-perpendicular-
to-plane geometry, CPP, to obtain this highly-localized measuring current. Since CPP
GMR is sensitive to the relative orientation of the magnetization in adjacent F layers, this
GMR can, in principle, be used to provide localized information about the domain state in
the F layers. Continuing with the work by Slater3, we have adapted one of the Ono et al.
CIP GMR methods for trapping domain walls‘“5 to CPP GMR measurements. Ono et al.
used a F(t1)/N(tN)/F(t2) spin valve, SV, to trap a domain wall in a speciﬁc place and
detect the wall’s presence, where t means layer thickness with t1¢t2. The dissimilar
thicknesses of the F layers make them have different switching ﬁelds. The SV was in the
shape of a long wire, and a constriction situated near its center acted as a trapping site for
a domain wall, see Fig.1.l (a). In our work, a similar F(t1)/N(tN)/F(t2) structure was used
with t1< t2 and tN thick enough to minimize magnetic coupling between F layers. At 4.2 K
two superconducting contacts, S, guarantee a uniform CPP current ﬂow that is conﬁned

to the region of the wall trapping in the constriction, but measurements at 295K using N

top contacts can also be done with non-uniform CPP currents. Away from the
constriction, the shape anisotropy of the wire constrains the magnetizations of each F
layer to be parallel to the wire axis and in a single-domain state. After application of a
strong H along the +x direction, H is then increased along -x, causing the DW to
propagate in the thin F layer until the wall becomes trapped in the notch as the

magnetization is reversed on one side of the notch.

(a) H mm

 

<—% —<'
H<—>

—>x

 

 

 

 

P AP Domain wall
fT‘t FD trapped in
S top contact constriction
(b) $."d: F

 

 

 

 

 

 

 

 

 

:Uniform current

Fig. 1. 1. Domain walls move in both ferromagnetic layers at different times because of the
different switching ﬁelds. As the wall moves in the thin F layer, past the top measuring contact,
the resistance changes in proportion to the location of the wall. Antiparallel magnetizations of the
F layers give higher value of resistance, and parallel magnetizations give a lower resistance.
Superconducting contacts guarantee uniform CPP current.

The magnetization of the thick F layer remained ﬁxed along +x. As stated before, the
GMR depends on the relative orientation of the magnetization in the two F layers: when

the magnetic moments of the F layers are aligned parallel, P, the resistance is lower, and

when they are aligned antiparallel, AP, the resistance is higher. The presence Of a trapped
wall could be detected because the CPP resistance is between the limits Of both
magnetizations being P or AP as the domain wall moves between the measuring contacts,
as shown in Fig. 1.1 (b). AS H continues increasing along —x, the DW leaves the notch
causing the thinner F layer to switch completely. Further increases in H along -x causes a
DW to move through the thicker F layer.

In this chapter a phenomenological review of the sources of GMR and a CPP
GMR outline, which are of direct relevance to this work, are given in Sect. 1.2. A more
detailed analysis of this theory can be found in Refs. 6-9, and in previous dissertations”
“. This chapter will also concentrate on magnetic domains and DW theory in Sect 1.3,
giving a review of the central mechanisms that dominate the formation and propagation
of domain walls. Thin ﬁlm studies will be emphasized which are the main interest of this

project.

1.2 Current Perpendicular to the Plane Giant Magneto-

resistance

Magnetoresistance, MR, is the change in electrical resistance, R, of a conducting
material in response to a ﬁeld H. In the case of a single F layer, the ordinary MR consists
mainly of two components: (1) a contribution from the bulk, part of which is anisotropic

MR, AMR, and Lorentz MR, LMR, and (2) a small contribution from the domain walls,

DWR. AMR has its origin in the spin-orbit coupling, and its main characteristic is that R
is different for current flowing parallel or perpendicular to H. LMR comes from the
Lorentz force that the magnetic ﬁeld, even in the absence of an externally applied ﬁeld,
exerts on the moving electrons. DWR arises from the electron scattering in the domain

walls”'”.

GMR refers to the MR of F/N multilayers, and it is much larger than the MR of each
constituent bulk material. Only in certain special cases is the GMR comparable or smaller
than the combination of AMR, LMR, and DWR7. GMR also arises in a variety of
magnetic systems including multilayers, spin valves, and granular materials. Their
common property is that they consist of separated regions of magnetic material capable
of adopting independent magnetization orientations in response to H. Viewed differently,
GMR arises from the transfer of magnetic information by the carriers from one magnetic
region to another across the intermediate non magnetic spacer metal, and the information
is coded in the chemical potentials of up and down electrons and also depends on the

decay of coding in transit.

The discovery of GMR effect in Fe/Cr magnetic multilayers in 1998 has initiated a
tremendous research effort on layered magnetic systems‘s's’ ‘5 "7. GMR stimulated interest

in understanding the physical processes involved and accelerated the emergence of new

18-19

technology, now called spintronics , which has the potential to replace much of the

traditional electronic technology based only on the charge of electrons. GMR is also used

as a sensor for probing other phenomena such as the coupling between F layers when

20.24

separated by N layers and the generation of magnons and magnetization switching by

a high-intensity spin-polarized electric current25 ' 32.

Since the earliest times, almost all of the MR experiments have been carried out
in the CIP geometry. The reason is simple; it is very easy to measure the fairly large
resistance of a thin ﬁlm or multilayer when the current flows in plane because the sample
length is typically orders of magnitude larger than its thickness. However, for CPP GMR,
the geometry is the opposite: the main length of the sample is just its thickness, while the
lateral dimensions of the sample are usually much larger than the thickness. Therefore the
resulting very low resistance can be measured reliably only by extremely sensitive
techniques. In order to increase the CPP R to easily observable values, microfabrication
or even nanofabrication technologies can be used to reduce the cross section of the
samples. The ﬁrst CPP GMR measurements were reported by W. Pratt and collaborators
at Michigan State University in 1991, and they showed that CPP GMR could be several
times larger than CIP GMR”. Because of its high symmetry, only simple equations are
necessary to describe CPP GMR theoretically7'8' 34‘35; and in contrast to C [P GMR theory,
this allows a straightforward analysis of multilayers. CPP transport analysis in F/N
multilayers began with a phenomenological two current mode135'36, and later on, more
rigorous theories were developed”. For convenience they can be divided into two
categories: Free Electron Based Models, semiclassical models neglecting quantum
effects, and Fermi Surface Models, inherent to quantum mechanics, and whose main
issue is the coherence of the electron scattering from adjacent interfaces.

Semiclassical models are appropriate instruments to analyze and explain the
results in this thesis. Thus, it is not necessary go deeper into quantum mechanic models;

further information on Fermi Surface Models can be found elsewhere36'37.

The development of semiclassical models started with Zhang and Levy”, who
pointed out that the free-electronic transport can be described in terms of two
independent parallel channels (spin-up and spin—down) in the diffusive regime. Here the
thicknesses involved in the system must be longer than the elastic mean free path of the
electrons, 1, (in contrast to the ballistic regime); and also weak spin-ﬂip scattering is
assumed, in which the electron spin-ﬂip scattering processes occur on a much longer time
scale than the elastic electron scattering events. It was Lee et al. who ﬁrst wrote down the

135. The scattering of the electrons

equations to describe a two parallel-channel mode
carried by each channel is spin dependant with different scattering rates and can be
described phenomenologically in terms of different resistivities for majority and minority
electrons, i.e. electrons with their magnetic moment pointing parallel or antiparallel to the
local magnetization, respectively. Later, Valet and Fert, VF, used the Boltzmann
formalism, to extend this model to include spin memory loss due to spin ﬂipping in the
bulk of the metals; this mechanism is measured by a quantity called the spin diﬁ‘itsion
length 38"", IFS; and INS; for F and N metals, respectively. Finally, one of the last steps in
the development of the semiclassical models was the inclusion of spin-ﬂip scattering at
the interface by Fert and Lee“, who generalized VF model by adding spin memory loss
at the interfaces through a modiﬁcation of the boundary conditions.

For samples in which no spin-ﬂipping occurs anywhere in the multilayer, the
Michigan State University group has demonstrated43‘“ that a ONO-channel-series-resistor-
model (two spin channels carrying currents independently), 2CSR, accurately described

the experimental data. This 2CSR model comes out as a particular case of the VF model

when lsp>>t in the F layer and N layers.

1.2.1 Giant Magneto-resistance. Semiclassic Analysis

GMR arises from spin dependent scattering in F metals and at F/N interfaces”.
Such scattering depends on impurities and crystal defects present in both F and N metals,
thermal vibrations of the lattice, mixing of the F and N metals at the interfaces, and the
band structures of the F and N metals. The band structure of a F material is magnetic
moment dependent. That is, the energy, 8, Of d bands with one moment direction are
shifted relative to the e of d bands with the opposite moment direction. At the Fermi
surface, this shifting leads to a difference in the density of states, 0(8), for each d band.

This situation is represented in Fig 1.2, where a simple sketch of 3 energy bands and d
energy bands of a N metal and a F metal is shown. Transport is carried by s electrons
because their effective mass is much lower than that of d electrons. If electrons do not
ﬂip their magnetic moments during scattering, the majority s electrons, moment up,
would scatter mostly into other majority s electron states, because there are few majority
d electron states available close to the Fermi energy. Minority electrons, moment down,
in contrast, can scatter more often into the larger number of minority d states at the Fermi
energy. These different scattering processes generate a different scattering probability for
electrons with magnetic moments parallel and antiparallel to the local magnetization.
This difference is called spin anisotropy.

To describe how GMR comes from the spin dependent scattering, consider a
F/N/F trilayer. The system is shown in Fig. 1.3, for two relative states of magnetization of
adjacent F layers: AP or P with respect to a ﬁxed direction in space. Electrons entering

the trilayer are divided into two groups: majority and minority electrons. If no Spin and

momentum are transferred between these groups, they can be treated as two separate spin
channels of conduction. This channel separation requires low temperature where
electron-magnon and electron-phonon scatterings are negligible. Then, the total R can be
calculated from the contribution of two different resistances in parallel for majority and
minority electrons. Usually the minority electrons are more strongly scattered in F metals

and at F/N interfaces, than majority ones.

    

/

a) Normal Metal j b) Ferromagnet
/'I’-’ ! \\\

   
  

~“\ Fermi Level
1.

   

    

V

    
 

wk

‘
\

N

R\\

  

\\\
\\\

.\\\\\\‘\\

\

    
    
 

\“

\\\\

 

45

Fig. 1. 2. Simpliﬁed diagram of the 4s and 3d energy, 2, bands vs. density of states, 17(8), of: a) a
normal metal, no net magnetic moment, and b) a ferromagnetic metal, there is a net magnetic
moment.

When the magnetizations are in the AP state, see Fig.1.3, one electron group will
scatter strongly in the ﬁrst F layer and weakly in the second F layer, and vice versa for
the other group, contributing equally to the total resistance, RAP. When the
magnetizations are in the P state, the up electrons will be scattered weakly in both F

layers, shorting out the total resistance, while the down electrons will be scattered

strongly in both layers. Consequently, the net resistance, Rp, will be smaller than that in

the AP state, Rp < RAP. GMR is usually computed as:

AAR
AR,

GMR:

 

(1.1)

where AAR = A x AR = A x (RAP-RP) is the difference of speciﬁc resistances for AP and

P states, and A is the area of the CPP current ﬂow.

 

(a) AP state (b) P state

 

 

e‘ .
“P' I MK

    

C PP-I

. T CPP-I
L r:
A 1' :‘\ e-downI

    

.-.... I

 

 

 

 

 

 

 

 

 

 

Fig. 1.3. Schematic explanation of the basic GMR effect for a particular magnetic conﬁguration.
a) When the magnetizations (arrows) of the magnetic layers are antiparallel, both moment-up and
moment-down electrons have equal resistance path. b) When the magnetizations of the F layers
are parallel, the moment-up electrons have a lower resistance path compared with moment-down
electrons, leading to a lower overall resistance

To produce P states, it is necessary to apply an external magnetic ﬁeld strong
enough to align the moments of the F layers along the ﬁeld. Because the AP state is more
elusive, there are typically three ways to produce it: i) Using an exchange-biased spin
valve, EBSV, consisting of two F layers separated by a N layer thick enough to prevent
coupling. The magnetic moment of a free F layer can be switched while the magnetic

moment of a F pinned layer is ﬁxed due to contact to an antiferromagnetic layer. 4546 ii)

11

Using antiferromagnetic exchange coupling between two adjacent F layers separated by a

15‘16'20'24 iii) Using a hybrid spin valve, SV. It is composed Of two F layers Of

N layer.
different switching ﬁelds, separated by a sufﬁcient thick N layer to prevent coupling.
Studies using such an asymmetric hybrid SV are part of this dissertation, and a more

detailed description of our system can be found in Chap. 2.

1.2.2 Total Resistance of an asymmetric FIN/F Trilayer using

the Two-current Series-resistor Model (2CSR)

In this simple model, the electrons travel through each layer and the interfaces,
sampling the magnetic order, regardless of the mean free path. The different scattering
rates make the bulk resistivity of the majority electrons, pl, and minority electrons, pl,
distinct. Similarly, the interfaces also have spin-dependent scattering, characterized by
speciﬁc resistances, for majority electrons, ART, and for minority electrons, ARl. Lee et
al.35 elaborated the ﬁrst equations of the 2CSR introducing parameters to describe what
happens in the bulk of N and F and at their interfaces. The most relevant ones are the

following two dimensionless parameters: bulk spin asymmetry B, and interfacial spin

 

asymmetry‘x
l T l T
p —p AR —AR
=—————— and = (12)
ﬂ pl+pT 7 ARi+ART

In addition to B and y, the measured bulk resistivities of the metals, p, the

interfacial speciﬁc resistances, AR, and layer thicknesses, t, are enough parameters tO

12

describe CPP GMR. The thicknesses of the layers are the only lengths taken into account;
the rest of the parameters are independent of t. Recall that spin-ﬂip scattering is assumed

to be negligible in the 2CSR model.

AP

Current

 

 

 

 

 

 

 

Fig. 1. 4._Diagram of the 2CSR model for the AP state of an asymmetric F/N/F trilayer with
superconducting contacts. Big arrows indicate orientation of local magnetization. F layers have
different thicknesses. The current is divided into two channels: moment up channel and moment
down channel. There is one resistance per channel that is the sum of each resistance in series. The
total resistance is the combination of the resistance of each channel in parallel.

Consider a relatively simple case that can be studied with the 2CSR model: two F
layers of different thicknesses, separated by a N layer, see Fig. 1.4. Two S contacts at the
ends guarantee uniform CPP current ﬂow through area A for T < Tc , where Tc is the
critical temperature of S. The dissimilar thicknesses of the F layers produces switching

ﬁelds different enough to allow AP alignment under ﬁeld reversal. The different F layer

thicknesses makes this F/N/F trilayer asymmetric, producing somewhat more complex
algebraic ﬁnal results for the CPP resistance.

We use the following notation: subscript N always refers to N metals and
subscript F always refers to F metals. The symbol T indicates majority electrons (moment
parallel to the local magnetization), and the symbol 1 indicates minority electrons
(moment antiparallel to the local magnetization).

A measure of the. average resistance for majority and minority electrons in the F

layers is given by the following:

p‘ =(pr‘ +p:)= p]: (13)
” 4 (l-ﬂi)

 

where pFT =2pp‘(1 -— ﬂF ), pFi = 2pF.(I + ,6). ), and ,BF is the bulk spin-asymmetry
parameter of the F metal.

In the case Of N metals, up and down electrons scatter at the same rate. Thus:

 

. (pl + pi) m
= = _—_ 1.4
p” 4 (I—ﬂi) p” ( l
where ,3” = 0, and p; = pi, = 2pN.
An equivalent analysis for the F/N interfaces deﬁnes the average interfacial

speciﬁc resistance for majority and minority electrons:

ARI/N +AR:N ARF/N
4 (1‘ 72m)
where Al”, =2AR'(1— 7W), At”, =2AR'(1+ 2W ), and rpm is the interface spin

ARF/N =

 

(1.5)

asymmetry parameter.

l4

It is assumed that the S/ F interface resistance is spin-independent, and thus 73/1: =

0. This gives:
T _ l _ ‘
AR S/F- AR S/F - 2 AR S/F (1-6)
where AR .s/p : ARs/F .

The speciﬁc resistance Of each channel is the series sum of resistivities of
individual layers times their thickness, plus the interfacial speciﬁc resistances. Thus, the
total CPP AR is equal to the parallel addition Of the sum of speciﬁc resistances of the two
spin channels as described in Fig. 1.4.

In case of the AP state, ARs for spin-up and spin-down electrons can be written

ARAP(up)=2AR.ST'/F +pAr’tN TP; tr, +pl£tF, +ARil/N +ARE/N (1'7'3)

ARAP(down)=2AR;,F +pfvtN +Pi~t5 +10%, +ARi/N +ARLN (11b)

Further steps can be taken by placing Eqs. 1.3 to 1.6 into Eqs. 1.7 to get the
speciﬁc resistance of each channel in term of the average speciﬁc interface resistances,

average bulk resistivities, thicknesses, and spin asymmetry parameters of the multilayer:
ARerup) = MR... + 2W, + 2p;~t.,(1— 3) + 2p;t.~,(1 + ﬂ) + 4AM...

(1.8a)

ARAP(down)=4ARS,F + 2pNtN +2p;t,.l(1+ﬂ) + 2p;tF"(I—ﬂ)+4AR;,N

(1.8.b)

15

Since the two channels resistances are in parallel, the total speciﬁc resistance Of

the system in the AP state is given by:

 

 

 

l 1 1
= + (1.9)
ARM, ARAP (up) AR”, (down)
Combining Eqs. 1.8 and 1.9, ARAp comes out as:
ARAP =2ARW +pNtN +p;.(t,. +tF:)+2AR;/N — (1.10)

(P1102; —tF,)ﬂ)2
(ZARSW +pNtN +P;(tp, +tF} )+2AR;/N)

Analogous treatment can be done to obtain AR for the P state. Combining the

speciﬁc resistivities and interfacial speciﬁc resistances of each channel, ARs for spin-up

and spin-down electrons become:

ARM up) = ZARsT/F + pit... + P; tr, + p; tr, + ZARl/N “-1 l-a)

ARP(down)=2ARSl/F +p§t~ +pﬁt, +pﬁtF, +2ARﬁ/N (1.11-b)

l .

Placing Eqs. 1.3 to 1.6 into Eqs. 1.1], ARs can be obtained as function of the
average speciﬁc resistivities, average speciﬁc interface resistances, thicknesses, and spin

asymmetry parameters:

ARP(up)=4ARs,F +2pNtN +2p;tFI(I—,B)+2p;.tFJ(I-,6)+4AR;,,,.(1—y)
(1.12.a)

ARP(down) = 4.4125,, + 2pm + 2p;.z,., (1 + ,6) + 2p;.tF2 (1 + ,6) + 4AR;./N(1 + 7)
(1.1212)

16

Then the total ARp is given by the sum in parallel Ofthe resistances in Eqs. 1.12:

1 = 1 + 1 (1.13)
ARP ARP(up) ARP(down)

ARP =2ARS/F +pNtN +pF(tF, +tF,)+2ARI:/N —

(p;(tp, +tr, )ﬂ'l‘ ZARE/Nl' )3
(2ARS/F +pNtN +pl:(tF, +th )+ ZARLN)

 

(1.14)
The difference between ARp and ARAp can be easily derived from Eqs. 1.10 and
1.14, giving AAR which is one of the most useful quantities to characterize a multilayer

system and determine its GMR.

 

o A 0 ' R.
AAR=ARAp-ARP= «WT/3+ RF/N’l.)(pptf’ﬂ+A "’37) (”5)
(ZARS/F +pNtN “Moran +tF, )+2ARF/N)

1.2.3 Inclusion of Spin Diffusion Length in a FIN/F Trilayer
Resistance Calculation

As we will show in Sect. 2.2, our actual trilayer system has tn >> IFS; and tn 5

lFsp. Thus, to compute ARM», ARp, and AAR, it is necessary to utilize models which

138, which can describe accurately our

include spin diffusion lengths, such as the VF mode
system. The VF model assumes that spin-ﬂipping occurs in the bulk of the F and N layers

and calculates AR for [F5]: and lep of any size with respect to t; and tN. In the limit that

11’s,.» tn and [NSF >>tN, the VF model agrees with the 2CSR model.

17

 

AP

Current

 

 

 

 

 

Fig. l. 5. Diagram of the 2CSR model for the AP state of a tri-layer F/N/F with superconducting
contacts. F layers have different thicknesses. The inclusion of the spin diffusion length in the ﬁrst
F layer, tn >> [F517 , shortens the two charmels. The current is divided into two channels:
moment up channel and moment down channels. There is one resistance per channel that is the
sum of each resistances in series. The total resistance is the combination of the resistance of each
channel in parallel plus the contributions of that part of F, not in the two-channel region and the
S/F boundary resistance on the left.

Without going through the VF formalism strictly with its complicated
calculations, a simple modiﬁcation of the 2CSR model is adequate to estimate the value
of the total AR,» and ARM), which agrees with those values given by the VF model. Since
tn >> IFS).- , only a thin region of thicknesess [Fsp , next to the F/N interface, participates
in the two spin-channel conduction. The rest of the F1 layer just looks like a single
resistor as illustrated in Fig. 1.5. Since tp2 2* IFS; we ignore spin—memory loss and apply
the usual 2CSR model to the F2 layer.

Under these conditions and following similar calculations to the ones described in

Sect. 1.2.2, ARM, and AAR come out as:

ARAP =2ARS/F +pr(tI-; _/.:I')+prvtrv "IPA“; +II; )+ 2AR;.N _

(pH/.5.- — r... )ﬂI"
(ARM + pit... + p21 1.5;. + II, )+ ZARI.-.)

 

(1.16)

_ 40021.53 + ARI-hwmitpﬂ + ARLNII

, . (1.17)
(ARSKF+pNtN +pF(I:F+tF1)+2AR,,/N)

AAR = ARM, — AR,

 

 

AP S

Current

119ml ’str
' RNIJNZ

 

 

 

 

 

{—tFl —’ l—tFl —’

Fig. 1.6. Diagram of the 2CSR model for the AP state of N2 right contact. The right Nb layer in
Fig. 1.5 is replaced by a N 1+ N2 layer. The inclusion of the spin diffusion length in the N2 layer,
1N2 >> lmsp, shortens the two channels.

Another system which is of interest for this work is shown in Fig. 1.6, which is
the result of modifying the system presented in Fig.1.5, where the right superconducting
layer is replaced by a N1+N2 bilayer. In this case, tN2 >> [~st, and similarly to what
happens in the F1 layer, only a thin region of thicknesess INZSF, next to the Nl/N2

interface, participates in the two spin-channel conduction. The rest of this N2 layer just

lOOks like a single resistor as illustrated in Fig. 1.6. For the N. layer, one assumes tm <<

INISF. The values of ARM and AAR can be calculated with Eqs. 1.18.

ARAP =ARS/F +pF(tF, —l.S[;‘)+pNtN +p;‘(lsFF +tF,)+pN,tN, +p~,’~, +

(My SEE-tr; )ﬂ_A}g‘/N,7F/N,)2
(2144/11; +P;( :F+tg)+WN+AK‘/M +pN,t.v, +va',/S\I" +A}§I,/Iv,)

 

+2A4/N +AE7N, +Algl,/N,

(1.18)

AAR = ARM, - AP, =
_ 4(p}1;ﬂ+AR;/~r)(p2~tp,ﬂ+ ARLINV+ARZ~/~,r)
(pm with, with”; win; +tp, )+2ARi~/~ + ARi/N, + MIL/M)
(1.19)

 

NOW if we assume that S = Nb, F = Py (permalloy = Ni34 Fe“), and N: Cu in Fig
1.5 and S = Nb, F = Py, N: Cu, Ni: Cu, and N2: An in Fig 1.6, these two systems
represent, as we will see in Chap. 2, our two types of actual samples with Nb-top contact
and Au-top contact, respectively, both with Nb bottom contacts. Calculations of ARAPS
and MRS of these systems using Eqs. 1.16, 1.17, 1.18 and 1.19, see Table 1.2, are very
useful to predict and analyze our experimental data. As mentioned before, these equations
are valid only for low temperature. At this point, we have to mention that our actual
samples have a lOnm-thin-Cu layer inserted between the multilayer and the bottom
superconducting Nb contact, and a 5nm-thick-Cu + 15nm-thick-Au layer next to the top
contact. We assume that the proximity effect, to superconducting Nb, allows Cooper
pairs to pass through the N metals, so that we only need to consider an effective Nb/Py

interface". The values of AR", p*, t, and 15; used in these calculations are shown in

Table 1.1. The spin asymmetry parameters are [3 = 0.73 and y = 0.7.48

20

 

 

 

 

 

P. ptpy= 0.263 uﬂm t,,,= 20 nm AR*p,,c.,= 0.51 fem2 mp: 5.5 nm
F2 pitpy= 0.263 119m (N 5 nm
N pc.,=' 0.006 uﬂm 1c”: 10 nm AR~W= 3.00 ram2 1%,; 450nm
N, pmﬂ 0.006 119m rc,= 5m
N2 [2MB 0.02 uﬂm IM- 107nm ARM“: 0.175 mm2 I‘“s,.= 35 nm

 

 

 

 

 

 

Table 1.1. Values of average bulk resistivities, p*, thicknesses, t, average speciﬁc interface
resistances, AR“ and spin diffusion lengths 15;. Values obtained from Refs. 48, 49 and 50.

Other helpful quantities to be considered in our calculations are RAP and ARAp,
also included in Table 1.2. They were obtained by dividing the calculated values of AR Ap
and AAR by an estimation of the CPP current ﬂow area. As we will see in Chap. 2,
basically two types Of constrictions were built in our nanowires. For the purpose Of our
calculations, they have different effective current areas. These two kinds of constrictions
are: U-shaped notches of current ﬂow area A ~ 1.5 x 10'13 m2 and V-shaped notches Of
current ﬂow area A ~ 2.2 x 10'13 m2. These areas were estimated by averaging over the
measured areas (using a scanning electron microscope) of 3 typical U-shaped-notch
samples, and 5 typical V-shaped-notch samples (considering the actual dimensions Of the
samples after SiO deposition, see Sect 2.2.4). Table 1.2 also contains the results of the

calculation of GMR percentages utilizing Eq. 1.1.

 

 

 

 

 

 

 

 

 

 

 

Contact ARM» (1'01?) AAR (fﬂnz) RAP (m0) AR(mQ) GIUR 1%)
Nb-U ~11.6 ~l.l ~77 ~7.2 ~10
Au—U ~ll.2 ~1.6 ~ 75 ~ 11 ~17
Nb-V ~11.6 ~l.1 ~ 55 ~ 5.2 ~10
Au-V ~ll.2 ~l.6 ~ 53 ~ 7.9 ~17

 

 

Table 1.2. Low temperature values of ARM and AAR calculated with Eqs. 1.17 and 1.18, for S =
Nb, F = Py, and N: Cu in Fig 1.5, Nb top contact; and S = Nb, F = Py, N= Cu, N1: Cu and N2:
Au in Fig 1.6, An top contact. RAP and ARAp, for the same systems with estimated area of A~ 1.5
x 10'13 m2 for U notches and A~ 2.2 x 10'l3 m2 for V notches. GMR percentage obtained with
Eq.1.1.

21

1.3 Magnetic Domain Structures and Domain Walls

1.3.1 Magnetic Domain Structures - Total Free Energy

In a F material the redistribution Of the magnetic domains is established by the
reduction of the overall total free energy of the sample, based on several competing
energies. In a perfect single crystal, the energy minimization calculations can be strictly
carried out. However, the presence of imperfections, such as strains, inhomogeneous
internal ﬁelds, grain boundaries in polycrystalline samples, etc., can radically change the

details of the domain conﬁguration, and thus complicate those calculations. Based on the

energy density’s dependence on the local value of the magnetization, .7 , direction,

[Kn

r71 = , the competing energies can be divided into two groups: local contribution terms,

which depend solely on If: , and non local contributions terms, which do not depend on

k1

Iii exclusively. Summing up those main contributions, the total free energy can be written

as an integral over the sample volume, V:

E ~j [Aa(Va)2 +F,,,(iii)-H .J—iH,.J—E..E°]dV

total =

T i i izi 1

Total energy 5 Ea, (exchange) + Ea( anisotr0py)+ Ez (ext. ﬁeld) +Ed (Stray ﬁeld) +E, (ext. stress)

(1.20)

Fm, is a function which collects all contributions from crystal and structural

magnetic anisotropies, andI-l and F], are the external and the stray (or demagnetizing)

22

ﬁelds, respectively. The symmetric tensor 6'“ collects all stresses of non-magnetic
origin, a” (Iii) is the free magneto-elastic deformation at any given points I.
The ﬁrst local energy contribution is the exchange energy, E”, which causes a

preference for a constant direction of the magnetization. Changes from this equilibrium

invoke an energy penalty which can be described by the stiffness expression:
15,, =A,, [(Vr‘hﬂdr (1.21)

where A” is the stiffness constant, which depends upon the material, giving a measure of
the strength of the coupling between the spins in the material.

The second local contribution is the anisotropy energy, Ea. This energy depends
on the direction of magnetization relative to the structural axes of the material. F crystals
have preferred axes of magnetization, easy axes, which arise from the band structure of
the material and the spin orbit interaction. This tendency of the F magnetization to align
along these easy axes is named anisotropy. The most relevant one is the crystal
anisotropy, but there are other types such as the surface anisotropy, and interface
anisotropy, etc. These various anisotropy effects can be characterized with a constant K.
In this work, all of them are ignored because of their small contribution to the total free
energy. As we will see later when analyzing the magnetostatic energy (or stray ﬁeld
energy), one of the reasons to neglect Ea is that stray-ﬁeld effects are much stronger than
those of the various anisOtropies. Another important reason arises from the structural
features of our samples. The sputtered Py (used to make our actual sample) grows in
randomly-orientated fcc-structured-columns which have in-plane grain sizes of ~ 5-15

nmsz'“. Columns grow with (111) texture” with their magnetization easy axes along the

23

(110) “in-ﬁlm-plane” directions. Since these grains are arbitrarily-orientated and also
smaller than the shortest lateral dimension of our samples (“the notch width”~ 100 nm),
the anisotropy effects are considerably reduced.

The third local energy contribution is the external ﬁeld or Zeeman energy, E; it

comes from the interaction of H and the magnetization:
E, =—J,jI?-ﬁz dV (1.22)

where J, is the magnitude of the saturation magnetization. For uniform H, this energy
depends on the average magnetization only.

There are three non local magnetic energy contributions: The largest is variously
called the magnetostatic energy, demagnetizing ﬁeld energy, stray ﬁeld energy, or dipole
energy, Ed, and comes from the energy of the magnetic ﬁeld created by the
magnetization. The usual form of this term is:

Ed=lu0 jdeV=—::- [rid-7dr (1.23)

all —space sample

where #0 is the permeability constant. The mechanism relating the preferred
magnetization direction with the external sample shape is called shape anisotropy, and it
is quantiﬁed through the magnetostatic energy. For example, consider the extreme case
where an inﬁnite plate of thickness t is uniformly magnetized perpendicular to its plane,

as shown in Fig.1.7. The resulting energy density for this uniaxial-like shape anisotropy,

 

can be quantiﬁed by:
2
ed=-1Hd-.7= J3 (1.24)
2 211..

24

This maximum energy density is

 

 

 

 

 

 

 

 

ii A A (l A (1
J2
-. —. ivenb K = S . =K/K measures
i x J J t g Y a' 2.110 Q «i
Y
He the competition between various

 

anisotropies, K, and this maximal shape
Fig. 1.7. Sketch of the demagnetization ﬁeld

for an uniaxial-like shape anisotropy in a plate anisotropy. When Q iS small, the maximal
of thickness t and inﬁnite extension in x-z
plane that is uniformly magnetized shape effects are stronger than the other
perpendicular to its plane.
anisotropy effects.

When there are stresses of non magnetic origin present, the last term in Eq. 1.20
describes the interaction of magnetization with external stresses, or non-magnetic
internal stresses resulting from dislocations, inhomogeneities in temperature, structure or

composition. For an isotropic material and uniaxial stress along the axis of unit vector 5 ,

the magneto elastic coupling energy can be expressed by:

E, =j—-:-;,6[(iii-a)2 -§] dV (1.25)

which describes a uniaxial anisotropy along the stress axis with an anisotropy constant of
Ku=3/2 40; where g", is a dimensionless material parameter indicating the strength of the
elastic interaction.

The weakest contribution, which is not included in Eq. 1.20, is the energy
associated with the elastic interactions between regions magnetized along different axes,
the so called magnetostrictive energy; it is neglected in this work due to its minor

contribution to the total balance of free energy.

25

As we stated before, the balance Of the mentioned energies determines the domain
structure in F ﬁlms. For a very thin magnetic ﬁlm, unless there is a magneto-crystalline
easy axis perpendicular to the plane of the ﬁlm, the magnetization will lie in the plane of
the ﬁlm due to the large shape anisotropy. For polycrystalline ﬁlms, there is no preferred
in-plane direction, since all orientations of the magnetization in the plane are equally
probable. For very thin ﬁlms, demagnetization effects over most of the plane of the ﬁlm
proper can be ignored. However, the edge of the ﬁlm may still show demagnetization
effects in order to minimize the energy, for example, 90° domains of closure. The best
way to understand this is through a simple example for a single-crystal ﬁlm. Consider a
rectangular thin-ﬁlm crystal magnetized entirely along the easy axis, as shown in Fig 1.8
(a). The magnetostatic energy of the sample is reduced by approximately a factor of two
if the conﬁguration is divided into two separate oppositely magnetized domains, see Fig.
1.8 (b). By adding more oppositely magnetized domains (Fig. 1.8 (c)), the magnetostatic
energy would reduce until the energy necessary to produce a new boundary between
domains is greater than the energy reduction. This is because the addition of a new
domain also creates a “domain wall”, which is the transition region of ﬁnite extent
between the two magnetization domains, where the magnetic moments vary in direction.
The creation Of a domain wall requires an increase of the exchange energy and anisotropy
energy of the system. In this simple example, we are ignoring possible magnetostatic
energy contribution to the domain-wall itself. Thus, at this point, the combination of the
exchange and anisotropy energies mainly rule the production of new boundaries and
adding opposite domains along the easy axis is not enough to reduce the total energy.

Formation of triangular closure domains at the edges of the rectangle with magnetization

26

at 90° to the original domains (Fig. 1.8 (d)) makes it possible to drastically reduce the
stray magnetic ﬁeld and thus the magnetostatic energy. However, those closure domains
are magnetized in the hard direction, introducing anisotropy energy to the system. Along
with the emergence of closure domains, new domain walls appear, whose formation adds
more exchange and anisotropy energy to the total free energy. Thus, the creation Of
closure domains helps decrease the total energy until the magnetostatic energy reduction
is equal to the increase of exchange energy and anisotropy energy of the system. In the
ideal case, poles Of magnetization disappear from the surface, making the magnetostatic
energy equal to zero. In a more realistic case, the magnetostatic energy is diminished but

residual poles remain on the surface.

(a) (b)

 

 

Easy axis
A

K11-

 

 

 

111111

Fig. 1. 8. a) Thin ﬁlm domain conﬁguration after saturation, with the subsequent reduction to
approximately zero ﬁeld. b) and c) Adding oppositely magnetized domains reduces the
magnetostatic energy. (1) Formation of triangular closure domains at the edges of the ﬁlm with
magnetization at 90° to the original domains reduces the magnetostatic energy.

 

 

 

 

 

 

27

When nO domains occur at the edges and no wall is present in the ﬁlm, a wall
must ﬁrst be nucleated somewhere before magnetization change can occur via wall
motion. Closure domains at the edges of a ﬁlm play an important role as nuclei for such

walls.

1.3.2 Type of Domain Walls in Unconstrained Thin Films

Shape anisotropy is very pronounced in a thin ﬁlm due to its extreme thinness
compared to the other two linear dimensions. As consequence, the energies and widths of
domain walls in thin ﬁlms are quite different from those in bulk materials. Consider a
ﬁlm of thickness t (along y) and inﬁnite extent in the x-z plane, with easy axis along 2, as
shown in Fig. l .9. A domain wall of width D, whose plane is perpendicular to x, is placed
in this ﬁlm and magnetizations on either side of the wall are antiparallel and along 2. If t
> D the sample is essentially three dimensional, and a “Bloch wall” occurs where the
magnetization rotates by 180° in the y-z plane within the wall“. as shown in Figl.9 (a).
(Bloch walls have no poles inside the wall.) As t —> D, the Bloch wall will generates
signiﬁcant magnetic pole density on the two opposite surfaces Of the ﬁlm, giving rise to
stray ﬁelds. Therefore, the magnetostatic energy cannot be a priori neglected. The
magnetostatic energy associated with these stray ﬁelds plays an important role in the
determination of the wall type

Néel demonstrated in an approximate calculation that in a very thin ﬁlm the
energy can be minimized by having the component of the magnetization normal to the

surfaces of the ﬁlm vanish. Thus, the spins within the domain wall rotate in the plane of

28

the ﬁlm, x-z in F igl.9 (b). Because the magnetization along x inside the wall is not zero,
magnetic poles are present. These domain walls are called “Néel walls”57 .
There exist other types of domain walls which are intermediate states between

these two ideal cases, the well-known N661 and Bloch walls; more information about

them can be found elsewhere”.

(8)

 

Bloch

 

 

 

 

(b)

 

 

 

 

Néel

 

 

 

 

Fig. 1. 9. Two domain wall conﬁgurations in a ﬁlm of thickness t, inﬁnite extent in x-z plane, and
easy axis along z: a) Bloch wall b) Néel wall.

As a simple example to establish what parameters deﬁne a DW of width, D,
consider the determination of a Bloch wall width in an inﬁnite perfect crystal by
minimization of DW energy in the semiclassical treatment. The magnetic moments are
treated as spins that in turn are considered as classical vectors, whose directions change

gradually. The reason for this gradual change is that the exchange energy is lower when

29

the change is distributed over many atomic planes instead Of discontinuously. Of course,
the anisotropy energy of the crystal is increased due to the fact that the spins within the
wall must by necessity point in directions other than that of the easy axis. A crystal with
uniaxial anisotropy, whose axis of easy magnetization is as shown in Fig 1.9 (a), has an

exchange Hamiltonian and an anisotropy energy density e). given by :

Hex=—ZIZS,-Sj and ekz-IIS-ID/Z

-2 _ﬂ
_D/2K,sm ¢dx— 2 (1.18)

j>i

where I is the exchange integral (which is a constant for this case), S. corresponds to the
ith spin, with i, j = 0 to N, K 1 is the ﬁrst order anisotropy constant and (Fax/D is the angle
between the spin and the easy direction in the plane Of the wall. If the change occurs in N
equal steps, the wall thickness is D=Na, where a is the lattice constant, and the total

energy per unit wall area becomes:

 

2 ( )

Differentiating E w with respect to N, the domain wall width is easily found as:

2 2 1/2 1/2
D=Na=[-2—ﬂ—B—] :44...) (1.27)

 

K10 K]

where Aex = 2IS'Z/a. If the exchange interaction is stronger, D gets longer; and
alternatively, if the crystal anisotropy is stronger, D shortens“.

In the previous straightforward example, the magnetostatic energy was not
included in the energy balance, but in a more realistic case its consideration is crucial for

determining the type of wall present in the system. To exemplify this, let us examine the

30

results by T. Trunk et al.”, who investigated the Bloch to Néel wall transition in a Py
ﬁlm. They directly integrated the Landau Lifshitz Gilbert equation in a three dimensional
cartesian lattice, considering that the dimensions of the sample are inﬁnite in two
directions but ﬁnite perpendicular to the ﬁlm plane. They also neglected the crystal
anisotropy, and only exchange and magnetostatic energies were included in their
calculations.

Fig. 1.10 (a) shows that three regimes can be distinguished based upon the
thickness dependence of the magnetostatic energy: “Bloch-type walls” when the ﬁlm
thickness is over 35 nm, a transition from “Bloch to Néel walls” as the thickness of the
ﬁlm is decreased between 35 and 30 nm, and “Neel-type walls” for ﬁlm a under under 30
nm. Trunk et al. provided precise values for this energy balance, as the wall transforms
from Bloch to Néel below 35 nm, the energy contribution changes from 76% exchange
and 24 % magnetostatic to 70% magnetostatic and 30 % exchange, respectively. This

means that, when the dipole interaction gets stronger, Néel walls are more likely to occur.

 

 

(a) j (b)

, / soo-
Bloch "‘

21 / E 250‘

\ ./ ° W

150-

   
 

   

: Neel Wall

\

 

 

 

 

 

 

1- Néel Bloch Wall
100~
50-
o -.., o . . - . . .
10 100 1000 10000 035100 200 300 400 500 600 700
t(nm) t(“I“)

Fig. 1.10. Results presented by Trunk et. al.” for a Py ﬁlm. a) Wall energy per unit area as
function of ﬁlm thickness. b) Wall widths in the center of the material, as a function of ﬁlm
thickness.

31

Fig. 1.10 (b) tell us, that in the center Of the material, the Néel wall width
increases typically from 35 nm to 100 nm, as the ﬁlm thickness is reduced. If we deﬁne a
Py ﬁlm as thin if its thickness is comparable to the Bloch wall width, Py ﬁlms under 20
nm can be considered very thin, in which case Néel walls are energetically more likely to

occur, with widths up to, at least, 3 times bigger than those of Bloch walls.

1.3.3 Domain Walls in Magnetic Fields and Shape Effects

The previous discussions were based on the inﬂuence of the exchange,
anisotropy, and magnetostatic energies only. Those DW conﬁgurations represent a
minimum free energy in the absence of an external ﬁeld. When an external magnetic ﬁeld
is applied, Zeeman energy also contributes to the energy balance. The angle between the
magnetization and the external magnetic ﬁeld becomes important because the
magnetization tends to align along the easy axis. For a perfect single crystal when a ﬁeld
is applied at an angle to the easy axis, the Sign of the ﬁeld component along the easy
direction establishes in which direction the walls will move5°. Analogously, for a
polycrystal with strong shape anisotropy, Q << 1, see Sect.l.3.l, we can conjecture that
the sign of the ﬁeld component along the shape anisotropy “easy” axis will establish in
which direction the walls move.

As just indicated, altering the external shape of a sample can signiﬁcantly affect
the preferred axis of magnetization; and by adjusting these external geometrical
parameters, it is possible to trap a DW. In our samples, composed of a long narrow wire

as shown in Fig 1.11, the magnetization prefers to align only along the longitudinal axis

32

of the wire due tO the shape anisotropy. A wider area or reservoir at one Of the ends
allows closure domains to nucleate a DW, a sharp tip on the other end prevents wall
nucleation, and a constriction in the middle of the wire ensures wall trapping. After
applying a fairly large H along +x, the magnetization of the sample will be pointing to the
right in Fig. 1.11. If the ﬁeld is then lowered until it changes Sign (pointing to — x), the
DW will ﬁrst move in the reservoir to accommodate the growth of a favorably oriented
domain and then a head-to-head domain wall (see Sect. 1.3.4) will be injected into the
narrow wire from the reservoir at the right and eventually will get trapped in the

constriction built into the middle of the wire. The presence of the notch creates a potential

 

 

Ii .9.... i

Rese oir

1.1 “m

 

Domain wall trapped in
constriction of width ~ 0.1um

Fig. l. 11. Top view of a sample used to trap a DW. A constriction placed in the middle traps the
wall while it is traveling from one end to the other. A reservoir creates closure domains which
nucleate the wall, and a sharp tip on the other side prevents wall nucleation.

barrier that must be overcome for the DW to continue moving. The wall will stay trapped
until the applied ﬁeld lowers the potential barrier sufﬁciently to drive the wall out of the
constriction. The magnetization on the right side of the wall is reversed, and pointing
along -x, while the magnetization on the left side is still pointing along +x. As H is
lowered further, the wall leaves the notch, and the magnetization of the whole sample

will point along —x. If the ﬁeld is now increased, at low H pointing along +x, 3 tail-to-tail

33

domain wall will be injected into the wire from the reservoir and become trapped at the

constriction.

1.3.4 Domain Wall Structure in a Ferromagnetic Wire and at a

Constriction in Presence of an External Magnetic Field

To interpret the results and understand the mechanisms that rule DW motion in a
long nanowire with a central notch, ﬁrst it is essential to analyze what domain structure
can be present in a long narrow F wire without a constriction, and then determine how a
constriction alters the dimensions and type of wall present in that geometry.

To understand what kind of DW structure is present in a F thin wire with “no
constriction”, let us refer to the work done by R. D. Mc Michael et al.°° They presented
calculations Of head-tO-head domain wall structures in magnetic strips of Py, by
minimization of the exchange and magnetostatic energies only (and neglecting
magnetocrystalline and magnetostrictive anisotropy energies). Two types of head-to-head
DW structures can be formed in a long Py strip: “transverse” and “vortex”, whose
characteristics are illustrated in Fig. 1.12 (a) and (b). A phase diagram was also proposed,
which exhibits under what dimensions these two types of structures exist, see Fig. 1.12
(c).

In Fig 1.12 (6), points A and B represent 500-nm-wide Py ﬁlms of two different
thicknesses, tA ~ 5 nm and t3 ~ 20 nm. As we will see in details in Chap. 2, these are the
dimensions of the Py layers of our samples. We can infer that only a “transverse” wall

can be present in our thinner Py ﬁlms, but a “vortex-type” wall might be present in our

34

thicker Py layer. However, in the constriction region of the thicker Py layer, the lower
effective strip width might cause a transverse wall to form, as inferred from point C in

Fig. 1.12 (c).

 

 

 

‘A“‘

(8) <:;};I

 

 

 

 

 

 

 

 

 

 

AAAA

 

I’ll/”///’//

AAA“

 

.(
l
11
10
MN

\\\
\\
\ss

‘ﬁA“

 

 

’I”/”””””/

[it

 

 

 

 

 

 

 

r \
”;”;’J”m\
III/I’llllﬂdﬁﬁﬂn-~\\

II

 

 

(b)

 

 

 

‘y‘r‘IIIII’I/llam\ \!
~ :2/[I/III’II/Iaaa~\\i

II
II
{I
J
Fig. l . 12. Results presented by Mo Michael et al. a) “Transverse” domain structure for a head-to-
head wall calculated for a 2-nm-thick, 250-nm-wide Py strip. b) “Vortex” domain structure
calculated for a 32 nm thick, 250m nm Wide Py strip. c) Phase diagram of head-to-head domain
structures. A and B points represent our samples, 500-nm-width Py ﬁlms of two different

thicknesses, tA~5nm and t3~20 nm. C represents the constriction region, width ~100nm,
for the thicker Py layer.

 

 

 

Py Strip Wiilth (nm)

§
..1

 

 

 

1‘1‘

1‘1 ‘1\\
1M‘1\\\\\
1h\\\\\\\
‘1 \\~\~ss\

 

\‘Sm‘1

‘3‘“0.“ “I
\\\\\\\ “I

 

 

 

 

 

 

 

a.“
E:
\
\
\\
\
\
\
\
\
\
\
\
\
7w

 

 

\\‘-'f”I/III/II[Iii—--—~————u ' ' ' ""H

\W’If’fffff [firm . .
"Jame—w Pystnp thicknesses (an)
_

 

I’
I
I“ \\'IIII III
E

 

 

 

 

 

If a constriction is now placed somewhere in these type of wires, the dimensions
of the strips will vary locally, and the drastic changes in the shape anisotropy will induce
variations of the magnetostatic energy. A treatment for wall characterization in these
kinds of geometries was developed by Bruno“, who theoretically studied a constrained
wall in a notch separating two wider ultrathin ﬁlm regions. In this work the
magnetizations of these two regions do not have the same structures as those studied by
Me Michael et al. In Bruno’s work the magnetizations are antiparallel (at 180°), but they
are not aligned as a head-to-head (or tail-to-tail) arrangement. Bruno pointed out that the
magnetic wall will tend to localize near the constriction to minimize its energy. When the

cross section of the constriction is much smaller than that of the wider region, the

35

structure becomes almost independent of the material parameters, such as exchange
stiffness, and anisotropy constant. Instead the structure is determined by “the geometry of
the constriction”. The wall energy consists mostly of exchange energy. Thus, he argues
that a geometrically constrained magnetic wall constitutes a new kind of magnetic wall,
in addition to the well known Bloch and Néel walls. The width of a geometrically
constrained magnetic walls is essentially given by the “length of the constriction”.

The most relevant calculation to

 

’l‘
1 121m" the geometry used in this work was done

50”“ i l bMM‘h 11162 h ‘ lthW
. 400m __’1 y c rcaeea. wosrmuae

trapping for 5-nm-thick Py wire with a »

 

, , central trapezoidal constriction that Opens
Fig. 1.13. Geometry used by Me Michael et al.

to simulate domain wall motion in a Snm thick

at 45°, see Fig 1.13. The wire is considered
Py layer.

to have semi-inﬁnite ends. Calculations were done using a micromagnetic model,
OOMMF, developed at NIST, which is based on the Landau-Lifshitz equation. The
model includes effects Of the exchange energy (characterized by the exchange stiffness
constant), the magnetostatic energy (characterized by the spontaneous magnetization),
and applied ﬁeld energy. The magnetization is assumed to be uniform across the
thickness of the ﬁlm to allow the use of a two-dimensional grid. The spins are free to
rotate in three dimensions, but the large magnetostatic energy required to tilt the spins out
of the plane results in predominantly in-plane spin conﬁgurations. They found that there
exist three conﬁgurations: one unstable, with the DW in the central region, and two
stable, with the DW at either end of the trap, see Fig.1.l4. In the unstable conﬁguration

the spins along the lower edge of the center region form a 180° wall. For the stable

36

conﬁgurations, when the wall sits at either corner, the magnetization only turns by 135°.
This later situation causes a reduction of exchange energy of the domain wall, which
stabilizes the wall at the ends of the constriction. Note that for all three conﬁgurations the

wall has a magnetization that is predominately perpendicular to x (“transverse” DW).

 

  
   
  

 

zero ﬁeld after;

" -0.2 - I
zero ﬁeld after _§ f

 

 

 

04 ’p/e
- ~06 - /
W
: _08 .1 l 1 1 1
zero ﬁeld after{_ , 4 -3 -2 -1 0 l. 2 3 4

Fig. 1.14. Calculations by Mc Michael et al. for spin conﬁgurations at zero applied ﬁeld. a)
Unstable state aﬁer application of H in the —y direction. b) and c) Stable conﬁgurations after
application of H in the +x and —x directions, reSpectively. d) A hysteresis loop for a domain wall
trapped in the constriction. The switching ﬁeld for moving the domain wall from one end of the
notch the other is 1.1 mT, and the domain wall is pushed out of the constriction at H = 3.2mT.
Note the linear behavior of the magnetization vs. H while the wall is trapped.

Fig. 1.14 (d) shows the hysteresis loop while a wall is trapped in the constriction.
The switching ﬁeld for the domain wall while it is trapped in the notch is 1.1 mT, and the
domain wall is pushed out of the constriction at H = 3.2 mT. The magnetization has a
linear behavior as a function of the magnetic ﬁeld while the wall is trapped.

In this simulation DW widths range between ~ 150 nm and ~ 250 nm. This means
that the DW width is basically bounded by the wire and constriction widths.

Mc MiChael’s simulations suggest that only Néel walls are likely to form in

constrictions placed in “single” thin Py strips of width tpy. However, when the width of

37

the constriction Wpy —> tpy, we need to be careful because the ﬁlm might no longer be
considered a thin ﬁlm locally. In this limit, the wall will probably differ from a pure Néel
wall. That is in agreement to what is claimed by Bruno, who believes that walls at
constrictions are a transitional stage between pure Bloch and Néel walls. This could be
the case of the thicker Py layer of our samples.

Combining some of the results by Me Michael and Bruno, it is possible to
estimate the width of the wall present at the constriction of our samples, see Fig. 1.11. A
lower DW-width bound would be deﬁned by the width of the constriction ~ 50 nm - 100
nm, and a upper DW-width bound would be determine by some value between the wire
width and constriction length ~ 600nm.

Single F-layer systems are easier to analyze than double F-layer systems. As we
will see in Sect.1.3.5, extra factors intrinsic to F coupling make the determination of

trapped DW structure more complicated in double F -layer systems.

1.3.5 Double F Films

Magnetic double films consist of two F layers separated by a N interlayer. Such
sandwich structures must be distinguished from strongly coupled systems, such as F ﬁlms
directly coupled to hard ferromagnetic or antiferromagnetic substrates. When the N
interlayer in very thin, typically less than 5 nm, quantum mechanical exchange rules the
coupling between the F layers. If the N layer is thick enough, a weaker coupling

dominates, called orange peel effect. This favors the parallel orientation of the two F

38

layers, and it occurs when the N interlayer is thin compared to the corrugations in the F/N
interfaces, see Fig.1.15 (a). If the N layer is free of pinholes and typically much thicker
than 10 nm (depending on the type and perfection of the N layer), the F ﬁlms have no
local coupling between the magnetization directions in the two layers. However, if a
shape effect makes the thickness and width of the F layers comparable, then the presence
of magnetic free poles at the layer edges can alter the stray ﬁeld and therefore induce

coupling between F layers. See Fig. 1.15.(b).

 

 

 

 

 

 

 

 

 

(a) (b)
’ + a -
W
a f‘ +

 

 

 

 

Fig. 1.15. a) Orange peel effect may lead to ferromagnetic coupling. It occurs if the interlayer is
thin compared to the corrugations in the magnetic ﬁlms. b) Free poles at the edge of the F layers
may alter the stray ﬁeld and induce antiferromagnetic coupling between F layers when the
thickness of the F layers are comparable to their lateral dimensions.

If the double F layer is in the form of a long wire (with a ~ lO-nm-thick N interlayer),
the magnetizations tend to align along the wire axis due to the strong shape anisotropy,
and no magnetic poles appear along the edges of the wire, essentially reducing the
possible coupling between the F layers to almost zero. However, placing a constriction,
as shown in Fig.1.11, introduces a new shape anisotropy which can induce pole
formation. These extra magnetic poles affect the magnetostatic energy mainly in their
vicinity and, in consequence, induce local coupling between F layers. This local coupling
will become stronger as the width of the constriction, wp, in the F layers is reduced so

that W}: -—> tp, where tp is the thickness of the thicker F layer. In this limit, it is unlikely

39

that the local magnetizations in the two F layers will be parallel to each other even when
no domain wall is present in the constriction. When a wall is trapped in the constriction,
this coupling will likely cause the wall to deviate from a pure Néel wall (and this is in
addition to the effect produced by w; —> t}: on a “single’ F layer, described in 1.3.4). For
our sample the worst-case scenario is for the thicker Py layer, where Wpy 2 2.5 tpy, and
this might imply a relatively small deviation from a pure Néel type wall. However, when
no trapped wall is present, the residual coupling may produce observable non-parallel

magnetizations in the two F layers.

1.3.6 Wall Displacement Calculation using a Simple Model of a

'h'apped Head-to-Head Domain Wall

To calculate the wall displacement, Ax, in a notch as H is varied, we have applied
a very crude adaptation of Me Michael et al. model60 to the F(t1)/N/F(t2) trilayer system
previously presented in Sect. 1.1, where t, < t2. The thicker F layer is saturated along +x,
and a head-to-head wall, in the thinner F layer, is trapped in a V-shaped constriction,
whose geometry is illustrated in Fig. 1.16. Based on the Me Michael et al. calculations
shown in Fig 1.12 (a) and 1.14 (a), we approximate the wall as a region of uniform
transverse magnetization and width, D, along x . Outside the wall, we assume that the

uniform magnetization J is parallel or antiparallel to x, as shown in Fig.1 . 1 7.

40

We consider that after the system

(a)

 

AL

is saturated along +x, H is reduced until

the wall is trapped Initially, the wall of

H<—>
—>x DOWN width Do and in-plane area Aw°, is placed
:22:

 

 

 

 

 

 

 

 

 

P AP
RH Aw trappedin , _
Stopwntact constriction at the center of the constriction, x = 0,
, » / N
(b) =9 ﬂ... F N within the CPP-current region of area A.
r ——N
. -> F The in—plane areas for the parallel state,
' —N
S AP, and the antiparallel state, AM, are

equal for Ax = 0. As H is decreased, the

Fig. 1.16. As a wall moves past the top wall moves toward the left (along —x),

measuring contact, the resistance changes in . _

Antiparallel-state resistance > parallel-state
resistance. At some value of H the DW leaves the
notch. The wall displacement Ax was computed for two cases: i) as the wall moves, the

DW width is constant, D = Do, and the DW area, Aw, changes; and ii) as the wall moves,

D varies and the DW area is constant, Aw = Aw°.

 

 

<— Wall --r

width _
<‘----
width
IA “1 A
I V

i I i Q
0 00 500 0 500

X ("I“) Ax x (nm)
Fig. 1.17. Conﬁguration of our model to calculate the wall displacement, Ax, of a head-to-head
wall within a V shaped constriction. Arrows mean magnetization direction. AM». Ap, and Aw are
the areas of the antiparallel region, the parallel region and the wall, respectively, where the CPP
current ﬂows.

1 1'

53
C:
CD
I
a...

>
2. T 1
l
Half Notch Width (nm)
e
I
>1
1 I IO...
“\
>
P;
l

1

Wall —+_

 

§
1
17>

 

Half Notch Width (nm)

 

 

 

 

H
l

 

 

 

 

 

9500

.ll

41

First let us deﬁne the following unitless parameter:

r421 (1,29)
Pp

where pAp and pp are the trilayer effective total resistivities of the antiparallel state and
parallel state, respectively. Theoretically, see Table 1.2, and experimentally, see Chap. 3,

we know that F is typically << 1.

It has also been found that the CPP resistance of a F(t1)/N/F(t2) trilayer system

follows R(0t) s (RAP-RP) (l-cosz(or/2)) + Rp, where or is the angle between the

magnetizations of the F layers.63 Thus for or = 90° where .7”, _L L, , we ﬁnd:

M=ér (130)

pp
Since the current ﬂows perpendicular to the plane of the sample, the contribution
to the total CPP resistance, chp, from each part of the notch, as shown in Fig 1.17, is the

sum of resistances in parallel, as follows:

 

 

t A A A
* =t,(—I-—+—L+ 1) A _1'2_+_A_r;+_1

= = (1.31)
RCPP RAP RP RW pep? pp pAP [’17

where t. is the total trilayer thickness, RAP and Rp are the resistance contributions of the
parallel and antiparallel states within the notch, RW is the wall resistance contribution, and
pcpp is the total effective CPP resistivity of the trilayer system.

Using Eqs. 1.29 and 1.30 into 1.31, we obtain:

A
A =—.I_[AP + AP + AW

] (1.32)
pm p, (1+0 ”,1”
2

 

 

42

Using the fact that F << 1 (to neglect second order terms in F) and the condition
that A 1' AAp+ Ap+ Aw, Eq. 1.32 can be transform into Eq. 1.33.

A,
A+—L
” 2

pCPP Epp[1+r(l—_7—)] (1'33)

From Eq. 1.33 we can deﬁne Rnorm, which is a normalized resistance :

A
AP+—’-V—

Rnom(AX)=———p“”” -p” =I-———2 (1.34)
pAP "pp A

Rnorm is associated with the wall position in the notch, because each term of Eq.
1.34 is a function of Ax, except for A (and Aw when assumed to be constant). When the
wall is centered in the notch, Ax = 0, and Rnom(Ax = O) = R°norm is a minimum. When the
wall is about to leave the constriction, Ax = Axmax, and Rnorm (AXmax) = Rm"norm is a

maximum. Given the difference between the normalized resistances of these two states:
A; — A,’,',"“

2

and subject to the constraint that SRnom, is ﬁxed, we can determine Axum. We obtain the

arm :11“: —R” :5”; —A,’:""" + ] (1.35)

roots of Eq. 1.35 for different values of the initial Do (using either of the mentioned
constraints: D = Do and variable Aw, or constant Aw = A°w and variable D).

As an example, let us assume that BRnorm ~ 0.1, which is a representative
experimental value, as we will discuss in Chap. 3. A Mathcad program was used to ﬁnd
the roots of Eq 1.35, and the results are presented in Fig. 1.18. The Axmax vs. Do curves,
for the two types of constraints, have similar behaviors. This means that for an initial Do

~ 50 nm - 100 nm, “both curves” show that the wall must move ~ 150 nm inside the

43

notch to keep SRmm1 ~ 0.1, and for an initial Do ~ 600 nm the wall must shift ~ 70 nm,

see Sect. 1.3.4.
A better analysis would be to solve the micromagnetics problem for the V-shaped

notch in a ﬁnite H using OOMMF and then use the CPP transport analysis to predict

5Rnom. Such as analysis has not yet been done.

 

200 1 1 I 1 1
Fixed D = 00, and variable A...

---------- Fixed Aw= NW, and variable 0

 

-

lSOr

 

 

 

 

E 100-
50 — ‘
0 I l l I l
0 100 200 300 400 500 600

Do (nm)

Fig. 1.18 Maximum wall displacement within the constriction as a function of the initial wall
width D. Curves for a ﬁxed D and for a ﬁxed wall area Aw do not exhibit large differences.

44

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47

 

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63 Personal communication.

48

CHAPTER 2

Experimental Methods

2.1 Introduction

Studying the behavior of a domain wall in a localized region of a ferromagnetic
layer requires high resolution measurements, which can only be provided by sensitive
techniques. Given its enhanced response to small motions of the wall, our current
perpendicular to plane, CPP, giant magnetoresistance, GMR, technique is an effective
method for detecting the presence and motion of a trapped wall. However, high quality
samples are needed, requiring very precise fabrication processes. In this chapter the work
done to optimize this new method, along with a summary of procedures to make and

measure good quality nano-fabricated spin-valve, SV, samples, are presented.

2.2 Sample Preparation

The overall sample fabrication can be summarized as follows: ﬁrst, Au leads were
deposited onto a Si substrate and Shaped using lithography. The dimensions of the Au

leads were gradually increased in the transition from the microscopic contacts of the

49

nanowires, to the macroscopic contact pads, that are used for external connections. After
that, a Nb/Cu/Py/Cu/Py/Cu/Au multilayer was sputter deposited onto the substrate and
patterned via lift off into ~30 um x ~60 1.1m rectangles that make contact with some of the
Au leads. (Py = “Permalloy” = N134F616.) Next e-beam lithography, evaporation of a 300-
nm-thick Al layer, and lift-off were used to deﬁne Al masks for subsequent ion milling to
form the ‘wire’ and its notch. After ion milling through the thick Py layer, a planar layer
of SiO was evaporated to insulate the top and bottom contacts. To remove possible
backscattered particle wall formation on both side of the Al masks, ion milling at small
angle was also done before the Al was removed by a chemical etch. Finally, e-beam
lithography, sputter deposition and lift-off were used to produce 3 Nb or Au top contact.
The procedure was mainly accomplished in a class 1000-100 clean room, and its result is
summarized in Fig. 2.1.

Constriction: notch , where domain .. .

wall trapping is observed Current ﬂow, I+

     

   

   

Current flow, 1‘ N

810 layer to insulate Nb bottom “N a-.- V '
contact and Nb top contact Uniform current density

Bottom Nb contact

  

Fig. 2. 1. Perspective view of a sample, illustrating the actual geometry. The superconducting top
and bottom Nb contacts, at 4.2 K, ensure a uniform CPP current density through the sample. For
some samples Au top contacts were used instead. Note that the vertical is exaggerated.

50

2.2.1 Design of a Mask for Photolithographic Patterning of Au

Electrical Leads

Sample preparation began by cleaning the Si (100) wafers. The wafers were ﬁrst
submerged in Alconox", and placed in an ultrasonic cleaner for 15 minutes. After rinsing
in deionized water, the substrates were immersed in acetone, and placed again in an
ultrasonic cleaner for 15 minutes. A ﬁnal bath of isopropanol alcohol, IPA, was used to
accelerate and improve the drying process. The wafers were visually inspected using a
Olympus BX60 optical microscope between 20 X and 100x. If non removable defects,
such scratches, were present, the wafer was discarded. Wafers, which passed inspection,

were placed in IPA and the preparation procedure was continued.

  

(a) Shadow Mask (b)

  

Si Wafer

Fig. 2. 2. a) Picture of the shadow mask used to make the Au leads prior to the deposition of the
multilayer onto the Si substrates. This shadow mask provided 24 (1.27 cm x 1.27 cm) individual
substrates from each Si wafer. b) Sketch of a Si wafer, which is positioned under the shadow
mask during exposure to ultraviolet light.

51

The photolithographic process was performed using a Shadow mask to pattern a
photoresist layer before deposition of the Au electrical leads onto the Si wafers. A picture
of the design of the shadow mask is shown in Fig 2.2 (a). This mask allows one to obtain
up to 24 (1.27 cm x 1.27 cm) substrates from each wafer. The majority of the mask is
transparent to ultraviolet light, and the dark chrome regions form features on the substrate
by projecting a shadow. In general, a positive radiation-sensitive resist, i.e. photoresists
or e-beam resists, has strong chemical bonds (also called cross linked bonds), and when
exposed to ultraviolet light or an electron beam, these bonds break down, making the
exposed area soluble in developers (acid based chemicals). The portion of resists
underneath the mask is still cross-linked and insoluble in developers.

To produce Au leads with smooth edges, 3 large enough undercut in the resist was
required to separate the evaporated (or sputtered) material lying on the top of the
photoresist from the portion of the material deposited directly on Si.

The optimum process, which had a success rate of ~ 100 %, is as follows:

1. The sample is positioned and held via vacuum on a Spinner. A large drop of positive
Shippley 1805 photoresist is placed using a pipette on the surface of the substrate and
spun for 45 seconds at a rate of 4500 rpm. Thickness ~ 0.5 um.

2. The sample is baked for 45 min at 95°C to harden the photoresist.

3. By using a previously designed photo mask fabricated by Photronics, the sample is
exposed to ultraviolet radiation of wavelength between 365 nm to 400 nm in selected
areas. Exposure of the sample was accomplished utilizing mask aligner from A MB,

Inc.

52

4. The sample is submerged in Chlorobenzene for 30 second to harden the surface of
the non-exposed areas to achieve the desired undercut.

5. The remaining Chlorobenzene is removed from the sample surface by rinsing the
samples in deionized running water for 20 seconds.

6. Each sample is immersed in a bath of Shippley 452 developer to remove the exposed

photoresist and then rinsed in deionized water for 20 seconds.

(i) Photoresist
/

 

 

 

 

(ii) Substrate
Au
(iii) 4
Au Leads

(iv) / \
H

Fig. 2.3. Cartoon of the Au leads deposition procedure. This technique can be used for any
process involving evaporation or sputtering. i) Photoresist over a Si substrate. ii) Developed
patterned photoresist after exposure to light. iii) Evaporated Au on a Si substrate and on the
photoresist. iv) Au leads on a Si substrate after lifting-off.

Once the photoresist mask was created, 150 nm thick Au leads were evaporated
onto the Si wafers after a previous deposition of 3 nm of Ti to improve the binding of the
Au to the substrate. Au has strong bond to Ti, and Ti adheres well on the surface of the Si

wafer due to the chemical bond to the naturally-occuring SiOz. The Ti evaporation rate

was ~ 0.04 nm/sec for a current of 3.6 A. The evaporation of Ti and Au took place in an

Edwards-Auto 306 evaporator at approximately 3 x 10'7 Torr. Au evaporation rate was
0.3 nm/sec for a current of 2.6 A. To lift-off, each wafer was submerged in acetone at 80
°C for 20 minutes and rinsed with IPA. Fig. 2.3 illustrates the different phases of the Au
deposition method. The ﬁnal geometry of the Au electrical leads is shown Fig 2.4. Note
that the central area, surrounded by the ends of the Au leads, is empty for subsequent
deposition of the multilayer, and that the Au contact pads are shorted via a Au bridge, to
prevent the nano samples from burning out due to static discharge during handling.

On the Au leads another layer of positive Shippley 1805 photoresist was spun for
45 seconds at a rate of 4500 rpm, to protect the surface of the wafers, and to keep them

clean during cutting. Si wafers were cut using a Micro Automation Dicing Saw model

1006, into 24 individual square substrates of 1.27 cm by 1.27 cm, see Fig. 2.4 (a).

 

Fig. 2. 4. a) Top view of the patterned Au leads on a single Si substrate of 1.27 cm by 1.27 cm.
Note that the Au contact pads are shorted to prohibit burning out of the samples due to static
charges. b) Magniﬁcation of the central region of the Si substrates; there is an empty area of size
40 pm by 60 um, surrounded by the Au leads.

With the Au electrical leads in place, the substrates were ready for deposition of

the multilayer.

54

2.2.2 Multilayer Thin Film Preparation via Sputtering

The basic sputtering process involves a large vacuum chamber and a low pressure
inert gas atmosphere. Upon applying a high current to a ﬁlament (cathode), the heated
ﬁlament emits electrons that accelerate toward an anode. These accelerating electrons
ionize the Ar gas molecules in their paths creating positive ions. The target is located
between the anode and cathode, and the whole assembly is coupled to a pair of parallel
magnets, that produce a magnetic ﬁeld that is parallel to the target surface and
perpendicular to the cathode-to-anode direction, which localizes the electrons to the
region above the target. Applying a negative voltage to the target causes the ions to
accelerate toward the target (ion bombardment). During bombardment, the ions transfer
their momentum to the atoms of the target and thereby physically eject these atoms from
the target surface, which flow toward the substrate where they adhere, creating a thin
layer of metal. Sputtering is a versatile process for making multilayer ﬁlms. In this part of
this chapter, only the essential details of the sputtering technique for this work are
described. Further information can be obtained elsewhere”.

A multilayer consisting of Nb(100)/Cu(10)/Py(20)/Cu(lO)/Py(5)/Cu(5)/Au(15),
units in run, was sputtered onto the central part of the substrates, as illustrated in Fig. 2.5.
The ﬁrst layer of Cu between the bottom Nb layer and the thicker Py layer acts as a
buffer layer between the fcc Py and the bcc superconducting Nb. The intermediate layer
of Cu is used as a spacer to reduce coupling between Py layers, see Sect. 1.3.5. The last
Cu layer provides identical interfaces on both sides of the thin Py layer. The Au layer on

the top is to protect the multilayer from oxidation and provides good electrical contact.

55

9% PMMA/MM Multilayer
(*0 (b (c)
e-beam Resists /2% PMMA

 

 

 

 

Fig. 2.5. Sputtered multilayer. 8) Sketch of the exposed area with different e-beam doses

(different size rectangles), to create a bigger undercut. b) Top view of patterned e-beam resist. c)

Top view of the actual sputtered multilayer. The upper cartoons show side views of the

lithographic process.

Before sputtering the multilayer, positive resist was spun on each Si substrate, and an
e-beam resist mask was lithographically built. To obtain each of the e-beam lithographic
features, the samples went through the same technique:

1) To create the mask, a layer of 9% Copolymer in Chlorobenzene (Copolymer is
Polymethyl methacrylate (PMMA), 495k molecular weight, and 85% methacrylic
acid (MAA)) is spun at 3000 r.p.m. onto the sample and baked for 5 min at 160 °C.

2) A second layer of 2% PMMA (in Chlorobenzene) is spun at 4600 r.p.m. and again
baked at 160 °C for 30 minutes.

These two layers of resist are used to broaden the undercut in the resists mask after
developing as shown in Fig. 2.5 (b). The ﬁrst layer of 9% Copolymer is more sensitive to
secondary electrons coming from the substrate than the 2% PMMA.

3) The features are drawn by exposing the samples to an e-beam in a JOEL 840 scanning

electron microscope, SEM, at a magniﬁcation of 850x, and at a working distance of

25 mm.

56

4) The samples are developed in a 1:3 methyl isobutyl ketone (MIBK) to IPA mixture,

then rinsed in [PA for 10 seconds and dried with N2 gas.

A rectangular area of 28 1.1m by 65 um, as shown in Fig. 2.5 (a) was drawn by e-
beam lithography following the above-described technique. To enhance the undercut
generated by the bilayer of resist, the samples were subjected to an exposure only on a
bigger rectangle (29pm by 66pm) with a dose of approximately 50 uC/cm2 and a current
of 50 pA. A second exposure of 180 uC/cm2 with 50 pA (smaller rectangle) created the
actual area for deposition of the multilayer. The center-to-center distance, together with
the line spacing of the e-beam, were set to 193.5 A. The latter parameters are not relevant
at this point of the sample preparation, and they were chosen to maximize efﬁciency.
Finally the samples were developed for 40 Seconds.

Deposition of the multilayer via sputtering was done following the standard
procedures described elsewhere”. Do note that quartz-crystal ﬁlm-thickness monitors
were used to determine the layer thicknesses. Typical deposition rates were: Au ~ 4.5
A/s, Py ~ 5.5 NS, Cu ~ 9 NS, and Nb ~ 6 A/s at an Ar pressure of 3 x 10'3 Torr. To lift-
off, each Si substrate was immersed in acetone at 80 °C for 20 minutes, rinsed with IPA

and dried with N2.

57

2.2.3 E-beam Lithography to Deﬁne the Required Geometry

(i.e., Wire with Central Notch) for Domain Wall Trapping

To make the wires for domain wall trapping, a portion of the multilayer is etched
by ion milling. An Al mask with the shape of the nanowire is used to shield the portion of
the multilayer which will constitute the sample and delimit the region of the multilayer to
be etched away. To control the shape of the notch properly, the e-beam lithography used
to create the Al mask must be carefully done because the smallest transverse dimension
of the constrictions is close to the resolution of the method, which is given by a spot size

of ~ 25 nm diameter.

_“___<—— Pointed End to Prevent Wall Nucleation

(a) ~+ *— 0.4 um - 0.5 um (b)

'1"_—‘ Z: ‘ 1+— Top Contact

19 pm
|

0.5 pm — 0.15 um """""""""

 

 

 

K Domain wall Reservoir
4;. " <

A 1.1ttm

Fig. 2.6. a) Sketch of a multilayer nanowire showing its typical shape and dimensions. The
reservoir helps nucleate the domain wall. b) Top view of the center of a substrate, showing the
wires drawn in the e-beam resist.

58

The shape and dimensions of the nanowires, see Fig. 2.6 (a), were based. on the
Japanese group’s work”, where trapping of a domain wall in a notch was shown using
current in plane MR geometry. They showed that attaching a reservoir pad at the end of
the nanowire causes a drastic decrease of the switching ﬁeld associated with the injection
of a domain wall from the reservoir pad into the nanowire. They also found that the wire
with a diamond-shaped reservoir pad, in comparison to other pad geometries, shows the
lowest switching magnetic ﬁeld at any temperature.

To trap the wall, two types of notch geometries were designed: a well-deﬁned V-
shaped notch, and a more elongated U-shaped notch. Fig. 2.7 shows scanning electron
microscope, SEM, images of the Al masks used to build these two different constrictions.
Their basic difference is given by their shape and dimensions: a V-shaped notch is
typically ~ 500 nm long by ~ 50 nm to 100 nm wide in the narrowest region, and a U-
shaped notch is ~ 800 nm long by ~ 50 tol 50 nm wide in the narrowest region.

The e-beam lithographic procedure utilized to make the Al masks followed the
technique described in Sect. 2.2.2, see also Fig. 2.8 (a) i-v. The samples were exposed to
a single dose for a current of ~12 pA. The center to center distance together with the line
spacing of the e-beam were set to 48.5 A. In this manner, this combination of parameters
produced the optimum pattern. One of the main concerns during this process was the
control of the developing time, which can vary signiﬁcantly depending on various factors
such as the SEM calibration (the most crucial one). Small variations of the working
conditions, i.e., a new SEM ﬁlament or temperature oscillations, can alter the ﬁnal result
considerably (even when the rest of the SEM parameters are not changed). To reduce

these undesired effects, we increased the exposure dose to 500 uC/cm2 so that only a 3-

59

sec developing time was necessary to obtain quality samples. After developing was done
in an ultrasonic bath, a 300 nm layer of Al was evaporated in the Edwards-Auto306
evaporator at a deposition rate of 0.5 nm/sec, 2.2 A current. When the deposition was
ﬁnished, the samples were placed in acetone at 80 °C to lift-off the Al not in contact with
the multilayer. The remaining Al wires were used as a shield, selecting the areas where
ion milling should not occur. Al has a lower ion-milling rate than the rest of the materials

of the multilayer, and, in principle, it can be easily removed with a photo developer.

n

"KMT’X’TWWW v .‘rvmar‘yfemK-n- ‘44."; _..;ggivg-
,.... .-.__.‘.~u, ._

-» ,q ,v. .
..._.....‘r,..-__‘ . 7

N; «misc-(i, 4.4.. we. wag

?‘

. 1:3..-
u-_
. (‘3’: ‘
3 .4
.8.
£0
.1 X
E
' E
. "‘E
. N?‘
y, '>’
. é.

 

Fig. 2.7. SEM pictures showing 300 nm thick nanowire Al masks on the multilayer. The two
typical geometries of the notch are displayed: a) V-shaped notch, and c) U-shaped notch. b) and
d) are magniﬁed views of the constriction regions.

60

(i) Multilayer (3)

(ii) e-beam Resists - 9% PMMA/MMA and 2% PMMA

(iii) Development

(iv) Al Mask Deposition A;

(v) Al Lift-off [A]
(vi) Patterned e-beam Resists for ion Milling /a--”
M ”I Al

 

Fig. 2.8. a) Sample preparation sequence prior to Ar+ ion etching. b) Top view of Al masks on
multilayer that select the area to be exposed to ion-beam etching, and of the e-beam resist layer,
that protects Au leads outside of the central open rectangular area.

To protect the Au leads and select the area where the insulating layer is deposited,
two new layers of e-beam resists were spun to create an open rectangle in the center of
the substrate as shown in Fig. 2.8 (a) vi and (b). To enhance the undercut and facilitate
SiO lift-off, a dose of 50 uC/cmz, 50 pA current, was applied on a bigger rectangle, 37
pm by 52 um. A second e-beam exposure of 180 uC/cmz, 50 pA current, forms the actual
rectangle of 35 um by 50 um. The center-to-center distance, together with the line
spacing of the e-beam, were set to 193.5 A.

With the Al masks and the e-beam resist in place, the substrates are ready to

proceed with the Ar+ etching and the deposition of SiO planar insulation.

61

2.2.4 Ion Milling and Planar Insulation of the Patterned Wire

In ion beam etching, an ion beam is directed against a surface, with the objective
of removing material from the surface. The etching is the consequence of physical
sputtering, which is the result of the momentum exchange between beam ions (normally
formed from an inert gas) and the target atoms or molecules. Additional information

about ion milling techniques, including particular descriptions of the equipment

3, 9-10

employed in this work can be obtained elsewhere

(I)

Magnetic Arm

 

Sample in holder (c)

810

     
 

 

Fig. 2.9. a) Sketch of the magnetic arm used to load the samples into the ion in g chamber and
to hold and rotate them during SiO deposition. b) Holders for top ion milling. The sample is
localized under a metallic mask with a hole in its center to select the area to be ion milled. c)
Cylindrical holders for side ion milling.

Samples to be ion milled were placed in holders consisting of a metallic mask, a
copper heat sink, and a magnetic disk, see Fig. 2.9 (b). With the help of a magnetic arm,
the holders with the attached samples could be situated in a vacuum chamber either above

an evaporation boat for SiO or a 3-cm ion Ar+ source made by Commonwealth Scientiﬁc

62

Corporation'g. AS shown in Fig. 2.9 (a), the holder is inserted into the chamber directly
above the SiO boat. For ion milling, the holder is detached in-situ from the magnetic arm
and located on a wheel that can rotate so that the holder is placed above the ion gun.

The system was continuously pumped down to l x 10'7 Torr. Etching was done by
ion milling at an Ar pressure of l x 10’4 Torr, ~ 7 mA current and at 300 V accelerating
voltage. Ar gas was bled into the chamber at 3 to 6 sccm. A shutter shielded the samples
while the ion gun was started. When the system was ready, the chosen sample was
rotated via a wheel over the ion mill, and the shutter was opened. Ion milling rates were
obtained from Refs. 3 and 9 and related to the Au ion milling rate provided by the same

references, as shown in Table 2.1.

 

Nb Cu Py
0.26 0.65 0.38

 

 

 

 

 

 

Table 2.1. Ratio ion milling rate / Au ion milling rate for Nb, Cu, and Py. Ion mill rates (including
Au) were obtained from Refs. 3 and 9.

Each sample was ion milled for a long enough time so that the bottom Nb should
be uncovered. With the help of the parameters in Table 2.1 and the in-situ measured Au
ion milling rate, ~ 0.85 nm/s, the thicknesses of Nb, Py, and Cu layers, Sec. 2.2.2, were
converted into effective Au thicknesses and summed up to obtain the total effective
thickness of Au (~ 130 nm) used to calculate the etching time ~ 153 s. Approximately
141 s of ion milling was usually sufﬁcient to remove all the Cu and Py; this additional ~
12 s of etching was done to ensure Nb exposure, during which only ~26 nm of Nb was
removed. To control the ion milling rates for these ﬁlms, the vacuum chamber contained

a quartz—crystal ﬁlm-thickness monitor, FTM, which was utilized to measure the Au ion

63

milling rate in-situ. Au was sputtered at ~ 0.6 nm/s onto the FTM quartz wafer and etched
away each time ion milling was performed. Proﬁles of the samples, acquired with an
Atomic Force Microscope, AFM, NanoScope Digital Instruments D 3100 SPM were used
to check thicknesses; and a SEM, Hitachi S-4 700 II FESEM, allowed each step of the

sample fabrication to be inspected.

(a)

   

 
 

Si substrate

 

 

Fig. 2.10. a) Typical proﬁle of a multilayer nanowire aﬁer the Al mask was removed. 810 was
evaporated leaving a ~13 11m high protrusion of Au. b) Top view of the patterned and planar
insulation of SiO.

Right after the samples were ion milled, and without taking the samples out of the
vacuum chamber (to prevent oxidation), a layer of SiO was evaporated to planarize and
insulate part of the micro-fabricated features from the top Nb or Au strip. Ar supply was
interrupted, and deposition took place at pressures of the order of 2 x 10'7 Torr. A
Tantalum boat containing SiO was heated up at a rate of ~13 A per 5 seconds, using a
secondary current from a Variac. When the secondary current trough the boat was ~ 222
A, the boat was hot enough to evaporate SiO. The deposition rate was between 0.2 to 0.6
nm/s. Details of the SiO setup can be found in Ref. 3. However, note that the FTM could
be used to check the SiO deposition rate. A 55 nm thick layer of SiO was evaporated

leaving a ~13 nm high protrusion of Au, after the Al mask removal, see Fig 2.10 (a). The

64

 

ix»

samples were held by the magnetic arm and the evaporation was performed while
rotating the sample half of the total time clockwise and half anticlockwise at 0.5 r.p.s.,
see Fig 2.9 (a). In this way a uniform SiO deposition is attained, reducing the chance of
pinhole formation.

The ﬁnal pattern shown in Fig. 2.10 is only obtained when Al masks are removed.
During ion milling, part of the backscattered material coming from the sample is
implanted in the Al, building a “particle wall” on its sides. Unfortunately SiO deposited
on top of the Al seals the masks completely. Thus simply dissolving A] using photoresist
developers becomes almost impossible, unless the wall is, at least partially, eliminated

tit’ﬁlll

ii
( ) Backseattered Particle Walls

/

    

(iV)

 

 

/h

 

 

 

 

(V) . , (vi) Nanowire

 
  
 

Edge Damage
/

SiO Insulation 1.

    

Fig. 2. 11. Cartoon showing the sequence followed to ion mill the substrates and deposit a planar
SiO insulation. i) Etching from the top. ii) Particle wall build up on the sides of the Al mask. iii)
SiO deposition. iv) and v) Ion milling from the sides to remove build up. vi) 810 liﬁ off via Al
removal.

65

To start “particle wall” removal, the samples were ﬁrst submerged in Acetone for
20 minutes at 80 °C to remove the resist and clean away the unnecessary SiO deposited
on the resist. Next, they were inserted into two grooves constructed in metallic cylindrical
holders, see Fig. 2.9 (c), that positioned the substrates in a almost vertical orientation.
The ion beam was perpendicular to the longitudinal axes of the wires and at 3° with
respect to the plane of the sample substrate. One of the sides of the nanowires was then
ion milled for ~ 2.5 min, affecting the “particle wall” only. Ion milling was performed
under the conditions described in Sect. 2.2.4. Next, the substrates were rotated 180 ° and
placed in holders to ion mill the other size of the nanowire for the same time. Later, the
samples were placed in a bath of photoresist developer for 10 minutes. Removal or at
least cracking of the “particle wall” allows the photo developer to penetrate into the A1
and dissolve it. A cartoon shown in Fig. 2.11 summarizes the main stages of this

procedure. Fig. 2.12 shows SEM images of the ﬁnal result, where the sample is ready for

deposition of the ﬁnal top contact strip.

    

Fig. 2. 12. a) SEM image of a nanowire aﬁer SiO deposition and Al removal was ﬁnalized. b)
Magniﬁcation of a U-shaped notch. c) Magniﬁcation of a V-shaped notch.

66

2.2.5 E-beam Lithography and Sputtering to Obtain the Final

Top Contact Strip

Following the usual e—beam lithographic step, as described in Sect. 2.2.2, a ﬁnal
0.9 um width Nb or Au strip was fabricated to make contact between the multilayer
nanowire and the Au electrical leads. Initially two resist layers were deposited, followed
by e-beam microscopy. The shapes of the strip were designed to avoid contact with
possibly damaged SiO on the bottom Nb layer edges, i.e., with pinholes produced during
ion milling from the sides, see Figs 2.11 (v) and 2.13 (a). Two basic strip shapes were
fabricated: S and U types. The latter allows tracking of wall motion in two different
regions along the wire. As we see in Fig. 2.13, along with the ﬁnal 150 nm thick Nb strip,
two extra 150 nm thick Nb rectangles were built on the ends of the of external Au leads
to optimize contacts with the central bottom Nb rectangle. Standard sputtering techniques
were utilized to deposit Nb, the sputtering rate was ~ 3 [Us at an Ar pressure of ~ 6 x 10'3
Torr (base pressure ~ 5 x 10'8 Torr). Deposition took place in the ion milling chamber
after the samples were ion milled for 10 seconds to eliminate a possible poorly-
conducting ﬁlm, the purple plague, formed between the Al mask and the Au surface
underneath. Ion milling followed the conditions described in Sect. 2.2.4. For Nb lift-off,

the samples were submerged in an acetone bath at 80 °C for 20 minutes.

67

\ri I tlﬂt'
”immut- Vxlmprll lop

i 'Nllélln'd lop

(tilll;lt‘i\ (onlzlt‘lx

I \il'.l \l) Ri'llsnglt-s

 

Fig. 2.13. a) Top view of patterned resist mask to create the ﬁnal top strip. The strips are designed
to avoid contact with the SiO-coated edges of the bottom Nb layer that could be damaged by Ar+
milling. U type strips allow tracking of wall motion in two different regions of the wire. b) Top
view of ﬁnal top Nb S-shaped strips. Extra Nb rectangles assure good connection between the
bottom Nb layer and the Au leads.

Because Au has better conductivity than Nb at 295 K, the CPP current-density
distribution with Au should be more uniform. In some cases 200 nm thick Au was used
instead of 150 nm thick Nb to build the ﬁnal contact strip, see Fig. 2.14. Very similar
procedures to those used for top contact Nb strip fabrication were employed to make the
Au top contacts; Au deposition is described in Sect. 2.2.4.

For H = 0, our “dirty” sputtered Nb, deposited in the ion-milling chamber, had a
critical temperature, Tc, of ~ 7.2 K, below which the Nb contacts become
superconducting equipotential surfaces which produce a uniform CPP current density. Au
is normal at all temperatures, and the CPP current density will be non-uniform. However,
if we expect good data from Au top contact samples at 295 K, we can also anticipate high
quality data from the same samples at 4.2 K because the resistivity of Au will be lower
(but not superconducting). To understand this situation of non-superconducting contacts,

in the Appendix we present a simple Ohmic model given by Lenczowski et al.”; who

68

amass :rerp‘ttrtsdtﬁt‘m»

it

 

Fig. 2.14. SEM image of three nanowires (V ~shaped notch) on the central area of a substrate and
S-shaped Au top contacts deposited over the SiO insulating layer. Au top contacts were used for
295-K-measurements mainly.

calculated the current distribution in small pillar like structures for CPP
magnetoresistance experiments. Application of this model to our systems shows, as
expected, that at 4.2 K the Nb top contact produces totally uniform distribution of
thecurrent. At 4.2 K the CPP current density in Au-top contacts is reasonably close to
uniform, ~27 % average change between edges of the constriction, and at 295 K its
uniformity is worse, ~ 45 % average change between edges. Very similar behavior is
shown by the current density distribution of Nb top contacts at 295 K. This is an
indication that at 295 K (because of the presence of the non-superconducting bottom Nb
contact) changing the top contact does not affect the current-density distribution
signiﬁcantly. These non-uniformities of the CPP current densities for Au top contact

samples at 4.2 K and 295 K, and for Nb top contact samples at 295 K, are signiﬁcant, but

69

not large enough to categorize the data obtained with these contacts as unreliable.
However, only superconducting Nb contacts guarantee to provide the “most uniform”

current density in the notch region.

2.3 Equipment and Measurements

F our-terminal resistance measurements were made at 295 K ﬁrst, and then the
sample was placed in liquid He at 4.2 K. Two types of setups were used :

(l) Nano-Volt Measurements: a multiplex system with 12 channels, six current
channels and six voltage channels, was used to measure samples with resistances bigger
than 100 1.10. This setup uses a DC current source and a DC nanovoltrneter to measure
samples .

(2) Lock-in Amplifier (LA): this system was used to detect and measure very
small AC signals (a few nano-volts), allowing comparable signal-to-noise ratios for
currents smaller than in (1). Due to this advantages of the LA over (1), most of the data
were obtained with it. The probe system is similar to (1) with 12 channels, 6 voltage
channels and 6 current channels. This system was also used to measure samples with
resistances bigger than 100 119. LA has the particular advantage that a DC current can be
added to the AC currents, allowing current dependence measurements. The LA ﬁlters the
DC current component, and only the AC component of the current is utilized to measure

the resistance of the sample.

70

2.3.1 Nanovolt Measurements

A Keithley 2400 current source supplied current and a Keithly 2182 nanovolrneter
measured the voltage. With the help of a Keithly 7001 multiplexer, the system was
designed to allow different samples to be measured on an single substrate without
removing the sample probe from the liquid He dewar.

The probe, which can be used at room temperature and at 4.2 K, consisted of six
current and six voltage Cu leads that were connected to the external measuring
equipment. Each connection included shorting and grounding switches for each
individual lead; it was possible to ground directly or ground through a 1 M0 resistor.
These switches prevent the small features of the e-beam samples from burning out due to
static charges effects. The current leads are connected to the probe via a Fisher seven-pin
connector, while three Cu Omega-Engineering thermocouple connectors are used to
connect the voltage leads. Each thermocouple connector has two leads plus a ground
connection. This kind of all-Cu wire system minimizes voltage offsets and drifts due to
the thermoelectric effects at room temperature. More information about this set up,

including construction details of the probe, can be found in Ref. 3.

2.3.2 Lock-in Ampliﬁer

Both an AC voltage signal, at a speciﬁc reference frequency (8 KHz), and a DC

voltage signal were supplied by a SR844 Stanford Research Systems Lock—in Ampliﬁer.

71

The voltages were added and converted to a current sent to the sample, (1+ and 1') via an
adapter. The AC voltage signals coming from the sample, (V+ and V'), were subtracted
and pre-ampliﬁed by 3 Stanford Research preampliﬁer SR552 and sent back to the Lock-
in Ampliﬁer, which uses a phase sensitive detection technique to extract the component
of the signal at the reference frequency and phase. A diagram of the measuring system is

presented in Fig. 2.15.

 

 

 

 

 

 

 

 

 

 

V+ and V' V+
i Preampliﬁer anmmmnml é
>
. I“ and I' g
Voltage-Current Box H
Input signal I I V‘
1

 

 

----.’t

 

AC signal DC signal

 

I-

 

Sample

 

 

 

--o--o---

17

Probe
Lock-in Ampliﬁer
1+

Fig. 2.15. Diagram of the measuring system. The Lock-in ampliﬁer is connected to the Voltage-
Current Box via two co-axial cables and from there a triaxal cable goes to an adapter. The adapter
is used to change the current triaxal cable into a Fisher seven-pin connector, which goes to the
sample probe. The adaptor is also used to change the Cu Omega-Engineering thermocouple
connectors into a triaxal cable which brings back the voltage to the preampliﬁer. The adapter
selects the channels to be used as well. The preampliﬁer is connected via a coaxial cable to the
Lock-in ampliﬁer.

 

 

 

 

 

The sample probe can be used with either the lock-in system or the Nanovolt
system. The probe allows contact to all three nanowires on the same substrate, but only
one nanowire is measured at a time. Each substrate was placed at one end of the long
probe, as shown in Fig 2.16 (a) and (b), in such a way that the nanowires were aligned

parallel to the longitudinal axis of the probe and the external magnetic ﬁeld. To protect

72

 

Fig. 2.16. a) Photo of the room temperature magnet with the probe not yet inserted. b) The
substrate is placed at one end of the long probe, and the samples are connected via indium
contacts to the probe Cu wires. 0) The probe is inserted into the sheath that contains a
superconducting solenoid, and the whole system is dipped into a He dewar.

Mam tic
Fiel

 

Fig. 2.17. Sample connections. a) The external Cu leads are connected with indium to the sample
via the external contacts at the outer edges of the substrate. V and I external contacts are shown
for connection to the central nanowire. b) Magniﬁcation of the central part of the substrate.

73

the sample from blowing due to static charges, the shorting switches of the voltage and
current leads were closed; and then after the samples were connected according to Fig.
2.17, the external shorting Au bridges on the substrate were cut. For low temperature
measurements, the measuring probe ﬁts inside a separate sheath that contains a
superconducting solenoid of coil constant 506.6 Gauss/A, see Fig 2.16 (c). This coil has a
persistence switch3 across it that produces a constant ﬂow of current through the coil,
thereby reducing the noise in the magnetic ﬁeld produced by the magnet current supply.
In the case of the LA system, this switch was kept open because each point was taken in
less than 4 seconds, comparable to the time necessary to open and close the persistence
switch. For room temperature measurements, the probe was separated from the sheath
and inserted into a standard electromagnet of coil constant 821 Gauss/A as shown in Fig.
2.16 (a) and (b). Two power supplies can control either magnet, one of 8 A range and
another of 2 A range. The external magnetic ﬁeld resolution was increased by changing
the original 12-bit GIPB card to control the magnet power supplies to a analog 16-bit
A/D card, National Instruments: PC1-6731. The external magnetic ﬁeld was applied
along the longitudinal axis of the probe and mainly swept between —500 Oe and 500 Oe.
Between data points the H sweep rate was ~200 Oe/s, and the time for each measurement
was usually 1 to 3 s. A Lab-View program automated the measurements and calculated

R. Studies of standard resistors indicate that the long-term drift of electronics were S 0.02

m!) at 4.2 K and S 0.2 m9 at 295 K.

74

REFERENCES

 

1 J .M. Slaughter, W. P. Pratt Jr., and P.A. Schroeder, Review of Scientiﬁc Instruments 60,
127 (1989).

2 Shang-Fan Lee, Ph.D. Dissertation, Michigan State University (1994).

3 Perpendicular Giant Magnetoresitance in thin Films with Microfabricated
Superconducting Top Contacts, R. D. Slater Dissertation (2001).

4 Qing Yang, Ph.D. Dissertation, Michigan State University (1995).
5 T. Ono, H. Miyajima, K.Shigeto and r. Shinjo, App]. Phy. Lett.. 72, 1116 (1998).

6 Y. Yokoyama, Y. Suzuki, S. Yuasa, K. Ando, K. Shigeto, T. Shinjo, P. Gogol, J. Miltat,
A. Thiaville, T. Ono, and T. Kawagoe, J. Appl. Phys. 87, 5618 (2000).

7 K. Shigeto, T. Okuno, T.Shinjo, Y.Suzuki, and T. Ono, J. Appl. Phys. 88, 6636 (2000).
8 K. Shigeto, r. Shinjo, and r. Ono, J. App]. Phys. 75, 2815 (1999).
9 Commonwealth Scientific Corporation One-CM Ion source manual.

10 Characteristics , Capabilities and Applications of Broad-Beam Sources, H R Kaufman,
R. S. Robinson and W. E. Hughes, Commonwealth Scientiﬁc Corporation (1987).

“ S.K.J. Lenczowski, R. J. M. van de Veerdonk, M.A.M., J. B. Giesbers , and H.H. 1. M.
Janssen, J. App]. Phys. 75, 5154 (1994).

75

CHAPTER 3

Results and Discussion

3.1 Introduction

As indicated earlier in this thesis, several current-in-plane magnetoresistance, CIP
MR, experiments have been performed to measure the localization and motion of
geometrically conﬁned domain walls in nanostructures. Since the pioneering work by T.
Ono et al. "2, showing trapping of a domain wall in a notch placed in a long wire without a
reservoir, subsequent work has shifted to using high CIP current densities to manipulate
the wall motion in such narrow structures”. A signiﬁcant contribution to this ﬁeld was
made by Klaui et al.3, who used a narrow single layer ferromagnetic ring with notches
where head-to-head walls could be manipulated by the orientation Of an in-plane magnetic
ﬁeld and by high current densities circulating around the ring.

In this chapter, we present the results of our various works done to study domain
wall trapping and motion using CPP MR as an alternative to CIP MR utilized until now.
As our data will Show, the utilization of a localized CPP current enhances the sensitivity
for detecting the presence and motion of a trapped domain wall, and allows us to choose

the measuring region almost independently of the sample geometry. The results presented

76

in this chapter principally consist of CPP resistance, R, vs. sweeping magnetic ﬁeld, H,
curves; but also studies of domain wall stability, time dependence of wall motion inside a

constriction and effects of high-density CPP currents are included.

3.2 CPP Resistance Data

The development Of this work can be divided into three periods. In the ﬁrst one,
no electron-microscope characterization, “NC”, of the notch geometry was done because
the CPP resistance measurements needed to be perfected ﬁrst, and only “proof of wall
trapping” from the CPP MR was required. In the second period, the design of the U-
shaped constrictions was well characterized with a Hitachi S-4 700 II F ESEM. In the third
period the constrictions were changed into V-shapes, which were also properly
characterized by means of the SEM.

Table 3.1 presents the CPP resistance data of all the samples which successfully
showed trapping of a domain wall. RAP, and Rp are resistances of the antiparallel, P, and
parallel, AP, states respectively, and GMR = RAP — Rp / Rp. Sample identiﬁcation
numbers provide information about the sputtering run number, substrate number and
nanowire employed. A single asterisk, *, indicates that the sample was measured using a
Au top contact ﬁrst, and then it was remeasured with a Nb top contact deposited on top of
the original Au contact. A double asterisk, **, indicates that the width of the top contacts
was increased by a factor of 1.5. Table 3.2 shows the average values of the data presented

in Table 3.1. These averages were calculated for eight groups of samples deﬁned by their

77

notch shapes, top contact types and measuring temperatures. Uncertainties were

[/2

estimated by a/(n) , where o is the data standard deviation and n the number of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

measurements.

Top Temperature AR=-RAer RA,» GMR
Sample Notch Type contact (K) (m0) (m0) PA)

1 470-1 B-a U Au 4.2 3.0 24.8 1 3.79
1470-1B-b * U Nb 4.2 5.0 62.5 8.70
1 470-2A-b U Nb 4.2 5.0 152.0 3.40
1470-58-a U Nb 4.2 1.9 47.3 4.1 9
1470-SB-b U Nb 4.2 4.0 1 88.0 2.1 7
1470-58-c U Nb 4.2 3.5 120.0 3.00
1 492-1 A-b U Nb 4.2 4.5 1 40.0 3.32
1492-1 A-a U Nb 4.2 3.4 62.5 5.75
1 470-68-a V Nb 4.2 3.6 143.6 2.53
1 563-7B-a V Nb 4.2 5.0 90.5“ 5.85
1459-7B-a NC Au 295 3.2 760.0 0.42
1470-1 A-a NC Au 295 1 6.0 1 242.0 1 .31
1470-1A-b NC Au 295 1 7.0 1 330.0 1 .29
1 470-1A-c NC Au 295 29.0 1440.0 2.06
1470-1 B-a U Au 295 1.5 653.0 0.23
1470-1 B-b U Au 295 2.3 760.6 0.30
1470-1B-b* U Nb 295 2.5 81 8.0 0.30
1470-2A-a U Nb 295 3.0 820.0 0.37
1470-2A-b U Nb 295 4.0 480.0 0.84
1470-3B-c U Nb 295 3.2 989.5 0.32
1 470-5A-c U Nb 295 0.8 290.0 0.28
1 563-7A-b V Nb 295 1 .3 655.0" 0.20
1 563-7B-b V Nb 295 2.0 946.0“ 0.21
1 563-7B-a V Nb 295 2.5 907.0” 0.27
1 563-88-a V Au 295 1.8 623.0“ 0.29
1 563-8A-b V Au 295 1 .2 391 .0“ 0.30

 

 

Table 3.1. Experimental data of samples showing trapping. RAP and R,» are resistances of the
antiparallel and parallel states, respectively. GMR = RAP — Rp / Rp. * means samples remeasured
with extra Nb strip over the original Au top contact strip. ** indicates that the width Of the top
contacts was increased by a factor of 1.5.

78

 

 

 

 

 

 

 

 

6 [I
it I Nb-U 295K
1’ o Au-U 295K
at in A Nb-V 4.2K
d‘ * Au-U 4.2K
/ o Nb-U 4.2K
4- -‘ :1 I
I
E." ' "A I
E * ]" '..
a: / peg;-
< ,i’ ,e'“
2- a;
I
, ,.
I
at ll 4" 9
’ "‘i
0 le" r l I l I I I [— U
0 200 400 600 800 1000
RAP(mQ)

Fig. 3.1. AR= (RAP-Rp) vs. RAp. Two least-squares ﬁts were performed: at 295 K (all the points
were considered); and at 4.2 K (Au-U and Nb-V were excluded). Lines were forced to go through
the origin.

Fig. 3.1 shows AR= (RAP-RP) vs. RAP at 295 K and 4.2 K. T wo least-squares ﬁts
were performed: at 295 K, in which all the points were considered, and at 4.2 K, in which
Au-U and Nb-V were excluded. These linear ﬁts were forced to go through the origin. In
the ideal case of a perfect sample with one value of CPP area, these data should coalesce
into one point for each temperature. This clearly not the casein Fig. 3.1. If the variations
in CPP area were the only source of RAP and AR ﬂuctuations, the data should follow the
two best-ﬁt lines in Fig. 3.1, where (0,0) correspond to an inﬁnite CPP area. At 295 K,
with the exception of the point at RAP = 480 m9 (1470-2A-b), these data do seem, to
follow this trend, but with large ﬂuctuations. At 4.2 K, the ﬁt appears to be worse. We
speculate that the contact region between the top and Au layer of the sample and the Nb

top contact may be “dirty”, introducing both a variable effective contact area and a

79

contact resistance that will cause RAP and AR to ﬂuctuate. Thus it may be important to

explore ways of making more reliable contacts between the upper surface of the sample

and the top contact.

 

4.2 °K 4.2 °K 4.2 °K 295 °K 295 °K 295 °K

 

RAM (m {2) ARAV ("7Q GMR Av(%) RAP-AV (”l-0) ARAV (m0 GMR A! 1%L
Nb—U 110 i 20 3.9 :t 0.4 4.3 :1: 0.8 680 :1: 128 2.7 :1: 0.5 0.42 :1: 0.11

 

 

 

 

 

 

 

 

 

 

 

 

 

Au-U ~ 25 ~ 3 ~ 13.8 507 i 116 1.5 i 0.3 0.3 0 i 0.01
Nb-V ~ 143*" ~ 3.6 4.2 i 2.7 717 :1: 92 1.8 :l: 0.3 0.25 :1: 0.02
Au-V 707 i 54 1.9 i 0.4 0.27 :i: 0.03
Au-NC 1193 i 113 16.3 i 4.0 1.27 :1: 0.25

 

Table 3.2. Average values of the experimental data presented in Table 3.1. The uncertainties
were estimated by o/(n)’ 2, where o is the data standard deviation and n the number of
measurements. *** sample 1563-7B-a was not considered in the average.

In spite of the data ﬂuctuation seem in Fig. 3.1, it is still worthwhile to compare
the calculated values of RAP , AR, and GMR using the 2CSR model, Sect. 1.2.3, with the
4.2-K experimental values of the same quantities. Surprisingly, the average experimental
value of Rep ~ 110 m!) for Nb-U samples, shown in Table 3.2, is reasonable close to the
calculated value, shown in Table 1.2, RAp-ca|c a 77 m0. However, Ach s 7.2 m!) and
GMR“.c E 10% are ~ 80% higher than the corresponding experimental values, see
Table 3.2. The inclusion of a contribution from the dirty Au/Nb interface in our
calculations could increase RAP“.c and reduce Ach and GMRcatc.

For Au-U samples at 4.2 K, comparing experimental, Table 3.2, and calculated
values, Table 1.2, is more suspect because there is only one experimental point.

Nevertheless, there are indications that our calculations match one aspect of the
experimental data: GMR,“c s 17% and the experimental GMR a 14% are rather close.

Unfortunately, experimental RAP ~ 25 1110 < Rem -:'-. 75 m0; and experimental AR 3- 3

80

m!) < ARC,“C E 11 m0. Thus, the experimental and calculated values of RAP and AR

differ by about a factor of three. This discrepancy is not understood at present.

3.3 CPP Resistance vs. Magnetic Field

Fig. 3.2 shows the CPP R as a function of the sweeping ﬁeld, H, for a V-shaped
notch. Near + 500 Oe, the cartoon shows that the magnetization of the thin and thick Py
layers are in the parallel state and pointing to the right (ﬁlled arrows along +x). This is
the low resistance, Rp, state. The ﬁeld is then lowered until a head to head domain wall is
injected into the thin Py layer of the wire from the reservoir at the right at —10 Oe and
becomes trapped at the notch. Such low injection ﬁelds agree with earlier work by Ono et
a].1 For the thin Py layer, magnetization, J, on the right side of the wall is reversed, as
shown (open arrow along —x). As H is lowered further, the CPP MR detects an average
motion of the trapped wall to the left. At H = —100 Oe, the wall leaves the notch, and the
two magnetizations are now in the AP, high R state, RAP. Further reduction of H causes a
head-to-head wall to be injected and trapped in the thick Py layer at H = —230 Oe.
Finally, by —400 Oe, the wall in the thick Py layer has left the notch, and the
magnetizations are now in the P state. Starting at -500 Oe and increasing the ﬁeld gives
very similar trapping behavior in R for the thin and thick Py layer, but with tail-tO-tail

walls.

81

 

144 - .
143
6:
E 142 / Magnetization
V t
CI of thinner Py layer
141
\ Magnetization
140 ’ of thicker Py layer

 

 

 

 

 

 

 

Fig. 3.2. CPP resistance R vs. magnetic ﬁeld, H, at 4.2 K for a V-shaped notch. Curved dashed
arrows indicate change in H. Sample1470-6B-a, Nb top contact.

In Fig. 3.3 we present AR(=R-Rp) vs. H for a U-shaped notch with a Au top
contact, which has a very respectable GMR of (RAP —- Rp)/Rp E 14%. In contrast to the V
notch of Fig. 3.2 where one trapping step occurs in the thin Py layer, here we see several
intermediate trapping steps that commence once the wall is injected into the wire at |H| ~
10 Oe. The direction of ﬁeld sweep affects these steps. We also see no trapping of the
wall at the notch in the thick Py layer. As opposed to the V notch case where the wall
pinning site is better deﬁned, the more elongated U notch can have wire edge roughness
and other defects which seem to act like multiple similar-strength pinning sites where
trapping of the DW can occur. This is somewhat similar to what was observed by Grollier

at et al.5, who detected domain wall pinning in defects of a Py stripe with no notch, and

82

by Giordano et al.“, who showed that magnetization reversal in very narrow Ni
nanowires (with no constriction) appears to be dominated by pinning of the domain wall
on defects. Studies of standard resistors at 4.2 K indicated that long term drifts of the

electronics were S 0.02 ml), signiﬁcantly less than the substeps seen in F i g.3.3.

 

 

 

 

 

 

3 — i -
E
e t _ . \ _
II Multiple substeps
a:
4 P

0 l

-300 -200 -100 0 100 200 300

H (Oe)
Fig. 3.3. AR (=R-Rp) vs. magnetic ﬁeld, H, for a U shaped notch. R is resistance, AP means
antiparallel state and P means parallel state. Arrows indicate different H sweeps. Sample 1470-
lB-a, at 4.2 K, Au top contact.

In Fig. 3.4 3 AR vs. H curve at 295 K for a NC sample type is shown. Here we
observe two wall-trapping substeps in the thin Py layer that are not affected by the ﬁeld
direction. We also see a single trapping step in the notch area of the thicker Py layer,
which is affected by the sweep ﬁeld, making the characteristic resistance value of the step

and its length differ between sweeps. The data also show that CPP detection of domain

83

wall motion can be measured at 295 K, even with non uniform CPP currents. See

Appendix.

20 . r
18

 

AP

'1

 ._.-...1” 3

"‘h.

 

 

{#-

 

Lllllllllllllllllll

I ' rj U I I I I I I l U l U I I I

I
/.I
raﬂl—I- l—I/ v\."‘I-l———I—ﬂp
. L 1 ‘ i 1 . r . r L r“. . 7

-30—0 -200 -100 0 100 200 300
H(Oe)

Fig. 3.4. AR(=R-Rp) vs. magnetic ﬁeld, H, for 3 NC notch. R is resistance, AP means antiparallel
state and P means parallel state. This curve has two reproducible wall-trapping substeps for the
thin Py layer. Arrows indicate different H sweep. Sample 1470-1A-a at 295 K, Au top contact.

.-I

 

 

Assuming that the top contact is perfectly centered on the constriction, R values
of the wall-trapping steps tell us what the position Of a wall in the notch is. For instance,
in Fig. 3.2, having R values of the wall-trapping steps that are almost halfway between P
and AP resistances means that walls are trapped near the middle of the constriction in the
thin Py layer. In Fig. 3.3, the resistance shows multiple jumps between the P and AP
states, and this means that the wall gets pinned at many different sites along the “entire”
U-shaped notch. If R shows reproducible pinning points, like in Fig. 3.4, we can
determine the position of these sites in the notch and with this information characterize an

unknown notch shape. In Fig. 3.4 only two wall—trapping substeps appear for the thinner

84

Py layer, which indicates that this NC constriction is close to a V-notch shape. The main
trapping seems to occur just before the wall leaves the constriction, which implies that

the notch is asymmetric.

3.4 Multiple Runs

Fig. 3.5 Shows two characteristic groups of R vs. H curves. The ﬁrst group is
shown in Figures (a) and (b) that correspond to U and V shaped notches with well
deﬁned geometry. These reasonably reproducible curves indicate that walls almost follow
the same path through stable pinning sites in the thin Py layer. In spite of this stability,
wall-trapping steps in the thicker Py layer are less reproducible in the thinner Py layer.
Constrictions with roughness and probable lack of symmetry belong to the second group,
inherent to U shape notches only. Figs.3.5 (c) and (d) Show no wall path reproducibility,
not only in the number of substeps but also in their resistance values. Even when these
different sweep curves do not exhibit the same behavior, they do Show signs of some
periodicity. For instance, in Fig. 3.5 (c) we observe that wall-trapping in the thinner Py
layer always takes place between ~ 10 Oe S 1 H 1 S ~100 Oe, and many runs present two
clear R jumps at ~1301 Oe and 1601 Oe. In Figs. 3.5 (c) and (d) we also see that wall
trapping in the thicker Py layer is rare.

It is important to note that for the thinner Py layer in Fig.3.5: (1) the injection

ﬁeld from the reservoir has a reasonable stable value of l H 1~10 Oe which is independent

85

of the notch type (since this injection ﬁeld depends mainly on the properties of the
reservoir and its connection to the nanowire, this notch-shape independence is expected),
and (2) the escape ﬁeld from the notch, is more variable from sample to sample but
mostly occurs for 50 Oe S 1H 1 S 150 Oe. Also note that in all these curves for |H| S 100
Oe and no trapping, MR readily detects a subtle readjustment of the magnetizations away

from the P state for the two Py layers (this is shown in an increase of R as |H| decreases).

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(81m .1 .,. .1. (b) ..................
47.2 L
47.0 1
46.8 i
I
46.6 g
a q A
g 45.4 ‘ E
m 46.2 a m
46.0 - ( .
- I -')
45.8 ~ 1 1 r
. Ila, _ ‘
. n- - - -) . —~i ._'; .2 1
45 6 ”I “LII”... "id—|H|.“ I ' “*1
45,4 1 - I - . . n - n 151 ...................
-200 -100 0 100 200 -500 400-300-200-100 o 100 200 300 400 500
H (Oe) H (Oe)
(c) (d)
25 ' r f r ' m r r v r ' - r r 1 ' 1 f r ' 1 '
' ’7‘ 62 1 "—7 A ' 4
t 4
F5 1 , l l l ‘
24 - ’ r . 61 t. L :
1
. I g . ’ i ‘
A A 60 _.. I .t
E v E I I l
v 23 b ' 4
m " d v 1 ‘0 V
J a: 59 - .
L
(— l 1 --> 1 ’ ‘
_- 1- ; 58 _6' -1:
22 1 _ a. A'_ - g a
“4% J. - - ‘
300‘200‘100‘0‘10OAIA 57 gltrﬁfj‘ ‘ L
' ' ° 20° 30° -300 -200 -100 o 100 200 300
H (09) H (Oe)

Fig. 3.5. Multiple CPP resistance, R vs. magnetic ﬁeld, H, curves. H sweeps move back and
forward between —500 Oe and 500 Oe. Samples a) l470-5B-a at 4.2 K, U-shaped notch, Nb top
contact, and b) l470-6B-a at 4.2 K, V- shaped notch, Nb top contact. Stable and reproducible
conﬁgurations. U-shaped notches only: samples c) l470-lB-a at 4.2 K, Au top contact, and d)
l470-lB-b at 295 K Nb top contact. More unstable conﬁgurations.

In Fig. 3.5, injection ﬁelds for a wall in the thicker Py layer typically vary

between 1H 1- 150 Oe and ~ 300 Oe, which are up to 30 times larger than those for a wall

86

in the thinner Py layer, 1H l~ 10 Oe. One would have expected injection ﬁelds to scale
with thickness, 20nm/5nm = 4.8 Perhaps dipole coupling between Py layers in the
reservoir (see Sect. 1.3.5) causes these “low” injection ﬁelds for walls in the thinner Py
layer, and variable high injection ﬁelds for walls in the thicker Py layer. Note that the
injection ﬁelds of the wall in the thinner Py layer are ~10 times smaller than their escape
ﬁelds, 1H l~ 100 Oe. In the thicker Py layer this ratio of escape ﬁeld to injection ﬁeld is
much smaller (< 2). High injection ﬁelds means that the barrier is already lower in the
notch region, and this might explain why it is more difﬁcult to trap walls in the thick Py
layer. This, plus the variability of the wall-injection ﬁelds in the thicker Py, would also

explain why the AP-—>P state transition ﬁeld can ﬂuctuate from run to run.

3.5 Sample with CPP Current outside Constriction

As we already mentioned in Sect. 3.4, in Figs. 3.2 to 3.5 for |H| S 100 Oe and no
trapping, the MR detects a slight alteration of the magnetizations away from the P state
for the two Py layers. This is likely due to residual dipolar coupling between these two
layers in the notch region. See Sect. 1.3.5. To conﬁrm that this behavior was only
associated with inside the notch region, we placed an extra Nb top contact well to the left

of a U-shaped constriction, as shown in the inserts of Figs. 3.6 and 3.7.

87

 

 

 

 

 

 

 

 

 

 

 

 

 

    

6 ' I ' l r l ' r I T r
+top contact
6% outside notch
5 " +top contact
- over notch
| | Upper Contact Strip
A 4 ' Iu/ i'
‘1 3 b 1! 11 _
m .. 1 I ‘ q
a = - 1 .
2 - g \ ‘ , -
'I ' . ‘ “
l u
m : L ‘1 No apparent coupling of
q 1 L V b ‘ . ferromagnetic layers .1
\ .
. <—-— . ‘ < ------------ a
.1: . i 4
O /I~$ {\‘_--.). rs.<'——".'-—
I 1 \o-o-oJ l\o

 

l a
-400 -300 -200 -100 0 100 200 300
H(Oe)

Fig. 3.6. AR (= R — Rp) vs. H for a sample with one Nb top contact placed to the leﬁ of a U-
shaped notch and the other contact over the notch. Solid and dashed arrows show direction of
ﬁeld sweep at 4.2 K. Sample 1470-lB—b‘, Nb top contact.

Fig. 3.6 shows for the top-contact-outside-notch, TCO, data that, for -70 Oe S H S
+300 Oe, AR = (R - Rp) = 0, indicating a lack of residual dipole coupling in the notch free
part of the wire, as expected, see Sect. 1.3.5. A similar behavior is Observed at 295 K for
-40 Oe S H S +300 Oe, see Fig. 3.7. Fig. 3.6 also shows that at H ~ -70 Oe, the wall
leaves the CPP current region of the U notch and begins entering the CPP current region
of the TCO. This situation is repeated in Fig. 3.7, but at a lower value of H ~ -50 Oe, as
expected (because of thermal effects). In Fig. 3.6, for -110 Oe S H S -70 Oe, there is
some evidence of trapping in the TCO curve before the AP state is attained, presumably
due to stress introduced during cooling of the sample. During material deposition,

interface stresses are generated between layers; and these stresses can increase during

88

cooling of the sample at 4.2 K due to differential thermal contraction. Seemingly the
main contribution to stress in the Py layer comes from the top contact Nb. These non
magnetic stresses can act like wall-pinning defects along the Py nanowire, see Sect.1.3. 1.
In Fig. 3.7 we also observed that, at 295 K, the expected lower stress and higher thermal
activation allow a cleaner transition to the AP state. In Fig. 3.6 the AP—> P state transition
is at H-270 0e for the TCO data and at H~-225 0e for the top-contact-over-notch curve.
This is explained, as we saw in Sect. 3.4, by the ﬂuctuation, from run to run, of the
injection ﬁeld of a wall in the thicker Py layer (recall that the injection ﬁeld of the thinner

Py layer is more stable). This would also explain the difference in AP—> P state transition

 

 

 

 

 

 

 

 

 

 

 

 

ﬁelds observed in Fig 3.7.
6.0 _ . l . l . , . . l . I .
5.5 - |L/UppchontactStrip +top contact "
' ' outside notch
5'0 . GWO +top contact .
4.5 - E " over notch -‘
A 4.0 - _"‘ -
C.‘ '. .I
g, 3.5 . _ ‘
0:“ 3.0 _. —A -
u 2.5 - -
m - No apparent coupling of .1
II 2.0 - . ‘ ferromagnetic layers
a: . - i
<1 1 5 . I b.
1.0 - §
L i '
0.5 rem-«"- v 1
0'0 w—h-oo . .0 . 4

 

 

 

-400 -300 -200 -100 o 100 200 300
H (Oe)

Fig. 3.7. AR (= R - Rp) vs. H for a sample with one Nb top contact placed to the leﬁ of a U-
shaped notch and the other contact over the notch. Solid and dashed arrows show direction of
ﬁeld sweep at 295 K. Sample l470-lB-b', Nb top contact.

89

The localized CPP current studies presented here clearly demonstrated the power
of this technique. We have conﬁrmed our assumption that the wall is injected from the
reservoir on the right and moves to the left, passing through the notch region ﬁrst and

then sweeping under the top contact outside the notch (located to the left).

3.6 Estimation of the Displacement of a Domain Wall

within the Constriction

The response of the trapped wall to H in the thinner Py layer produces an
approximate linear variation of R that has a maximum value 5R ~ (9 X(RAp - Rp), where
(9 is determined by the “strength” of the pinning site. This is clear consequence of the
enhanced sensitivity for domain wall motions given by CPP MR, which cannot be
obtained by using CIP MR instead. Earlier CIP results showed no linear variation of R
with ﬁeld for trapped walls.l

As we saw in Sect. 1.3.5, Mc Michael et al.9 have done macromagnetic
simulations for a head-to-head wall of transverse magnetization (.L x) that is trapped in a
trapezoidal notch cut into one side of a narrow wire in a very thin Py layer. Such
simulations indicate that the average magnetization Jx varies linearly with H during
trapping. Since the CPP MR varies approximately as the average Jx for the thin Py layer
within the area deﬁned by the top Nb contact (while J of the thick layer remains ﬁxed),

the simulations would predict the linear response in R that we see.

90

 

 

 

 

 

 

3,5 M ' _ _
_ 5R] (RAP'RP) ~ 0.1 dR -0.02mQ .
3O _ dx=4-8nm_
a 2.5 - -
E - 5R=0.385mQI .
V 2 0 - -
Q.
m r q
i 1.5 - (RAP-Rp)=3.55mQ —
II ’

% 1.0 '- 1
0.5 - ‘_ q
. .‘.‘.*:

0.0 1 i L ‘

-100 0

H(Oe)

Fig. 3.8. AR= (R-Rp) vs. magnetic ﬁeld, H, data showing the displacement of the wall trapped in
the thin Py layer within the constriction. 8R value from the V shaped notch puts a constraint on
the relationship between the width of the domain wall and the distance the trapped wall moves as
the ﬁeld changes. Sample1470-6B-a, Nb top contact, Fig. 3.1.

Such simulations also indicate that the width (along x) of this transverse region for the
head-to-head wall is approximately equal to the width (_L to x) of the notch region. One
can use the 5R value from a V shaped notch to put a constraint on the relationship
between the width of this transverse region and the distance the trapped wall moves
(along x) as the ﬁeld changes. As seen in Sect. 1.3.6, we adopt a very crude model where
the head-to-head wall (of ﬁxed width D or ﬁxed wall area, Aw) is uniformly magnetized
transverse to x and elsewhere the uniform J is either parallel or antiparallel to x. For
instance, for the V-shaped notch of Fig. 3.2, we have 9 s 10%, see Fig 3.8. Therefore,

this simple model predicts that, if the initial domain width, D0, is ~100 nm (~ the width

91

of the notch .l. to x), then the 6R corresponds to a ~ 150 nm displacement of the wall.
However, if Do 5 600 nm (comparable to the length of the notch along x or to the width
of the wire), then the displacement is ~ 70 nm.

Note that at 4.2 K the long term drifts of the electronics were S 0.02 m0. This
means that, based on the correspondence between SR and the wall displacement

discussed above, we can detect with the CPP-MR subtle average wall motions of ~ 4-8

nm.

3.7 Stability of a Wall within the Constriction

Fig. 3.9 shows motions of a wall trapped in a U-shaped notch at 295 K, Au top
contact sample. H is ﬁrst increased to 500 Oe to attain the P state, point 1, and then is
sweept back until a head-to-head wall in the thinner Py layer gets trapped in the
constriction, H~-20 Oe. A further decrease in H causes the wall to jump signiﬁcantly,
ending up at point 2, H~-4O Oe. After that, the sweeping ﬁeld is increased gradually, and
R indicates that the wall varies its position within the constriction but stays trapped until
the sweeping ﬁeld rises above 10 Oe, point 3 in Fig. 3.9 (b). When H is progressively
swept back to -50 Oe, the wall gets trapped in the notch again, and then leaves it,
achieving the AP state at point 4 in Fig 3.9 (b). Even when H is swept between —50 Oe

and 20 Oe, points 4 and 5 in Fig 3.9 (b), AR(= R-Rp) maintains a constant value. Thus

92

once the wall has left the notch, the AP state is quite stable over this range of ﬁelds

because the wall does not return.

 

 

 

 

 

 

 

 

 

 

 

 

(a) (b)

4 v , v 1 . , . 4 v r ' T ' I V l

4 SM «mm
._\m
l-I_I- / 2 =I"—kl=l"~I-=I>I‘ISI=-I\. 5

3 L A 1" 3 P '\\1§'—.-.-"I-I-I ‘
"E L E“
v 2 . :1 2r
or“ a;
CE (I

u 1 _ ll 1 .
% II %
-I
0, unnu- ..."\I—I-4 0 _
‘—
an an 400 0 1m 60
H (0e) H (Oe)

Fig. 3.9. AR (= R - Rp) vs. magnetic ﬁeld, H. Head-to-head wall motion in a U-shaped notch of a
An top contact sample at 295 K. a) Overall major ﬁeld sweep. b) Detail of minor ﬁeld sweep.
Sample l470-BB-c at 295 K, Nb top contact.

Fig. 3.10 exhibits wall motion in a NC notch of 3 Au top contact sample at 295 K.
After achieving the P state at —500 Oe, the ﬁeld is swept back to various values to: get the
wall trapped in the thin Py layer, Fig. 3.10 (a); attain the AP state, Fig. 3.10 (b); and get
the wall trapped in the thicker Py, Fig. 3.10 (c). Fig. 3.10 (a) shows totally reproducible
cycles of AR vs. the sweeping ﬁeld between 0 0e and 40 Oe. The wall moves back and
forth inside the constriction following the same path. In Fig. 3.10 (b), AR depicts stability
of the AP state for 0 0e S H S 180 Oe after the wall left the constriction. Fig. 3.10(c)
indicates that the wall in the thicker Py layer is trapped in the constriction for H sweeps
between SOOe and 180 Oe; and even when H is reduced to 0 0e aﬁer the sweeps, the

wall remains trapped inside the notch.

93

(a) (b) (0)

 

 

18» 18» s --------------- 13

T
i
l

 

 

 

 

 

 

 

 

- x7 - . ,’
15 r- K” , 15 r r- 15 ” (’- $ '
J f i x i
a 12 - I 12 ~ 12 - fﬁL “““ ti
1% ' " r' ““41? ........
a. ‘ 4 . ““1251
A I
3:? 9 - 9 - 9 ~ E +
.. : i
a: . : ‘ :
Q ' ' E E I
6 - 6 - 5 6 _ : .
3 - 3 ~ 3 ~ .
I I x" I
all u" 5"
/‘ ””” ' Vix”' /f
0 ’1 . 1 . 0 "1 L 4 . o 1 A I
0 1 00 0 100 0 100
H(Oe)

Fig. 3.10. AR (= R-Rp) vs. H, a head-to-head wall motion in a NC-shaped notch of a Au top
contact sample at 295 K. a) Reproducible cycles of AR vs. H between 0 0e and 40 0e occurs,
aﬁer wall-trapping. The wall moves back and forth inside the constriction following the same
path. b) AR depicts stability of the AP state, once the wall has leﬁ the notch. c) A wall in the
thicker Py layer is trapped in the constriction, and even when H is reduced to 0 Oe, the wall has
not left the notch. Sample l470-lA-a.

In Fig. 3.11 we see the response of a wall trapped in the thin Py layer to ﬁeld
variations for a U-shaped-notch sample with Nb top contact at 4.2 K. After setting H = -
500 Oe (P state), a wall moves in the notch region for 10 Oe S H S 150 Oe. At 150 Oe the
wall is very close to leaving the notch. Sweeping the ﬁeld back and forth between 150 Oe
and 0 0e reproducibly shifts the wall between the same two pinning sites within the
constriction and with hysteretic motion. These observations suggest that the constriction

is elongated and rough having at least two pinning sites between which the wall can

94

move with hysteresis. In contrast, in Fig 3.10 (a), the motion of a wall between the two

pinning sites does not exhibit hysteresis, which is probably due to the higher thermal

 

 

activation at 295K .
2.0 . , , ﬁ ' I . I
1 5 — ........ v? -
A ,I/I’,
G e
3.5, 5’
0;“ 1.0L , r _
(I .
l| /‘
“45 0.5 . :I _
.’
i .................. . .l
0.0 . | . ,_._./ .

 

 

 

Fig. 3.11. AR (= R — Rp) vs. magnetic ﬁeld, H. Sweeping H back and forth between 150 Oe
and 0 0e shifts the wall between the same two points within the notch. Back and forward
motions follow different paths. Sample 1470-SB-a at 4.2 K, U-shaped notch and Nb top
contact.

These observations along with those of other samples imply that, in general, when
any system “with a trapped wall” is relaxed by changing H to 0 Oe, the wall continues in
the notch region. Without the wall irreversibly leaving the constriction, it can move to a

different point in the notch which gives a lower energy state.

95

3.8 Time Studies

Figs. 3.12 and 3.13 show the time dependence of R after the ﬁeld sweep was
stopped at the values of H indicated in Fig. 3.12 (a) as A-C and in Fig. 3.13 (a) as A-F.
Letter A indicates the ﬁrst value at which a positive ﬁeld sweep was interrupted, and then
R was monitored for long periods of time to assess the stability of wall trapping. Next the
ﬁeld sweep was started again at -500 Oe (or 500 Oe) and stopped at another value of H,
points B—C in Fig. 3.12 and points B—F in Fig. 3.13.

In Fig 3.12 the stability of the trapped wall in a V notch of both Py layers was of
interest. In Fig. 3.12 (b) curves A-C clearly show no change of AR(= R — Rp) in time. This
means that the wall does not move out of its original pinning site when H is ﬁxed. This
system is very stable, as expected.

In Fig. 3.13 (a) we see the overall curve of a U notch sample; but after repeated
ﬁeld sweeps from —500 Oe to +500 Oe, AR became more stable. The open circles
represent one of these more stable sweeps that happens to exhibit wall trapping in the thick
Py layer. In Fig. 3.13 (b) curves A-F exhibit signiﬁcant changes in R with time, this
implies that the wall is unstable moving or jumping between weak pinning sites inside the

U-shaped notch. These changes are signiﬁcantly larger than the electronics driﬁs of S 0.02

mi).

96

(a)

 

 

 

5 I l I I j I I I I
l A
4- l -
HT A
a. h -l
a: \r
o':2~ '- B

 

 

4
'1.

.JK'
‘---_--------

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

m d
<
1 - -
ﬂ— ‘ "“* .
o Lézrri-i . . ."H- — ,
-5oo 400-300-200-100 o 100 200 300 400 500
(b) H(Oe)
5 . ......, . -.......
4 - A -
. /
I I—I—I-I-I>II
A 3 '— d
g I I—I—I-I-III / C
“F“ 2 - e
m I I—I—I—I-III
ll ’ ‘
051 1 "' \ -
l B
0 — _
10 . ......1.00 - .....1.600
Time (s)

Fig. 3.12. a) AR(= R — Rp) vs. magnetic ﬁeld, H, at 4.2 K for a sample with a V-shaped notch. H
sweeps start at -500 Oe and then stopped for about 1000 s at a given H represented by A and B.
Then the ﬁeld sweep is started again at 500 Oe and then stopped for about 1000 s at a given H
represented by C. b) Resistance, R, vs. time, commencing 10 s after magnetic ﬁeld sweep is
stopped at A-C. Sample l470-6B-a, Nb top contact.

97

 

 

 

 

 

.4 i

2 " I; if :I l "
A I I A: |
G k : :
é ' : :
a: 1 - 1 V _
<1 b. B-D )9

‘— E F -->
0 - ----- ﬁned

 

-300 -200 -100 o 100 200 300
H (Oe)

 

I IIIIIII l IIIIIII I IIIIII' I

9‘

 

<—1mQ

‘

 

 

l
I I 1111111 I l 1111]]!

l l lllllll l

10 100 1000 104
time (s)

Fig. 3.13. a) AR (= R — Rp) vs. H, at 4.2 K for a sample with a U-shaped notch. Open circles: H
sweeps start at -500 Oe and then stop for over 1000 s at a given H represented by A—F. Then the
ﬁeld sweep is started again at —500 Oe. b) AR vs. time, commencing 10 s after magnetic ﬁeld
sweep is stopped. A—F correspond to values of H shown in (a). The ordinate values of these

curves have been shifted somewhat for clarity, but they share the same incremental resistance
scale. Sample 1470-lB-a, Au top contact.

98

These domain wall motions inside the U notch are somewhat similar to what was
observed by Giordano et al.“, who proposed that domain wall depinning in very narrow
Ni nanowires (with no constriction) occurs by thermal activation over a barrier above 2
K, as opposed to tunneling through a barrier. This idea is also sustained by a theoretical
study of quantum domain wall depinning of by Chudnovsky et a1. '0, who established that
for a ferromagnetic layer with uniaxial anisotropy the crossover temperature between
thermal activation and quantum tunneling regimens is typically 0.1-1 K. Due to the
geometrical similarities of these works and our system, we presume that at 4.2 K when H
is ﬁxed and a wall moves between pinning sites of a notch, as shown in Fig. 3.13 (b),
thermal activation takes placed over time scales > 80 3. However, during a rapid ﬁeld
sweep and 3-sec R measurement, the time scale to thermally activate a wall to escape
from a particular pinning site must be within ~ 35. As H increases, the potential barrier
lowers until this thermally-activated escape can occur. Thus, the change in H associated
with each trapping step is a measure of the original barrier height just after the wall got

trapped at that step.

3.9 Current Driven Studies

As mentioned earlier, many of the recent domain wall trapping studies
emphasized the use of high “in plane” current densities to manipulate the wall motion in
narrow structures. 3'5 Analogously, we are interested in knowing if, by applying a CPP

density current, we would be able to control, or at least perturb, the position of a wall.

99

Fig. 3.14 (a) shows an example of R vs. H data for a U-shaped-notch sample at
4.2 K. After starting in the P state at H = -500 Oe, the sweeping ﬁeld is gradually
increased to ~125 Oe, point A, where the wall in the thinner Py layer is trapped in the
constriction. H is then set to 0 Oe, the system relaxes but the wall remains trapped, as
seen in Sec 3.7. The resistance is then monitored for progressive DC current increments,
in cycles between 0 mA —> 4 mA —> -4 mA —) 0 mA. This CPP DC current is added to
the AC current used to read sample resistances. The resistance drop seen in Fig 3.14 (b)
(circular red symbols) indicates that the wall has shifted from position A to position B,
which is another pinning point within the notch.

Note that the DC current scale in Fig. 3.14 (b) does not display high values of
current. This is because R shows drastic changes when the DC current in the Nb contact
exceeds the critical superconducting current density, see Appendix. Only the states before
and after the DC-current application are of interest.

In Fig. 3.14 (a), the system is similarly carried from the P state at H =- 500 Oe to
H~ 50 Oe, point B, which is also in the trapping region of the wall in the thinner Py layer.
H is set to zero and R is then measured following the same DC cycles described above,
but no motion of the wall is observed, see square black symbols in Fig. 3.14 (b). This is
an indication that point B is a lower-energy pinning site, since the wall relocates from
another place in the notch to this point but once it is there it does not move.

Point C in Fig. 3.14 (a) corresponds to trapping of the wall in the constriction of
the thicker Py layer. This second step did not occur in the particular overall run of Fig.

3.14 (a). The system is taken through the P and AP states to trap the wall at H ~ 200 Oe,

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) 6 I I 1 I I i T I I I
5 — B\ MA—I-T d
a» \
l— .—
e 4 r A
e /
me 3 - u -
a if *
ll 2 - f C -
m I t,\\ d
< d.‘ \4 D
1 — ”.4 I —
I-I-I-I-I’..---’ \l/ l
O '- 1 1 1 1 1 1 1 1 I 1 . L Lr'q
-100 -50 0 50 100 150 200 250
H (Oe)
(b) 6 I T I ﬂ I ‘ I f I
5
4
2‘
Va 3
“F
a:
ll 2 - C ...... > -
I
<1 1 _ O—WO‘OWO‘:
l- ‘( ---------- ) D ‘( """ J
o —o=——o—0052:5>625§39—c3-——o——o———o—=
-o.04 -0.02 obo 0.02 0.04

DC Current (mA)

Fig. 3.14. Wall motion by applying a CPP DC current density of 3 x 1010 A/mz. a) AR(= R — Rp)
vs. magnetic ﬁeld, H. H sweeps start at —500 Oe, stop at a given H represented by A and C, and
ﬁnally go to 0 Oe. A and C indicate wall trapping in the thinner and thicker Py layers,
respectively. B represents relocation of wall trapped in the notch of thinner Py layer. D represents
P state after the wall has left the notch in the thicker Py layer. b) AR vs. DC current. Sample1492-
lA-b at 4.2 K, Nb top contact and U-shaped notch.

10]

and then H is set to 0. R is measured while a DC current is applied as explained before.
R, in Fig 3.14 (b), shows that the wall moves off the constriction to point D, P state.

These preliminary DC-current investigations showed that only 2 out of 5 U-
shaped-notch samples studied in this way exhibited indications of a wall being driven by
a DC current. In Figs. 3.14 there is no indication of preferred wall motion direction
(along x) other than to lower energy points.

The mechanisms of wall motion due to a CPP DC current density is not yet
understood. The maximum applied DC current density, ~ 3 x 1010 A/mz, is an order of
magnitude lower than the characteristic spin torque mechanism current densities, ~10ll
A/m2 ”. This suggests that perhaps other mechanisms are responsible for this wall
motion. For example, if one were to consider the ﬁeld generated by the DC current as a
possible cause, one must know the actual non uniform current density distribution.
Remember that the critical current of the top Nb contact was exceeded in these studies,
which additionally complicates the analysis. In spite of this, for an “initial” analysis,
simple numerical calculations, for a uniform current ﬂow through the contacts and the
sample, indicate that this ﬁeld is non-uniform and could be locally important, ~ 25 Oe.
However, further studies must be done to understand better CPP-current—driven wall

motion.

102

REFERENCES

 

‘ r. Ono, H. Miyajima, K.Shigeto and r. Shinjo. App]. Phy. Lett. 72, 1116 (1998).

2 T. Ono, Y. Ooka, S. Kasai, H. Miyajima, N, Nakatani, N. Hayashi, K. Shigeto, K. Mibu
and T. Shinjo, Mater. Sci. Eng. B 84, 126 (2001).

3 M. Klaui, C. A. F. Vaz, J. A. C. Bland, W. Wemsdorfer, G. Faini, E. Cambril and L. J.
Heyderman, App]. Phys. Lett. 83, 105 (2003).
4 M. Tsoi, R. E. Fontana and S. S. P. Parkin, App]. Phys. Lett. 83, 2617 (2003).

5 J. Grollier, P. Boulenc, V. Cros, A. Hamzic, A. Vaurés, A F ert and G. Faini, Appl. Phys.
Lett. 83, 509 (2003).

6 N. Giordano and J. D. Monnier, Physica B 194-196, 1009 (1994).
7 K. Hong and N. Giordano, J. Magn. Magn. Mater. 151, 396 (1995).

8 J.Z. Sun, L. Chen Y. Suzuki, s.s. Parkin, R. H. Koch, J .Magn. Magn. Mater. 247,
L237-L241 (2002) and references therein.

9 RD. Mc Michael, J.Eicke, M.J. Donahue, and D.G. Porter, J. Appl. Phys. 87, 7058
(2000).

'0 E. M . Chudnovsky, o. Iglesias, P. c. E. Stamp, Phys. Rev. B 46, 5392 (1992).

11 Katine J .A., Albert F .J ., Buhrman R.A., Myers EB, Ralph D.C., Phys. Rev. Lett. 84,
3149-3152 (2000).

103

CHAPTER 4

Summary and Conclusions

We have successﬁrlly adapted the Ono et a]. method for trapping domain walls"2 to
current perpendicular to plane, CPP, giant magneto resistance, GMR, measurements. The
multilayer sequence was Nb(100)/Cu(l0)/Py(20)/Cu(l0)/Py(5)/Cu(5)/Au( 15), where Py =
Ni34FC|6 and the thickness are in run. We shaped the Py/Cu/Py/Au part of the multilayer
into a long 500-nm-wide long wire with a U-shaped or V-shaped constriction near its
middle, acting as a wall-trapping site. A sweeping magnetic ﬁeld, H, was applied along + x
and parallel, P, to the axis of the wire. After saturation, this H direction was inverted
(along —x), and magnetization reversal started by nucleation of a magnetic (head-to-head)
domain wall in the thinner Py layer at low values of H while the magnetization of the
thicker Py layer remained ﬁxed. Closure domains initially nucleated the wall in a diamond-
shaped reservoir placed at the +x end of the nanowire, and then the wall was injected in the
—x direction from there into the thinner Py layer of the nanowire. At this very low ﬁeld, we
could very-effectively observe wall trapping because the CPP current is conﬁned to the
notch region by a 900-nm-wide top contact made of 200-nm-thick Au or lSO-nm-thick Nb.
At 4.2 K, the latter provided a more uniform CPP current density because the bottom and
top Nb layers became superconductors, but measurements at 295K have also been
successﬁrl with non-uniforrn CPP currents. The notch geometry affected the wall motion,
which we were able to detect by subtle GMR changes between P and antiparallel, AP,

relative orientations of the magnetizations of the two Py layers. The response of a trapped

104

wall to H in the thinner Py layer produced an approximate linear variation of R in each
trapping step. This was consequence of the enhanced sensitivity for domain wall motions
given by CPP GMR, which cannot be obtained by using the current-in-plane technique of
Ono eta]. Resistance changes with H showed that in V-notches one trapping site occurred.
In contrast, for U-notches several pinning sites were seen while the wall remained trapped
in the constriction. This behavior depended upon the wire edge roughness and other
defects, which acted like similar-strength pinning sites where trapping of the wall could
occur. Using the change in R associated with the position of the wall in the notch region,
unknown constriction geometries could be characterized. The ﬂexibility provided by this
new method allows the CPP current region to be chosen independently of the long
dimension of the wire. This helped us detect the presence of the wall even outside the
notch region, right after the wall had escaped from the notch, and also verify that the subtle
readjustments of the MR associated with coupling between the Py layers are clearly sensed
in the constriction region only. This detection scheme allowed us to conﬁrm the expected
-x direction of the wall propagation after the wall was injected from the reservoir into the
nanowire. As the magnetic ﬁeld continued increasing along -x, a second wall in the thicker
Py layer was injected from the reservoir into the nanowire, and it sometimes got trapped in
the notch. Finally, if the magnetic ﬁeld was raised ﬁrrther, the wall in the thicker Py layer
escaped from the notch and the P state was attained. Successful pinning of a wall at the
constriction in the thicker Py layer was less likely because this wall was injected at a
higher ﬁeld, meaning that the energy barrier for escape was already lower in the notch.

In all cases, when a system with wall trapped in its constriction was relaxed by

sweeping the ﬁeld to 0 Oe, the wall did not have to leave the constriction, but instead it

105

moved to a different point in the notch seeking a lower energy state. Many of these
changes were reversible. In a stationary regime, when the magnetic ﬁeld is kept ﬁxed, the
time dependence of the wall position within the constriction could be determined with high
precision using our CPP GMR technique. We believe such wall motions at 4.2 K are
driven by thermal activation.

We observed in some samples motion of domain wall driven by high-density CPP
currents of ~ 3 x 1010 A/mz. Since the current density is one order of magnitude less than
the typical current density,~10ll A/mz, reported for spin torque mechanism3, the
particular mechanisms of DW motion driven by a DC CPP current is not yet understood.

In conclusion, we have used localized CPP GMR to detect the occurrence and
small motions of a trapped domain wall in a narrow ferromagnetic wire. This different
wall-detection scheme that we developed provides enhanced sensitivity to small wall
motions. It will also facilitate the study of a wide range of interesting wall-trapping
geometries. For example, (1) we could investigate the motion of a magnetic vortex, in a
disk-shaped thin ferromagnetic ﬁlm of diameter < 1 pm, due to the application of an in-
plane magnetic ﬁeld. (2) We could examine wall motion in a major constriction with two
trapping sites, producing a double potential well, that can be modiﬁed by changing H and /
or exciting with a high-frequency H. This system would also allow us to inspect motion,
between the two pinning sites, of a wall driven by high-density CPP current. (3) By
lowering the temperature, we will be able to study quantum tunneling as a possible

mechanism of wall motion at ﬁxed H.

106

REFERENCES

 

‘ r. Ono, H. Miyajima, K.Shigeto and T. Shinjo, App]. Phy. Lett. 72, 1116 (1998).

2 T. Ono, Y. Ooka, S. Kasai, H. Miyajima, N, Nakatani, N. Hayashi, K. Shigeto, K. Mibu
and T. Shinjo, Mater. Sci. Eng. B 84, 126 (2001).

3 Katine J.A., Albert F.J., Buhrman R.A., Myers EB, Ralph D.C., Phys. Rev. Lett. 84,
3149-3152 (2000).

107

APPENDIX

Uniformity of the CCP Current Density

The distribution of the current density is expected to differ considerably between
Au and Nb top contacts samples. At 4.2 K the Nb top contact becomes a superconducting
equipotential which produces a uniform current density. Since Au remains normal, the
CPP current density will be non uniform. To understand this latter case, let us make use
of a simple Ohmic model presented by Lenczowski et all, who calculated a current
distribution in a small pillar-like structure for CPP magnetoresistance experiments. Fig
A.l shows one of the square pillar geometries studied by Lenczowski that is similar to the

geometry used in this work .

 

 

d, : ‘ > V >
—1< \ /
\Current leads Voltage leads /

a, El: ' 1 4 1 ‘

x=0 x=L

 

 

 

 

 

 

 

 

 

 

Fig A. 1. Sketch of the current density in the nanopillar Ohmic model studied by Lenczowski.

This one-dimensional model assumes that in the current leads the current density
decreases monotonically from a certain value at one of the edges of the pillar, x=0, to
zero at the other edge, x=L, see Fig. A. l.

The current density in the pillar, j(x), is given by the following expression:

108

'(x)=-l——I——cosh(L——i] (A l)
J Lk sinh(L/k) k '

where x represents position along the axis perpendicular to the current in the pillar, and L

is the width of the square pillar. k is deﬁned as:

—I/2
k=C’/2[§L+-§i] (A. 2)
l b
1
c=-2-(p,d, + p,d,,)+ ARA, (A. 3)

where pt and p1, are the resistivities of the materials of the top and bottom contacts
respectively, and d, and db are the thicknesses of the top and bottom contacts. ARM: is the
speciﬁc resistance of the multilayer pillar in the antiparallel state of U-shaped notches of
area 1.5 x 10''3 m2. ARA)» were calculated following the 2CSR model at 4.2 K, Au-ARAp
~1 1.2 fﬂm2 and Nb'ARAp ~11.6 me2, see Table 1.2, and estimated from the
experimental data at 295 K, Au-ARAp ~76 film2 and Nb-ARAp ~105 fﬂmz, see Table 3.2.
The following contact resistivities were used: at 4.2 K pm, = 0 tram and pAu= 0.02 pﬂm,
and at 295 K, N = 0.145 uQm and pAu= 0.04 unmz L was taken to be equal to 0.1 pm,
in the center of the notch, and 0.5 um in both ends of the CPP current flow, where the

width of the notch is a maximum and the worst-case scenario for the current density

distribution.

109

(b)

_Tooewo

 

 

 

8.00E-01

 

§e.ooe-or
S

 

)1
34.00501 ‘

200501 .-

 

 

 

 

 

 

 

 

 

0. 00900

 

 

 

0 0.1 0.2 0.3 0.4 0.5
_ X (11ml

 

 

 

 

Fig A.2. Simulation of the current density through a multilayer pillar using Lenczowski and et a].
method.l a) L was taken to be equal to notch width at the center ~ 0.1 jun. b) L was taken to be
equal to 0.5 um, the maximum width of the notch area, which is the worst-case scenario.

Fig. A.2 shows, as expected, that at 4.2 K, the Nb-top contact produces totally
uniform distribution of the current. On the contrary, for Au-top contacts at 4.2 K the
change in current-density is ~ 50 % at the at both extremes of the CPP current ﬂow see
Fig. A.2 (b). However, it is ~ 5 % in the center of the constriction, see Fig. A2 (a). Thus,
the “average change” of the current-density distribution over the whole notch is ~ 27 %.
This suggests that R is rather-uniformly sensed over the entire CPP current ﬂow region
and therefore the data obtained with Au-top contacts can be considered reliable at 4.2 K.
At 295K, Nb contact current-density changes are ~ 80 % at the ends of the constrictions,
see Fig. A.2 (b), and ~ 10 % in the center of the constriction, see Fig. A2 (a). Thus, the
“average change” in the current-distribution over the whole notch is ~ 45%. Comparable
behavior is observed for the Au-top-contact current-distribution at 295 K. We should
expect the least-uniform current-density for the any contact to occur at 295. However the
observed non uniformities in the average current-density-distributions are not “drastic
enough” to lead one to conclude that R is not representative of the whole constriction and

that these contacts are unreliable.

110

Even though Nb is the best material for the top contacts at 4.2 K, we need to be
aware that there are limits to the current density that the superconducting contacts can
support while maintaining an equipotential. If this critical current density is exceeded,
causing these contacts to become “normal”, the CPP current density will become non
uniform as shown in Fig. A2. The critical in-plane current of our “dirty” Nb top strip
was measured to be ~ 1.6 mA at 4.2 K, for the Nb sputtered in the ion-milling chamber.
For a superconductor the current ﬂows close to the surface in a region approximately

equal to penetration depth, 9». At 4.2 K, 1 is ~100 nm,3 for our Nb. Since the thickness of

the Nb strips is ~ 150 nm, the in—plane current will be close to uniform over the cross-
section of the strip. This gives a critical current density of ~ 1.2 x 10 6 A/cm2 for our Nb

strips, a reasonable value for our sputtered Nb.

111

REFERENCES

 

' S.K.J.Lenczowski, R. J. M. van de Veerdonk, M.A.M., J. B. Giesbers , and H.H. J. M.
Janssen, J. App]. Phys. 75, 5154 (1994).

2 Kittel, Introduction to Solid State Physics, 7th Ed., and personal communication.

3 T. P. Orlando and K. A. Delin, Foundation of Applied Supeconductivity, Addison-
Wesley, 6, 259 (1991).

112

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