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Thesis

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

STUDY OF PROXIMITY-INDUCED SPIN-TRIPLET PAIR
CORRELATIONS IN FERROMAGNETIC JOSEPHSON
JUNCTIONS

presented by

Trupti S. Khaire

has been accepted towards fulfillment
of the requirements for the

PhD. degree in Physics and Astronomy

 

 

flmflfié»

Major Professor’s Signavture

%Qj/jO/O

Date

MSU is an Affirmative Action/Equal Opportunity Employer

PLACE IN RETURN BOX to remove this checkout from your record.
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STUDY OF PROXIMITY-INDUCED SPIN-TRIPLET PAIR CORRELATIONS IN
FERROMAGNETIC JOSEPHSON JUNCTIONS

By
Tmpti S. Khaire

A DISSERTATION
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Physics and Astronomy

2010

ABSTRACT

STUDY OF PROXIMITY-INDUCED SPIN-TRIPLET PAIR
CORRELATIONS IN FERROMAGNETIC JOSEPHSON JUNCTIONS

By
ITrupti S. Khaire

In conventional superconductors, superconducting correlations are due to spin-
sz'nglet Cooper pairs that are correlations between electrons of opposite spin, whereas
ferromagnetism on the other hand favors parallel alignment of electron spins. When
a superconductor is placed in contact with a ferromagnet, Cooper pairs can cross
the interface into the ferromagnet. When they do so, the two electrons from the
spin-singlet Cooper pair enter different spin bands and rapidly lose phase coherence
over a short length scale. This is called the conventional spin-singlet proximity effect.
In contrast, spin-triplet Cooper pairs are not subject to this-constraint, and hence
the spin-triplet proximity effect should extend much further into ferromagnet. The
generation of spin-triplet correlations has been predicted to occur in superconduct-
ing / ferromagnetic hybrid systems, but is known to be very sensitive to the presence of
magnetic inhomogeneities in the ferromagnet. The major part of this work was aimed
at studying materials and conditions necessary for the generation of long range triplet
correlations. Once generated, there are several factors that pose difficulty in their
long-range propagation. Our major task therefore was to separate the “generation”
and “propagation” of the triplet correlations in our system. All these studies imple-
ment Superconductor/ Ferromagnet / Superconductor Josephson junction as a tool for
the observation of the long-range effect.

We have observed a long-range spin-triplet supercurrent in S / F / S Josephson junc-
tions containing Co(d)/Ru(0.6 nm)/Co(d) trilayers as thick as 2d = 50 nm. The
spin-triplet pair correlations are induced only when a thin layer of PdOBgNIOJQ alloy

is placed between the central Co and outer Nb layers. The spin-triplet critical super-

current in our Josephson junctions was nearly 100 times greater than the supercurrent
in similarly-prepared junctions without PdNi alloy. This provides strong evidence of

long-range triplet correlations in our system.

DEDICATION

To the reader

iv

ACKNOWLEDGMENT

I am thankful to many people who I have come across all these years.

I am very thankful to my advisor, Prof. Norman O. Birge for everything. I admire
your systematic approach in all things professional and personal. Thanks for seeing
it through all the ups and downs and the worst struggle during my primitive years.
The gradual change from being there for us to letting us decide what to do next, was
indeed nice.

Also, many thanks to Prof. William Pratt, Jr. your enthusiasm is always conta-
gious. Your excitement while looking at some of my worst possible measurements,
really helped me in keeping my spirits high.

Thanks to Dr. Reza Loloee for making the basement a place to learn and laugh,
a second home in every sense. Thanks for helping me even during odd hours. Apart
from the technical expertise, I thank Dr. Baokang Bi for helping me see the fun
behind “problem-solving”.

Thanks to my senior colleagues, to Ion Moraru for introducing me to experimental
techniques, and thanks to Gassem Alzoubi, the little time we overlapped was fun
indeed. I would also like to thank to my current lab colleagues Mazin, Yixing, and
Kurt for keeping me company. Special thanks to Yixing for the Fraunhofer-analysis
program you made for us. Many thanks to my friends Sheenu, Neelam and Poonam
for being there with me all these years. And special thanks to my best friend - my
Mom.

Thanks to Machine shop personnel Tom Palazzolo, Jim Mums and Tom Hudson.
I also thank the Keck Microfabrication Facility for its extensive use in our sample

fabrication process. This work was supported by DOE grant DE—FG02-06ER46341.

1

TABLE OF CONTENTS

List of Tables .................................
List of Figures ................................
Introduction ...........................
1.1 Proximity Induced Odd Triplet Superconductivity ...........
1.2 This Work .................................
Theoretical Background .....................
2.1 Superconductivity .............................
2.1.1 London Penetration Depth ....................
2.2 Proximity effect ..............................
2.2.1 Superconductor/ Normal metal (S/ N) ..............
2.2.2 Superconductor / Ferromagnet (S / F) ...............
2.3 Short Range Correlations .........................
2.4 Long Range Triplet Correlations (LRTC) ................
2.4.1 What are LRTCs? ........................
2.4.2 A Simplified Picture of Triplet Generation Mechanism . . . .
2.4.3 Previous Experimental Hints of LRTC .............
2.4.4 Ways to induce LRTC in S/ F Systems .............
2.4.5 Ways to detect LRTC ......................
2.5 Theoretical Predictions for LRTC ....................
2.6 Josephson Junctions ...........................
2.6.1 Definition .............................
2.6.2 Resistively Shunted Junction (RCSJ) ..............
2.6.3 Effect of Magnetic Field .....................
2.6.4 Josephson Penetration Depth ..................
2.7 Ferromagnetic 0—7r Josephson Junctions .................
2.8 Domain Structure of Ferromagnetic Interlayer .............
2.9 Our Approach ...............................
Experimental Methods .....................
3.1 Sample Fabrication ............................
3.1.1 Sputtering .............................
3.1.2 Photolithography .........................
3.1.3 Ion Milling ............................
3.1.4 SiOx Deposition ..........................
3.1.5 Liftoff ...............................

vi

ix

[\D

0‘

\INODCfl

9
11
12
12
13
17
18
19
19

32
35

37
37
38
42
43
44
45

3.1.6 Top Leads ............................. 45

3.2 Fabrication Issues ............................. 46
3.2. 1 Undercut ............................. 46
3.2.2 Back Sputtering .......................... 47
3.2.3 Dust particles ........................... 48
3.3 Reactive Ion Etching (RIE) ....................... 48
3.4 Magnetic Force Microscopy (MFM) ................... 50
3.5 Measurements ............................... 52
3.5.1 Energy Dispersive X—ray Spectroscopy (EDS) ......... 52
3.5.2 Magnetic Measurements ..................... 53
3.5.3 Resistivity Measurements .................... 54
3.5.4 Temperature Variation Measurements .............. 56
Spin-Singlet Superconductivity ................. 59
4.1 CuNi Josephson Junctions: (Nb/CuNi/Nb) ............... 59
4.1.1 Characterization of CuN i Josephson Junctions ......... 59
4.1.2 Magnetizing CuNi Josephson Junctions ............. 61
4.1.3 Disadvantages of CuNi Alloy ................... 63
4.2 PdNi Josephson Junctions (Nb/ PdNi/ Nb) ............... 64
4.2.1 Characterization of PdN i Alloy ................. 65
4.2.2 Characterization of PdNi Josephson Junctions ......... 67
4.2.3 Magnetizing PdNi Josephson Junctions ............. 70
4.2.4 Critical Currrent vs Thickness: O — 7r Josephson Junction . . . 72
4.2.5 Resistivity of PdNi ........................ 74
4.3 Theoretical Analysis of PdNi Josephson Junctions ........... 76
4.4 Discussion of Results ........................... 78
4.4.1 Estimate of Mean Free Path in PdNi .............. 78
4.4.2 Estimate of Exchange Energy in PdNi ............. 79
4.4.3 Comparison to Other Experiments ............... 79
4.4.4 0 — 7r Josephson Junction: Temperature Dependence ..... 80
4.5 No Sign of LRTC! ............................. 84
4.6 Conclusion ................................. 85
GMR Experiments ....................... 87
5.1 Magnetoresistance (MR) ......................... 87
5.2 GMR Theory ............................... 87
5.2.1 Simplified GMR Model ...................... 88
5.2.2 Two-Current Series-Resistor Model (2CSR) .......... 90
5.3 Spin Diffusion Length in PdNi Alloy .................. 94
5.3.1 Spin Valves: Py/Cu/PdNi .................... 94
5.3.2 Spin Valves (Spoiler Geometry) ................. 98
5.3.3 Discussion of the Results ..................... 100
5.3.4 Strong spin orbit coupling in PdNi alloy ............ 101
5.4 Spin Diffusion Length in PdFe ...................... 103

vii

5.4.1
5.4.2
5.4.3
5.4.4

6 Spin-Triplet Superconductivity

Characterization of PdFe Alloy .................
Magnetic Anisotropy .......................
Double Exchange Biased Spin Valves ..............
Discussion of Results .......................

6.1 Ferromagnetic Josephson Junctions using Ni ..............
6.2 Reduction of Flux .............................

6.3 Synthetic Antiferromagnet (SAF) ....................

6.3.1
6.3.2

Josephson Junctions using SAF of the form Co/Ru/Co . . . .
Other Experiments using SAF Configuration ..........

6.4 Long-Range Triplet Correlations in Our Experiment ..........

6.4.1
6.4.2
6.4.3
6.4.4

7 Discussion and Further Work

Strength of Triplet Correlations .................
Where are the Triplets Generated? ...............
Temperature Dependence of the Triplet Samples ........
Discussion of the Results .....................
6.4.4.1 Comparison between Theory and Experiment . . . .
6.4.4.2 Confirmation of Triplet Correlations .........

7.1 Our Aim ..................................
7.2 Overview of Our Work ..........................
7.3 Future Directions .............................
7.4 A Year of Tfiplet Correlations! ......................

A Appendices

A.1 Photolithography Recipes ........................
A.1.1 Single Layer Photolithography ..................
A.1.2 Bilayer Photolithography .....................
A.1.3 Trilayer Photolithography ....................
A.1.4 Image Reversal Photolithography ................

Bibliography

Bibliography

viii

oooooooooooooooooooooooooo

104
106
107

109
110
113
115
116
119
121
127
129
130
131
131
133

135
135
136
137
139

140
140
141
142
143
144

147

147

LIST OF TABLES

2.1 Exchange symmetry for 2—particle fermionic correlation function . . . 13
4.1 Summary of PdNi parameters, 221:, ple, p and le ............ 80
4.2 Summary of PdNi parameters {171, {1:12, E63; and TCurz‘e ....... 81

ix

LIST OF FIGURES

Images in this dissertation are presented in color

2.1 Andreev Reflection ............................ 7
2.2 Simplistic electron dispersion explanation ................ 9
2.3 Triplet generation mechanism ...................... 14
2.4 Equivalent circuit of RCSJ model .................... 24
2.5 Tilted washboard potential ........................ 26
2.6 Underdamped and Overdamped Josephson junctions ......... 27
2.7 Josephson junction schematic ...................... 28
2.8 Airy pattern for circular Josephson junction .............. 30
2.9 0 — 7r Josephson junctions ........................ 31
2.10 Ferromagnetic domain structure ..................... 33
2.11 Neel and Bloch domain walls ....................... 34
2.12 Our approach for the study of LRTC .................. 36
3.1 Overall fabrication process ........................ 38
3.2 Sputtering chamber ............................ 40

X

3.3

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

3.12

3.13

3.14

3.15

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

Sputtering holder and mask ....................... 40

Sputtering gun .............................. 41
A special alloy target ........................... 42
Photolithography ............................. 43
Baffled-box ................................ 45
Nb top leads ................................ 46
Back-sputtering .............................. 47
Issue of dust particles. .......................... 48
Magnetic Force Microscopy (MFM) on Ni film ............. 51
SQUID magnetometry .......................... 53
Current comparator circuit ........................ 55
Lead configuration ............................ 56
Temperature variation measurement set-up ............... 57
Fraunhofer for CuNi Josephson junction ................ 60
Magnetizing CuNi Josepshson junction ................. 62
Curie temperature of PdN i ........................ 65
M vs H for 100 nm PdNi film ...................... 66
I -V characteristics of PdNi ........................ 68
Ic vs H for PdNi Josephson junctions .................. 69
Magnetizing PdNi Josephson junctions ................. 70
Magnetic field shift (H shz‘ ft) vs. PdNi thickness (d pd Ni) ....... 71
Critical current density (Jc) vs PdNi thickness (d pd Ni) ........ 72

xi

4.10

4.11

4.12

4.13

4.14

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

5.10

5.11

6.1

6.2

6.3

6.4

6.5

6.6

Linear Plot: Jc vs. dpsz‘ for 32.5 to 58 nm .............. 73
Linear Plot: Jc vs. d pdm for 55 to 85 nm ............... 74
ARN vs. dpsz' .............................. 75
Temperature dependence of critical current for PdNi Josephson junction 82

Anomalous temperature dependence of critical current for a PdNi J oseph—

son junction using 47.5 nm thick PdNi ................. 83
Giant Magnetoresistance ......................... 88
Schematic for a Py/Cu/PdNi spin valve ................ 94
AR vs. H for a Py/Cu/PdNi spin valve ................ 96
AAR vs. dpdNi for a Py/Cu/PdNi spin valve ............. 97
Schematic for a Py/Cu/PdNi/Py/FeMn spin valve ........... 99
AAR vs. d psz- for a Py/Cu/PdNi/Py/FeMn spin valve ....... 100
Spin—orbit coupling ............................ 102
Curie temperature of PdFe alloy ..................... 105
M vs H for 80 nm thick PdFe film .................... 105
Schematic for FeMn/Py/Cu/PdFe/Cu/Py/FeMn spin valve ...... 107
AAR vs. d pd Fe for the double exchange biased spin valve ...... 107
Fraunhofer for SFS junction using Nickel ................ 111
Oscillatory Exchange Coupling ..................... 115
Schematic for Josephson junction using SAF configuration ...... 117
ICR N vs. DCo for Josephson junction using SAF configuration . . . . 118
SEMPA picture for Co/Cu/Co ...................... 119
Haunhofer for Josephson junction using Co/Cu/Co .......... 120

xii

6.7

6.8

6.9

6.10

6.11

6.12

6.13

A.1

A2

A3

A4

Generation and Propagation of Triplet correlations .......... 122

Schematic of Triplet sample ....................... 123
Fraunhofers for Triplet samples ..................... 125
IcR N vs 1900 for Triplet samples .................... 126
Effect of PdNi thickness variation in Triplet samples .......... 128
16 vs H (Fraunhofers) measured at different temperatures ....... 130
Temperature Dependence of critical current in Triplet samples . . . . 131
Single layer Photolithography ...................... 141
Bilayer Photolithography ......................... 143
Trilayer Photolithography ........................ 144
Image Reversal Process .......................... 145

xiii

Chapter 1

Introduction

According to the Bardeen, Cooper and Schrieffer (BCS) theory [1], superconductivity
in conventional metals and their alloys is due to s-wave spin-singlet pair correlations.
For several decades this type of superconductivity was the only one observed experi-
mentally. In the last two decades several other types of superconductivity have been
discovered. In particular, the high—Tc superconductivity discovered by Bednorz and
Muller [2] in cuprates is still an extensively studied area, where the pairing is now
believed to be an s-wave or a mixture of s-wave and d-wave. Both the s-wave and
d-wave ordering usually imply spin-singlet pair correlations. Recently a p-wave spin-
triplet pair correlations have been found in strontium ruthenate SrgRuO4 [3] and in
heavy fermion intermetallic compounds. Because of the p-wave symmetry, these ma—
terials are highly sensitive to the presence of impurities. But what strikes our interest
here are a new form of spin-triplet correlations, which are symmetric in momentum
(s-wave) and hence insensitive to impurities. The novelty of these new type of super-
conducting correlations lies in the fact that they satisfy the spin-statistics theorem
of quantum mechanics by being odd under time-reversal (or odd in frequency) and
hence they are also known as “odd-triplet correlations”. This type of pairing corre-

lations were first proposed by Berezinskii [4] in 1975 as a possible explanation for

1

superfiuidity in He3. However, later years saw that the superfiuidity in He3 was in
fact a result of p—wave spin triplet correlations, which are even under time-reversal.
The odd-triplet correlations therefore remained a theoretical possibility that had no
counterpart in the real world. But a series of experiments performed in the late 1990’s
[5, 6, 7] renewed the possibility of observing odd—triplet superconductivity in real sys-
tems. These were experiments conducted by different groups studying the proximity

effect in superconductor/ferromagnet (S / F) structures.

1.1 Proximity Induced Odd Triplet Superconduc-
tivity

The word proximity eflect defines an interplay between a superconductor and any
other metal brought in close contact with each other. When a BCS superconductor
is placed next to a normal metal, the superconducting correlations are known to pen-
etrate the normal metal over a distance as large as few microns at low temperatures.
If instead of a normal metal, a ferromagnet is placed next to a conventional supercon-
ductor, the spin-singlet correlations are known to oscillate and decay rapidly inside
the ferromagnet on a length scale of just few nanometers. This short length-scale of
decay was known to be a general characteristic of the S / F proximity effect until some
unusually long range effects were observed by a few groups in the late 1990’s [5, 6, 7].
In 2001, two theoretical groups [8, 9] published papers indicating proximity-induced
odd-triplet correlations in S / F systems, provided that the F-layer has magnetic inho-
mogeneities. It is now believed that the long-range proximity effect observed in S / F
systems is a result of proximity-induced odd triplet correlations. Another promising
hint of these spin-triplet correlations was reported recently in a half-metallic ferro-
magnet Cr02 by Keizer et al. Since Cr02 [10] is a fully spin-polarized magnet (where

the electron transport is metallic for spin-up electrons, while it is insulating for spin-

2

down electrons), the observation of long-range proximity effect was considered an
unequivocal indication of triplet correlations. However, there was no confirmation
of these results for a long time. The difficulties in reproducing the result lie in the
complex nature of CrOg that is sensitive to its growth conditions. Bergeret et al.
[8, 11] recently proposed several mechanisms that lead to inhomogeneous magnetism
in S / F systems, such as: magnetic disorder, non-collinear magnetic domains, spin ac-
tive interfaces, etc. Since then several other theory papers suggesting different ways

to study proximity-induced odd-triplet superconductivity have emerged in this area.

1.2 This Work

The presence of proximity-induced odd-triplet correlations can be tested either by
measuring the density of states or by measuring the Josephson effect. Each method
has its own pros and cons, however in our search for this new symmetry prediction,
we have chosen to work with Superconductor / Ferromagnet / Superconductor (S / F / S)
Josephson junctions. Our experiments were aimed at studying the conditions and
materials suitable for the observation of odd-triplet correlations. In this thesis I will
explain the various considerations that went into creating the final S / F / S Josephson
junction which showed strong evidence of odd-triplet correlations.

The brief outline of this thesis is as follows— Chapter 2 focuses on the physics be-
hind the S / F proximity effect. It also discusses in detail the conditions necessary for
the generation and observation of long-range odd-triplet correlations. Chapter 3 gives
the details of the fabrication procedure and the measurement techniques used in our
experiments. Chapter 4 shows the results of our first Josephson junction experiment
using a weakly ferromagnetic alloy- PdNi. The absence of odd-triplet correlations in
this experiment led us to investigate the spin memory length in this alloy using stan-

dard Giant Magnetoresistance techniques, which are described in Chapter 5. Chapter

3

6 talks about our much awaited results—the observation of spin-triplet superconduc-
tivity in our Co—based Josephson junctions using PdNi alloy near the Nb interface.
The final device modeled and reported in this chapter is a result of a series of con-
clusions drawn from different experiments performed in Prof. Birge’s group, I will
therefore also give a brief overview of those experiments in this chapter. Finally in
Chapter 7, I will discuss the possible mechanism behind the generation of odd-triplet
correlations in our experiment. I will also talk about the interesting experiments that
are currently in progress in the group. We believe these experiments will help us
improve our understanding of the microscopic mechanism behind the generation of

odd-triplet correlations.

Chapter 2

Theoretical Background

2. 1 Superconductivity

Superconductivity is manifested as a sudden drop in resistivity below a certain critical
temperature (Tc). It was discovered in 1911 by Heike Kamerlingh Onnes in mercury
at liquid helium temperatures [12]. Later many materials were found to show a similar
transition at various temperatures. The superconducting material we use in our work

is Niobium; it undergoes a superconducting transition at a temperature of about 9.25

K.

Among the most striking properties of the superconductors are: 1) Ideal dia-
magnetism that leads to magnetic flux expulsion from the superconductor (Meissner
effect); 2) Macroscopic quantum nature of superconductivity including phase coher-
ence that leads to zero resistivity and the Josephson effect; 3) Quantization of mag—
netic flux passing through a superconducting loop, a practical application of which is

SQUID (Superconducting QUantum Interference Device).

A microscopic explanation for superconductivity was not fully known until John
Bardeen, Leon Cooper and Robert Schrieffer [1] put forth their epoch-making theory

of superconductivity called BCS theory in 1957. In this theory it was shown that

5

a phonon-mediated weak attractive interaction between electrons can lead to the
formation of bound pair of electrons with opposite momenta and spin. Such pairs
of electrons act as superconducting charge carriers in the material and are known as
Cooper pairs. The BCS ground state wave function consisting of the bound state
electrons (Cooper pairs) is given in terms of the electron creation operator cJr as

follows,

We) = H (Uk + kaLTCLjHW) (2-1)
k=k1,k2....,kM

with chl2 + Ink]2 = 1 .Here [vkl2 is the probability that the pair state (k T, —k I) is
occupied, [uh]2 is the probability that it is unoccupied and |¢0) is the vacuum state.

Using this ground state, the single particle excitation spectrum is given by,
E2 = efi + |A,,|2 (2.2)

where, Ak is the minimum excitation energy or the superconducting energy gap
and ck is the kinetic energy measured from the Fermi energy. An excitation in a
superconductor is described in terms of a quasiparticle (electron-like or hole-like)
excitation above the gap in the superconductor. The gap, Ak is determined by the

self-consistency equation,
A ——V"’k'A"' 2 3
k — _ Z 2Ek’ ( ~ )
kl

where, V is the weak negative constant interaction that leads to pairing of electrons.

2.1.1 London Penetration Depth

When a superconductor is placed in a uniform magnetic field of flux density Ba applied

parallel to its surface, the flux density at distance :1: inside the superconductor is given

6

b ,
Y B(a:) = Baexp (E) (2.4)

where, B0 is the flux density at the surface of the superconductor. The equation shows
that the flux density decays exponentially inside a superconductor falling 1 / e of its
value at the surface at a distance AL. This distance is called the London penetration

depth and is given by,
m

A = —
L #071582

(2.5)

where, n 5 is the density of Cooper pairs, m is the mass, and e is the charge.

2.2 Proximity effect

2.2. 1 Superconductor / Normal metal (S / N)

 

 

 

Nu(E)f(E) Ns(E)f(E)

Figure 2.1: Andreev reflection. A process by which electrons penetrates from N to S
at energies less than the superconducting gap, A.

7

When a superconductor (S) is placed in good electrical contact with a non-
superconducting, non—magnetic (N) metal, the prOperties of both the metals are
modified. The appearance of superconducting correlations in the N metal near N / S
interface is called the proximity eflect. The weakening of superconductivity in the
S-metal near the interface is sometimes referred to as the inverse proximity effect.
The microscopic mechanism responsible for the proximity effect is Andreev reflection.
The schematic of this process is shown in Fig. 2.1. When an electron near the Fermi
energy approaches the S / N interface from the N-side, it cannot find a single-particle
state with the same energy on the S-side due to the energy gap A. If the initial
electron with energy 6 (measured with respect to the Fermi energy) can find a time-
reversed partner with energy —6, then the two electrons can enter the superconductor
as a Cooper pair. The disappearance of the partner can be viewed as creation of a
hole on the N-side, which follows the time-reversed trajectory of the incident electron
in the limit 6 —+ 0.

In a simple language, Andreev reflection can be viewed as penetration of two elec-
trons from N—side to S-side to form a Cooper pair, whereas inverse Andreev reflection
can be viewed as “leakage” of a Cooper pair from S-side to N-side. The two electrons
of the Cooper pair enter N-side with nearly opposite momenta as seen in Fig. 2.2a.
The wavefunctions of the two electrons in N-side remain in phase with each other
for times of order 71/ 6. This translates into the length hop/e in the clean limit or
W in the dirty limit, where v F is the Fermi velocity and D is the diffusion
constant.

Andreev reflection leads to pair correlations in the N-metal near the S / N interface.
At finite temperature, the characteristic decay length of these correlations in the
normal metal is called the normal metal coherence length €N~ In the clean limit it is

given by [13],
6 _ th
N — 27rkBT

 

(2.6)

8

In the dirty limit it is given by,

hD
5N = V —_27rkBT (2-7)

The clean limit here is defined as a regime when l N > f N and the dirty limit is a
regime when l N < 5N: where l N is the electron mean free path in the N-metal. The
spatial extent of the correlations depends on whether the system is clean or diffusive.

At low enough temperatures it can be ~ few microns.

2 . 2. 2 Superconductor / Ferromagnet (S / F)

 

 

 

   

 

 

 

 

'kF

Figure 2.2: (a) 10 free-electron dispersion relation in a normal metal, showing two
electrons that have ”leaked” into N from S (In the Andreev reflection picture, the
electron below the Fermi surface would be shown as a hole). (b) Same situation in a
ferromagnet. In this case there is a shift between the Fermi waueuectors of the two
electrons due to the exchange energy of the ferromagnet.

The main difference between the proximity effect in N / S and F / S systems can
be illustrated using the simplistic model of a ferromagnet shown in Fig. 2.2. On a
microscopic level, 3 Cooper pair is transferred from S to F in the absence of significant
spin-orbit coupling. When a Cooper pair leaks from S to F, the two electrons must

enter opposite spin bands. Due to the exchange energy E833, the Fermi wavevector

9

of the spin—down band is different from the spin-up band. In a Cooper pair, the
electron with spin parallel to the exchange field is decreased in potential energy, and
the electron with spin anti-parallel to the exchange field is increased in energy by the

same amount. The conservation of total energy requires,
’12 kl2 h? k2

: 2Eex (2.8)

 

 

As a result the total momentum of the C00per pair is not zero but is given as
Q = k], — k]? z 2Eex/vp. The order parameter acquires a term proportional to
exp(iQx/h). Fermionic antisymmetry requires consideration of the above pair as well
as the pair which has the down-spin and up-spin electrons interchanged in momentum
space, the latter gaining a center of mass momentum -Q. Now, if one considers the
effect of Cooper pairs incident on the interface at an arbitrary angle 0, then the
net gain of momentum of these pairs will be 2Q/cos 6. In 1D clean limit this leads
to the oscillation of the superconducting correlations. In 3D clean limit, averaging
over all possible angles leads to an oscillation as well as an algebraic decay of the
superconducting correlations, given by sin(x/€F)/(x/£F), where 5 F = hop/2Eem. In
dirty limit in the presence of strong disorder scattering, the superconducting pair
correlations oscillate and decay exponentially as sin(x/{;«)exp(—x/{;~), where f}; =
\/h—D/E—ex [14]. Thus the S/F proximity effect is characterized by a decaying, but
oscillating, order parameter. The characteristic decay length of these correlations in
the ferromagnet is called the superconducting coherence length in ferromagnet and
is given by 5 F in the clean limit and 5} in the dirty limit. For strong ferromagnets
such as Fe, Co or Ni, the large exchange energy causes the coherence length 6;. to be
around 1 nm in the dirty limit, whereas in weak ferromagnets the coherence length
can be relatively longer ~ few nm. Thus the proximity effect in S/ F systems can

be considered to be an extremely short ranged effect in comparison to the proximity

10

effect in S/ N systems.

2.3 Short Range Correlations

Although the penetration depth of the superconducting pair correlations in F-metals
is small, the physics of the proximity effect is S / F structures is not exhausted by this
suppression. In fact, the oscillatory nature of this short ranged proximity effect has
been reported to give rise to very interesting effects is S / F experiments. For example,

these oscillations are known to result in,

o Oscillation of critical superconducting temperature (Tc) as a function of F-layer

thickness (dp) in S/F structures [15, 16, 17, 18, 19, 20].

o Oscillation of Josephson critical current as a function of F-layer thickness [21,

22, 23, 24, 25, 26, 27, 28, 29, 30].

o Oscillation in the sign of the proximity effect corrections to the density of states

(DOS) [31].

However interesting may be the effects seen in the above experiments, the short
ranged nature of the S/ F proximity effect in these systems is a well known and an
extensively studied area. Studying these effects therefore was not the prime goal of
our project. Our interest in S / F systems on the other hand stems from an exotic
long-range proximity effect that is predicted to occur in such systems under certain

conditions. The next section will describe more about this effect.

11

2.4 Long Range Triplet Correlations (LRTC)

2.4.1 What are LRTCs?

A new exotic type of proximity induced superconductivity is predicted to occur in
S / F systems in the presence of magnetic inhomogeneities and is called “odd-triplet
superconductivity” [9, 8]. This type of superconductivity, causes a long-range prox-
imity effect which is not governed by the strength of the exchange field but is only
limited by the temperature and could be as long as that in the case of S / N systems.
The long-range proximity effect occurs in S / F systems only under certain condi-
tions. In the case of homogeneous magnetization in F-layer only a singlet component
(3 = 0, m = 0) and a short range triplet(s = 1, m = 0) component of the pair correla-
tions arises in the structure. These components decay very fast in the F-layer because
the strong magnetization makes the spins of a pair to be parallel to each other, thus
destroying the superconducting correlations over the length, figmglet = W in
dirty limit. However in the case of inhomogeneous magnetization in F-layer, alongside
with the singlet component, all types of triplet Cooper pairs arise (s = 1; m = 0, 21:1).
The components with s = 0, m = :l:l can penetrate longer distances in a ferromagnet
since both electrons in the Cooper pair can enter the same spin band in the ferromag-
net. In addition, the superconducting correlations with non—zero orbital momentum
are generally sensitive to disorder, whereas the s-wave (l = 0) nature of such triplet
correlations should be robust even in the presence of disorder (according to Ander-
son’s theorem). This component (3 = 1,m = i1 and l = 0) therefore penetrates
much longer distance in ferromagnet, over the length, {griplet = W in dirty
limit and is referred to as Long-Range Triplet Component ( or correlations), LRTC.
According to the spin-statistics theorem of quantum mechanics, two spin half
particles, i.e. fermions, should have a wavefunction that is antisymmetric under

the exchange of particles. Conventional BCS superconductivity is attributed to spin

12

singlet correlations (antisymmetric spin part) which obey this fermionic antisymmetry
by being even in orbital angular momentum state (l = 0). Similarly there exists a
‘p-type’ superconductivity that is attributed to triplet correlations (symmetric spin
part) and which obeys the fermionic antisymmetry by being odd in orbital angular
momentum state (l = 1). This is seen in materials like SrgRuO4 and UPt3. The
odd nature of triplet superconductivity we are studying here, lies in pair correlations
that have an even orbital angular momentum (l = 0) while still being spin triplets
(s = 1,m = 21:1). This may seem like a violation of the Pauli exclusion principle
which demands an overall antisymmetry of the wavefunction. However it turns out
that the Pauli exclusion principle is not violated, because the overall antisymmetry
of the wavefunction in this case is maintained by pair correlations that are odd under
time reversal and hence the name “odd—triplet superconductivity”. The blank boxes
in Table 2.1 indicate the “rare” cases that are allowed only if the pair correlations are

odd under time reversal.

 

[ [ s=0 (antisymmetric) I 321 (symmetric) ]

 

 

0 BCS superconductors —
l=1 — SrRuO4
2 High-Tc superconductors —

 

 

 

 

 

 

 

Table 2.1: Combinations of 2-particle fermionic correlation functions allowed by the
exchange symmetry. The blank combinations are not allowed normally, but they be-
come available if pair correlations are odd under time ( or frequency)

2.4.2 A Simplified Picture of Triplet Generation Mechanism

The following section gives a simplified picture of the triplet generation mechanism.
This however is not a rigorous derivation, but is a mere attempt in explaining the
importance of non-collinear magnetization or magnetic inhomogeneities in the gener-
ation of long-range triplet correlations.

As discussed earlier, when a Cooper pair enter a ferromagnetic region, it acquires

13

 

Figure 2.3: A ferromagnet(F1) placed next to superconductor generates spin-
singlet{s = 0, m = 0) as well as short range spin-triplet (s = 1,m = 0) correlations in
the system. In presence of magnetic inhomogeneities (shown by a second ferromagnet
F2 with a rotated magnetic moment), rotation of short range spin-triplet component
into long—range triplet—components (s = 1,m = :l:1)

a center of mass momentum Q. The fermionic antisymmetry requires us to consider
this pair along with a pair which has down spin and up spin electrons interchanged in
the momentum space [14] with a center of mass momentum —Q. One can therefore

write down the following wavefunction,

IXm) = {/3 expense)! n) — emu—low)! m] (2.9)
le) = cos(Qx)(li>7__2-Il—T)—) + i sin(Qx)g—T£>7+§I—lD—) (2.10)

le> is not the full wavefunction. It only shows the spin part and the center of mass

part. If x1 and x2 are the co—ordinates of two electrons, then x = (x1 + x2) / 2.

For two spin-1/2 particles one can also use eigenstates of total spin and its 2-

14

component ,

M) = (I u) + I mwi (2.11)
I0,0> = (I n) — I iT>)/\/§ (2.12)

One can rewrite the Eqn. 2.9 as follows,

le) = cos(Qx)|0, 0) + isin(Qx)|1, 0) (2.13)

The above shows that in case of homogeneous magnetization in the F-layer, not
only spin-singlet correlations (s = 0, m = 0) but also short-range triplet correlations
(s = 1, m = 0) are generated by the virtue of exchange field. This can be explained by
the schematic shown in Fig. 2.3. The F1 layer in the figure represents the ferromagnet
with homogeneous magnetization, whereas the F2 layer represents the ferromagnet
with inhomogeneous magnetization. The presence of homogeneous ferromagnet F1
induces spin-singlet as well as short-range triplet correlations. However, it is this
s = 1, m = 0 triplet component that in the presence of non—uniform magnetization
gives rise to long-range triplet components (3 = 1, m = :I:1). This inhomogeneity
is provided by a different orientation of magnetization, present either in the same
ferromagnet or provided artificially by placing a separate ferromagnet with different
direction of magnetization (as shown by layer F2 in Fig. 2.3). To understand the
role of short range triplet component and the magnetic inhomogeneities better, let us

consider the rotation matrix for total angular momentum j = 1 case,

%(1+cosfi) ——‘}—-2-sin6 %(1— cosfi) l
R(5) = 63919 (—z;y8) = fi Sinfi cosfi —71§- sinB (2.14)

%(1—cosfi) sinB %(l+cosfi)

 

 

 

SI”

15

The components 3 = 1, m = 0, :l:1 can be written down in the matrix form as follows,

 

 

 

 

 

 

 

 

 

 

 

 

' T
I
l1,1) = | TT) = 0 (2.15)
0
- 0 .
M) = (I n) + I lT>)/\/§= 1 (2.16)
0
. 0 -
I1,-1>= Ill) = o (2.17)
1
Consider rotation of the state [1, 0) gives,
.0. -%(1+cosfl) —%sinfi %(1—cosfi)q p0-
B(5) 1 = fisinfi cosfi —%sinfl 1 (2.18)
0 %(1—cosfl) -\}—§sinfi %(1+cosfl) _0_
- O I ' —%sinfi -
3(5) 1 = cosfl (2.19)

 

 

 

 

0 71§sin5

 

 

 

 

 

 

 

 

'01 -—1/\/2- P11 ’0]
RM) 1 = 0 = n}; 0 +713- 0 (2.20)
0 1N2 0 _1

16

From above, one can see that under rotation the triplet components (3 = 1, m =
0, 21:1) transform amongst themselves just like the three components of a vector. The
presence magnetic inhomogeneities in S / F systems serves as a mechanism that causes
the rotation of short range triplet component (3 = 1, m = 0) into long-range triplet
components (3 = 1, m = :lzl).

It is instructive to notice that the Eqn. 2.10 has a symmetric and an antisymmetric
spin part, according to Pauli exclusion principle the overall antisymmetry of the total
wavefunction is satisfied by a conjugate antisymmetric and symmetric spacial part
respectively. However, this is not necessarily true since the Pauli exclusion principle
can also be satisfied by demanding that both the spacial and spin part have an
identical symmetry (either both even or both odd) under the interchange of particles,
and that the fermionic antisymmetry is respected by being odd under time reversal
(or odd in frequency). A detailed theoretical analysis is beyond the scope of the

simplified picture explained above and needs to be worked upon in the future.

2.4.3 Previous Experimental Hints of LRTC

This phenomenon of LRTC as described above cannot be expected from the simple
picture of a superconductor in contact with a ferromagnet. As we said before, LRTCs
are predicted to occur only when the exchange field is not homogeneous. However
in 1990’s, much before this prediction, three groups observed an unexpected decrease
of the resistance of a micron sized ferromagnetic wire attached to a superconductor,
when the temperature was lowered below the superconducting transition temperature
To [7, 5, 6]. Given the short-range nature of spin-singlet correlations, this long-range
proximity effect was initially a surprise and was attributed to anomalous interface
effects. However, in later studies theorists [8, 9] pointed out that the long-range effect
in these experiments was a natural outcome of proximity-induced odd spin-triplet

correlations rather than spin-singlet correlations. In addition to these experiments,

17

similar long-range effect were observed by Klapwijk’s group [10] working on S / F / S
Josephson junctions using NbTiN as the S-layer and CrOg as the F-layer. Since Cr02
is a half-metallic ferromagnet (fully spin-polarized ferromagnet), it was considered as
an unequivocal experiment ruling out all the other explanations. However, large
sample-to—sample variations seen in this experiment made it difficult to analyze their
result. Another experiment reporting phase-dependent conductance oscillations of
a Holmium (Ho) wire attached to superconducting electrodes on its both side were
attributed to the presence of triplet correlations [32]. It was believed that the spiral
magnetization in H0 is responsible for triplet correlations.

After the above mentioned experiments, there was a huge surge in the number
of theory papers suggesting possible ways to generate LRTC. In spite of such large
number of possibilities suggested by these papers, it is not only difficult to find new
systems that generate LRTC, but it is also equally difficult to reproduce the results

of the handful of experiments that are mentioned above.

2.4.4 Ways to induce LRTC in S / F Systems

If magnetic inhomogeneities exist one should be able to see long-range effects in the
S / F structures. These magnetic inhomogeneities needed for the generation of LRTC

can be provided by any of the following mechanisms,

1. Intrinsic Inhomogeneity: Intrinsic magnetic inhomogeneities provided by
the domains and/or the domain walls at the S/F interface [8, 33, 34] or the
spiral magnetic order in certain ferromagnets (For e. g. Holmium), are predicted

to result in LRTC. [35, 36, 37, 38]

2. Extrinsic Inhomogeneity: Magnetic inhomogeneities can be induced exper-
imentally by manipulating the multilayers such that different F-layers have dif-

ferent directions of magnetization. For example, it has been suggested to use

18

F/ S / F trilayer structures such that magnetization in two F—layers are inclined
at an angle :ta with respect to the z-axis. If the distance between the two
F-layers is less than the superconducting coherence length, {3, then the triplet

correlations can get induced in the central layer. [39]

3. Spin Active Interfaces: Inhomogeneous magnetization can also be obtained
through a spin active interface that allows for spin-flip processes. [40, 41, 42,

43,44,451

2.4.5 Ways to detect LRTC

A reliable experimental signature of induced triplet superconductivity can be obtained

by doing one of the following experiments,

1. By measuring the proximity-induced changes in density of states (DOS). How—
ever since such changes in DOS are extremely small [31], we have chosen not to

use this method for the detection of LRTC.

2. By measuring the Josephson effect in S / F/ S junctions. For all the experiments

described in this thesis, we have chosen to work with Josephson junctions.[10]

2.5 Theoretical Predictions for LRTC ,

A large amount of theoretical work devoted to the study of odd-triplet correlations
uses equations based on the quasi-classical Green’s function formalism that was first
recognized by Eilenberger [46]. In the dirty limit, these equations are simplified
further by Usadel [47] and are therefore known as Usadel equations. There are some
excellent review articles that discuss various types of S / F structures suitable for the

generation of LRTC [48, 11].

19

In some papers, special attention is paid to the nature of the S/ F interface. In
particular a large number of theory papers are devoted to the study of LRTC gen-
erated by the spin-active interfaces [40, 41, 42]. The approach used in these papers
describes the spin-active interface by a scattering matrix, the elements of which are
considered as phenomenological parameters, i.e., in this approach one does not need
to know a lot about the detailed structure of the interface, but one can proceed with
the calculations based on these phenomenological parameters. Materials with large
spin-orbit scattering can be treated as forming a spin-active interface. Also, there is
another point of view which considers an interface with domain walls smaller than the
Fermi wavelength as a spin-active interface. This allows to invoke the quasi-classical
approximation and simplifies solving the problem. This point of View was taken by

various theorist in Ref. [33, 49].

Similarly, there is a huge amount of literature devoted to the study of LRTC
based on the domain structure in the F-layer. In particular, Ref. [8] discusses the
generation of LRTCS in diffusive S / F structures with a Bloch-type domain wall. The
LRTC in Neel-type domain wall was analyzed in Ref. [33] A general case of domain
wall with a width arbitrary with respect to the mean free path and an arbitrary

impurity concentration, was studied in Ref. [34].

The interface transparency has been treated differently in several of these papers.
For example, Braude and Nazarov have studied LRTC in S / F structures with highly
transparent interfaces. This is termed as strong proximity effect. In other papers,
LRTC has been studied assuming weak proximity effect. This assumption allows one

to linearize the Usadel equations which simplifies the calculations [50, 49].

A lot of stress has been laid on generating the inhomogeneities by creating ar-
tificial structures using F / S / F trilayers such that different F layers have different
direction of magnetization. In particular the Ref. [39] studies F/ S / F/ S / F structure

with different magnetic orientation of F and F’ layers. Similarly structures of the

20

form of S/ F / I/ F / S have been analyzed when the magnetic moments in the F-layers
are antiparallel and parallel. A larger critical current is predicted for the antiparallel
case than the parallel case [11]. In addition, the critical current in antiparallel case
was found to be larger than for the case without any ferromagnets, indicating that
ferromagnetism can enhance critical current [51]. Also, diffusive Josephson junctions
of the form of S/ F/ F’ / S are studied in Ref. [52, 53]. Since it is not possible to have
Josephson current due to the interference between the singlet and triplet components,
two sources of triplet components are needed in Josephson junctions to observe the
long-range Josephson effect. Accordingly the long-range Josephson effect is not pos-
sible in Josephson junctions with only two F-layers. This led two groups to suggest
the geometries of the Josephson junction of the form S/ F’ / F/ F” / S [54, 49]. We find
this geometry most relevant to our triplet experiment discussed later in Chapter 6.
Temperature dependence of the LRTC has also been studied by some papers for
the triplet case [40, 41, 50, 49]. The nature of triplet dependence is sensitive to
the relative magnitudes of various energies. If Egg; > EF, anomalous temperature
dependence is expected, whereas standard temperature dependence is expected if
Eex < E F- However, a few experiments performed in this category do not seem to

follow these predictions.

2.6 Josephson Junctions

2.6.1 Definition

A Josephson junction consists of two superconductors separated by a non-superconducting
layer which is so thin that electrons can tunnel through the barrier. A number of
interesting phenomenon occur in such a junction. The simple analysis given in the
following section is taken from The Feynman’s Lectures on Physics- Volume III.

Consider a macroscopic superconducting wavefunction, 7,01, as a common wave

21

function of all the electrons on one side, and 2122 as the corresponding wavefunction

on the other side. These superconducting wavefunctions satisfy the Schrodinger equa-

tions,
2'77. (%) = Eula + KI/Jg (2.21)
if}. (gal-biz) = 1321/12 + K1491 (2.22)

where, E1 and E2 are ground state energies of two superconductors, and K is a real
coefficient that describes the coupling between two superconducting wavefunctions.
If a constant potential difference V is applied between the two superconductors, the

ground state energies are shifted such that,
E1 — E2 = e*V (2.23)

where, e* = 2e is the charge carried by a Cooper pair. For the ease of calculations
let us redefine the zero of energy mid-way between E1 and E2, then the shift caused
by applied voltage is such that E1 = eV and E2 = —eV. The resulting Eqns. 2.21

and 2.22 can be re-written as,

. 51/11

m (951?) = —eVzl)2 + mm (2.25)

€V¢1 + K 1/42 (2.24)

Substituting the superconducting wavefunctions of the form, 1121 = [#21] exp(i61) and

$2 = [102] exp(i62), where 01 and 02 are the macroscopic phases in superconductor 1

22

and 2 respectively; and separating the real and imaginary parts one gets,

 

 

 

71% = 2K|¢1||1I92| Sinso (226)
hey" = -2Klvlllv2|sinr (2.27)
% = -—K 31% cosp — eV (2.28)
(3:72— : —K -::—: 00890 + eV (2.29)

 

 

where we have used (,0 = 62 — 61. The current densities flowing into each supercon-

ductor are given by,

 

_ all/M2
J1 — 2e at (2.30)
_ 5|¢2|2
J2 — 2e at (2.31)
h=—h=h am)

If we substitute the density of Cooper pairs in each superconductor equal to p0, i.e.

|¢1|2 = |zp1|2 = p0 and JG = 2622”” ”w ' av. 2e3‘fi/L0. Equation 2.26 and 2.27 yield

the first Josephson relation,

J3((,o) = Jc sincp (2.33)
Equation 2.28 and 2.29 yield the second Josephson relation,

ago V

2.6.2 Resistively Shunted Junction (RCSJ)

The first Josephson relation gives the current-phase relation for a Josephson junction,

Is = 10 sin (,0 (2.35)

23

where [C is the maximum supercurrent that a junction can withstand. According
to this equation, the applied current controls the phase-difference between the two
superconductors. For I < 10, the phase-difference stays constant, but for I > IC, a
voltage V appears across the junction as the phase evolves according to the second
Josephson relation,

, _ 2:): _ 27rV

h _ <I>o (2.36)

 

A typical I-V characteristics of a Josephson junction is shown in Fig. 2.6b. Even

 

. . .l .
T

 

Figure 2.4: The equivalent circuit of RCSJ model. The cross in the figure represents
Josephson junction (J J )

a high quality tunnel junction sometimes shows a hysteretic I-V characteristics. For
most of the practical applications of a Josephson junction it is important to elimi-
nate the hysteresis, which is done by shunting the junction with an external shunt
resistor. The resulting circuit is called Resistively Shunted Junction (RSJ) model.
The equivalent circuit of RCSJ model is shown in Fig. 2.4. The self-capacitance of
the junction is indicated by the capacitance C. If one assumes a current noise I N(t)

associated with the resistor, the resulting equation of motion is given by,

CV + 316+ 1, sin ,0 = 1 + IN(t) (2.37)

24

Setting V = hgo/ 2e, and ignoring the noise yields,

Ch -- h , . 2e BUJ
where,
(1’0
UJ = %[Ic(1— cos cp) — [(0] (2.39)
UJ = EJ(1— cosp — igo) (2.40)

where <I>o = h/ 2e is the magnetic flux quantum, E J = Ic<I>o/27r is the Josephson
energy, and i = I / Ic. The dynamics of the Josephson junction given by the above
equations is analogous to the motion of a ball of mass m and friction 77 moving on
a tilted washboard potential. Fd is the external driving force that tilts the potential
w(x) [55].

8w(x)
8x

8[w(x) - Fdx]
8x

 

 

mat + 772 = — + Fd = — (2.41)

Comparing Eqn. 2.38 and Eqn. 2.41, one can say that the Eqn. 2.38 represents the
equation of motion of a ball of mass Ch/ 2e moving along (,0 axis and subjected to a
viscous drag force given by (h/2e)2(1/R)d(p/dt. The effective potential experienced
by the ball is given by U J. The form of U J is sketched in Fig. 2.5. One can also
write Eqn 2.38 as,

95 9'9 . . 8w
_ —— = — = --— 2.42
a212, + we 2 Singo 84p ( )
OR
95 90 _ . . __ BuJ
[BCZJg-l-UJ—c —Z—SlI1<p-— —-5:5' (2.43)

25

 

 

 

 

V
V

Figure 2.5: (a) When I < IC, it is a static case where the particle is confined to one
well and it oscillates back and forth with plasma frequency, cop. (b) When I > IO,
the local minima disappears and the phase evolves in time. This dynamic case is
what is associated with a finite DC voltage V across the junction which increases with
increasing bias current.

where, we introduced Stewart McCumber parameter ,BC,

56 = (5)2 = $61ch6” (2.44)
with wp = W as the plasma frequency, wc = (277ICR) / (1)0 as the Josephson
frequency at the characteristic voltage VC 5 [CR and u J = U J / E J as the normalized
potential. In the static case, I < 16, the particle is confined to one well and it oscillates
back and forth with plasma frequency top. If I > [6, the local minima disappears and
the phase evolves in time. This dynamic case is what is associated with a finite DC
voltage V across the junction which increases with increasing bias current.

Overdamped vs Underdamped Junctions
Based on the relative size of cup and we, one can identify two different kind of

Josephson junctions.

o Underdamped Josephson Junctions: When the barrier is an insulator, the

26

(a) (b)
Underdamped ' Overdamped
BC >1 pc<<1

    

 

 

 

 

 

I—o

Figure 2.6: ( a ) I-V characteristics of a hysteretic underdamped junction (fie > 1) (b)
I-V characteristics of an overdamped junction (5c << 1).

junction’s internal resistance is very large. In this case BC > 1 and the junction

characteristic is hysteretic. This is also shown in Fig. 2.6.

o Overdamped Josephson Junctions: When the barrier is conducting, the
effect of the junction’s internal resistance will be large compared to its small
capacitance. In this case BC << 1 and the Josephson effect looks like as shown
in Fig. 2.6b. All of the Josephson junctions studied in this thesis showed

overdamped junction characteristics.

2.6.3 Effect of Magnetic Field

Fraunhofer Pattern for a Circular Josephson Junction

To understand the effect of an applied magnetic field on the Josephson effect, we
will consider a circular Josephson junction with a non-superconducting layer i.e. with
an insulating or a normal barrier. Apply a magnetic field of induction B(x)2 along

the z-axis in the plane of the junction as shown in Fig. 2.7. The vector potential in

27

2A+dNiW Hx,
V
V

 

 

+--. 2R _--_,

Figure 2.7: Circular Josephson junction in a magnetic field. Field applied in the plane
of the junction penetrates the London penetration depth A L into both the supercon-
ductors.

London’s gauge is,

A = -B(x)yx (2.45)

In the insulating layer, B(x) varies only slightly, and so one can consider B (x) 2 8(0).
Whereas, in the superconducting layer, magnetic field decreases as exp(—x/)\L). The

phase difference induced by the magnetic field is therefore given by,

[A Axdx = B(0)yl (2.46)
B

with l = 2/\ L + d, where A L is the London penetration length and d is the thickness of

the insulating layer. The total phase difference across the junction is therefore given

by,

27r A
’7 = A9 + — Axdx (2.47)
(pa B

where A9 = 61 — (92 and (1)0 = h / 2e. The Josephson supercurrent density is therefore

28

given by,

 

J(y )= Jc sin(7 )= JC sin( (A0 + 21/1: Amdx) (2.48)
B
J(y) = Jcsin(A9 + 27:1) yl) (2.49)
The critical current that we measure is given by,
I = /J(y)dydz (2.50)

I = 2 f: (m2 — y2J(y)dy (2.51)

Substituting Eqn.2.49 in the above equation gives,

R 27rB l
I = 4 V 2 — 2 ' A y .
cho R y sm( 6 + (1)0 u)dy (2 52)

For simplification let us substitute u = y/ R,

 

 

 

1
I = 4JCR2/ \/1 — u2 sin(Ab’ + 27:fiuBuMu (2.53)
0 0 .
J1(RlB/<I>0)
I I = .

 

 

where, J1 is the Bessel’s function of first kind and IC = JcnR2. The resulting pattern

is called an Airy pattern, and it is as shown in Fig. 2.8.

29

 

 

 

 

1W-
o.s- -
8 . .
:606- -
E“: i
-°o.2- -
0.0....,,,..-...

524012 3

(D/(Do

Figure 2.8: Dependence of the critical current on enclosed flux for a circular Josephson
junction yields an Airy diffraction pattern.

2.6.4 Josephson Penetration Depth

I C(H ) can be also modeled for non-uniform current flow, which is an important case

when the junction dimensions are greater than the Josephson penetration depth, x\;.

(1’0
A) =
\/27WOJC(2)‘L + 01F)

 

 

(2.55)

If )(J < w / 4, where w is the junction diameter, then the flux is screened from the
center of the junction, and the effect of self field of the current cannot be neglected
[56]. The Ic(H) can become asymmetric, and deviate from an ideal Fraunhofer-Airy

pattern.

2.7 Ferromagnetic O-rr Josephson Junctions

The current-phase relation of a conventional Superconductor / Insulator / Superconductor
(SIS) Josephson junction is given by, Is = Icsingo, where (p = 61 — (92 is the phase

difference between the macroscopic superconducting wavefunction in each supercon-

30

 

 

 

 

 

   

Nb-Co-Nb‘

3 4 5
dF(nm)

 

 

 

Figure 2.9: (a) Oscillatory dependence of critical current density as a function of CuNi
thickness, ( Taken from Oboznou et a1. [26]). (b) Oscillatory ICRN as a function of
Co thickness. ( Taken from Robinson et al. [27])

ductor and Ic is the critical current. The Josephson coupling energy is given by
U = —EJcos<p, where, E J = (Iccp0)/27r is the Josephson energy. For conventional
Josephson junctions the minimum Josephson energy occurs at (,0 = 0. In 1977, Bu-
laevskii et al. [57] calculated the critical current through a Josephson junction with
magnetic impurities in the barrier and predicted a 7r-shift in the current phase rela-
tion for the certain concentration of impurities. The current phase relation of such
junction is then given by I3(<p) = —Icsin<,o = Icsin(<,o + 1r) and the Josephson energy

is given by U = —EJcos(<,o + 71') = E Jcos(<,o), indicating the existence of go = 1r in the

31

ground state. Such a junction is called a n-junction.

The transition from O to 7r state in a S / F / S junction is the consequence of change
in the sign of the oscillating pair correlations in the F layer. This leads to oscillation in
the critical current as a function of ferromagnet thickness. This was first observed by
Ryazanov and his co-workers [21, 26] using a weak ferromagnetic alloy CuN i, and later
by Kontos et al. [23] using another weak ferromagnetic alloy, PdNi. Recently Blamire
and his co—workers [27, 28] have published data showing the oscillatory Josephson
critical current [C as function of F-layer thickness using strong ferromagnets, Ni, Co,
Fe, Py. Figure 2.9 shows oscillatory critical current as a function of F-layer thickness
for the case of weak ferromagnet, CuNi [21], and for the case of a strong ferromagnet
Co [27]. The data clearly show the transitions between the “0-state” and “ir—state”

as the F-layer thickness is increased.

2.8 Domain Structure of Ferromagnetic Interlayer

For quite a long time theoretical studies of ferromagnetic Josephson junctions and
the effect of the exchange field disregarded the domain structure of the ferromagnetic
interlayer. But recently there have been studies on how the domain structure would
affect the junction properties. Throughout the course of this project our idea was
to work with macroscopic samples. We believed that the multidomain structure
in macroscopic samples can provide us the magnetic inhomogeneities necessary for
the generation of LRTC. In this section I will talk about the domain structure in a
ferromagnetic layer.

In a ferromagnet, the exchange energy tends to align the electron spins and hence
the magnetic moments parallel to each other. A magnetized ferromagnetic mate-
rial containing a single domain has a macroscopic magnetization, as shown in Fig.

2.10(a). It causes the block to behave as a magnet with a magnetic field around it.

32

(a) (b) (C)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.10: Reduction of the magnetostatic energy by domain formation in a ferro-
magnet.

This configuration has large magnetostatic energy. The magnetostatic energy can
be reduced by formation of domains as shown in Fig. 2.10(b). This increases the
exchange energy as the neighboring electron spins in the interface between the two
domains cannot point in the same direction. To reduce the magnetostatic energy
further, one needs the magnetic pattern as shown in Fig. 2.10(c). The domains near
the end are called closure domains. Various other contributions to the total energy
such as magnetocrystalline and magnetostrictive energy also influence the shape and

the size of the domains.

The boundaries between the adjacent domains are called domain walls. The width
of the wall is determined by the competition between the various energies. The
exchange energy is optimized if adjacent spins are parallel and so the system tries
to minimize the angle of moments between adjacent planes of atoms, thus forming a
wide wall in which the angle changes gradually. But magnetocrystalline energy tends

to point the magnetic moments along certain preferred directions called easy axes

33

and hence prefers to have an abrupt change in the direction of magnetization.
There are two kinds of domain walls, Bloch walls and Neel walls. In a Bloch wall
the magnetization rotates around the axis perpendicular to the domain wall, whereas
in a Neel wall, the spins rotate around the axis normal to the surface of the film.
This is shown in Fig. 2.11. The existence of one of the two kinds of walls depends
on factors such as magnetostatic energy, thickness of the film, anisotropy of the film,

etc.

(a)

 

 

 

 

 

 

 

gun «I? 1 V
///-+\\\l l 1 x
///—*\\\l l

Figure 2.11: Assume that X—Z is the plane of the film. Schematic of (a) Bloch Wall
and (b) Neel wall.

As the thickness of a magnetic film decreases, the magnetostatic energy of a Bloch
wall that extends through the thickness of the sample increases as a result of free polas
at the top and bottom of the wall. To reduce this magnetostatic energy, the spins
in the domain wall rotate parallel to the film plane. Although this indicates that
Neel walls are more likely in the thin films we are studying, there is no way to know
definitely the exact nature of the domain walls in our sample. Generation of LRTC
in various S/ F structures with Neel and Bloch—type domain walls has been studied

theoretically [33, 8].

34

Thus in a realistic situation, the magnetization of any ferromagnet can be quite
inhomogeneous due to the existence of domains walls. Existence of such inhomo-

geneities can cause triplet correlations to arises in the domain walls and spread into

 

the domains over a distance of the order 5T = \/hD/(27rkBT), as predicted in Ref.
[8]. The correlations are very sensitive to the thickness of the wall. A very thin do-
main wall will cause the magnetization vectors in the adjacent domains to be nearly
collinear and will lead only to the penetration of singlet and short-range triplet com-
ponent. A very thick wall on the other hand causes the magnetization that is nearly
uniform on the scale of superconducting coherence length (£3). It is therefore impor-
tant to have a wall thickness of an order of the superconducting coherence length for

the odd triplet correlations to occur in the superconductor.

2.9 Our Approach

Our primary strategy in the detection of long-range triplet correlations was to create
S / F/ S Josephson junctions and systematically increase the F-layer thickness to the
point where the conventional spin-singlet correlations are exponentially small. If
we observe a supercurrent that continues to persist for thicker F-layers, it will be
a strong evidence of spin-triplet correlations. Since the length-scale of decay for
singlet correlations is different from the length scale of decay for triplet correlations,
one should also observe a clear change in slope as is shown in Fig. 2.12. In the
absence of magnetic inhomogeneities in the F-layer, no LRTC will be generated and
consequently there will be no change in slope. Also, as said earlier, the spin singlet
correlations are known to show an oscillatory behavior of critical current as a function
of F-layer thickness, however no oscillations will be observed when the supercurrent

is dominated by spin-triplet correlations.

35

 

Singlet correlations genvelope)

|C a exp(- dF/F, I:)

Homogeneous M

.an“.'

  
   

\
\. Long range triplet correlations
' \

T
IC or ’5.pr dF/é’; F)

/|nhomogeneous M

 

 

 

—>

Figure 2.12: Our approach for the study of LRTC using S/F/S Josephson junctions.
For small thickness of F—layer, IC oscillates and decays on a short length scale 5F-
For large thickness of F -layer and in the presence of magnetic inhomogeneities, LRTC
takes over and Ic decays over a longer length scale without any oscillations. A change
of slope would be a clear indication of LRTC. In absence of magnetic inhomogeneities
in F-layer only short-scale oscillatory decay will be observed.

36

Chapter 3

Experimental Methods

This chapter will discuss the details of the sample fabrication process. During the
course of this work several different kinds of sample were made - but here, I will
specifically discuss the sample fabrication process used in making Josephson junctions.
As for the GMR samples, the sample fabrication process has already been discussed

in recently published theses [58, 59].

3. 1 Sample Fabrication

The sample fabrication process can be roughly divided into following parts (See

Fig.3.1),
1. Sputtering the multilayer
2. Photolithography
3. Ion milling

4. Silicon monoxide (SiOm) deposition

5. Lift-off

37

6. Sputtering top leads

A 3” Si (100) wafer is obtained from Silicon Quest International. It has a thickness
of around 400 ,um and resistivity of about 1-10 Qcm at room temperature. The wafer
is spin coated with $1813 resist at 4000 RPM for 40 sec and baked at 95°C on a
hotplate for 2 minutes. The resist layer in this step just acts as a protective layer,
protecting the samples against any damage during the wafer cutting process. The 3”
wafer is out then into 0.5” x 0.5” substrates. The substrates are then ultrasonically
cleaned in hot acetone (60 °C) to remove the resist, followed by an ultrasonic cleaning

in alcohol and DI water. The substrates are then blow-dried using nitrogen gas.

Photoresist pillars Ar ions

L Multilayer I Multilayer I l Multilayer [
. L-‘|1__‘ . 1 [ r'..".’LL'l'_‘fl’.E.,é ]

'AJLLALALA‘_ . I [ xLJAdnnh-

a) Sputter S/F/S b) Photolithography C) '0" Mi”

S'°\>‘<I IIIII

 

 

 

Top Nb leads

  

 

 

 

 

'nnm'i'rmj

._.l. "“4L;4llu

 

 

 

 

 

 

 

d) Silicon monoxide e) Lift off 1‘) Deposit top Nb leads
deposition

Figure 3.1: (a) Sputtering Multilayer, (b) Photolithography, (c) Ion milling, (d) 5203,-
Deposition, (e) Lift-ofl', (f) Top-Leads Sputtering

3.1. 1 Sputtering

We use the sputtering method to create a thin film multilayer of S/ F/ S type. Our

sputtering chamber has six gun positions that allow us to sputter six different mate-

38

rials in a single pump-down. Four out of the six gun positions are large triode sources
whereas the remaining two are small magnetron sources. The required sputtering
targets and the target housings are mounted into the chamber as shown in Fig. 3.2.
The sputter confining chimneys are placed over the target housings to avoid any cross
contamination between different targets. A computer controlled rotating target plate
is placed just above the chimneys which either opens or closes all the target positions
simultaneously. Another computer controlled rotating substrate plate (called SPAMA
plate) hangs upside down from the top of the chamber. This substrate plate has 8
substrate-holder positions. The typical substrate holder used for making Josephson
junctions is shown in Fig. 3.3. A metallic multilayer of any desired shape and size can
be made by placing a thin metallic mask (shadow mask) in close proximity with the
substrate. The shadow mask used for creating Josephson junctions is a long rectangu-
lar strip of size 10.10 mm x 0.16 mm. Each substrate holder has a rotating mask that
can be rotated in-situ. This allows us to selectively open a single substrate at a time
while still protecting the rest. The SPAMA plate also has two Sycon Instruments
quartz crystal monitors that are used to monitor the deposition rates prior to depo—
sition of each individual sample. The entire sample cleaning and loading procedure
is done in a Class-100 clean room to avoid any dust particles on the substrate, which
if present could possibly lead to shorts in the multilayer. Prior to the sputtering, the
system is baked for 10—12 hours and pumped for 1-2 days. The base pressure thus
obtained using a CTI Cryo—Torr high vacuum pump is about 3-4 X 10’8 torr. In
addition, a cold trap (Meissner trap) operating at liquid nitrogen temperatures (77
K) is used to freeze most of the water vapor in the system an hour before sputtering.
This achieves a pressure of 2 x 10‘8 torr or better. A capillary tube in contact with
the trap carries 750 - 1000 psi of cold nitrogen to heat exchangers on the substrate

plate, thus maintaining the temperature of the substrate between —30 and +30°C.

After achieving the desired base pressure, argon gas is slowly leaked into the

39

 

Figure 3.2: The sputtering chamber showing sir: gun positions- four of them are large
triode sources whereas the remaining two are small magnetron sources. In order to
avoid the cross contamination, the plasma is confined using chimneys.

 

Figure 3.3: This figure shows a typical substrate holder and a mask used in the Sput-
tering chamber. The substrate holder {shown on the right-hand—side) has two sample
positions, only one sample is opened during the sputtering using the rotating mask
{shown on the left-hand-side).

chamber at a rate enough to maintain the pressure at about 2.5 x 10‘3 torr. The
sputter guns are then turned on and stabilized for 25-30 minutes. A side cross-

sectional view of typical sputtering gun set-up is shown in Fig.3.4. Once the current is

40

passed through the tungsten coil, the magnets confine and direct the flow of electrons
towards the anode. On their way to anode, the electrons strip the Ar gas atoms of
the orbital electrons thus ionizing the gas and creating a plasma close to the target
to be sputtered. Once the plasma is stabilized, a large negative voltage is applied to
the target. This causes the positive ions of Argon to accelerate towards the target.
This high-speed bombardment of Argon ions causes the sputtering (ejection) of target
atoms. The resulting material gets deposited on the substrate when both the target
plate and the mask of the substrate holder are opened and when it is sitting right

above the desired target.

Magnetic confinement shield Aluminum gun housing
Ar Plasma
Ar —> Target material
——>

 

 

 

Tantalum filament

Anode

Cooling water

Aluminum ring

Figure 3.4: Side cross-sectional view of typical sputtering gun set up, consisting of
filament (cathode), anode, and target. The magnets are placed on the sides ( not shown
here) such that the magnetic field is perpendicular to the plane of the paper.

Special Alloy Targets

When using alloys like PdN i or PdFe, the target material is in itself not an alloy
of desired combination. Special kind of targets were designed for such alloys. A base
target of Palladium was drilled with holes of varied sizes. Ni (or Fe) and Pd plugs

of the right dimension are then inserted into these holes to get the alloy with desired

concentration. One can easily change the concentration of the alloys by replacing

41

some Ni plugs with Pd shots or vice versa. One such specially designed sputter-
target is shown in Fig. 3.5. Our large tn'ode source as opposed to the magnetron
source of any form ensures the uniform mixing of the alloy components when they

reach the substrate.

 

Figure 3.5: The base target is made up of Palladium with Nickel plugs placed into the
holes.

3. 1.2 Photolithography

After sputtering the S/F/ S multilayer, the next step in the device fabrication is a
photolithography process.

What is photolithography? In Greek, it literally means writing on a stone using
light [Photo - light, lithos - stone]. Lithography was invented in 1796 by Aloys
Senefelder. Lithography at that time was an artist’s work. In the scientific world
or in the IC industry photolithography is a process by which geometric shapes are
transferred onto a Silicon chip.

The basic process is shown in Fig. 3.6. It involves coating the substrate with a

photo—sensitive material called photoresist. The photo-resist is then baked at a certain

42

temperature that is characteristic of the kind of resist used. The baking process
drives out the solvent from the resist and makes it photosensitive. The sample is
then selectively exposed using a mask which acts like a stencil with desired features.
The sample is then developed in a developer solution. If the resist belongs to “positive
photo-resist” category, the exposed resist dissolves in the developer leaving the sample
with unexposed resist in desired shapes and sizes. This process creates the circular
resist pillars of varied dimensions on our metallic multilayer. We have experimented
with different kinds of resists during the course of this experiment to find the optimum
resist and the method that best suits our junction fabrication process. Details of this
photolithography process using different resists are given in the Appendix-A. The
resist pillars created in this step act a masks for the next two processing steps—Ion

milling and SiOl- deposition.

 

Spin photo-resist

.0. £232.15;

 

Deep UV exposure

of selective regions W

using a photo mask

F i, After chlorobenzene
soak and Developing

Figure 3.6: Basic steps in the creating resist pillars are- (a) Resist coating, (b) Deep
UV exposure using a photo—mask, (c) Developing in a photodeveloper.

3. 1.3 Ion Milling

After creating the photoresist pillars, samples are loaded into an ion mill chamber.
Base pressure of 2 x 10"8 torr or better is achieved by pumping overnight using

a turbo pump. Ion milling is done at 2 x 10‘"4 torr argon pressure using a 3”

43

Commonwealth Scientific Argon Ion beam source. The resist layer created via the
photolithography process serves as a mask in the ion milling process. Ion milling being
purely a physical process results in a high-resolution anisotropic etching of materials.

Our substrate plate is also equipped with a film thickness monitor. Prior to ion
milling a sufficient amount of Au is deposited on the film thickness monitor, which
later is used to measure the ion mill rate by placing it just above the ion mill gun.
Test samples were made to measure the etch rates of different materials relative to
Au etch rates. Knowing the Au etch rate and the relative etch rates of different
materials, the milling time for our samples could be easily calculated. In order to
avoid shorts due to back sputtered Nb, milling was done only until the middle of the

ferromagnetic layer.

3.1.4 SiOa, Deposition

After ion milling, SiOx deposition is done in the same chamber without breaking the
vacuum. This avoids shorts in the junctions due to exposure of substrates to the dust
particles in air.

During evaporation, 8103; has a tendency of spitting and spalling, which leads
to pinholes in evaporated thin films. To avoid this problem, boats in the form of
“baffled boxes” are obtained from the RD. Mathis Company. The baffled box has
two cavities, of which one contains SiOx crystals and is closed, while the other is
open. When heated, the SiOx travels an indirect path via a series of baffles from the
closed cavity into the open cavity, which then acts like an exhaust chimney for the
vapors. The substrate never sees the bulk material. This avoids particulates from
the vapors and reduces the chance of pinholes in the evaporated thin films. A typical
baffled-box used here is shown in Fig. 3.7.

The SiOm layer acts as an insulating layer that separates the bottom Nb layer

from the top Nb layer sputtered in the end.

44

Exhaust chimney for
SiOX vapors
/

    

Figure 3.7: A typical “bafi‘led-bor” used for SiOm deposition obtained from R.D. Mathis
Company is shown here.

3.1.5 Liftoff

After the resist pillar fulfills its job as a mask during the ion milling and the SiOm
deposition process, it is removed by dissolving it in Remover-PG. This process is called
a lift-off. The 8101; deposition covers the substrate uniformly. To be successfully able
lift off the photoresist pillar, it is important that the lift-off liquid finds a way to
reach the resist pillar. Having a negative resist profile or an undercut (an umbrella
like structure) in the resist profile facilitates the lift—off process. This is also shown

in Figure A3 in Appendix-A.

3.1.6 Top Leads

After lift—off, the substrates are ion-milled to remove a thin layer of top Au (~5 nm).
This step removes the residual—resist and the oxides from the top Au surface. 200 nm
of Nb leads are then sputtered over the pillars using a shadow mask as shown in Fig.
3.8. The layout of the lithographed features is designed such that each lithographed
pillar aligns well with each open window in the top mask. In the end a thin protective

Au layer (15 nm) is sputtered over the top Nb leads to prevent oxidation.

45

multilayer

 

 

\

Shadow mask

SI substrate SiOx

Figure 3.8: (a) The multilayer pillars ( exaggerated sizes) after the lift-off step. (b)
A metallic shadow mask used for the deposition of top Nb. (c) Final sample after
sputtering the top Nb leads on the multilayer pillars.

3.2 Fabrication Issues

A successful photolithography technique is not one that merely yields a successful de-
sign transfer on to the chip, but is one in which resist can be successfully stripped off
after serving its purpose. The prime factors that decide the appropriate photolithogra-
phy process are undercut in the resulting resist profile, uniformity and reproducibility
of the technique used, and sustainability of that structure under various experimental

conditions.

3.2.1 Undercut

Ideally, a single layer photolithography is expected to yield a resist pattern with
straight side walls that are perpendicular to the substrate. However when working
with single chips of 0.5” x 0.5”, the resist accumulation at the edge of the substrate
can be as thick as 30-40 pm. This makes it difficult to make a hard contact between
the substrate and the photomask, thus resulting in resist side walls with positive

slopes. During the process of material deposition, the material gets accumulated on

46

the top as well as on the side walls of the resist, thus leaving no possible pathway for
the lift-off liquid to reach the resist. Special techniques are therefore used to get a good
undercut. The undercut structure protects the resist side walls from the deposited
material (SiOx) and thus facilitates an easy lift-off of the resist (see Appendix A, Fig.
Al-A3).

3.2.2 Back Sputtering

*7 [iflum
10 RV 15.0:1‘m x ll 0mm \fLUl

 

Figure 3.9: ( a ) The resist pillar before ion milling, ( b ) Back-sputtered material accu-
mulated at the edge of a resist pillar (picture taken after an attempted lift-017‘).
During the ion milling process back-sputtered etched material can land on the
side walls of the resist pillars and render it difficult to be dissolved in the liftroff
liquid. Fig. 3.9 shows an SEM picture of the back-sputtered material at the edge of a
resist pillar after the lift-off process. Using an ultrasonic process during lift-off helps
in breaking off the back-sputtered material but is not guaranteed. Usually having a
large undercut solved the problem of hardened resist edges. In addition, special care
was taken to avoid etching the bottom Nb—layer, which if back-sputtered could lead to
a short-circuit in the Josephson junction. In all the samples made during our studies,
the etching process was discontinued after etching halfway through the ferromagnetic

layer.

47

3.2.3 Dust particles

   

Sputtered Multilayer

Figure 3.10: (a) Dust particles seen as seen the dark field under optical microscope.
(b) A multilayer strip with dust particles.

A dark field image of samples that were not processed in the cleanroom showed
dust particles as seen in the Fig. 3.10 below. This was a big step in realizing that the
dust particles were the major cause of shorts in multilayers made during the initial
stage of our project. After this finding, all our samples were processed in a Class-100

cleanroom.

3.3 Reactive Ion Etching (RIE)

One of the ways to etch materials is to use reactive ion etching (RIE) process. RlE
uses a chemically reactive plasma to etch the materials. Purely physical etching
processes like ion milling are anisotropic, whereas chemical etching processes like wet
etching are highly isotropic. RlE implements both chemical as well as physical etching
of the sample. Physical anisotropic etching processes like ion milling yield ideal sharp
features, however such processes are not material sensitive which make the end—point

determination difficult.

48

We use a PX—250 Plasma Etcher for the RIE process. It is equipped with a solid
state RF generator with a fixed frequency of 13.56 MHz. The chamber consists of
three Aluminum plates; the center plate acts as a powered shelf, whereas the outer
two act as ground shelves. Plasma is generated under low pressure (vacuum) by an
electromagnetic field. High-energy ions from the plasma attack the wafer surface and
react with it. Since RIE is a chemically sensitive process, different gases can be used
to etch different materials. For example, SF6 gas is used to etch Nb. Prior to the
actual etching process, the chamber is cleaned by running an oxygen descumming
process. In the descumming process, oxygen is bled into the chamber and a pressure
of 500 mtorr is obtained. RIE is turned on for 10 min with an applied power of 300 W
to clean the resist debris and the other organic impurities in the system. The sample
to be etched is then loaded on the powered shelf and the system is pumped to its
base pressure. In order to ensure complete removal of impurity gases in the system,
it is then purged with SF6 gas and pumped again. This process is repeated 2-3 times
prior to the actual etching of the sample. For the actual etching process, SF6 is bled
into the chamber at the rate of 50 sccm (220 mtorr). RIE is then turned on with
a power of 65 W and the etching is performed for a fixed amount of time. After
several etching attempts, we found that the etch rates varied from sample to sample
as well as from run to run. Currently our RIE system is equipped with an ordinary
mechanical pump that allows us to reach a base pressure of only about 20 mtorr. The
possibility of contaminating gases in our system cannot therefore be ruled out. We
believe this as a possible reason for our process inconsistencies. Although it is hard to
identify the source of the polymeric residues found on our samples, we suspect them
to be the reaction bi—products of the silicon substrate. In future, a better vacuum
pump and use of quartz substrates instead of silicon substrate could possibly help in
solving the current problems. However, due to the absence of any consistent results

with the current set-up, we decided not to pursue this etching method any further.

49

3.4 Magnetic Force Microscopy (MFM)

In our search for odd triplet superconductivity in SF S systems, it was essential to
search for appropriate ferromagnetic materials that have inhomogeneous magnetiza-
tion. In as-deposited thin ferromagnetic films, the magnetic inhomogeneity could
arise due to rotating magnetic moment in the domain walls or due to inhomogeneous
spatial variation of the magnetization in adjacent domains. The length scale of these
inhomogeneities is not known a priori, however various techniques can be used to
probe this information. In order to understand the magnetic structure of the ferro—
magnetic materials, we choose to do Magnetic Force Microsc0py (MFM). MFM is a
technique which gives an image of magnetic structure of the sample surface. It is a
form of atomic force microscopy where a sharp magnetic tip is used to scan the sur-
face of the magnetic sample. The image taken contains information about both the
topography as well as the magnetic structure of the sample; which effect dominates
depends on the sample-tip separation. The strong magnetic forces that reflect the
magnetic structure of the surface persists for greater tip-to-sample separations than

the weaker van der Waals forces that give the topographic image of the surface.

In a standard AFM operating mode that gives the topography, the cantilever
is operated near its resonance frequency. The vertical position of the scanner that
corresponds to constant oscillation amplitude of the cantilever is stored to form the
topographic image of the sample surface. Tip-sample interaction is maintained by
using a feedback that keeps the oscillation amplitude constant. The resulting variation
in the tip height forms the topographic image of the sample surface. On the other
hand in MFM mode, the phase of the oscillation is measured while keeping the tip
height at a constant but larger value than that of the previous scan. Typically each
single line scan is first made in topographic mode, which is then followed immediately

by a MF M mode scan. The information obtained in the topographic scan mode is

50

used to maintain the constant but longer tip-sample distance in the MFM scan mode.
This prevents breaking of the tip due to strong magnetic tip-sample interaction while
still exploiting the long-rang nature of magnetic forces. The phase shift thus detected
can be solely attributed to magnetic interaction between tip and sample. Most of
the scanning probe microscopy techniques are based on the force or force derivative
detection. If the Etip— sample is an energy of the tip-sample interaction, the force on

the tip is given by:

F = VzEtip—sample (3-1)

In MFM, the phase shift is proportional to the gradient of the magnetic force in the
vertical direction,

A 90 (X sz 0‘ VgEtip—sample (3'2)

MFM was done using the cantilevers with magnetic Co-Cr coating (NSCl3/Co—Cr)

Lowpass

 

Figure 3.11: An MFM image of 7 nm thick Ni layer using a magnetic Co-Cr coated
MFM tip.

51

obtained from MikroMasch. Fig. 3.11 shows the MF M image obtained for 7 nm of
Ni deposited on 40 nm of Nb. Although it was hard to identify the orientation of
magnetization in the domains walls in this picture it was clear that the domain size
was no larger than a half a micron. It was not possible to find the domain wall width
from the MF M study. But our calculations show that the wall thickness should be
about ~12 nm or less in Ni films at 4.2 K.

The currently housed facility allows us to do MFM only at room temperature.
Since weak ferromagnetic alloys of our interest (PdNi, CuNi, etc.) have Curie tem-
peratures that are below room temperature, a low temperature MFM measurement
is necessary for such materials. The other available techniques that are not feasible in
our laboratories include the Bitter method, magneto-optic Kerr method and SEMPA

(Scanning electron microscopy with polarization analysis).

3.5 Measurements

3.5.1 Energy Dispersive X-ray Spectroscopy (EDS)

When a high energy beam of charged particles at 20 keV is focused onto the sample,
the X—rays characteristics of the elemental composition of the sample are emitted.
The elements in a sample can be determined by measuring the energy of X-rays
produced. This technique is called as Energy Dispersive Spectroscopy. Typically
an EDS system is attached to a Scanning electron microscope (SEM), Transmission
electron microscope (TEM) or Scanning transmission electron microscope (STEM).
The EDS system we use here is attached to a SEM system. SEM is used to create
and focus a beam of electrons. A SiLi crystal detector operating at liquid nitrogen
temperature is used to convert the X—ray energy into voltage signals. The signal
is further processed by a pulse processor, analog to digital convertor (ADC), and a

multichannel analyzer (MCA) which is then analyzed and displayed on the computer.

52

We have performed systematic EDAX measurement studies for weak ferromagnetic

alloys like PdNi and PdFe.

3.5.2 Magnetic Measurements

 

 

Amplifier Integrator

 
 

 

  
   

Lock-in
Detector

 

Oscillator 6

 

 

 

Shield

 

 

 

Figure 3.12: Superconducting pick-up coil couples the external flux to the input ter-
minal of the SQUID. The SQUID acts as a linear current to voltage convertor. The
magnetic moment of the sample causes the current variation in the detection coil Lp
which then leads to corresponding variations in the SQUID output voltage.

For all the magnetic measurements we have used a superconducting quantum in-
terference device (SQUID). The commercial system MPMS XL from Quantum Design
provides the temperature in range from 2-400 K and magnetic fields up to 5.5 Tesla.
The sample is mounted in a plastic straw and the measurement is performed by mov-
ing the sample between the superconducting detection coils. If the detection coil were
a simple single or multiple-loop pick up coil (a magnetometer coil), it would be more
susceptible to the environmental noise, i.e. noise due to sensitivity to the tilt in the
earth’s magnetic field, power line noise, RF interference, etc. Therefore the detection
coil in this system is a second order gradiometer. Since magnetic fields fall off quickly
(inverse cube(1/r"3)) with the distance, gradiometers take advantage of the fact that

the field gradient due to a local source will be stronger than the field gradient due

53

to any distant source. The change in flux associated with the coil produces current
that is inductively coupled to the SQUID via an input coil. The SQUID acts as a
linear current to voltage convertor. The magnetic moment of the sample causes the
current variation in the detection coil which then leads to corresponding variations
in the SQUID output voltage. Fig 3.12 shows the dc-SQUID schematic used for our
magnetic measurements. The sensitivity of the instrument was better than 1x10—8
emu. By changing the externally applied field, the magnetic moment of the sample
changes, thereby causing a change in the SQUID response. This allows us to mea-
sure magnetization as a function of applied field (M vs. H). Measurements can be
performed at any set temperature in the range from 2—400 K. In order to mimic the
actual growth condition in Josephson junctions, most of the ferromagnetic thin films
used for the magnetization study were also grown on thin niobium films. Care was
taken to avoid the diamagnetic contribution of Nb by measuring these samples at

temperatures higher than the superconducting transition temperature of the Nb.

3.5.3 Resistivity Measurements

The Josephson junctions studied in this work had lateral dimensions in the range of
10—40 am with their resistances varying in the range of 9-150 ,uQ. They require an
extremely sensitive low noise measurement technique which is provided by a SQUID.

Our sample is mounted on a Quick dipper probe, which is a long stainless steel
metallic probe consisting of a sample holder with four probe leads, a superconducting
magnet, a SQUID detector and a persistent switch. All the measurements are done
at 4.2 K by dipping the Quick-dipper (QD) into a liquid helium dewar. Our SQUID-
based resistance measurements rely on a “current-comparator” circuit which is shown
in Fig. 3.13. The voltage sensitivity of our set up was about 1 pV. A small DC current,
1,, (Imam: 100 mA) is passed through an unknown sample with resistance R3. The

current through the reference resistance (Rgef) is varied via the feedback circuit so as

54

 

 

 

 

Low noise DMM
current A Voltmeter
source

 

 

 

 

 

 

 

 

 

 

 

% be

Transformer

 

 

 

 

RS Rref

 

 

 

Figure 3.13: Schematic of the SQUID based current-comparator circuit used to mea-
sure resistances in the pi) range.

to balance the SQUID-based potentiometer setup. The voltage across the feedback
resistance is recorded. The sample resistance can then be calculated by using the

relation,

_ V0 Rre f
Rs .- (Is) (be (33)
Where V0 is the feedback output voltage of the SQUID electronics, R¢ef=95 a!)
is the reference resistor, R fb=10 k9 is the feedback resistance. Every sample has

six Josephson junctions. Since all the Josephson junctions have a common bottom

Nb layer, in order to measure any single pillar it’s imperative to have three working

55

 

0” I(+) V(+) I(-) V(-)

Di Era 1" f3

A ,

 

Figure 3.14: (a) Schematic of a S/F/S Josephson junction. (b) The critical current
measurement of a single Josephson junction (#1) in fact requires us to make the lead
connections to two of it ’s neighbors {#2 and #3).

pillars on the sample. The Fig.3.14 shows the lead connections made to the three
pillars. The contact to be measured (Pillar #1) is connected to both the current (1+)
and the voltage lead (V+). The second contact (Pillar #2) is connected to another
current lead (I-) and the third contact (Pillar #3) to another voltage lead (V-). The
current flows from contact 1 to contact 2 without creating any voltage drop across the
contact 3. Since Nb is superconducting at the temperatures we measure, the voltage
leads measures only the drop across contact #1. The leads can be permuted so as to

measure all the junctions on the sample.

3.5.4 Temperature Variation Measurements

A few experiments during this course of work were carried out to measure the critical
current variation of the Josephson junction as a function of temperature.
The sample is mounted on the quick dipper rod as shown in Fig. 3.15. A vacuum-

can is then sealed over the sample and pumped using a mechanical pump. The can

56

 

 

 

 

 

 

 

 

 

,, iii“ T° Pl‘mp I: mania He
__________ [i fl { were.
..... [I //\,/ Vapor lock
Vacuumican 77777 — fl CUP—QR pot

Sam le ' ' _
/ P

H
\

 

 

{substrate

 

 

 

Exchange gas
Ar+H2
/

 

 

 

 

Figure 3.15: Schematic of low temperature measurement set-up. Measurements can
be performed for the temperature range of 1.6-8.5 K.

is then filled with exchange gas containing Ar (90%)+ H2 (10 ‘76). The exchange gas
acts as a heat exchange medium between the sample holder and the liquid helium
outside the vacuum-can thus decreasing the temperature of the sample holder by the
mere heat exchange process. A magnet and a heater is mounted by sliding them over
the vacuum-can such that sample sits right in the middle of magnet. This heater
is used during the dipping process to avoid freezing of the exchange gas. The 1K
liquid He pot is then pumped and filled with He gas just before dipping the probe
in liquid He so that the positive pressure prevents the air from entering the pot via
the capillary connection to the He bath. When inside the liquid He, the 1K pot get
filled with liquid He, and sample is at the liquid He temperature (4.2 K). To get the

57

temperatures lower than the liquid He temperature, the 1K pot is pumped. As the
vapor pressure of the liquid He decreases, the temperature decreases. Temperatures as
low as 1.6 K can be achieved by pumping on the liquid He. To work at temperatures
higher than 4.2 K, a vapor lock is Operated at the end of capillary connected to the
1K pot. This prevents the flow of liquid into the 1K pot. A balanced pumping and
heating is used to achieve the desired temperature. Temperatures as high as 9 K can
be achieved using one heater or as high as 20 K using two heaters. We have used this
system to study the temperature dependence of the critical current for our S/ F/ S

Josephson junctions.

58

Chapter 4

Spin-Singlet Superconductivity

When dealing with a fairly new physics problem, it is important to be able to sepa-
rate out the known physics issues from the new unknown physics issues. Since this
was our first experience working with Josephson junctions, we realized that it was
important for us to establish a standard procedure that guarantees reliable Josephson
junctions. In the past Ryazanov [21, 26] and his co—workers have extensively worked
on Superconductor / Ferromagnet / Superconductor (S / F / S) Josephson junctions using
a weak ferromagnetic CuNi alloy. Their work, apart from being a pioneering work
in the S/ F physics, has shown I-V characteristics and Fraunhofer patterns that are
identical to the standard S / N / S (N—Normal metal) Josephson junctions. We therefore
decided to take the plunge into this field by creating S/ F/ S junctions using a CuNi

alloy and compare our results with those of Ryazanov.

4.1 CuNi Josephson Junctions: (Nb/CuNi/Nb)

4.1.1 Characterization of CuNi Josephson Junctions

Our CuNi sputtering target consists of a 5.6 cm diameter target of pure Cu with

several 6 mm diameter Ni plugs inserted into the target. This sputter target looks

59

identical to the one shown in Chapter 3, Fig. 3.5. CuN i alloys have been intensively
studied in the past, and are known to show a transition from paramagnetic to fer-
romagnetic behavior with the increasing concentration of Ni. The past experiments
have shown that the alloy is ferromagnetic for concentrations greater than 44 % [60].

EDAX measurements on our sample indicated Ni concentration of 52 i0.5%.

 

 

 

 

 

  
 

 

 

 

25
A 6
Z 3
20- a) 0-
Es
e s
A15‘ > -1'o-5 0 51'0
< Current(mA)
E
v 10-
_o
5.
0- . . . j
-20 -1O 0 10 20 30

H ext (0e)

Figure 4.1: Critical current I0 vs applied field He“ for Nb/C'uNi/Nb Josephson junc-
tion with dCuNi=16 nm. The lateral dimension of the pillar was 50 am. The inset

shows I-V characteristics for the same junction.

Fig.4.1 shows characteristic Ic vs Hem (Fraunhofer pattern) obtained for a Nb/
Cu0.43Ni0,52/ Nb Josephson junction using Cu48Ni52 alloy. (The inset in Fig. 4.1
shows the I — V characteristic of the junction.) The thickness of CuNi alloy was 16
nm and the lateral junction dimension (diameter of the circular pillar) was 50 ,am.
The extremely low values of critical current at the minima indicate the absence of any
shorts in the surrounding insulator. The qualitative nature of the Fraunhofer pattern
as well as the I-V characteristic seen here is identical to what Ryazanov and co-workers

have seen in Josephson junctions using CuNi alloy of a similar concentration.

60

4.1.2 Magnetizing CuN i Josephson Junctions

Since we were working with ferromagnetic Josephson junctions, we realized that it
was important for us to understand the influence of the magnetic barrier on the
observed Fraunhofer pattern. To study this, we decided to intentionally magnetize
one of our Josephson junctions. Large in-plane magnetic field of 1000 Oe was applied
to magnetize the CuNi layer at 4.2 K. To ensure that there are no trapped Abrikosov
vortices in the Nb, the sample was then raised in the Helium dewar so that the
temperature of the substrate was greater than the Nb transition temperature (Tc)
but less than the Curie temperature (Tam-e) of the ferromagnet. The sample was
then lowered back into the liquid helium dewar and Ic vs Hext (Fraunhofer pattern)
was then measured. We saw that the Fraunhofer pattern of thus magnetized samples
shifts in field to the point where the flux due to an externally applied field cancels

the intrinsic trapped flux of the magnetized layer. This is shown in Fig. 4.2.

To understand more about the observed shift, let us assume the F-layer to have
a uniform magnetization M throughout the junction. The intrinsic magnetic flux in
the junction is then given by, <I> F = 47erFw, where d F is the thickness of the F-
layer and w is the lateral dimension junction (i.e. diameter of the circular junction).
The total magnetic flux (PM through the F-layer is therefore the contribution from

intrinsic magnetic flux (13 F and the flux due to an external magnetic field,

(ptot = 47TIl’Ide + Hext(2)‘L + dp)w (4.1)

Since the field penetrates the London penetration length A L in the superconducting
electrodes on both sides, the effective thickness seen by the magnetic field is 2);, +dF.
The expected value of /\ L for our Nb was 86 nm.

When the sample is completely magnetized by applying a magnetic field in the

positive direction, the observed peak of the Fraunhofer pattern shifts in field to a

61

 

 

 

 

 

 

 

-45 -30 -1 5 0 1 5
Hex, (0e)
Figure 4.2: Critical current 10 vs applied field He“ for Nb/CuNi/Nb Josephson junc-

tion with dCuNi =16 nm. Black Triangles: Virgin State, Red Circle: After magnetiz-
ing, Blue Ttiangles: After demagnetizing sample

point where the flux due to the external field cancels out the flux due to the intrinsic
magnetization of the CuNi layer. This shift in the field can be calculated from the

above equation by setting <I>t0t=0.

47erF

HShift = __
(2AL+dF)

(4.2)

Fig. 4.2 shows 30 Oe shift in the Fraunhofer peak when CuN i is magnetized. Using
the observed shift, one can then calculate the remnant magnetization (M R) in the
junction using Eqn. 4.2. The M R thus calculated from the observed shift was 32
emu/cm3. This value is much larger than the M R of 10 emu/cm3 seen in M vs. H
measurements for an identical thickness of ferromagnet. This discrepancy may arise

because the samples used in the M vs. H measurements were grown on a thin Cu layer

62

~ 5 nm rather than on a thick Nb layer. We also observed that upon demagnetizing
the sample, the Fraunhofer pattern returned close to its original position.

It is important to notice from Eqn. 4.2, that even in an absence of external
magnetic field, the trapped flux in the junction can cause the Fraunhofer pattern to
shift. This can cause the maxima in critical current to occur at non zero magnetic
fields. Such a shift is also apparent in our virgin state Fraunhofer pattern seen in Fig.
4.2.

Our data were consistent with the work done by Ryazanov [61, 21], and this clearly
demonstrates that our Josephson junction fabrication process is sound and reliable.
Despite the excellent nature of the junctions, CuNi alloy was used only to test the

device reliability.

4.1.3 Disadvantages of CuNi Alloy

Many groups have successfully studied S / F / S junctions using weakly-ferromagnetic
alloys to reduce the exchange energy and consequently increase the characteristic
coherence length ép. Although using weakly ferromagnetic material allows us to
increase the thickness of the ferromagnetic material, such alloys suffer from strong
spin orbit and/or spin-flip scattering which is likely to destroy both the spin-singlet
and spin-triplet correlations. In the past, Ryazanov and his co—workers [26] have
worked with Cu47Ni53 and found that the Josephson supercurrent in the CuNi layer
decays over a length scale of only 1.4 nm. They also found that the supercurrent
oscillates on a length scale of 3.8 nm. The fact that the length scale of decay is
smaller than the length scale of oscillations indicates strong spin-flip scattering in
this alloy [62, 63, 14, 33]. Several such experiments have been performed by other
groups using weakly ferromagnetic alloy [22, 23, 64, 24]. Although no long range
triplet corrections were seen, these experiments have successfully studied the 0 — rr

transition of the critical current as a function of the F-layer thickness.

63

4. 2 PdNi Josephson Junctions (Nb / PdNi / Nb)

As discussed in the previous section, there is strong spin-flip scattering in CuNi alloy
[21, 26] which makes it an unfavorable candidate for the study of long range triplet
superconductivity. In contrast, Kontos et. al. [23] worked with PdNi alloy and saw
the same length scale of decay and oscillation (5 F1 z .5 F2 z 2.8 nm), which implied
a possibility of less spin-flip and spin-orbit scattering in this material. We therefore
decided to pursue this as our next possible candidate in the study of long range triplet
correlations. The following sections in this chapter are based largely on our published

paper Khaire et al., Phys. Rev. B 79, 094523 (2009).

It’s important to recognize here the different nature of magnetism in CuNi and
PdN i alloy. Since Pd is “nearly” ferromagnetic itself according to the Stoner criterion
it takes only a small concentration of Ni to make it ferromagnetic. By the virtue of
small Ni concentration, one can expect the magnetism to be more uniform in PdNi
alloy than the CuNi alloy, where the magnetism results from large clusters of Ni

atoms.

In the past, Aprili [31, 23] and others [64, 65, 66, 67, 68] have extensively studied
Pd1_xNi$ with Ni concentration of 12 at% but only with the PdNi thicknesses less
than 15 run. As mentioned earlier, the goal of our work is to increase the thickness
of the F-layer and see the clear transition from the spin-singlet correlations to the
spin-triplet correlations as the thickness of F-layer is increased. Our choice for this
material was therefore governed by 2 factors: 1) A weak ferromagnetic alloy allows us
to increase the thickness of the F-layer without introducing large amount of flux in the
junction (Large flux in the junction can pose severe problems, this issue is discussed
in detail in Chapter 6); 2) A possibility of less spin-flip and spin-orbit scattering in
PdNi alloy compared to CuN i alloy allows the triplet-correlations to survive for longer

distances in the F-layer.

64

4.2.1 Characterization of PdNi Alloy

The Ni concentration in our PdNi sample was confirmed by three different methods:
1. EDAX
2. Curie Temperature
3. Saturation magnetization.

Energy dispersive X—ray analysis of 1.5 ,um thick PdNi film yielded a Ni concen-
tration of 12i0.5 at.%. A thick film was used to ensure the large signal to noise
ratio for the Ni-K peak. Similar EDAX measurements performed on a 200 nm PdNi
sample yielded an identical concentration provided the signal was accumulated for

long enough times to ensure large signal to noise ratio.

 

160—
140: \
120—-

100:

80-
60-

M (emu/cma)

4o-
20—

     

 

 

0 _ . , , .v.,._.., r

0 50 100 150 200 250 300
Temperature (K)

Figure 4.3: Magnetization vs. temperature for a 100 nm thick PdNi film. Then the

magnetic moment was measured by applying magnetic field of 5 kOe while heating to
room temperature. Black circles: In-plane field, Red squares: Out—of-plane field.

65

To confirm the measured concentration value, the magnetization M vs temperature
of a 100 nm thick PdNi sample was measured using a superconducting quantum
interference device (SQUID) magnetometer. The film was grown on 150 nm of Nb to
have identical crystalline properties as our Josephson junction samples. The film was
first cooled in zero field to 10 K, then the magnetic moment was measured by applying
an in—plane field (or out-of—plane field) of 5 kOe while heating to room temperature.
These curves are shown in Fig. 4.3. The cooling curves were also measured, and were
found to follow the same curves as during heating (Not shown in Fig. 4.3). A clear
change of slope is seen around the Curie temperature of the sample at around 175
K, independent of whether the field is applied in-plane or out-of-plane of the sample.
According to the pervious literature published by Beille [69] and cited by Kontos [70],

this Curie temperature corresponds to a Ni concentration of about 12%.

 

150

.3

o

o
1

01
O
r .

 

 

 

 

.4600 ' 4500 T b ' 20'00 ' 4600
Field (Oe)
Figure 4.4: Magnetization vs. in-plane field for 100 nm thick PdNi sample. Black

circles: In-plane field and Red squares: Out-o -plane field. The measurement was
done at 10 K.

66

Figure 4.4 shows M vs H measured for the same 100 nm thick PdNi film at 10
K by applying field either in—plane or out-of-plane of the sample. In both cases the
same saturation magnetization is obtained, but a larger field is required to attain
the saturation when the field is applied in plane of the sample than when the field
is applied out-of-plane of the sample. (Note: The saturation field is not visible
in the field range plotted in Fig 4.4.) This indicates that the magnetic anisotropy
of PdNi films is out-of—plane. Similar measurements performed on 30 and 60 nm
PdNi films also indicate an out-of-plane anisotropy. Recently, similar out-of-plane
anisotropy was observed in CuNi alloy [71, 72]. This is in contrast with what is
usually seen in thin films. In thin films, the strong shape anisotropy dominates the
magnetocrystalline anisotropy, which results in an overall in-plane magnetization of
the film. The saturation magnetization of PdNi was about 150 emu/cm3 = 0.23
u B / atom (See Fig. 4.4), which according to Beille [69] and Kontos [70] corresponds
to the Ni concentration of about 12%. Thus all the three methods of concentration

determination indicated a Ni concentration of 12:l:0.5% in our samples.

4.2.2 Characterization of PdN i Josephson Junctions

For a fixed thickness of PdNi, several S/ F/ S Josephson junctions of varying lateral
dimensions (10 to 40 ,um) were made on the same sample. Depending on the lateral
dimensions, the normal state resistance of samples varied in the range from 2.4 to 152
at). Resistance in this range require an extremely sensitive low noise measurement
technique which is provided by a SQUID. All the four probe measurements were done
at 4.2 K by dipping the sample into a liquid helium dewar. The measurement set-up

has been described in detail in Chapter 3, section 1.5.
Figure 4.5 shows the typical I — V characteristics obtained for Nb/ PdNi/ Nb

Josephson junction with diameter of 20 ,am and using dpsz' = 62 nm and Heat = —19

67

.3
o

 

      
 

J

«#0303
1.1.1

N
1 .

‘ .
V «an...»nm.yn.~..u~.w..-..._

L l 1

Voltage (nV)
115 o

 

 

 

-0.3 ' -0.2 ' 0.1 ' 0:0 ' 0:1 . 0:2 . 0.3
Current (mA)

Figure 4.5: Voltage vs. Current for a PdNi Josephson junction with diameter 20 um,
dpdNi= 62 nm and Hext = -19 Oe. The red solid line is a fit to Eqn. 4.3

Oe. The red line is a fit to the standard I-V relation given by,

W) = l—fi—IRNReKI2 — 131/21 (4.3)

Occasionally, we have observed I-V curves that are shifted horizontally, so that the
critical current in the positive is not exactly the same as the critical current in negative
current directions. In such cases, we average the critical currents in the two current

directions.

Figure 4.6 shows the typical Ic vs Hem (Fraunhofer patterns) obtained for Nb/
PdNi/ Nb junctions with different thicknesses of PdNi (35, 50, 70, 85 nm). The ex-
tremely small values of critical current at the minima indicate absence of any shorts
in the insulating material surrounding the Josephson junctions. Also it is impor-
tant to note that the maxima in Ic are observed close to Hext z 0. This indicates

that the PdN i layers in the junctions have a multidomain structure which leads to a

68

1.6 0.20

 

 

 

 

 

 

 

 

 

 

. a) ‘ b
1_2_ 0.16: )
' 0.12«
0.8« .
. 0.03-
0.4-] 004:
l i
Aao ............. 0.00.........
E -45 -30 -15 0 15 30 45 -40 -20 0 20 40
v ‘ 0.05]
—0 0.12‘ c) 004. d)
0.03- 0.03:
. 0.02.
0'04" 0.01.
. fl

 

 

 

 

00- 0.00«
-45 -30 -15 0 15 30 45 -30 -15 O 15 30

Hext (Oe)

Figure 4.6: Critical current, Ic vs. applied magnetic field Hem (Fraunhofer patterns)
obtained for PdNi Josephson junctions with difi'erent thickness of PdNi interlayer a)
35nm, b) 50nm, c) 70nm, d) 85nm. The pillar diameters are 10, 10, 10, and 20 um,
respectively.

highly homogeneous flow of current through the junctions. Occasionally Ic(H) was
distorted or the central peak was shifted due to the residual magnetic flux trapped
in the junction during the cooling process. The ,u-metal shield currently employed
in shielding the sample from external fields is small and is sitting at the bottom of
the dewar. When the liquid helium dewar is full, the sample undergoes a ferromag-
netic transition (Tam-e of PdNi = 175 K) even before it reaches the u-metal shield,
thus trapping residual magnetic flux due to extraneous sources. Usually heating it to
the room-temperature (i.e. Pulling the sample to the top of the helium dewar) and

re—dipping it in liquid helium, gains back the demagnetized state.

69

4.2.3 Magnetizing PdNi Josephson Junctions

 

 

 

 

 

 

 

 

0.04- «E
0.00 6 , I - T

-200 11130 -1'20‘ so -40 0 40
Hm(0e)

 

Figure 4.7: Fraunhofer pattern in the virgin state (red circles) and after magnetizing

(black diamonds) a Nb/PdNi/Nb Josephson junction with diameter w = 10 um and
dpsz' =47.5 nm.

Ic vs H at measurements were also performed on all our samples after magnetizing
the Josephson junctions. The samples were magnetized by applying a large in-plane
field of 5 kOe and the sample was carefully lifted in the cryostat to just above the
liquid helium level until the Nb electrodes showed a transition to the normal state.
This step removed any trapped flux from the Nb electrodes or the superconducting
magnet. Sample was then dipped back into liquid He and the Fraunhofer pattern was
measured. As observed earlier in the case of CuN i, the peak of the Fraunhofer pattern
was found to be shifted in field. One such shifted Fraunhofer pattern is shown in Fig.
4.7. The maximum critical current measured for magnetized samples matched closely

with the maximum critical current obtained for virgin state samples.

Samples were magnetized by the procedure described above and the field shift

70

 

A 200-

H-shift (0e

 

 

 

100 T l ' I 7 I ‘ l ' l ' I ' l ‘ l '
20 30 40 5O 60 70 80 90 100 1 10
PdNi thickness (nm)

 

Figure 4.8: Magnetic field shift of Fraunhofer patterns of magnetized samples vs. PdNi
thickness tip. The line is a fit of Eqn. 4.2 to the data points with d F < 75 nm, with
A L = 86 nm. The red stars indicate H shi ft values calculated using the same Eqn. 4.2
but using Mrem values obtained directly from [W vs. H data obtained for 30, 60, and
100 nm thick PdNi films.

(Hshift) of the Fraunhofer pattern was measured for all our Josephson junctions
with varying PdNi thickness. Fig. 4.8 shows the field shift of the Fraunhofer pat-
terns obtained for Josephson junctions with varying thickness of PdNi layer. As the
thickness of PdNi is increased, the field shift saturates at around 200 Oe. This is
because, in thin films dominance of shape anisotropy leads to a strong preference
for in—plane magnetization, however as the film thickness increased, dominance mag-
netocrystalline anisotropy over shape anisotropy leads to an increased tendency of
magnetic moments to align perpendicular to the plane of the sample. This leads
to a decrease in the in-plane component as the thickness is increased. Since Hshi ft
is a measure of Mrem (in-plane component), increasing PdNi thickness leads to the
saturation of the Hsh, ft as seen in the Fig. 4.8. The solid line is fit to the data using
Eqn. 4.2, using remnant magnetization Mrem as the only free parameter. The fit

gives Mrem = 55 emu / cm3. This value is comparable to the remnant magnetization

71

of 76 and 62 emu/cm3 measured directly for PdNi films of thickness 30 and 60 nm
respectively. The red stars in the figure are Hsh, ft values calculated using the same
Eqn. 4.2 with Mrem values obtained directly from the magnetization measurements

done on PdNi films of thickness 30, 60 and 100 nm.

4.2.4 Critical Currrent vs Thickness: 0 — 7r Josephson Junc-

tion

 

 

 

 

 

 

 

l ' l ' l ' I ' l ' I ' l ' l
30 40 50 60 70 80 90 100
deNi (nm)
Figure 4.9: Critical current density (Jc) vs. thickness of PdNi (deNi) for all of our
Nb/PdNi/Nb Josephson junctions. Each data point is the average taken over multiple
pillars on the same substrate and the error bars represent the standard deviation of
the mean. Black points (squares) are virgin state data, while red points (circles) were
measured after magnetizing the samples (see Fig. 4.8). The solid line is a fit of Eqn.
4.6 to the virgin state data, while ignoring the last two data points with dpsz- = 95
and 100 nm.

10 vs Hext measurements as described in sections 4.2.2 and 4.2.3 were performed

on several samples for which the PdNi thickness was varied from 35 to 100 nm.

72

The maximum critical current density (JG) obtained for all such devices in virgin as
well as magnetized samples is plotted as a function of PdNi thickness (dpsz') in
Fig. 4.9. Each data point represents the average over multiple Josephson junctions
measured on the same substrate. The error bars are the standard deviation of the
measurements. The critical current density is seen to decrease exponentially over five
orders of magnitude over the measured range of thickness. To our knowledge this was
the widest range of ferromagnet thickness in S / F/ S Josephson junctions studied to

this date.

 

3.0x108
2.5x108-

A 2.0x108-

 

 

 

 

 

30 ' 3'5 1 4'0 ' 4'5 50 ' 55

deNi (nm)

Figure 4.10: Linear plot of Jc vs. dpsz' for the thickness range 32.5 to 58 nm. The
line is the same fit shown in Fig. 4.9.

It is important to notice here that the critical current density, Jc does not decrease
monotonically but in fact shows the oscillations that are characteristics of 0 — 7r
junctions. Fig. 4.10 and Fig. 4.11 show linear plots of Jc vs dpsz' for the thickness

ranges 32.5-58 nm and 55—85 nm respectively. The local minima are clearly seen

73

 

1 .75x107
1 .50x107-
1 .25x10’-

1 .00x107~

W)

q

°7.50x106-

J

    

5.00x106~

   

 

 

 

2.50x1064: i

ii

55 60 65 ' 7'0 ' 75 so 85
(nm)

 

deNi

Figure 4.11: Linear plot of Jc vs. dpsz' for the thickness range 55 to 85 nm. The
line is the same fit shown in Fig. 4.9.

in these figures in the neighborhood of 35, 48, 60, and 75 nm. Such an oscillatory
behavior representative of 0 — 7r transition has been observed previously by various

groups [26, 27, 23, 22, 24, 73, 29, 30] working on CuNi, PdNi, Ni, Co, etc.

4.2.5 Resistivity of PdNi

Figure 4.12 shows a plot of specific resistance ARN vs. d pdm, where RN is the
normal state resistance of our Josephson junction. The specific resistance AR N has

barrier and bulk contributions which can be written in the following form,

ARN = 2ARB + PPdNidF (44)

where R3 is the PdNi/ Nb boundary resistance, p pd N,- is the resistivity of PdNi, and
tip is the thickness of the PdNi layer. A linear fit of the data to Eqn. 4.4 yields

74

 

 

 

 

 

12.0-
“E
10.5-
g
2
CE 9.0-
X
<
7.5-
6.0 4.........f.,.,.
30 40 50 60 70 80 90 100110
deNi(nm)

Figure 4.12: Area times normal-state resistance vs. deNi for all of our Joseph-
son junction samples. The slope provides the resistivity of PdNi and the y-intercept
provides twice the Nb/PdNi boundary resistance

the boundary resistance of ARB = 2.31 :l: 0.07 film2 and the resistivity of PdNi
p pd N,- = 68 i 3 an. Independent in-plane Van der Pauw measurements performed
on 200 nm thick PdNi film yielded a resistivity value of ppsz- = 116 :t 2 an. It is
possible that the in—plane resistivity could be higher than the perpendicular resistivity
due to columnar growth of PdN i; although measurements on other sputtered metals

often find a close agreement between these two methods of measurement.

75

4.3 Theoretical Analysis of PdN i Josephson J unc-
tions

The three energy scales of importance in understanding S/ F / S results are, Eex, the
exchange energy in the ferromagnet; A, the superconducting gap; h/r, where r is
the mean time between collisions of an electron propagating in the ferromagnet. The
relative magnitude of the energies determine the 3 distinct regimes. For all the known
ferromagnetic materials used in S/ F/ S studies to this date, E83, >> A. However,
depending on the magnitude of h/r relative to these two energies, the system could

either be in,

1. Clean limit where Eexr >> It and Ar > h
2. Intermediate limit where Eexr > h and Ar < h

3. Dirty limit where Eexr << h and Ar < h.

These three regimes can also be characterized by comparing the relative length scales:
the mean free path le = vpr, the superconducting coherence length {5 = hDs/A,
clean (dirty)limit exchange length, 5 F = twp/2E” (5 F = W).

In the dirty limit, when d F is of an order of E F or greater, the superconducting
correlations decay and oscillate on a length scale given by the dirty-limit exchange

length 5;. = ,/ hD F / E63. In this case, the thickness d F dependence of superconduct—

 

ing critical current JC is given Buzdin et al. [74] and is of the form,
—d
Ic(dF) = Ico€33p( F)

sin (95 + z)
6} 6} 4

In the presence of spin-flip and spin-orbit scattering, the length scale of oscillation is

 

 

(4.5)

not equal to the length scale of decay [14, 62, 63, 33]. The general equation in that

case is given by,

76

Ic(dF) = Icoemp (—)

€F1

 

sin (FL +¢)[ (4.6)

£132

In general, the effect of spin-flip and spin-orbit scattering is to increase the length scale
of oscillation (€F2) relative to the length scale of decay (5 F1)- In the past, an equation
similar to this was used to fit [C vs dp data from S/ F/ S junctions containing CuNi
alloy, with {F1 = 1.3 nm and 5 F2 = 3.5 nm. The smaller value of {F1 compared to
5 F2 indicated that the spin-flip scattering is strong. We too used the above equation
as a fit to our data, and the fit is as shown in Fig. 4.9. But surprisingly we found that
the length scale of oscillation (6 F2 = 4.4 :l: 0.1 nm) was smaller than the length scale
of decay (5 F1 = 7.7 :l: 0.5 nm). Thus the dirty limit assumption that led us to using
this equation is not valid in our case. After digging further into the experiments done
in the past, we noticed the condition {F1 > é F2 has been observed in S / F / S junctions
using strong ferromagnets like Ni, Fe, Co, and NigOFe20 [27, 28].These materials have
large exchange energy and they satisfy the intermediate limit condition, Eexr > h
and Ar < 5.. Our observation of {F1 > 5 F2 in our S / F / S junctions using PdNi alloy

suggests that PdNi may also be in the intermediate limit.

Bergeret et al. [8] provides a general formula for the critical current behavior in
both the dirty limit as well as in the intermediate limit. When dF > le, (le is the

mean free path) the formula for the intermediate limit is given by,

Ic(dp) oc 7rT Z A

A2 sin(dF/ér )exp (“dF
w>0

2 + v.22 dF/éF le (1 + 20.27)) (4.7)

where the summation is done over the positive Matsubara frequencies, to = 7Tl€BT (2m+
1) with T as the temperature. Asymptotically at large values of tip, Eqn. 4.7 is sim-
ilar to Eqn. 4.6. The fit parameters obtained using Eqn. 4.7 are, é F = 4.01 :t 0.1
nm and le = 10.6 :l: 1 nm. Although 5 F is comparable to {1:2, le is somewhat larger

than the 51:1 obtained from the fit using Eqn. 4.6. The mismatch is due to the sum

77

over Matsubara frequencies in Eqn. 4.7. In an another theoretical approach taken
by Kashuba et al. [75], the authors solve for the case of intermediate limit taking
into account the spin-flip and spin-dependent scattering in F layer. The result thus

obtained is nearly identical to Eqn. 4.7 stated above.

4.4 Discussion of Results

4.4.1 Estimate of Mean Free Path in PdNi

For many metals the product ple, which is inversely proportional to the Fermi surface
area, is known and tabulated [76]. It is therefore straightforward to estimate the mean
free path in metals from the measured resistivity. In the past people working on PdNi
have tried to estimate its mean free path using the ple value in Pd. The reported
values [66, 65, 70] vary widely in the range 0.33—4.0 f sz. The difficulties in getting
a right estimate for ple value lies in the complex band structure of Pd. The detailed
discussion of Fermi surface in Pd has been given in several papers [77, 78, 79, 80].
Pinski et al. [77] states that at 10 K, 97% of the transport current is carried by
light electrons on F-centered sheet of the Fermi surface, whereas specific heat is
dominated by heavier holes on the open portion of the Fermi surface. The lower
estimate 0.33 film2 [66, 65] is a result of using Einstein’s relation, 0 = n(EF)e2D,
with density of states at Fermi level n(EF) obtained from specific heat coefficient
"7 = («z/skimp).

We estimate the ple product for PdNi in two ways. Since the electronic transport
in Pd is dominated by the electrons on the F-centered sheet, we use the total number
of carriers 11, the density of states at the Fermi level n(EF), the effective mass m*,
and the Fermi velocity vp on that sheet. These values have all been tabulated by
Dye et al. [79] based on deHaas van-Alphen measurements of the Fermi surface of Pd.

Using 17. = 0.375 carriers/atom = 2.54 - 1028m‘3; n(Ep) = 0.189 states/(eV atom

78

spin) = 2.56 - 1028ev-1m-3; m* = 20772.; up = 0.6- (2rr/a) - (ii/2m) = 5.6- 105
m/s and using the Drude formula, 0 = nezr/m“, we find ple = 1.55 me2, while
using the Einstein relation we find ple = 1.31 f sz. The slight difference between
the two values is likely due to the non-parabolic character of the F-centered sheet.
We also estimate ple product using a second method, where we use our own measured
resistivity, p = 68 an and the mean free path from the Jc vs. d F fit, le = 11.2
nm and obtain ple = 0.76 me2. Thus both our methods yield ple values that are
comparable.

In his Ph.D. thesis [70], Kontos found that the resistivity of thin PdNi films with
a: a: 12% varied linearly with inverse thickness 1/d once the films were thinner than
about 8 nm, indicating that the mean free path is limited by the film thickness. The
SIOpe of the graph gives the product pd = 1.7 f sz which is not very different from

the estimates we have obtained from above.

4.4.2 Estimate of Exchange Energy in PdNi

As shown earlier, the fit to our Jc vs. at F indicated a longer length scale governing the
exponential decay compared to the length scale governing the oscillation (5 F1 > 51:2).
This suggested that our PdNi was in intermediate limit. Using é F2 = 4.0 :t 0.1 nm
and the Fermi velocity of the dominant carriers, Up = 5.6 - 105 m/s [79], gives an
estimate for the exchange energy in our PdggNilg alloy of E63; = twp/251:2 = 44

meV.

4.4.3 Comparison to Other Experiments

It is important to mention here that a similar experiment was performed by Kontos
et al. [23] using a PdNi alloy of similar concentration to ours. They studied S / I/ F / S

Josephson junctions with a PdNi alloy and found the length scale governing the decay,

79

g H, was similar to the length scale governing the oscillation, 6 F2 a: (PI = 2.8 nm.
The values of 6 F2 in their experiment and ours are rather close to each other, but
the values of {F1 are not. It is not clear if that discrepancy is significant or not.
The thickness range covered in the earlier work was 4.5 - 14 nm, whereas the range
we covered was 32.5 - 100 run. If the mean free path in the PdNi alloy is indeed
in the range of 11 run, then the samples studied by Kontos et al. [23] were in the
crossover regime with d F m l6, where the thickness dependence has not yet obtained
the asymptotic exponential decay, JC 0: exp(—d F / l6). But then one would expect a
less steep decay of .10 with dp, rather than a more steep decay. We believe that this
could be because the PdNi films deposited in different laboratories may have different
polycrystalline structures, and hence very different mean free paths. A summary of

the parameters estimated by previous workers, as well as by our work, is given in

Table 4.1 and 4.2.

 

 

 

Source Experiment Ni conc. v F ple p le
(at. %) (105m/s) (fflmz) (nflm) (nm)
[31] S/F DOS 10 2.0 4 - a: dp
[23] S/I/F/S 12 2.0 4 - z (11:
[66] Tc of S/F 14 2.0 4 240 16.6
[67, 68] Tc of S/ F 14 2.0 0.96 240 4
[65] Tc of S/ F 15 2.0 0.3256 220 1.48
[64] S/ F/ S 18 2.0 - - -
this work S/F/S 12 5.6 0.76 68 11

 

 

 

 

 

 

 

 

Table 4.1: Summary of PdNi parameters, vp, ple, p and le from several groups. The
superconductor used in all the above experiments was Niobium.

4.4.4 0 — 7r Josephson Junction: Temperature Dependence

Throughout the course of this work, our aim was to search for signs of spin-triplet
superconducting correlations in our samples. At first glance, the data in Fig. 4.9 show

no sign of spin-triplet superconducting correlations, which if present, might manifest

80

 

Source {F1 é F2 Eex formula to Tam-e
(nm) (nm) (meV) extractEex (K)

[31] 2.8 2.8 35 (hp/Em”? 100
[23] 3.5 3.5 13 (hD/Eex)1/2 260
[66] 6 6 15 (rip/Eat)”2 156
[67, 68] 3.4 3.4 13 (rip/Eel)”2 185
[65] 3.5 3.5 13 (hD/Eex)l/2 260
[64] 2.4 2.4 52 (hD/Eex)l/2 200
this work 8.0 4.0 44 hvp/Eez 175

 

 

 

 

 

 

 

 

 

Table 4.2: Summary of PdNi parameters from several groups. Note that the most
workers have used the diffusive formula 5 F2 = (liD/Eex)”2 to extract E61; from the
measured value of {152, whereas we have used the ballistic formula, E F2 = hula/2E”.

themselves as a crossover to a less-steep and non-oscillatory exponential decay of Jc
at large values of (11:.

However, it is intriguing to find that the length scale characterizing the exponential
decay of Jc in our samples, 5 F1 = 8— 11 nm, is substantially longer than that observed
previously in S / I / F / S junctions with PdNi [23] The natural question to ask ourselves
was - Could it be that we are already observing the triplet Josephson effect throughout
the whole range of d F reported here? The strongest evidence against spin-triplet
correlations in our Josephson junctions is the nearly-periodic set of local minima we
observe in Jc vs. dF, shown in Fig. 4.10 and Fig. 4.11. We believe that those
local minima signal crossovers between 0-junctions and rr-junctions, which are due to
the effect of the exchange splitting on spin-singlet superconducting correlations. A
Josephson supercurrent dominated by spin-triplet correlations would not exhibit such
minima, but rather would decay monotonically with increasing d F- However looking
at the uncertainty in our data points, the next natural question to ask was whether
the local. minima we observe truly represent 0 - 1r crossovers than just an unlucky
distribution of sample-to-sample fluctuations?

We realized that there are three ways to probe the local minima observed in our

Jc vs. dp data:

81

1. By a direct measurement of the current-phase relationship of the junction [81].

2. By extension of Jc vs. dp measurements to smaller values of dp, to see if the
slope of the Jc vs. d F semi-log plot changes to a value close to that measured by
Kontos et al.. This would require reducing the lateral size to of our junctions,

so as to maintain the condition AJ > w/ 4.

3. By measuring Jc vs. temperature T for samples very close to a 0 — rr crossover.
In S / F / S junctions with very weak ferromagnets, the 0 — 7r crossover has been
observed in the T-dependence of Jc [21, 26, 24, 30]. As the exchange energy
increases, however, the thickness range over which one can see a non-monotonic

T-dependence of JC gets progressively narrower [30].

 

1 08
3 —<— 35 nm
' “\¢.-_¢ —O— 55 nm
. . “‘6‘ + 47.5 nm
\ ‘ __ _
] \e.-.‘ ‘ v 68 nm

\.\“~e- K. + 60 nm

 

 

 

 

Temperature (K)

Figure 4.13: Critical current density vs. temperature for five Nb/PdNi/Nb Josephson
junctions with dpsz- as listed in the figure. The anomalous temperature dependence
for the sample with dpdN, = 47.5 nm indicates that its thickness is very close to a
0-7r transition.

Each of these checks presents its own set of challenges. But when posed with

several different possibilities, we decided to use the tool at our disposal—Prof. Pratt’s

82

 

+T=7.99 K
+T=7.49K
+T=7.03K
0.20.. _ -v-T =6.49 K

' —<—T=6.00K
—>-—T=5.50K
+T=5.00 K
+T=4.50K
+T=4.00K
+T=3.84 K
—O—T=3.54 K
+T=3.05 K
—o—T=2.54 K
+T=2.06 K
+T= 1.71 K

  
 
 
 
 
 
 
 
 
 
   

 

 

 

Figure 4.14: Raw data showing 16 vs. H for ferromagnetic Josephson junction with
47.5 nm thick PdNi layer. The largest critical current is seen at ~4K

home-built Quick-Dipper probe-III. This probe allows us to vary the temperature in
the range from 1.6 to 8.0 K. The details of this experimental setup are given in Chap-
ter 3. Section 3.5.4. We were therefore quickly able to measure Jc vs. temperature T
for some of our Josephson junctions. Fig. 4.13 shows the temperature dependence of
critical current for Nb/ PdN i / Nb Josephson junctions with d Pd Ni: 35, 55, 68, 47.5, 60
nm. (Fig. 4.14 shows [0 vs H measured at different temperatures for a Nb/ PdNi/ Nb
Josephson junction with 47.5 nm thick PdNi layer.) A clear non-monotonic behavior
is seen for the 47.5 nm sample which was close to a 0 — 1r transition. Whereas, no
such behavior was seen for the 35 nm and 60 nm samples, in spite of their closeness
to our anticipated 0 — rr crossover. A non-monotonic temperature dependence of the
critical current observed for the 47.5 nm sample confirms 0 - 7r oscillations that are
characteristic of the standard singlet proximity effect in PdNi. In the past, simi-
lar non-monotonic dependence indicative of 0-7r transition was observed by various

groups[21, 26, 24] working with CuNi alloy. This led us to believe that the local

83

minima seen in our data (Fig. 4.9) do indeed represent 0 — 7r crossovers, rather than

sample-to-sample fluctuations.

4.5 No Sign of LRTC!

As is evident from Fig. 4.9, the critical current density in our Nb / PdN i / Nb oscillates
and decays over a characteristic length scale of ~ 10 nm. There is no sign of a
crossover to a slower non—oscillatory decay of the type shown in Chapter 2, Fig. 2.12

Our data are therefore consistent with singlet proximity efl'ect. There is no indication

of LRTC.

The most natural question to ask here is: Why don’t we see long range triplet
correlations? As mentioned earlier, the weak ferromagnetic systems suffer from strong
spin-flip and / or spin-orbit scattering, which could be detrimental to the observation
of long range triplet correlations. To investigate the spin diffusion length (lsf) in PdNi
alloy, a separate experiment was carried out using the techniques borrowed from the
GMR (Giant Magnetoresistance) community. The details of this experiment are given
in Chapter 5. The measured value of the spin diffusion length, lsf = 2.8 nm, was
shorter than the length scale characterizing the decay of the Josephson supercurrent
in the present work (5 F1 as le m 11.7 nm). This was surprising, since normally, one
assumes that spin-flip and spin-orbit scattering processes occur on length scales much
longer than the mean free path. This assumption is also the basis of the diffusive
model used in discussing the spin diffusion length in Valery—Fert theory [82]. When we
were dealing with this puzzling issue, we also discovered an out-of—plane anisotropy in
our PdNi films. Nevertheless, we now believe that the short value of lsf as well as the
out-of-plane anisotropy in our PdNi films is a result of strong spin-orbit scattering in
this alloy. A detailed exposition of this conclusion in given in Chapter 5. And the

said discrepancy in the relative magnitude of le and lsf, (18 > lsf), is perhaps due to

84

the magnetically inhomogeneous nature of PdN i, which destroys the spin memory by
rotating the spin on a length scale much smaller than the mean-free path, le. This
possibly points to PdNi as a ferromagnetic material with the much needed magnetic
inhomogeneities that are essential for generating LRTC, but which unfortunately is
rendered useless because of the short spin-diffusion length. The scientific irony here is
that the origin of this short spin-diffusion may perhaps lie in these inherent magnetic
inhomogeneities!

Apart from having a long spin-diffusion length, it is equally important that the
length scale characterizing the magnetic inhomogeneity (say 6m) in PdNi should be
comparable to the Cooper pair coherence length 53 in Nb. If 6m << £3, then a
Cooper pair will experience the magnetization averaged over the length {3, and triplet
correlations will not be produced efficiently. If 6m >> £3, then a typical Cooper
pair experiences no magnetic inhomogeneity. Unfortunately at this point, the typical
domain sizes and domain wall widths in our PdNi alloy are not known. Since the Curie
temperature of PdNi is well below room temperature, obtaining information about
magnetic structure requires a low temperature magnetic visualization technique, such
as low-temperature magnetic force microscopy (MFM) or Bitter decoration. And
even then, the former method is not well-suited to weak ferromagnets, because the
magnetization of the MFM tip may influence the domain structure of the sample.
Unfortunately, no such measurements have been performed on PdNi alloy, to our

knowledge.

4.6 Conclusion

Here we have measured the critical current of Nb / PdNi / Nb Josephson junctions and
have seen it drop by five orders of magnitude over a thickness range from 32 to 100

nm. We have also seen and confirmed that the periodic array of local minima, are in

85

fact 0 - 7r oscillations that are characteristic of the standard singlet proximity effect
in PdNi. We have discussed possible reasons for the absence of induced spin-triplet
correlations, such as spin-flip scattering or a poor match of length scales between
the magnetic domains and the superconducting coherence length. Although this
experiment did not lead us to our most coveted goal of observing long spin-triplet
correlations, it definitely helped us in understanding the obstacles in reaching towards

it.

86

Chapter 5

GMR Experiments

5.1 Magnetoresistance (MR)

The term magnetoresistance (MR) refers to the change in resistance of a material
when a magnetic field is applied. The MR ratio is defined as the ratio of the change

in resistance in when the field is applied, to the resistance at zero field.

RH-RO _ £5?

The materials which have large resistance in the presence of field than in the absence

MR-ratio =

of field are said to have positive MR, whereas, if the field reduces resistivity, the

materials are said to have negative MR.

5.2 GMR Theory

Giant magnetoresistance (GMR) is seen in the so called magnetic multilayers, where
layers of magnetic and non-magnetic materials are stacked on each other. It was
discovered almost simultaneously in 1988 on Fe/ Cr multilayers by Albert Fert [83]
and on Fe/ Cr/ Fe trilayers by Peter Grunberg [84]. Depending on the thickness of

87

the non-magnetic layer, the magnetic layers either couple ferromagnetically or anti-
ferromagnetically. Fig. 5.1a. shows the case where the magnetic layers are antiferro-
magnetically coupled. That is, in the absence of the magnetic field the magnetization
of the ferromagnetic layers is antiparallel. The change in the resistance of the mul—
tilayer arises when the applied field aligns the magnetic moments of the successive

ferromagnetic layers. This is shown in Fig. 5.1b.

5.2.1 Simplified GMR Model

a. H=O b. Haeo

 

 

 

 

 

 

 

 

 

R R; R a

LA AAAAAL A AA

1" VIII" vvv '1'
1“... “‘ AAAAAA AAAAAA
'V'I'V v I I 'V"" V""'

R.» R? R~b as

Figure 5.1: A cartoon representing GMR effect. A circuit diagram is shown at the
bottom of each cartoon, where the magnetic layers are represented by resistances.
If the electron moment is parallel to the direction of magnetization in the F-layer,
the resistance experienced by it is given by RT. Similarly, if the electron moment is
antiparallel to the direction of magnetization of the F -layer, the resistance experienced
by it is given by Hi.

88

As said before, GMR device consists of ferromagnetic (F) layers separated by non-
magnetic (N) layers. The resistance of such a device can be explained by using Fert’s
simplified picture. In absence of magnetic field, the magnetization of two F-layers is
such that they have the net magnetization pointing in opposite directions. Whereas,
when the field is applied, the magnetization in two F layers becomes parallel to each
other. This is shown in Fig. 5.1a. An electric current sent through the system is
composed of two type- majority and minority spin current, without being very specific
we can also refer to them as moment-up and moment-down current. In ferromagnets,
the moment-up and moment-down particles have different densities of states at the
Fermi level. This causes the moment-up electrons to scatter differently than the
moment-down electrons both in the F -layer as well as at the F / N interface. Because
of this spin dependent scattering, the resistivity of one channel of electrons is less
than the resistivity of the other spin channel in the F-layer. For most ferromagnets,
the resistivity of the moment-up channel is less than the moment-down channel, but
this is not always the case. The Fig. 5.1 explains the GMR using the circuit diagram
with an assumption that R] << R j. Consider the case where both the F-layers are
parallel (See Fig. 5.1b). In this case, the resistance experienced by the moment-up
electrons in first F-layer is R¢ the same as the resistance in second F-layer, so that the
total resistance experienced by moment-up electrons is 2R]. Similarly the resistance
experienced by moment-down electrons as it traverse two ferromagnetic layers is 2R l'
Standard addition of resistances for a parallel (P) magnetic configuration gives the

total resistance for R p,
R
R P _R’I_L_ (5.2)

Now consider the case where the magnetization in F-layers is antiparallel as shown

in Fig. 5.1a. In this case the resistance experienced by moment-up electrons in

89

the first and second F-layers is R”? and R [ respectively, so that the total resistance
experienced by the moment-up electrons as they traverse the two F-layers will be
R]: + R]. The moment-down electrons will be affected in the same but opposite
way and its resistance will be R j + R]. The total resistance in antiparallel magnetic

configuration will be R A p,

RAP: -;-(R¢+R[) (5.3)

The difference between the two cases gives the Giant Magnetoresistance (GMR),

—R 2
ARzRP—RAPZ—éfl- (5.4)

The larger the scattering asymmetry for two spin channels, the larger is the difference

between RT and R j and the larger is the magnetoresistance.

In the N layer, both the moment-up and moment-down electrons experience the
same resistance and it is generally much less than the resistance in F layers and the

F / N interfaces and can therefore be neglected.

5.2.2 Two-Current Series-Resistor Model (2CSR)

The models used for the analysis of CPP-GMR (Current perpendicular to plane-Giant
magnetoresistance) data depend on the relative size of spin diffusion length, lsf and
the layer thickness, t. When lsf > t, the model used for analysis is called the two
current series resistor model (2CSR model) [85, 82, 86]. The extension of the model
was developed by Valet and Fert [82] for lsf 2 t. The details of the Valet-Fert theory

can be found in the theses written by past students [59].

The 2CSR model that we will discuss here is an extension of the simplified Fert
model described in the previous section. In this model, one divides the current sent

through the system into two independent moment-up and moment-down channels.

90

Each bulk and interface resistance can be thought of as an independent resistor. The
total resistance experienced by each spin channel is therefore a series contribution of
these resistors. The origin of GMR lies in the fact that the moment-down channel
experiences different resistance (in bulk or at interface) than the moment-up channel.
This is what gives rise to bulk scattering asymmetry or interface scattering asym-
metry. To calculate the total resistance experienced by the current flowing through
the multilayer, one then combines the overall channel resistances in parallel. The
difference in resistance experienced by the current for parallel (P) and antiparallel

(AP) magnetic configuration of the magnetic multilayers is called Magnetoresistance

(MR), MR=RAp — Rp.

Before going into the details of 2CSR model, we define several parameters used

to make calculations and model the multilayer.

The resistivity of the majority and minority channels is given by p}. and pi“

respectively. A useful parameter p}; is defined as,

T+p[p

p
pi? = ‘FT— (5-5)

p} is a measure of the average resistivity for moment-up and moment-down electrons.

In addition, the bulk spin-scattering asymmetry is defined by the parameter 6 as

follows,
i T
p - p
a =—- ————-—f f (56)
PF + PP

The resistivity experienced by moment-up and moment-down channels can be written

in terms of a bulk spin-scattering asymmetry parameter S and p" using the following

91

equations,

.0} = 2pi~(1— a) (5 7)
pi = 215:0 + 6) (5 8)
One can therefore also write,
air 10F
= 5 9

where, p F = (1 / p} + 1/pf7)—1 is the usual resistivity.

Similarly, the spin-scattering asymmetry at an interface is given by the parameter
7. The specific resistance of moment-up and moment-down channels, given by ART
and ARJr can be written in terms of the spin-scattering asymmetry at interface as

follows,

ARE/N = 2AR;/N(1— 7) (5.10)
ARfi/N— _ 2AR;/N(1+ 7) (5.11)

Consider the simplest case of an F / N / F spin valve. Let t N and t F represent the
thickness of the individual N and F layers respectively. Now, if one considers the case
where two ferromagnetic layers have antiparallel configuration, the specific resistivity

for the moment-up channel is given by,
Similarly, the specific resistance for the down channel is given by,

AIDE”,=pJfitF+ARi/N+pNtN+ARF/N+p}itp (5.13)

92

The total specific resistance of the anti-parallel state is,

1 1 1
= —+
T
ARAP ARAP ARhP

 

 

(5.14)

In the non-magnetic metals, both the moment-up and moment-down electrons expe-

rience the same resistance and hence the bulk spin scattering asymmetry in normal

metal 6 = 0 or in other words, pITV = pi, = 2pN

Substituting ARI1 P and ARfi P from Eqn.5.12 and 5.13 and using p}, = pi, =

2p N, one gets the following equation,
pr F + ARF/N ' WV N ‘ ’mF/N + PF F

A =
RAP 2

 

(5.15)

Using Eqns. 5.7,5.8, 5.10 and 5.10, one can then write the specific resistivity for the

anti-parallel case AR A p in terms of p}, 'y, B, and ART/N“
ARAP = 2p}(1—B)tp+2AR}/N(1w)+2pNtN+2AR}/N(1+7)+2p}(1+fi) (5.16)
Which after simplification gives,
ARAP = 2p}tp+2AR}/N+pNtN (5.17)

For the case where two ferromagnetic layers have parallel configuration, AR p can be
computed in the similar manner[85]. Finally, AAR for a bilayer of F /N / F form is

given by,
[Bristle + 27F/NAR}/Nl2
AR A p

 

ARAp-ARP= (5.18)

As explained earlier, this model holds true as long as, lsf >> t. When lsf as t, one

must then take into account the spin relaxation[82]. The 2CSR model in that case

93

needs to be modified, and for many cases only the numerical solution exists.

5.3 Spin Diffusion Length in PdNi Alloy

During the course of this project, some experiments were performed to measure the
spin-diffusion length in certain ferromagnetic materials of interest to us. The exper-
iments described here were not the primary goal of my project, and I will therefore

focus my discussion only on the relevance of results obtained through them.

5.3.1 Spin Valves: Py/Cu/PdNi

 

Py Cu PdNi

Figure 5.2: Schematic for PdNi spin valve. Because of the large coercive field of PdNi
layer, it essentially acts like a pinned layer. The overall parallel (P) and antiparallel
(AP) state is dominated by the low field switching action of Py layer.

Spin flip and spin orbit scattering in weak ferromagnetic alloys could be detrimen-
tal to long range triplet penetration, and hence a separate experiment to measure the
spin diffusion length lsf in PdNi was initiated in our group by a senior undergradu—
ate student, Hamood Arham. Hybrid spin valves of the form Cu(10)/Py(24)/Cu(20)
/PdNi(dpdN,-)/Cu(10) were sputtered, where all the thicknesses are specified in run.
Because of the large coercive field of PdNi (Hc z 1.5 kOe) compared to Py (Hc < 15

Oe), PdNi essentially acts as a “pinned” layer, switching magnetic state only for large

94

applied fields. The overall magnetic state of the spin valve, parallel or antiparallel,
is dominated by switching action of the “free” Py layer in small fields. Our spin
valves are sandwiched between two superconducting electrodes, and measurements
are performed at liquid He temperature (4.2 K) using superconducting quantum in-
terference device (SQUID) electronics in a current comparator bridge. The details of

the measurement set-up are given in Chapter 3, section 3.5.3.

The standard CPP-GMR (Current perpendicular to plane - Giant Magnetoresis-
tance) measurements are performed, where current is passed perpendicular to the
plane of the sample and the change in resistance is measured as a function of applied
magnetic field. One such R(H) plot is shown in the Fig. 5.3. This figure shows the
measurement performed at liquid helium temperature (4.2 K) on a spin valve with
d psz- = 12 nm. The sample is first subjected to large field, H = —5 kOe so as
to magnetize the PdNi layer in the negative direction. The field is then set to zero
and the sample is pulled to the top of the cryostat, just above the liquid helium level
until the N bTi wire near the sample transformed into the normal state. The sample
is then lowered back into the liquid helium. This process removes any trapped flux
from the Nb electrodes and the superconducting magnet. Our previous experience
in magnetizing PdNi based Josephson junctions (See Chapter 4, section 4.2.3), has
indicated no significant loss of M pd N, in the warming up process. Once the sample
was inside the cryostat the field was slowly scanned from H = —500 Oe to H = 500
Oe. Since the PdNi layer has large coercivity, the layer stays pinned in the negative
direction when the field is slowly scanned, whereas Py which has a low coercivity
switches it’s orientation relative to the PdN i layer from it’s initial parallel state to an
antiparallel state. Since, the switching field of Py layer (5 Ce) is less than the field
step size of 7.5 Oe, an abrupt increase in the resistance is seen very close to zero field
when the Py layer switches. The field was then slowly scanned back from H = 500
Oe to H = —500 Oe. Figure 5.3 shows only the region between -100 to +100 Oe for

95

clarity. The reproducibility of data in two directions indicate that M pd N,- does not
change significantly by applying fields as large as -500 Oe due to the large coercivity
of the PdNi layer.

 

10.15‘ a

 
 

 

 
 

 

 

 

 

 

M (arbbunits)
\“t

 

 

 

10.05-
-5 0 5
. _ . H (kDeL
-80 -40 40 80

H (Go)

Figure 5.3: R vs. H data at 4.2 K for a Py/Cu/PdNi hybrid spin valve with dpdNi =
12 nm. Before starting experiment, PdNi layer is magnetized in the negative direction
by applying a large field of -5 kOe. The increase in resistance is seen when the relative
orientation of Py layer changes from parallel to antiparallel state. Because of the large

coercivity of PdNi layer, it acts as a pinned layer. The inset shows the large coercive
field of PdNi (HG z 1.5 kOe.)

Several such samples are measured with varying PdN i thickness and the specific
magnetoresistance AAR = A(R A p - R p) is plotted as a function of the PdNi thick-
ness (See Fig. 5.4). When the thickness of the PdNi layer dpdm is much less than

lgdm, the two-current series-resistor model gives,

AAR 0< flpdNiPiadNideNi + 7PdNi/CuARl9dNi/Cu' (5-19)

, PdNi
When (1})sz >> lsf ,

AAR OC fiPdNipadeNilfidei + VpdNi/CUARPdNi/Cu' (5.20)

96

0.20 i i l

 

 

 

 

 

/
I
/
/
/
0.15- I -
/
/
A q /
NE I
0.10- ’ J -
«El ,’ 1 2
a: ,’ r
E 0.05 _
0.00 T T ' l ' I ' fi
0 5 10 15 20
deNi (nm)

Figure 5.4: AAR vs. d PdNi. The solid line represents a fit to the data of the Valet-
Fert equations. The fit provides an estimate of the spin memory length in PdNi of

lfdm = 2.8 :l: 0.5 nm. The dashed line shows the result of a calculation assuming
indNi = so.
8

According to the above equations, a plot of AAR vs. dpdm should be linear at
small values of the PdN i thickness and then saturate at large values. Valet-Fert[82]
theory interpolates between these two limiting cases, and the crossover between the
two behaviors is used to extract the spin diffusion length, 13f. Several material
parameters required for fitting the data to Valet-Fert equations were obtained from
previous experiments. The resistivity of PdNi alloy, p pdNi = 121 :l: 6 nflm was
obtained by performing Van der Pauw measurements on 200 nm thick PdNi films.
Also, a separate experiment performed to determine the dead layer between PdNi
and Cu interface indicated, 5deod=1-1 :t 0.4 nm [87].

Fig. 5.4 shows the specific magnetoresistance, AAR, vs. PdN i thickness, for all of
our samples. The data start out increasing nearly linearly with d PdNi, then flatten

out when dpdNi exceeds about 10 nm. The solid line is a fit to the data of the

97

Valet-Fert equations [82]. The fit yields the spin-diffusion length of l 3 f = 2.8 nm. To
illustrate the role of the finite spin memory length in the fit, the result of calculation
using 1:13” = 00 is shown by a dashed line in Fig. 5.4.

This small value of spin-diffusion length (13f = 2.8 nm) in PdNi was initially a
surprise, because it was much shorter than the mean free path (1,; = 10.6 :l: 1 nm)
obtained through our measurements on PdNi based Josephson junctions. Whereas in
a standard picture of diffusive transport in metals, the spin-flip and / or the spin-orbit
scattering happens on a length scale much larger than the mean free path in that
metal, i.e. lsf > le. After this experiment was performed, Hamood graduated but
this puzzle lingered on for a while. During this period, we accidently found that
our PdNi films have an out-of-plane magnetic anisotropy. This cast some doubt on
our ability to attain P (parallel) or antiparallel (AP) states in Hamood’s spin valve
samples. This led us to believe that the small spin-diffusion length in our PdNi alloy
could be a result of out-of-plane magnetic anisotropy in PdN i. We believe that the
out-of-plane magnetization of PdNi can cause precession of spins initially aligned
along in-plane (Py magnetization direction), thus enhancing the spin memory loss in

our samples.

5.3.2 Spin Valves (Spoiler Geometry)

In order to suppress the influence of out—of-plane component, a new experiment was
proposed by Prof. Pratt. Although Hamood had graduated by then, the accu-
rate measurement of spin diffusion length in PdNi alloy was very crucial to our ex-
periment. All the experiments henceforth were done by me. According to Prof.
Pratt’s new idea, exchange biased spin valves of the form Cu(10)/Py(24)/Cu(20)/
PdNi(dpdN,-)/Py(8)/FeMn(8)/Cu(10) were made, with dpdN, varying from 0 - 15
nm. The aim was to pin the PdNi layer via the thin Py layer so that the magne-

tization in PdNi is forced to lie in—plane. After deposition the samples are heated

98

 

Figure 5.5: (a) Schematic for Hamood’s spin valve showing the possible out-of-plane
component of magnetized PdNi. (b) Schematic for our new spin valves, where PdNi
layer is force-pinned “in-plane” via an exchange-biased coupling to Py/FeMn.

to 170°C, above the blocking temperature of FeMn, in a vacuum pumped pinning
chamber and cooled to room temperature in an in-plane field of 190 Oe. This causes
PdNi layer to be exchange coupled to the thin Py layer, which in turn is exchange
biased in-plane (in the direction of the applied field) by the FeMn layer [88]. Magne-
tization measurements performed on PdNi/Py/FeMn Show that both PdNi and Py
are exchange-biased by this procedure. The in—plane magnetization of the pinned Py
layer also constrains the PdNi magnetization to be in-plane. Effectively, the overall
structure is such that Py layer on the left side acts as a “free” layer whereas PdNi
acts as an in-plane “pinned” layer because of it’s proximity with a strongly exchange
biased Py layer. The schematic of this geometry is shown in Fig. 5.5. We call this
the spoiler geometry[89] because, with Spy >> fipdNi, AAR is largest in the absence
of PdNi layer, whereas as the PdNi thickness is increased, the signal diminishes until
it finally reaches a much smaller value corresponding to that of a Py/ Cu / PdNi spin

valve. For d pd N,- > leNi the Valet-Fert theory approximately gives,

AARapdNi) —AAR(oo> oc expi—dpdNi/lstii (5.21)

Figure 5.6 shows that in the spoiler geometry AAR decreases rapidly with deNi

99

 

 

 

 

 

 

25_ E195
‘ §185
NA 20-i g
g ______ §18'°-8'0-40'0'40'80
a: 15 -------- H(Oe)
n: .
E 1.0-
0.5:
0.0 ,
0

 

Figure 5.6: AAR vs. d 13sz“ for “spoiler” spin 'valves of the form
Py/Cu/PdNi/Py/FeMn. Without PdNi, these are high-performance Py/Cu/Py spin
valves with large AAR. As the 'PdNi thickness increases, AAR drops because of the
low spin-scattering asymmetry in PdNi relative to Py, i.e. flPsz‘ << ,pr. The
black dot-dashed line shows a linear interpolation between first two points. The
black solid line is a fit to the Valet-Fert equations for the rest of the points, giv-
ing lidei = 5.4 :l: 0.6 nm. The red large-dashed line is obtained with lngi = 00.

Inset: Raw magnetoresistance (R vs H) data for the sample with d pdNi = 2 nm.

and then saturates. The figure in the inset shows raw GMR data for the sample
in spoiler geometry with dpdNi=2 nm. The black line shows the numerical data fit
using Valet-Fert theory. The fitting is done to all the data points excluding the first
point where dpsz- = 0, since it does not have PdNi/ Cu or PdNi/Py interface. The
spin-diffusion length obtained from the fit is 13:de i = 5.4 d: 0.6 nm.

5.3.3 Discussion of the Results

We obtain two different values of spin-diffusion length via two different methods.
Hamood’s spin-valves indicated a smaller spin diffusion length in PdNi in comparison
to the spin-diffusion length measured later in the exchange-biased spin valves. The

longer value of lidei obtained from our second experiment supports the hypothesis

100

that the magnetization in the first set of samples was highly non-uniform due to the
out-of-plane magnetic anisotropy in PdN i films. The exchange bias in the second set
of samples forced the PdN i magnetization to lie in the plane of the film, which led to
a decreased inhomogeneous magnetization while increasing the spin diffusion length.
The fact that lsf < le even for the second set of samples indicate that the PdNi
magnetization is still inhomogeneous even after being exchange—coupled via the Py
layer.

During the course of work, we learned about the work done by Campbell and
co—workers[90, 91] 30 years ago demonstrating that Ni impurities in Pd exhibit strong
local orbital moment, which is indicative of strong spin-orbit coupling. This led us
to believe that both the origin of out-of-plane magnetic anisotropy as well as small

spin diffusion length in our PdNi alloy is a result of strong spin-orbit coupling.

5.3.4 Strong spin orbit coupling in PdNi alloy

In ferromagnets, the magnetization tends to align along certain preferred directions
called ‘easy’ axes. This property of having preferred direction is called magnetic
anisotropy. The magnetic anisotropy can have its origin in sample shape, crystal
symmetry, stress or directed atomic pair ordering. Normally in thin films the shape
anisotropy dominates the preferred direction of magnetization, thus causing it to lie
in the plane of the film. But our magnetization studies have shown that the preferred
magnetization direction in PdNi films is perpendicular to the plane of the film thus
indicating that the magnetocrystalline anisotropy rather than the shape anisotropy
dominates the preferred direction in PdNi alloy. To understand how the perpendicular
anisotropy is indicative of strong spin-orbit coupling, it important to understand the
origin of magnetocrystalline anisotropy.
Origin of Magnetocrysalline Anisotropy

What happens microscopically when fields are applied to rotate the spin system

101

b.

La, #4“ I; .‘LI 4‘. L

.. v‘ a." :5: ‘4 .‘

3 r] . -I-l . 5
‘ 1']. 'l E 1. 1

.‘ l - ' _I I It .-i -
'. 'i il 1., Ll 3,. i."
1 "I ’ '- 'i ' V ‘v 5..
‘1? “3’ ‘IIJ’ “It?" ‘f...

Figure 5.7: Fig. (a) shows the magnetization pointing in the easy direction (say) with
the orbital components aligned along the long axes (x-axis). The orbital components
(which are no longer spherical because of the spin-orbit coupling) favor the overlap.
Fig. (b) Shows the result of forcing the magnetic spins perpendicular to the easy axis.
The orbital components no longer have favorable overlap with each other. Taken from
Nicola Spaldin’s book [92].

of a domain away from the easy axis?

That is, microscopically when a field if applied to re—orient the direction of spins in
a domain, not only the electron spin but also the orbit needs to be reoriented, because
of the spin-orbit coupling. However, if the orbit is also strongly coupled to the lattice
(or to the electric field created by all nearby ions-also known as “crystal field”), any
attempt to rotate the spins is also resisted by the orbit. This is also explained by the
schematic shown in Fig. 5.7. This directional nature of the bonding causes certain
crystallographic directions to be more favorable than the others. It is possible in case
of PdNi that the film grows with a uniform strain. It is perhaps this strain-induced
crystal field along with a strong spin-orbit coupling that leads to a preferential out-
of—plane magnetocrystalline anisotropy seen in this material. Most of the materials in
fact have fairly weak spin-orbit coupling, and so the magnetocrystalline anisotropy is
not particularly strong. The perpendicular anisotropy in PdNi thin films is therefore

a strong indication of a strong spin-orbit coupling.

102

We believe that the strong spin—orbit coupling is not only manifested in perpen-
dicular anisotropy seen in PdNi thin films but also in the short spin-diffusion length
of the alloy. Furthermore, local inhomogeneities in the strain due to crystalline de-
fects or grain boundaries could cause local fluctuations in the magnetic anisotropy
direction, which further adds up to an enhanced spin memory loss. Our two methods
of measuring spin diffusion length resulted in the values 1551M = 2.8 :l: 0.5 nm and
5.4 :t 0.6 nm. The smaller of this values is a result of unpinned PdNi layer, which
we now believe is a result of conflict between the shape induced in-plane anisotropy
and the out-of-plane magnetocrystalline anisotropy. Nevertheless, it could be equally
argued that the larger of these values (seen for the pinned PdNi layer), could be a
result of enhanced in-plane homogeneity than due to the reduction of out-of-plane

component.

5.4 Spin Diffusion Length in PdFe

In our search for the right conditions and materials needed for the survival of long-
range triplet component, we realized that if we want to work with weakly ferromag-
netic systems (mostly alloys), it’s important to estimate the spin-diffusion length
a priori. Measurements performed by Campbell and co—workers in the 1970’s, in
addition to implying strong spin-orbit coupling in PdN i alloy also showed that spin-
orbit coupling in dilute PdFe alloys is comparatively weak. In fact, the past studies
have described PdFe alloy with Fe concentration of 1.4% as a nearly ideal Heisenberg
ferromagnet [93]. This motivated us to measure lsf in PdFe, with the hope that it

would be much longer than in,PdNi.

103

5.4.1 Characterization of PdFe Alloy

PdFe films were sputtered using a 5.6 cm diameter Pd target with a single Fe plug
of diameter 6.6 mm in the center. The Fe concentration in our PdFe sample was

confirmed by three different methods:
1. EDAX
2. Curie Temperature
3. Saturation magnetization.

An energy dispersion X-ray (EDX) experiment performed on a 400 nm thick PdFe
film indicated Fe concentration of about 1.6 at. %, but with a very large uncertainty
due to the very small Fe concentration. In order to get accurate concentration of Fe
in PdFe alloy, the magnetization M vs temperature of a 80 and 400nm thick PdNi
sample was measured using a superconducting quantum interference device (SQUID)
magnetometer. This is shown in Fig. 5.8. The 80 nm film showed smaller magnetiza-
tion and Curie temperature compared to the 400 nm film, which could be due to strain
during growth. The Curie temperature of 44K obtained from the 400nm thick film
provides an estimate of the Fe concentration of 1.1 at. % [93]. In yet another method,
the concentration was obtained from the saturation magnetization measured for the
same 400 nm sample. The measured magnetization of M pdN, = 63 emu/cm3=0.1
p B / Fe atom, according to ref. [93] corresponds to an Fe concentration of z 1.4 %.
These three determinations of the Fe concentration are reasonably consistent, and

lead us to our best estimate of 1.3 at. %.

5.4.2 Magnetic Anisotropy

Samples in the form of Nb(150)/Cu(10)/PdFe(x) /Cu(10)/Nb(25), with variable thick-

ness of PdFe layer were made for the magnetic measurements. Fig. 5.9 shows M vs.H

104

 

 

 

 

 

60-

"E

g 40—

3 l

E

Q)

V20-

2

”a,
0' _-..._ w» . -
' l ' r ' l l '
0 20 40 60 80 100

Temperature (K)

Figure 5.8: Black squares are the data points for M vs. T for samples of the form
Nb(150)/Cu(10)/PdFe(x)/Cu(10)/Nb(25), with 80 nm thick PdFe layer. Red circles
are the data points for .M vs. T for a 400 nm thick PdFe film. The films were zero-
field cooled to low temperature and then the magnetization was measured by applying
an in-plane field of 500 G. The temperature was then increased gradually to 100 K
keeping the field constant. The Curie temperature of the 400 nm film indicated an Fe
concentration of about 1.1%.

 

40

N
o
I
I

M (emu/cm3)
f’

-20 -~

 

 

 

 

4o . , . , . T . T , .
-750 -500 -250 o 250 500 750
H (De)

r

Figure 5.9: M vs. H at T = 10 K for a 80 nm thick PdFe film grown as
a Nb(150)/Cu(10)/PdFe(80)/Cu(10)/Nb(25) multilayer, with H pointing in-plane
(black squares) and out-of-plane (red circles)

data at T = 10 K for one such sample with a 80 nm thick PdFe—layer. Measurements

were made with H both in-plane and out-of-plane. One can clearly see a sharp switch-

105

ing to the saturation magnetization when the field is applied in-plane, whereas a large
field of z 300 06 is required to attain the same saturation magnetization when the
field is applied out-of-plane. The strong preference for in—plane magnetization in-
dicates dominance of shape anisotropy over magnetocrystalline anisotropy in these
PdFe thin films. Similar results confirming in-plane magnetic anisotropy were seen

in 60 nm and 400 nm thick PdFe films of similar geometry.

5.4.3 Double Exchange Biased Spin Valves

(Spin Valves of Type FeMn / Py / Cu/ PdFe / Cu / Py / FeMn)

In order to measure lsf of PdFe, we sputter hybrid spin valves of the form
Cu(5)/FeMn(8)/Py(8)/Cu(10)/PdFe(dpdpe)/ Cu(10)/Py(8)/FeMn(8)/Cu(5). These
spin valves are sandwiched between two thick Nb electrodes. After sputtering, the
two Py layers are pinned to the FeMn via exchange bias process as described in the
earlier section. These samples can be thought of as two FeMn/Py/Cu/PdFe hybrid
spin valves set back-to-back, with their MR signals adding. The advantage of this ge-
ometry relative to the first geometry we used with PdNi is that the magnetoresistance

signal is twice as large.

Raw magnetoresistance data are shown in the inset to Fig. 5.11 for the sample
with d pd Fe = 15 nm. The coercivity of PdFe layer is z 15 — 20 Oe, the magnetization
of PdFe layer is seen to switch at small fields. A plot of AAR vs. d pd Fe is shown
in Fig. 5.11. A fitting procedure using Valet-Fert equations yields the spin diffusion
length, lfidee = 9.6 :l: 2 nm. Although this value is larger than that obtained for the

PdNi, it may not be long enough for our study of LRTC.

106

FeMn Cu Cu FeMn

are 1“an

   

Py Pd Fe Py

Figure 5.10: Schematic for double exchange biased spin valve of the form
FeMn/Py/Cu/PdFe/Cu/Py/FeMn. A antiferromagnetic layer (FeMn) is used to pin
the outer Py layers via an exchange bias mechanism. The PdFe layer acts as a free
layer.

 

0.9

 

 

 

 

 

 

 

30.05 g
0.8 - a
130.00 g
0.7 - a
A -29.95 8
N 0.6 - ’5 ——————
E .2990 :9 ,x/
G 0.5-I - - i - - ,w”
2:, 430 -40 0 40 80 I,/
m 0.4 — H (09) III’
2 0.3 -' I” I
I
0.2 - ’
0.1 -
0-0 ' l ' I I I I I I l
0 20 40 60 80 100
deFe (nm)

Figure 5.11: AAR vs. deFe for the double hybrid spin valves containing Py and
PdFe alloy. The black solid line is a fit to the data of the Valet-Fert equations, with
the spin memory length in PdFe of QdFe = 9.6 :t 2.0 nm. The red dashed line shows

the result of a calculation assuming lQ-dFe = 00. Inset: Raw magnetoresistance data
for the sample with ddee = 15 nm.

5.4.4 Discussion of Results

We chose to work with a weakly ferromagnetic alloy with the hope that it would be

less detrimental to the observation of long—range triplet correlations. A clear signature
107

 

of LRTC would be the observation of Josephson current penetrating the F-layer over
a distance much longer than the length scale associated with conventional spin-singlet
correlations. This length scale in the clean limit is indicated by the mean free path,
le, and in the dirty-limit it is indicated by the exchange length, g F = W.
In our past experiments with PdNi alloy, we have seen that le > lsf. We believe
that the magnetically inhomogeneous nature of PdNi destroys the spin memory by
rotating the spin on a length scale much smaller than the mean-free path le. This
eliminated any hope of observing long-range triplet correlations in PdNi alloy. The
spin-diffusion length measured in PdFe alloy lfidee = 9.6 i 2nm is slightly larger
than the spin diffusion length measured in PdNi alloy lstdNi z 2.8 — 5.3 nm, however
the situation is still not ideal. Even if we expect the mean free path of the 1.4% Fe

alloy to be longer than that of the 12% Ni alloy, the long-range triplet penetration

will be damped by any process that changes the electron spin.

108

Chapter 6

Spin-Triplet Superconductivity

In Chapter 4 we presented the results obtained for S/ F /S Josephson junctions us-
ing a weakly ferromagnetic alloy PdNi. Our results show that the critical current
density in our junctions oscillates and decays as the F layer thickness is increased.
Both the oscillations as well as the short length scale of the decay (£ F=10 nm) are
indicative of standard spin-singlet correlations in our experiment. We concluded that
the short-spin memory length in our PdN i alloy or an unfavorable domain structure
were possible reasons behind lack of long range triplet correlations. A separate GMR
experiment as described in Chapter 5 was performed to measure the spin memory
length, the results of which indeed confirmed the short spin diffusion length in PdNi
alloy (l8f= 2.8 nm). This directed our search towards ferromagnetic materials that
will support propagation of the LRTC. Past studies have shown long spin memory
length in strong ferromagnets like Ni and Co. For e.g. Pure Co has indicated a
spin memory length of 40 nm [94, 95] whereas Ni gives a value of about 21 nm [89].
This led us to focus our attention towards making Josephson junctions using strong

ferromagnets.

109

 

6.1 Ferromagnetic Josephson Junctions using Ni

Figure 6.1 shows Ic vs H obtained for a S/ F/ S Josephson junction using a strong fer-
romagnet, Ni. The pattern differs significantly from the standard Fraunhofer pattern
observed earlier for Josephson junctions using weakly ferromagnetic alloys (See Chap-
ter 4, section 4.1). Aware of our adeptness in making reliable Josephson junctions,
we realized that the origin of irregularities in our Fraunhofer pattern was a result
of our choice of F-material. Later, similar results were observed by my colleague
Mazin when he was working on Josephson junctions using Co-layer [96]. Several
other groups studying S / F / S Josephson junctions have seen similar random-looking

Fraunhofer patterns [97].
Physics Behind the Irregularities Seen in Fraunhofer Pattern

In Chapter 4, section 4.1, we studied Josephson junctions using weakly ferromag-
netic alloys CuNi and PdNi. We saw nearly an ideal Fraunhofer pattern in virgin as
well as magnetized state of the sample. However, the results obtained using strong
ferromagnet varied drastically from our earlier observation using weak ferromagnet.
To understand this better, let us refer back to the equation for critical current given

in Chapter 2, section 2.6.3,

Is = /J(x,y)dxdy (6.1)
where,
J(x,y) = Jc siny = JC sin(Al9 + %/A(x,y).dl) (6.2)
O

In macroscopic samples the magnetization breaks into domains. Due to the do-
mains pointing in random directions, the term containing the vector potential per-
forms a random walk as one moves across the sample. In order to solve the above

equation, one must therefore integrate the current density across the area of the junc-

110

 

 

'c (mA)

0.4 -

0.2 -

n

0.8 -

0.8 -

 

c. 6A2

= 472'M

 

 

W 5y

 

.v

Figure 6.1:

 

A2
0 l I 1—ffi7 I I I I
-240 -200 450 —120 50 4o 0 4o
Hext (0e) ‘

<——>'\/ \v:

domain size

(a) Critical current Ic vs. in-plane magnetic field Hem for a Nb/ Ni/ Nb

Josephson junction of diameter 10 pm, with sz‘ = 11 nm. The black points (squares)
represent the virgin state measurement, whereas the red points (circles) are obtained
after magnetizing the sample in an external field of 1000 De. (b) The large magnetic
domains in ferromagnetic layer. (c) The vector potential taken across the red line
shown in part (b). The large domain sizes cause the vector potential to deviate
severely from the zero.

111

tion, taking into account the spatial dependence of the magnetic vector potential A
due to the domains. If the magnetic domains are very small and/ or the magneti-
zation is very weak as in the case with weak ferromagnetic alloys, then the vector
potential term stays near zero in all parts of the junction, and the critical current is
hardly affected. This leads to nearly ideal Fraunhofer patterns for Josephson junc-
tions using weak ferromagnets like CuN i and PdNi. But if the magnetic domains are
large and/ or have large magnetization as in the case of strong ferromagnets like Ni
or Go, the vector potential deviates far from zero even as it crosses a single domain
as shown in Fig. 6.1. This large vector potential variation across the sample leads to
a positive contribution to the overall phase 7, thus severely suppressing the critical

current. This can lead to complete destruction of the Fraunhofer pattern as seen in

Fig. 6.1.

In principle, a regular Fraunhofer pattern can be recovered if the sample is com-
pletely magnetized. For a sample magnetized by applying large positive field, a regular
Fraunhofer pattern should be obtained when the flux due to an external magnetic
field cancels the flux in the junction. This however should lead to a shift in the
Fraunhofer pattern as observed earlier in the case of Josephson junction using weak

ferromagnetic alloys. This shift is given by,

-M0MdF

Hshift = m (63)

However, the above argument holds only if the coercive field of the magnetic mate-
rial is large enough. For small coercive fields the applied field can lead to variation in
the magnetic domain structure even as one is attempting to measure the Fraunhofer
pattern. For the case of the Ni sample shown in Fig. 6.1, the largest peak in the
critical current Ic vs. field Hext after magnetization is found near —160 Oe, whereas

the expected shift calculated from the known saturation magnetization of Ni is ~ -207

112

 

Oe. Since the coercive field in our film was expected to be around 180 Oe, we believe
that the observed discrepancy is caused either by some rotation of the magnetization
in the domains or some domain wall motion. [The coercive field of 180 Oe was in fact

measured in a different 9 nm thick Ni film]

6.2 Reduction of Flux

With the distortions seen in the case of Josephson junctions using Ni, it is difficult
to get a good measure of the maximum critical current. To reduce the distortion of
the Fraunhofer pattern it is important to reduce the flux in the junction. We suggest

the following mode of operation to reduce the flux in the junction:

1. Reducing Thickness of the F-layer: Use of ultra-thin ferromagnetic layers
ensures reduction in flux in the junction. Under this condition, the flux enclosed
in the junction due to a single large magnetic domain can be much less than
one flux quantum, and one then safely ignore the contribution to flux from the
magnetization of the junction. Since a positive indication of LRTC can only
be sought at thicker values of F-layer, this option was not available to us. In
addition, the magnetically dead layers formed at the interfaces form an added

disadvantage in working with ultra-thin ferromagnetic layers.

2. Reducing Lateral Dimension of the Junction: Fabricating devices with
ultra small lateral dimension reduces the flux in the junction. This option was
pursued by Blamire and his co—workers while working on Josephson junctions
with strong ferromagnets like Ni, Co, Fe and Py [27 , 28]. A similar approach
was taken by Strunk and his co—workers while working with Cd [18]. This
method becomes less effective as the thickness of the ferromagnetic layer is
increased, and hence was not favored in our study of LRTC. In addition, working

with smaller lateral dimension restricts the possibility to introduce magnetic

113

 

inhomogeneities via multidomain structure that is naturally present in devices
of larger dimension. Such inhomogeneities may contribute to the generation of
LRTC as predicted by various theory papers [8, 33, 34]. Our aim during the
course of this study has been to exploit such inhomogeneities in the observation

of LRTC.

. Use Ferromagnets with Small Domain Size and/or Small Eem: This
gives another way to reduce the flux in the junction. This option was recently
pursued by us using a weakly ferromagnetic alloy, PdNi. We have obtained
excellent Fraunhofer patterns for demagnetized samples as well as for the uni-
formly magnetized samples. The latter patterns were shifted in field, but the
maximum value of the critical current was nearly unchanged. This indicated
that the magnetization of the PdN i layer makes very little contribution to the
total magnetic flux of the sample. The details of this experiment are given
in Chapter 4. The same is true for another weakly ferromagnetic alloy CuNi.
However there was no indication of LRTC in our experiment. Our later mea-
surements indicated that the short spin diffusion length (le z 2.8 nm) in this
alloy restricted the long range propagation of spin-triplet correlations. Simi-
lar options utilizing weak ferromagnetic materials were also pursued earlier by

various other groups [21, 23, 66], however no long-range Josephson effect was

observed.

. Engineer the F-layer to have Zero Net Magnetic Flux: One can engi-
neer the F-layers such that the net magnetic flux in the junction is zero. This
can be done using antiferromagnetically coupled F/ N/ F layers. We call this
configuration, “synthetic antiferromagnet”. This method not only reduces flux
in the junction but it also gives us an opportunity to work with strong ferro-

magnets. The next section will describe in detail the experiments undertaken

114

 

by our group using this method.

6.3 Synthetic Antiferromagnet (SAF)

The idea of using a synthetic antiferromagnet in our Josephson junction stems from
the GMR expertise of Prof. Pratt working in this field for a long time. Most of the
work henceforth utilizes antiferromagnetically coupled F-layers in reducing the flux
in the junction. Here I will give a brief overview of the physics behind antiferromag-
netically coupled F-layers.

Oscillatory Exchange Coupling

 

O

a)
l

O)
I

a.
l

 

 

Saturation Field (kOe)
N
1

 

 

 

Ru thickness (A)

Figure 6.2: Field needed to saturate the magnetization at 4.2 K vs Ru thickness for
Si(111)/(100 A) Ru/[(20 A) Co/tRu Ru/zo/(50 A)Ru deposited at temperature of 40
C (filled circles), 125 C(Empty circles) and 200 C(cross). Taken from Parkin et
al., 1990 [98].

It has been known for a long time that when an impurity is placed in an electron
gas, the background charge is redistributed to neutralize the impurity charge. This
disturbance gives rise to decaying oscillations of electron density as a function of

the distance from the impurity. These are called Friedel oscillations. It turns out

115

 

that something similar happens when a magnetic impurity atom is in a metallic
surrounding. In this case, the magnetic impurity gives rise to an oscillatory spin
polarization of the electron density that decays as a function of the distance from
its source. As a result the magnetic coupling of the next atom placed close to the
magnetic impurity can either be parallel or antiparallel to the magnetic moment of
the impurity atom depending on the sign of the induced spin polarization at that
particular distance. This physical mechanism leads to the long range oscillation in
exchange coupling between magnetic moments. The model described here is called
the RKK Y model. Such a mechanism is known to exist in rare-earth metals like
Gadolinium (Gd). In 1986, Majkrzak et al. [99], while working on Gd/Y/ Gd found
antiparallel magnetic moments in the Gd layers, the origin of which was believed to
be RKKY interaction. In 1988, Baibich et al. [83] found a similar anti-ferromagnetic
coupling in Fe/ Cr/ Fe structures. A detailed study of such structures later led to the
discovery of oscillatory dependence of the coupling on the thickness of the central
layer. In particular, Parkin et al.(1990) [98] observed that the coupling in [Co/ Ru] N
(and [Fe/ Cr] N) structure oscillates between ferromagnetic and antiferromagnetic as
the thickness of the spacer layer Ru (and Cr), is increased. Fig. 6.2 shows the Ru
thickness dependence of the field needed to saturate [Co/ Ru] N multilayers. Large
fields are required to saturate the multilayer when the Ru thickness is 6, 16 or 30
A. The large saturation fields are indicative of antiferromagnetic coupling between
the Co layers, whereas small saturation fields effect imply ferromagnetic exchange

coupling between the Co layers.

6.3.1 Josephson Junctions using SAF of the form 00/ Ru/ Co

In this sub-section I will talk about the results obtained by my colleague Mazin while
working on Josephson junctions using a synthetic antiferromagnet. These results are

published in Phys. Rev. B 80, 020506(R) (2009). Josephson junctions of the form

116

 

   

Nb——>

Co/Ru/Co

Nb

Figure 6.3: Schematic of the Josephson junction using a strong ferromagnet Co in
Synthetically antiferromagnetic form (i.e. Co/Ru/ Co form). In this configuration the
domain in the top Go layer are antiparallel to the domains in the bottom Co layer,
which leads to zero net flux in the junction. The antiparallel configuration is sensitive
to the thickness of the Ru.

Nb/Cu/Co/Ru/Co/Cu/Nb were made using the techniques described earlier in this
thesis. We refer to the central Co/Ru/Co trilayer as a synthetic antiferromagnet.
The schematic of this junction is shown in Fig. 6.3. The magnetization of the two
outer Co-layers is exchange—coupled in antiparallel direction via the 0.6 nm thick Ru
layer in the center. As a result, the total magnetic flux in the junction is nearly zero
and the junctions exhibits nearly ideal Fraunhofer patterns as shown in the inset of
the Fig. 6.4. The data for critical current vs. total Co thickness are shown in Fig.
6.4.

As seen from the graph, Ic decreases by four orders of magnitude as the total Co
thickness varies from 2 to 23 nm. The overall decay fits well to a simple exponential
decay. N o discernible oscillations were seen. This is in accordance with several theory
papers based on this topic [100]. However there was no indication of the LRTC,
which as said earlier would manifest itself as a crossover to a slower decay at large Co
thicknesses. The lack of LRTC in Mazin’s experiment was attributed to two possible
reasons: i) Large spin memory loss at the Co/ Ru interface that restricts the long

range propagation of triplets, ii) Lack of magnetic inhomogeneities in the Co layer,

117

 

 

 

 

  

 

 

         

 

 

9 . . -
E, 103 0.0920 -10 o 10 2
Z 3
E0 1:
0.1,
o 6 1'0 1 1'5 2'0 2'5

DCO (nm)

Figure 6.4: Product of critical current times normal resistance ICRN vs. total 00
thickness D00 = 2dCO in the Josephson junction using SAF configuration. The solid
line is a fit to an exponential decay, with the decay constant of 2.34 :l: 0.08 nm. The
inset shows the excellent Fraunhofer obtained for Nb/Cu/Co/Ru/Co/Cu/Nb circular
Josephson junction with total Co thickness D00 = 25100 = 18 nm. The pillar diameter
is 20 pm.

which as said earlier are essential for the generation of LRTC.

Figure 6.5 shows scanning electron microscopy with polarization analysis (SEMPA)
done for a [00/ Cu] N multilayer structure by John Unguris’ group at NIST [101]. The
samples used for this study were made in our sputtering system. The picture shows
the magnetic domain structure with domain size ~ 3 pm in Co films. The domains
are mostly oriented antiparallel, indicating lack of collinear magnetization needed for
the generation of triplet correlations. However, when we started with this study our
hope was to exploit the regions of non-collinear magnetization present in the domain

walls.

118

If

 

 

 

 

 

lo P(A¢) (arb. units)

 

Figure 6.5: SEMPA images of the topmost Co layer magnetization (a) and topography
(b) and second 00 layer magnetization (c) in the [00(6 nm)/Cu(6 nm)/20 sample.
The magnetization direction is mapped into color as indicated by the color wheel in
the center. A histogram of the difiemnce in the magnetization direction between the
two layers, A45, is shown in (d). { Figure taken from Borchers et al. [101])

6.3.2 Other Experiments using SAF Configuration

Not knowing if the spin memory loss is large at the Co/ Ru interface, we decided to
substitute Cu for Ru in our SAF Josephson junctions. We know that spin memory
loss at the 00/ Cu interface is only about 25% [102]. Here I report the results of
the experiment identical to one performed by Mazin, but using SAF of the form
Co/Cu/Co. Josephson junctions of the form of Nb/ Cu/ 00/ Cu/ 00/ Cu / Nb were made

119

 

 

 

 

 

 

 

-2'o ' -1'o - b 1 1b 30
Hex.( (09)
Figure 6.6: Critical current vs. applied magnetic field obtained for

Nb/Cu/Co/Cu/Co/Cu/Nb circular Josephson junction with total Co thickness of 14
nm. The pillar diameter is 20 pm. The distortion in the Fraunhofer pattern is a
result of incomplete flue: cancellation in the junction.

with the variable Co thickness. The magnetization of the two outer Co layers is
exchange-coupled in antiparallel direction via the 0.6 nm thick Cu layer in the center.
Fig. 6.6 shows the Fraunhofer pattern obtained for one such junction using total Co
thickness D00 of 14 nm.

The [C vs Hem differs significantly from the ideal Fraunhofer pattern obtained for
the Josephson junctions employing the SAF of the form of Co/ Ru / Co. This is because
the antiferromagnetic exchange coupling in 00/ Cu/ Co trilayers is not as strong as
in Co/Ru/Co trilayers. We also know this from magnetic measurements performed
by Mazin, which showed a regular hysteretic loops with low saturation fields ~ 200
Oe. This leads to an incomplete flux cancellation inside the Josephson junctions,
which in turns leads to significant distortions in the Fraunhofer pattern. Past studies
done by other groups have shown that the antiferromagnetic coupling strength in

00/ Cu systems is sensitive to the crystalline orientation of the as grown films, which

120

 

 

according to the literature can be improved by implementing an appropriate buffer
layer. However, we did not pursue this route any further at this time. Shortly after,
Mazin performed GMR experiments to measure the spin-memory loss at the Co/ Ru
interface, the preliminary results (unpublished) of which indicate no more loss of
spin-memory at the Co/ Ru interface than at the Co/ Cu interface.

Other systems including N i / Ru / Ni, Ni/ Ag/ Ni were made and magnetic measure-
ments were done to check for antiferromagnetic coupling. Our measurements of these
showed regular hysteresis loops with low saturation fields indicating large ferromag-
netic contribution from the coupled structure. They were therefore not found to be

suitable SAF candidates in our study of LRTC.

6.4 Long-Range Triplet Correlations in Our Ex-
periment

At this point, it was essential to put all the information together and realize that there
are two important aspects to the study of spin-triplet correlations: the “generation” of
spin triplet correlations and their “survival / propagation” in our Josephson junctions.
Any further progress in this search implied a careful consideration of both aspects.
Fig. 6.7 shows the basic idea behind this experiment.

Propagation of the LRTC (Central SAF Layer):

Although working with a weak ferromagnet allows us to measure junctions with
thicker ferromagnet materials, the spin—flip and/ or spin orbit scattering in weak fer-
romagnetic alloys limits the survival possibility of the long-range component of the
supercurrent. The current information on the spin diffusion length in PdNi, PdFe,
CuNi did not look very promising. The strong ferromagnets on the other hand have
long Spin-memory length, however the aforementioned difficulties in getting a good

Fraunhofer pattern indicate that they can be used only in Synthetic antiferromagnetic

121

 

 

   

Nbfi

Triplet Generator (X)
Trlplet Propagator
Triplet Generator (X)

Nb

Figure 6.7: Conceptual diagram representing the division of labor in our junction
— the X-region close to the Nb interface is to facilitate the ‘generation’ of triplets,
whereas the central SAF layer employing strong ferromagnet is essential in long range
‘propagation’ of the triplet correlations.

(SAF) form. We therefore chose to rely on our SAF system as a propagator of triplet
correlations. In the experiment that I will describe in this section, we have chosen to

work with Co/Ru/Co as our SAF system.
Generation of the LRTC (X Layer):

Generation of the LRTC was another critical issue for this project. Although
there are several theory papers that suggest different methods of generating LRTC,
our approach during the course of this study was to utilize the naturally occurring
magnetic domain structure in macroscopic samples. As described in earlier section,
Mazin’s Josephson junctions using Co/Ru/Co failed to show any LRTCs indicating
that Co may not have the right kind of inhomogeneous magnetization needed to
induce the LRTC. On the other hand, although short spin diffusion length in weakly
ferromagnetic alloy like PdNi and CuNi is known to limit long range propagation
of LRTC, nothing conclusive could be said about their ability to generate triplet
correlations. A recent experiment performed by Vashchunov et al. [72] on CuNi alloy

revealed that the material has perpendicular magnetic anisotropy and has a small

122

 

a)

__§i_q(____-le (200 nm)
:::::::::::::: Nb (25 "ml

f

    
  
 
 

50
Au (15 nm) *:::::£:’§:::

Nb (150 nm)l F

b) F layer:

Cu (5 nm) ——r , ., 4 X=PdNi
Cu (10 nm) _.,
Co (dco) A’ .31.». " ""““"'_.';'fif'2‘§./ Ru (0.6 nm)

.———-—. “—__J-—__‘.l-_...-ru__u .I.

Cu (10 nm)_p

.4 X=PdN'
Cu (5 nm) —>. . |

Figure 6.8: (a) Schematic diagram of Josephson junction samples. (b) Details of the
F-layer shown in a). PdNi is used at the Nb interface is to facilitate triplet generation,
whereas the central SAF layer, Co/Ru/Co, is to propagate the triplet correlations.
The Cu buffer layers play no active role in the device, but are important to isolate the
magnetic layers—PdNi and Co.

domains of the size ~100 nm. Although there is lack of information on the exact
nature of the domain structure in PdNi alloy, we suspect that PdNi alloy has similar
domain structure as CuNi. As said earlier, if the domain size is not much larger
than the superconducting coherence length in Nb (~ 14 nm), the long-range triplet
correlations could be induced. However, as measured earlier in Chapter 5, PdNi alloy
also has a short spin memory length. But if we keep the PdNi layer sufficiently thin,
the extent of spin memory loss will be small, and propagation of the LRTC will not
be completely suppressed. Apart from PdNi and CuNi alloy, we believe that there

could be many other ferromagnets that could be used as a generator of LRTCs.

A schematic diagram of our Josephson junction samples is shown in Fig. 6.8a.

Figure 6.8b shows the detailed sequence of internal layers of the labeled F—layer in

123

 

Figure 1a. Here I will discuss the role of each layer in brief:

1. The purpose of the weakly ferromagnetic alloy PdNi or CuNi— inserted between
the Co and Nb layers is to introduce magnetic inhomogeneity and thus facilitate

the generation of triplet correlations.

2. The purpose of the central SAF layer, Co/Ru/Co, is to propagate the triplet
correlations. The advantages of using Co—based SAF are three-fold: 1) The long
spin diffusion length in Co helps in propagation of long range triplet correlations,
2) Using Co in SAF form ensures zero net flux in the junction. As a result, our
data exhibit nearly-ideal Fraunhofer patterns (See Fig. 6.9) thus helping us
in getting a reliable measure of the maximum critical current. 3) Co being a
strong ferromagnet, destroys the spin singlet correlations on a length scale of
only few nanometers, it however favors the propagation of long range triplet
correlations. It therefore also acts as a filter of spin singlet correlations for large

thicknesses.

3. The Cu layers between the X-layers and the Co layers serve two purposes. 1)
They isolate the X and Co layers magnetically, so the magnetization of the X
layers is not exchange-coupled to that of the Co layers. 2) The lower Cu layer
used close to the Nb interface improves the growth quality of our sputtered Co
[96].

Figure 6.10 shows the product of critical current and normal state resistance
(ICRN) vs. total cobalt thickness (D00 5 2dCO) for a series of samples with fixed PdN i
layer thickness, dpdm = 4 nm. For comparison, Fig. 6.10 also shows Mazin’s data
for identical junctions but without the PdNi layers. As the Co thickness is increased,
the critical current of the Josephson junctions with the PdNi alloy decays very slowly
which is in sharp contrast to the very fast decay observed in the junctions without

PdNi alloy. In samples without PdN i, ICR N decays very rapidly with increasing DCO,

124

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12-a)
8.
4.
A OM' 10
< ' .
E 06 _
v c)
o l
— 0.4-
0.2- \
0.0 mm 0.00 fies T . . ..
-30 -20 -10 0 10 20 30 -20 -10 0 10 20
Hext(0e)

Figure 6.9: Critical current (16) vs. applied magnetic field (Hat) for Josephson junc-
tions with fixed PdNi-layer thickness dpsz- = 4 nm and variable Co-layer thicknesses
(6100) a) 2nm, b) 7nm, c) 13nm, d) 18nm. The pillar diameters w are 20, 20, 10, 20
mm respectively.

125

 

 

 

 

l unsung}

 

 

 

A

>

t: . o

v . i .

z :
m .
—o I

1.
l I I ‘
30 4o 50
DCo (nm)

Figure 6.10: Product of critical current times normal state resistance, IcRN, as a
function of total Co thickness, DCo = 2dCO. Red circles represent junctions with
PdNi and dpdNi = 4 nm (fired), whereas black squares represent junctions without
PdNi layer (taken from Ref. [96] ) ( The solid line is a fit of the data without PdNi
to a decaying exponential, also from Ref. [96]. In [96], data from multiple junctions
with the same value of D00 were represented by a single data point with an error
bar; here, each device is represented by its own data point.) The blue stars represent
measurements performed on Josephson junctions with triplet generator- PdNi placed
only on one side of the junction.

126

 

 

on a length scale of just 23410.08 nm [96]. The long-range character of the Josephson
current in samples with PdNi is a strong evidence for spin triplet correlations in our
system. There is a clear enhancement in critical current for the samples with PdNi
over those without PdNi. For example, when D00 = 20 nm, ICR N is over 100 times

larger in the samples with PdNi than in the samples without PdNi.

6.4.1 Strength of Triplet Correlations

Effect of PdNi Thickness Variation

Apart from the above mentioned clear indication of spin triplet correlations, we
found that the strength of the triplet correlations can be controlled by varying the
thickness of the PdNi layer.

Figure 6.11 shows IcR N vs. dpdNi for samples with 000 fixed at 20 nm. Without
any X-layer, ICR N is very small, whereas when the thickness of PdNi is increased the
[CR N increases until it reaches a maximum for dpsz- z 3 — 6 nm, after which it
decreases again. The decrease in [CR N for large thicker PdNi signals the destruction
of the spin-triplet correlations. This is perhaps because of the spin memory loss in
the bulk of the PdNi when the layer thickness is increased. As measured in our
GMR experiment, the spin memory length in PdNi was only about 2.8 nm [87]. This
would therefore explain why there was no evidence for spin-triplet correlations in our
Josephson junctions containing only PdNi layer [103]. However, having PdNi layer is
essential in generation of triplet correlations in our experiment described above.

Additionally, we have also measured samples without the Cu buffer layer between
PdNi and Co. Our measurements indicate no enhancement of the critical current
in this case. The Cu buffer layer ensures magnetic isolation of layers, removing Cu
leads to exchange coupling of the PdNi and Co layer. It is possible that the out-of-
plane magnetization in PdNi is the source of magnetic inhomogeneity in our system.

However, when PdNi is placed next to Co—layer, the exchange coupling of the layers

127

 

 

 

 

 

 

 

100 I I I I I I I
j
A 101 1
> 3 3
5 ; .
z .
m
11 3
0.1- . d
I ' I f r fi I I I ' I ' I
0 2 4 6 8 10 12
deNl (nm)

Figure 6.11: ICR N product as a function of d pd N,- for a series of junctions with fixed
000 = 20 nm. The ICRN first increases, then eventually decreases with increasing
dpsz'. Lines are guides to the eye.

force the PdN i moment to lie in-plane of the sample thus reducing the inhomogeneities
essential for the generation of triplet correlations. However it is hard to definitively

conclude anything about the microscopic mechanism that leads to triplet generation.

Since it is not possible to have Josephson current due to the interference between
the singlet and triplet components, we decided to test our Josephson junctions by
removing the PdNi layer from one side of the junction. These measurements are
indicated by blue stars in the Fig. 6.10. We have seen an enhancement in the critical
current that was five times larger than the spin-singlet current. However looking at
large sample-to-sample fluctuations, it is hard to attribute this enhancement to any

definite effect.

128

 

Hunt“ 1. A -
i

 

 

6.4.2 Where are the Triplets Generated?

Although a clear distinction was made in Fig. 6.7 indicating the region that generates
triplet and the region which propagates triplet, in reality it is hard to strictly classify
the process into two distinct events. We believe that there are two possible sources

of non-collinear magnetization in our samples.

1. If the Cooper pairs experience non-collinear magnetization between adjacent
domains in the X-layer, then domain size and out-of-plane magnetocrystalline
anisotropy are likely to be key ingredients in generation of LRTC. Although
PdNi [103] and CuNi [71, 72] alloy are known to have out-of-plane magnetic
anisotropy, there is no information on the domain structure in PdNi alloy.
Cu0,47Ni0,53 alloy on the other hand is known to have domains that are of
the order of 100 nm, which is not so different from the Nb coherence length
6 S = 14 nm [104]. It is also known that the competition between out-of-plane
magnetocrystalline anisotropy and the in—plane shape anisotropy in thin films
can lead to stripe domains with canted magnetization [105]. This could also be

a possible cause of non-collinear magnetizations in our films.

2. It is also possible that the C00per pairs experience non—collinear magnetization
between the X layers and the Co layers. If this is true then almost any ferro—
magnetic layer could work in place of the X layers, provided the magnetization
directions of the X and Co layers are independent. However the advantage of
using weakly ferromagnetic alloys as our X—layer is to preserve good Fraunhofer

I patterns. Using a strong ferromagnet as the X layer increases the flux trapped

in the junctions, which then leads to destruction of Fraunhofer pattern.

129

r_\'79...‘_u:1w'lT

 

 

6.4.3 Temperature Dependence of the Triplet Samples

We have also studied the temperature dependence of the critical current in a couple
of our samples that show long range triplet correlations. Fig. 6.12 shows IC vs H
measured at different temperatures for our Josephson junctions with DCo = 26 nm

and D00 = 50 nm; for a fixed thickness of PdNi dpsz' = 4 nm.

0.05

 

 

  
  
 
 
  

{1.66K'
01.9“.
.5251 K
v3.0“:
+4.10K,
+4.0“

 

 

 

 

 

 

 

V

Hext (09)

Figure 6.12: [C vs H measured at temperatures in the range from 1.6-8 K for: (a)
Josephson junction with D00 = 26 nm and dpdm = 4 nm, (b) Josephson junction
with D00 = 50 nm and dpsz- = 4 nm

Figure 6.13 shows monotonic decay of the normalized ICR N as a function of tem-
perature. The nature of the decay is independent of the F-layer thickness.

According to theory for diffusive S/ N / S junctions, the junctions are said to be in
“short junction regime” if A < Eth, or they are said to be in “long junction regime”
if A > Etha where Eth = hD/d2 is the Thouless energy, D is the diffusion constant,
and d is thickness of the N-layer. In long junctions ICR N is limited by the value
of Eth, or in other words it is sensitive to the change in thickness of the N-layer.
However, qualitatively our measurements indicate no significant change in the nature
of the decay for D00 2 26 nm and 50 nm, indicating that we are in the short junction

regime where 1012 N is dominated by the gap A. We were therefore not able to measure

130

 

 

0.11

Normalized 'cRN

 

 

 

0.01 1

 

1'é'é'l'é'é'i'a'9
Temperature (K)

‘

Figure 6.13: Monotonic decay of critical current as a function of temperature. Our
samples are in the short junction regime.

the Thouless energy, which is another way to gauge the strength of our junctions. To
get a reliable measure of the Thouless energy we need to measure junctions in the
long limit. Such a measurement requires measuring the temperature dependence of a
triplet sample with a very thick Co layer. Our measurements however indicate weak
antiferromagnetic coupling for thicker samples, leading to poor Fraunhofer patterns,

whence getting a reliable measure of critical current becomes difficult.

6.4.4 Discussion of the Results
6.4.4.1 Comparison between Theory and Experiment

Comparison of our results with theory is problematic because the magnitude of the
spin-triplet supercurrent depends on the details of the PdNi or CuNi domain struc-
ture, while theoretical calculations exist only for idealized magnetic configurations.
Nevertheless, there are three recent theory publications that are relevant to the sample

geometry studied here. Our samples can be viewed as realizations of the S / F’ / F / F” / S

131

 

junctions studied theoretically by Houzet and Buzdin [54], but with Cu buffer layers
separating the three ferromagnetic layers. This paper assumes that the magneti-
zation in three layers have same amplitude (same exchange energies) but different
orientations and goes on to show the that triplet contribution to the critical current
is sensitive to: 1) The relative orientation of the magnetization in successive F-layers;
2) The thickness of outer F’ and F” layers. They predict maximum triplet super-
current when the F’ and F” layer thicknesses are of the order of {F- We do observe
the predicted maxima in the triplet current for a certain thickness of outer PdNi-
layer. There is an apparent qualitative agreement between the prediction and our
result as seen in Fig. 6.11. More recently another two theorists, Volkov and Efetov,
have worked on our sample geometry [49]. This paper assumes a sample geometry
of the form S/F ’/F / F”/ S, but with the central F-layer composed of two domains
with parallel or antiparallel magnetization. In contrast to Houzet and Buzdin paper,
this paper assumes different exchange energies for central and outer F-layers. The
qualitative dependence of the triplet current on the outer F-layer thickness is simi-
lar to the Houzet and Buzdin paper. Both the above mentioned papers work in the
regime where E81; < E F- A third paper that is relevant to our sample geometry has
just appeared in cond—mat [50]. In addition to the above geometry considerations,
this paper has worked out problem in the clean limit and for moderately diffusive

ferromagnets using the Eilenberger equations.

In conclusion, the comparison between theory and experiment is difficult because
of the triplet sensitivity to: 1) size of domains and the domain walls, 2) orientation of
magnetization in these domains and the domain walls, 3) relative orientation of mag—
netization between two adjacent F-layers, etc. More theoretical as well experimental

work is therefore needed to understand this issue in detail.

132

 

 

.37 I‘ll!

 

6.4.4.2 Confirmation of Triplet Correlations

In the “dirty” limit, where the mean free path, le, is the shortest relevant length
scale in the problem, the spin-singlet supercurrent should decay on the length scale
5 F = (fit—WE, where D F and Eex are the electron diffusion constant and exchange
energy in the ferromagnet. However Mazin’s Co—based Josephson junctions containing
Co were in the “intermediate” limit, with le longer than fip, but shorter than {3, the
superconducting coherence length. In that limit, the spin-singlet supercurrent decays
on the length scale le. Mazin’s data gives an estimate of this length scale to be ~ 2.4
- 3.0 nm; which is agreement with previous measurements done by Blamire and his
co-workers [27]. This rapid decaying spin-singlet supercurrent for Mazin’s samples is
also shown in Fig. 6.10. In contrast, when the PdNi-layer was added close to the Nb
interface, we observed a huge enhancement in the critical current—for example, when
000 = 20 nm, the observed critical current was about 100 times larger in samples
with PdNi than for the samples without PdNi. This gives us a clear confirmation of
triplet supercurrent in our Josephson junctions. However, it is important to note how
our samples shows no discernible decay until ~ D00 = 30 nm, which then is followed
by large sample-to—sample fluctuations for thicker samples. This is because for the
samples with larger D00, the Fraunhofer patterns were poor, which made it difficult to
get an accurate measure of maximum critical for those junctions. We believe that this
is because the antiferromagnetic coupling of the Co/Ru/Co trilayer is less effective
for thicker Co layers. As said earlier, the spin-triplet supercurrent should decay over

a much longer length scale given by the smaller of the normal metal coherence length,

 

€N = \/hDF/27rkBT, or the spin memory length, Lsf = JhDF/rsf, where rsf is
the mean time between spin-flip or spin-orbit scattering events. However the large
fluctuations seen in our samples makes it impossible to get an accurate measure of

the triplet decay constant for our samples.

133

 

Looking back, there were hints of long-range proximity effects in S / F hybrid sys-
tems, some of them as early as 10 years ago [5, 106, 7, 107, 10, 32], but there was no
way to control the observed effects. For a long time the main problem in obtaining
definitive and reproducible evidence of LRTC was to identify and invent a mechanism
that creates LRTC. Our results give a strong evidence of induced spin-triplet corre-
lations, the magnitude of which can be controlled by varying thickness of the PdNi
layer.

The spin-triplet pair correlations observed here and discussed in Ref. [11] are quite
different from those believed to occur in materials such as SrzRuO4 [3]. The Cooper
pairs responsible for the LRTC effect seen in this experiment are believed [9, 8] to be a
result of unusual s-wave triplet pairing mechanism that is odd under time reversal, or
odd in frequency. Nevertheless, the observation of enhanced supercurrent in itself does
not provide a conclusive evidence of this unusual symmetry of the pair correlations.
More experiments need to be done to affirm. the symmetry of observed long-range

pair correlations.

134

 

. is 1'4"..-

.é". . "

 

IAI‘K ‘u' ._'.f

 

Chapter 7

Discussion and Further Work

7.1 Our Aim

The main aim of our project was to present an irrefutable, reproducible indication of
LRTC in our S / F/ S Josephson junctions. According to the theory, such spin-triplet
correlations are known to generate in a system only in the presence of magnetic
inhomogeneities [9, 8]. In the absence of magnetic inhomogeneities, only spin-singlet
and short-range triplet correlations exist which cause the critical current to decay
and oscillate on a length scale given by {Emmet = m in the dirty limit.
Because of the large exchange energy, Eex, this length scale is only of order of a
few nanometers. However, if the system has magnetic inhomogeneities, then apart
from the singlet correlations, long range triplet correlations can be induced. These
LRTC correlations are known to decay (without oscillations) on a length scale given
by égriplet = W in the dirty limit. Since this length scale is independent of
E33, and is only governed by the temperature, this causes the critical current to exist

for a length scale as long as few hundreds of nanometers at low enough temperatures.

135

 

 

 

7 .2 Overview of Our Work

During the initial stages of the project, it was important for us to separate the fabrica-
tion challenges from the real physics problems. A well known CuNi-based Josephson
junction served as our working template during the fabrication stage. After gain-
ing sufficient confidence in our fabrication technique, we ventured into this field by
creating S / F/ S Josephson junctions using a weakly ferromagnetic PdNi alloy as the
F-layer. Our junctions showed an oscillatory short length decay of the critical current
as a function of PdNi thickness. This short length oscillatory decay was indicative of
spin singlet correlations in our junction. The lack of LRTC in this experiment was
attributed to a short spin memory length in PdNi alloy, measured later in a separate
GMR experiment. Our further efforts in this field therefore concentrated on working
with strong ferromagnets which are known to have a long spin memory length. As
soon as we started working on Josephson junctions using strong ferromagnets, we
realized that the large flux contribution from strong ferromagnets made it impossible
to get an accurate measure of the maximum critical current. We therefore decided to
use them in a SAF configuration. A separate experiment was therefore conducted by
my colleague Mazin using Co/Ru/Co as a SAF layer in a Josephson junction. The
results of his measurement also showed a short length decay of the critical current as
a function of Co layer thickness. We suspected lack of inhomogeneities as a possible

reason behind the lack of LRTC in this experiment.

At this point we realized that the ferromagnetic materials helpful for the gener-
ation of LRTC may or may not support it’s long range propagation. A new device
was therefore designed where the role of LRTC generation was assigned to a thin
ferromagnetic X layer placed close to the Nb interface, and a central SAF layer con-
sisting of a Co/Ru/Co trilayer, because of the virtue of long spin memory length in

Co, was used for the long range propagation of thus generated LRTC. Our resulting

136

 

 

junction was a multilayer of the form Nb/Cu/X/Cu/Co/Ru/Co/Cu/X/Cu/Nb. We
observed that our junctions with X=PdNi layer showed a huge enhancement in the
critical current over the junctions without the X-layer, thus confirming the generation
of triplet correlations as a result of an added PdNi layer. A similar effect was seen

when Mazin replaced PdNi alloy with a CuNi alloy [108].

7 .3 Future Directions

After the successful observation of triplet correlations in our experiment, much of our
research efforts were directed towards understanding the exact mechanism behind
the generation of long range triplet correlations in our experiment. As discussed
in Chapter 6, we speculate two possible sources of non-collinear magnetization in
our junctions. 1) Non-collinear magnetization experienced by the Cooper pairs in
the PdNi layer, 2) Non-collinear magnetization experienced by the Cooper pairs in
between the PdNi and the Co layer.

It is possible that the out-of-plane magnetic anisotropy and the small scale do—
main structure in the PdNi (or CuNi) alloy are the key ingredients providing the
non—collinear magnetization that lead to the generation of LRTC in our experiment.
To rule out this possible role of PdNi (or CuNi) alloy, we decided to replace PdNi
layer with a strong ferromagnet such as Ni or Go. These strong ferromagnets, apart
from having a large scale domain structure, are also known to have in-plane mag-
netization. Currently Caroline Klose, a summer visiting student from Germany, has
started working on this problem. The S/ F/ S Josephson junctions of the form of
Nb/Cu/X/Cu/Co/Ru/Co/Cu/X/Nb, with X=Ni are currently being measured in
the lab. In the past, the flux contribution from the strong F—layer had led to destruc-
tion of the Fraunhofer pattern, however, we believe that if the Ni layer is kept thin,

the large destructive flux contribution can be avoided. Another way to avoid the large

137

 

flux contribution, is to use a SAF multilayer as the X—layer rather than using a strong
F-layer. With this issue in focus, Caroline will also be working on S / F / S Josephson
junctions using Co(tCo)/Ru/Co(tco) as a X-layer, where tCo is the thickness of the
Co layer. If Caroline observes LRTCs in her samples, it would be a strong indication
refuting PdNi or CuNi alloy as the sole generators of the LRTC in our experiment.
In that case, our second speculation, the non—collinearity experienced by the Cooper

pairs in between the X layer and the Co layer holds a strong ground.

Another way to ameliorate the effect of non-uniformity introduced by PdNi alloy
is to magnetize the PdNi-layer by applying a large in—plane magnetic field. This
will decrease the magnetic inhomogeneities arising in the structure due to the out-
of-plane magnetic component. The central Co/ Ru / Co layer being strongly exchange
coupled is known to remain unaffected by fields as large as 5 kOe. We plan to do
a systematic study of magnetized Josephson junctions by varying the magnetizing
fields, and measuring the resultant change in the maximum critical current of the

junction.

My colleague Mazin has been working on Josephson junctions similar to the ones
mentioned above, but with Co-platelets as the X-layer. The Co—platelets are formed
as result of deposition of extremely thin Co/ Cu multilayers, so that the Co—atoms '
interdispersed in the Cu form Co—platelets. It would be interesting to see if such an

unusual configuration can lead to the generation of triplet correlations in the system.

Another group member William Martinez is working on making the triplet sam-
ples using a lateral geometry. He will be making samples identical to our triplet
samples described in Chapter 6, however, instead of using antiferromagnetically cou-
pled Co—layers to reduce the flux in the junction, his geometry implements the use
of a thin narrow Co wire in order to reduce flux. One can therefore expect to see
an ideal Fraunhofer pattern for his samples even for longer Co lengths. As indicated

in Chapter 6, section 1.4.3, our attempts to measure the temperature dependence of

138

 

the critical current were restricted to the short-regime because of the destruction of
the Fraunhofer pattern for thicker Co—layers; we believe that William’s geometry will
allow such measurement in the long regime. Additionally, this sample geometry will
also help Bill to measure the temperature dependence of the resistance.

Apart from knowing the microscopic origin of triplet correlations in our experiment
and finding the different X materials that can generate long range triplet correlations,
a new Birge group member Kurt Boden is also working on measuring the density of

states (DOS) of the samples with triplet correlations, using tunneling spectroscopy.

7.4 A Year of Triplet Correlations!

Apart from our experiment, this year saw several other publications in this field. It
is several years since Keizer et al. [10] reported the evidence of triplet correlations
in Cr02 based Josephson junction that the Aarts group in Leiden finally decided
to revisit the problem [109]. Their experiments confirm the observation of triplet
correlations in Cr02 based Josephson junctions. However, the authors of this paper
also indicate a low success of their junctions, attributing it to the complicated nature
of CrOg that is sensitive to the growth conditions. Interestingly another group at
Penn State also reported an observation of proximity induced superconductivity in
Co-nanowires [110] that are hundreds of nm long. Similar evidence for triplet su-
perconductivity in Josephson junctions with ferromagnetic CugMnAl-Heusler [111]
barriers was also reported recently. All these experiments support the generation of
proximity-induced long-range triplet correlations in S / F systems. It really nice to see

so many positive results in this field after a long time.

139

 

 

 

Appendix A

Appendices

A.1 Photolithography Recipes

This section will describe various ways of doing optical lithography, also known as
photolithography. The basic process involves coating the substrate with a photo—
sensitive material called photoresist. The resist is then baked at a certain temperature
that drives out the solvent from it and makes it photosensitive. It is then selectively
exposed using a mask. If the resist used is a positive photoresist, the exposed resist
can be dissolved in a developer thus leaving the unexposed resist features on the
sample. Instead if it is a negative photoresist, the unexposed resist can be dissolved
in the developer thus leaving the exposed resist features on the sample. The mostly

widely used 81800 series resist is a positive tone photoresist.

Every resist attenuates the light passing through it so that the top layer devel-
ops faster than the bottom resist. This causes the sidewalls of positive resist to
have positive slope (80/90 degrees) unless special techniques are used. The use of
chlorobenzene in single layer photolithography, LOR (lift—off resist) layer in bilayer
photolithography, a metal layer in trilayer photolithography, or using a special im-

age reversal (IR) resist AZ 5214-E ensures either a well defined sharp undercut or a

140

 

 

negative sloped resist profile.
This section will give recipes for different kinds of photolithography techniques

used during the course of this work.

A.1.1 Single Layer Photolithography

Single layer photolithography is the fastest of all the processes described here. Ob-
taining a guaranteed, well—defined large undercut is difficult using this process. The
undercut obtained using this method is nominal and it strongly relies on having a
good contact between the substrate and the mask as well as a the exposure timing.
Since the desired features needed were relatively large (10—80 um) compared to the
minimum features sizes possible using the photolithography process (1-2 pm), using a
higher exposure time ensured sufficient exposure of the resist without compromising

on the expected dimensions.

15. ll M’ 1‘: (mm x 3‘; Uk SEW)

 

Figure A.1: SEM image of a resist pillar obtained using single layer photolithography

1. Spin coat S1813 resist at 5000 RPM for 40 sec.
2. Bake it at 100°C on hotplate for 1.5 min or 95°C in oven for 45 minutes.

3. UV expose with a mask for 10 sec.

141

 

 

4. Soak in chlorobenzene for 5 min and rinse with DI water.
5. Bake it at 95°C on hotplate for 1 min.

6. Develop in Microposit 352/452 for about 30-45 sec and rinse it with DI water.

Important note: In order to increase the robustness of photoresist against the
harsh ion milling process, the sample with photoresist features was baked on hotplate

for 2 min at 95°C and flood exposed for ~ 100 sec.

A.1.2 Bilayer Photolithography

A bilayer photolithography process uses two different kinds of photoresist. Since the
solvent liquids in the two resists are different, the layers don’t intermix and can be
treated independently. The bottom layer of resist is Lift-Of-Resist (LOR). As the
name suggests, this resist does not need an UV exposure for it’s development. The
second/ top layer can be a resist of user’s choice. We have worked with both 81813
and S1805. The development time of LOR resist is sensitive to it’s bake temperature;
higher bake temperatures yield slower development rate.

It was found that LOR is sensitive to the ion milling process even when it was
protected by the top resist. It is therefore advised that this resist should not be
used as a ion mill mask; it can but be safely used for metallization processes. This

photolithography process therefore had to be ruled out in our experiments.

1. Spin coat the substrate with LOR-5A at 5000 RPM for 40 sec.
2. Bake in oven at 170°C for 45 min.
3. Spin coat 81813 at 3000 RPM for 40 sec.

4. Bake in oven at 95°C for 30 min.

142

 

 

 

 

Figure A.2: SEM image of a resist pillar obtained using bilayer photolithography. The
bottom layer is Lift off resist (LOR) and the top layer is a $1805 resist.

5. UV expose the pattern for 10 sec.

6. Develop in Microposit 352/452 for about 20—30 sec and rinse it with DI water.

A.1.3 Trilayer Photolithography

The resist survival posed a big problem with the large undercuts obtained in the
bilayer lithography process. A trilayer photolithography process was therefore opti-
mized to get large undercuts. This process implements use of $1800 series resist as
the top and the bottom layer, where the layers themselves are separated by a thin
metallic Au layer. The scheme takes into consideration the fact that the solvents of
top and bottom layer being same, a thick enough Au layer can be used to avoid the

intermixing of the two layers.
1. Spin coat the substrate with 81813 at 5000 RPM for 40 see. This acts as layer-1.
2. Bake on hotplate at 100°C for 1.5 min or in oven at 95°C for 45 min.
3. Flood expose the resist for 4.5 sec.

4. Evaporate 10 nm Au. This acts as layer-2.

143

 

 

Figure A.3: SEM image of a resist pillar obtained using trilayer photolithography.
The two layers of resist {51813) is separated by a 10 nm of Au layer.

01

0':

CD

10.

. Spin coat the substrate with 81813 at 5000 RPM for 40 sec. This acts as layer-3
. Bake on hotplate at 100°C, for 1.5 min or in oven at 95°C for 45 min.
. UV expose the pattern for 4.5 sec.

. Develop in Microposit 352/452 for about 30 sec and rinse it with DI water. This

develops the layer-3.

. Etch the exposed Au using Standard Gold Etchant (KI+I2+H2O). This removes

layer-2.

Develop in Microposit 352/452 for about 30 sec and rinse it with DI water. This

develops the bottom layer, layer-3.

A.1.4 Image Reversal Photolithography

Since every resist attenuates the light passing through it, it is hard to obtain a negative

resist profile or a sharp undercut unless one the the above techniques are implemented.

But this very disadvantage can be turned into an advantage if one uses an image

reversal technique. Image reversal process uses a special kind of positive tone resist

144

 

 

which after a second bake at higher temperature can act like a negative tone resist. It
reverses the positive sloped profile to leave the opposite-a negative sloped profile on
the sample. A natural consequence of this is that an underexposure which normally
causes a positive resist profile now acts as an advantage when using an image reversal
process. This is can also be clearly understood from Figure A.4. This also meant

using a negative mask instead of a positive mask when using image reversal process.
a) Positive photoresist b) Image reversal photoresist

Ling; ways

2.. Expose using _,

 

 

 

 

/////////////// Ph°t°m35k ///////////////
\~. / <_ Light Intensity __> .l/ ’\
\v/ at mask / \_
1 Exposed region
<—— _ ——>
/////////////// ofrESISt ///////////////

--- Image Reversal ---

W- J _ )F— .—

1 ‘<— After developing ——>
/////////////// ///////////////

 

Figure A.4: A comparison of how the light attenuation in resist layer can be used to
advantage in an image reversal process.

1. Spin coat AZ 5214-E at 4000 RPM, 40 sec.
2. Bake on hotplate at 95°C for 1 min.

3. UV expose the pattern using a dark-field mask for 2.5 sec. [An underexposure

145

in this step gains a large negative slope in the resist profile!]
4. Bake on hotplate at 120°C for 1.5 min.
5. Flood expose the substrate for 20 sec.

6. Develop AZ Developer 352 for 40 sec and rinse it with water.

Of all the methods given above, it was found that the bilayer method was incom-
patible with our process. Of all the methods studied here, the trilayer photolithogra—
phy process gave the largest undercuts. Nevertheless because the trilayer method was
the most time consuming method, we preferred to work with a single layer method

or sometimes an image reversal method.

146

 

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