TOWARD 𝜑0 PHASE-TUNABLE FERROMAGNETIC JOSEPHSON JUNCTIONS

By

Robert Michael Klaes

A DISSERTATION

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

Physics—Doctor of Philosophy

2024

ABSTRACT

The interplay between superconductivity and ferromagnetism is a source of rich physics. Spin-

triplet supercurrent with long-range propagation through ferromagnetic layers has been well estab-

lished in theory and experiment and the use of magnetic layers for switching the ground state phase

across Josephson junctions between 0 and 𝜋 has been experimentally demonstrated. Combining the

two effects to observe 0-𝜋 switching in a Josephson junction containing three noncolinear magnetic

layers has also been experimentally demonstrated. Expanding on this idea, with careful control

of magnetic layers in a noncoplanar configuration, it has been theoretically proposed that a device

can be created which imparts an arbitrary phase difference across the junction. This demonstration

of the anomalous Josephson effect, a so-called ‘𝜑0 junction’, however, has yet to be realized in a

system of conventional ferromagnets. In this thesis, a battery of notable stepping stones toward

this goal are presented in the form of characterization of candidate patterned and unpatterned thin

magnetic materials and transport measurements of candidate Josephson junction device structures.

Copyright by
ROBERT MICHAEL KLAES
2024

To my father and the lasting legacy of his far too short life.

iv

ACKNOWLEDGEMENTS

I would like to begin by thanking my advisor, Norman Birge. From the moment I started working

with him in my undergraduate years, he has been a constant source of guidance, inspiration, support,

and intellectual stimulation. He is a seemingly superhuman intellectual powerhouse tempered with

self-awareness, humility, and a side of the proverbial ‘absent-minded professor’ that makes him

incredibly approachable and fun to work with. Meeting him was certainly a pivotal moment in my

life. I quite simply could not have asked for a better advisor.

I also thank the members of my advisory committee, beginning with Stuart Tessmer. Stuart is

the first professor I met in condensed matter physics and helped connect me with Norman in the

first place, for which I will be forever grateful. Thank you to Johannes Pollanen, rock-star in the

basement and all around great guy, a conversation with him is always fascinating and rewarding.

And to Kirsten Tollefson and Remco Zegers, who guided me through my tumultuous first few years

of coursework with extraordinary compassion and understanding.

I thank, too, Reza Loloee, facilities coordinator for the physics building and wizard of all

laboratory equipment in the basement. I can’t count the number of times he fixed something by

magic of his proximal aura, not to mention his undying patience and thirst for knowledge. To

Baokang Bi, microfabrication expert and clean room manager, whose wisdom and personability

were critical to my success. Thank you to Dan Edmunds, electronics genius and encyclopedia of

knowledge. I would like to thank our wonderful support staff, in particular the ‘Fab Four’: Kim

Crosslan, Cathy Cords, Jennifer Roberts, and Jessica Dellinger. They have helped me in countless

ways– clerically, emotionally, and spiritually. To Vladimir Zelevinsky, Mohammed Maghrebi,

Andreas von Manteuffel, Scott Pratt, Luke Roberts, and Steve Hsu for challenging me academically

almost to the point of breaking. And to the professors I had the great joy of teaching alongside–

Chong-Yu Ruan, Saul Beceiro Novo, Joey Huston, Pengpeng Zhang, and Xianglin Ke.

Thank you to the graduate students in the Birge group that proceeded me and helped to mentor

me: Joseph Glick and Bethany Niedzielski. And to Victor Aguilar, Alex Madden, and Swapna

Sindhu Mishra, who I had the privilege of working with long enough that they also became good

v

friends. Thanks to visiting researcher Demet Korucu for adding a unique perspective and delightful

culinary infusions to the group. Thanks also to our undergraduate students for always adding a dose

of levity and for building their own understanding by challenging mine: Anna Osella, Ben Byrd,

Thomas Bertus, Jacob Crawford, Jacob Kingsley, Nick Emtage, Fanlin Meng, and Sara Sawford.

I would also like to thank all of the extraordinary friends and colleagues I have met at Michigan

State: Eric Goodwin, David Greene, Justin Lane, Niyaz Beysengulov, Mark Olson, Eric Macaulay,

Danny Paz, Joe Kitzman, Camille Mikolas, Camryn Undershute, Josh Wylie, Mohamed Hassan,

Cami Monsalve, Carissa Myers, Kelly Anderson, Heat Uranin, Nick Cariello, Maya Bostock, Alper

Korucu, Pranaya Rath, Liz Tuttle, Chris Emery, and Victor Rodriguez-Pereira, just to name a few.

Thanks next to my best friends and stalwart companions. To my guardian angels Hannah Berg

and Julia Hinds, who shepherded me through my most challenging times in the program with their

unrelenting kindness, compassion, wisdom, humor, and infectious propensity to have fun. Thank

you to Michael and Albertina Gottschalk for being extraordinarily good friends and pandemic

survival champions. Our time together was among the most cherished of my entire time at MSU.

Thank you to Prof. Nathan Satchell, former post-doc extraordinaire, true friend, and beacon of

an ideal researcher who was largely responsible for the period of peak productivity and fun in

Norman’s group. And to Josh ‘Jeffrey’ Willard, my true best friend and longtime Birge group lab

mate. Without you I don’t know under which bridge or cemetery I would be aslumber, but I know

it’s worlds away from where I am now. Your example of a fine human being, scientist, husband,

father, and friend is something that will guide me for the rest of my days.

Thank you to the surrogate families of my youth in Seattle: Paul and Dene Napolitan and Clyde

and Betty Lince, for stepping up to the plate at a crucial time and helping to make me who I am.

Likewise to my local support from The People’s Church of East Lansing, graciously led by Rev. Dr.

Shawnthea Monroe, for providing unwavering spiritual guidance and a nurturing community. And

to my family to be– Debra Whitaker-Volturo and John Volturo and all the lovely Whitaker’s and

Swift’s– of which I am fortunate to officially become a member next summer. The love, warmth

and kindness you have shown has meant the world to me and will continue to drive me.

vi

Thanks to my wonderful mother Chris and her exceptional parents, Bill and Luanne, who

managed to give me a solid foundation in the face of unenviable circumstances. To my late father

Daniel, whose absence was felt stingingly, but whose presence still shaped me. To my brother Ken,

his wife Naomi, and their young daughter Ramona who always elicits a smile. To my brother John,

his partner Greta, and their incredible daughters Julianne and Emily for their unrestrained passion.

To my uncle David, his wife Sheree, and their remarkable son Grayson. And to all of my amazing

aunts, uncles, and cousins that make the Klaes side so vibrant, and the late Frank and Patricia, from

whom they sprung.

Finally, thank you to my lovely new family unit: my buddy Basilton, you have warmed my heart

ever since you came into my life with your indelible curiosity and playfulness. I am so grateful

to you for taking care of your mom before I had the privilege of meeting you both. And most

especially to my phenomenal fiancée Jena Layne Whitaker (soon to be Klaes). You have made

my life so much more meaningful and have opened up a new dimension of happiness that I never

thought possible. You keep me grounded; you inspire me; you motivate me; you make me a better

man every day. I am so blessed to share my journey with you! I fully love you!

vii

TABLE OF CONTENTS

LIST OF TABLES .

. .

LIST OF FIGURES .

. .

.

.

.

.

.

.

LIST OF ABBREVIATIONS .

.

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.

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.

.

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x

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

CHAPTER 1

.

.

.
JMRAM Application .

.
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
1.1 S/F Background .
1.2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Spin-Triplet Pair Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Phase-Tunable Josephson Junctions . . . . . . . . . . . . . . . . . . . . . . .
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Chapters Overview .

1
1
2
2
3
3

CHAPTER 2

2.1 Ferromagnetism . .
2.2 Superconductivity .
2.3

.
.
Josephson Junctions .

5
THEORETICAL BACKGROUND . . . . . . . . . . . . . . . . . . . . .
5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

CHAPTER 3

.
.

.
.
.

SAMPLE FABRICATION AND MEASUREMENT . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 27
.
. 28
3.1 Wafer Dicing .
.
. 29
.
.
3.2 Chip Cleaning .
3.3 Photolithography .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Sputtering Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Electron Beam Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.6
. 37
3.7 Side Ion Milling and Lift-off . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.8 Top Lead Photolithography and Sputtering . . . . . . . . . . . . . . . . . . . . 41
Josephson Junction Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.9
3.10 SQUID Magnetometer Measurement . . . . . . . . . . . . . . . . . . . . . . . 42

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ion Milling .

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.

CHAPTER 4

NI-MN PROJECT . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 43
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1 Exchange Bias .
4.2 Past Work . .
. 45
.
4.3 Magnetic Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4
. 50
4.5 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Josephson Junctions .

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.

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CHAPTER 5

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PROGRESS TOWARD PHASE-TUNABLE JJS . . . . . . . . . . . . . 53
5.1 Methods .
. 54
5.2 Ni/Co Multilayer Sheet Films . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3 Ni/NiFe/Ni Elliptical Arrays
. . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.4 Spin-Triplet Josephson Junctions . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.5 Addition of Switchable Permalloy Layer . . . . . . . . . . . . . . . . . . . . . 62
5.6 Ni/[Ni/Co]/NiFe SQUIDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

viii

CHAPTER 6

CONCLUSIONS AND OUTLOOK . . . . . . . . . . . . . . . . . . . . 69

REFERENCES .

. .

. .

.

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APPENDIX A

ADDITIONAL WORK . . . . . . . . . . . . . . . . . . . . . . . . . . 79

APPENDIX B

LABORATORY NOTES . . . . . . . . . . . . . . . . . . . . . . . . . 95

ix

LIST OF TABLES

Table 5.1 Ni/Co magnetics summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Table A.1 NiFeCr resistivity .

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Table A.2 Chiral molecules JJ data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

x

LIST OF FIGURES

Figure 2.1 Ferromagnetic domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.2 Anisotropy .

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Figure 2.3 Addition of anisotropies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

8

9

Figure 2.4 RCSJ Model .

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.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 2.5 Overdamped I-V Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 14

Figure 2.6 Airy interference pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 15

Figure 2.7 Airy interference pattern of a magnetic JJ . . . . . . . . . . . . . . . . . . . . . 16

Figure 2.8 Andreev reflection .

Figure 2.9 Spin bands .

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.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Figure 2.10 Pair correlation graphic . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 20

Figure 2.11 SQUID .

.

.

.

.

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Figure 2.12 SQUID IC vs. flux .

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.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 2.13 Triplet JJ design .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 23

Figure 2.14 Triplet spin bands .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 2.15 𝜑0 JJ design .

. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure 3.1 Fabrication overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 3.2 Photomask pattern .

Figure 3.3 EBL lift-off .

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Figure 4.1 Exchange bias .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Figure 4.2 FeMn/NiFe bilayer JJs .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Figure 4.3 NiFe/NiMn thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Figure 4.4 Ni/NiMn thin films

Figure 4.5 NiMn Fraunhofer

Figure 4.6 NiMn JC decay .

.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

xi

Figure 4.7 Simplified JMRAM cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 51

Figure 5.1 Triplet JJ sizes .

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 5.2 Ni/Co n=6 thick base .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 5.3 Ni/Co n=10 thin base .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Figure 5.4 Ni/Co n=10 thick base .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Figure 5.5 High in-plane field data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Figure 5.6 Elliptical arrays

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.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Figure 5.7 Ni dusting magnetics

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 5.8 Ni/Co triplet JJ .

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 5.9 Triplet critical current

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 61

Figure 5.10 Permalloy triplet JJ

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Figure 5.11 Permalloy triplet ICRN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Figure 5.12 Permalloy triplet initialization, medium area JJ . . . . . . . . . . . . . . . . . . 64

Figure 5.13 Permalloy triplet initialization, medium area JJ breakout . . . . . . . . . . . . . 65

Figure 5.14 Permalloy triplet initialization, large area JJ

. . . . . . . . . . . . . . . . . . . 66

Figure 5.15 SQUID bottom lead pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Figure A.1 NiFeCr magnetics .

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Figure A.2 Saturation magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Figure A.3 Nb top cap .

.

.

Figure A.4 Top cap ICRN .

Figure A.5 Top cap RN .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

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. 83

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 84

Figure A.6 Top cap width . .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 85

Figure A.7 Top cap Hshift

.

.

Figure A.8 Chiral molecules .

Figure A.9 Batch I data .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 86

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

xii

Figure A.10 Batch II data .

Figure A.11 Batch III data

Figure A.12 Crinkling . .

.

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.

.

Figure A.13 More crinkling .

Figure A.14 Contamination .

Figure B.1 Triplet JJ .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Figure B.2 Sputtering logbook format . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 100

xiii

LIST OF ABBREVIATIONS

AF

antiferromagnetic

ALD

atomic layer deposition

CISS

chiral-induced spin selectivity

EBL

electron beam lithography

FTM

film thickness monitor

HUJI

Hebrew University of Jerusalem

IARPA Intelligence Advanced Research Projects Activity

IEEE

Institute of Electrical and Electronics Engineers

IPA

isopropyl alcohol

I-V

JJ

current-voltage

Josephson junction

JMRAM Josephson magnetic random-access memory

LOR

lift-off resist

MRAM magnetoresistive random-access memory

PMA

perpendicular magnetic anisotropy

RCSJ

resistively capacitively shunted junction

RPM

revolutions per minute

SAF

synthetic antiferromagnet

SEM

scanning electron microscope

SQUID Superconducting QUantum Interference Device

TMAH tetramethyl ammonium hydroxide

VSM

vibrating-sample magnetometer

xiv

CHAPTER 1

INTRODUCTION

Je n’ai fait celle-ci plus longue

que parce que je n’ai pas eu le

loisir de la faire plus courte.

Blaise Pascal

This thesis focuses on superconductivity and ferromagnetism, and the interplay between these two

effects. The early work described has a direct practical application in the form of a proposed

superconducting memory cell. The work evolved in search of funding opportunities, resulting in

many tangential projects (some of which are outlined in the appendices), and culminates in a project

for which there is not an immediately obvious application, but is arguably more interesting from a

pure science perspective, the 𝜑0 junction.

1.1 S/F Background

At the interface of a superconductor and a normal metal, there is some length scale over which the

Cooper pairs will ‘seep’ into the normal metal layer and exhibit some superconducting properties.

This normal metal coherence length describes the exponential decay of the pair correlation function

and is on the order of hundreds of nanometers at cryogenic temperatures. In the 1980’s, early theory

work predicted how this effect would translate to a superconductor/ferromagnet interface [1]. In

short, because of the exchange splitting of the spin bands within the ferromagnet, the electrons

comprising the spin-singlet Cooper pairs enter different spins bands within the ferromagnet and

acquire a net center-of-mass momentum. This imparts a rapid oscillation and decay of the pair

correlation function.

Because this decay occurs over such a short length scale in a ferromagnet (on the order of

nanometers), it took quite some time to experimentally observe. In 2001, two groups were able to

detect the signature of this oscillation through density of states vs. thickness measurement (Kontos

1

et al. [2]) and critical current vs. temperature (Ryazanov et al. [3]). Shortly after this, oscillations

in critical current vs. thickness were also observed [4].

1.2

JMRAM Application

This oscillatory behavior implies that a Josephson junction containing a ferromagnetic interlayer

can impart a 0 or 𝜋 ground state phase difference across its barrier according to the barrier

thickness. An ingenious potential application of this property came with the proposal to create

a memory device based on control of this phase difference called Josephson magnetic random-

access memory (JMRAM) [5]. The design included a two magnetic layer system, one fixed in its

magnetization direction, and the other switchable. According to the relative orientations of the

magnetizations, this could impart either a 0 or 𝜋 phase difference, which would form the basis of

a binary memory cell. This phase control was demonstrated in 2016 in the Birge group [6], and

its operation within a memory array was demonstrated shortly thereafter by Northrop Grumman

Corporation [7]. This collaboration toward optimization of this memory device funded the work in

this group for many years, resulted in many advancements and publications [8, 9, 10, 11, 12], and

forms the basis of the early work in this thesis.

1.3 Spin-Triplet Pair Correlations

An interesting and totally unexpected idea was posited by theorists in the early 2000’s whereby

magnetic inhomogeneities could impart long-range spin-triplet pair correlations within a ferromag-

netic material in contact with a conventional spin-singlet superconductor [13, 14]. If spin-singlet

Cooper pairs could be transformed into spin-triplet pairs with like-paired spins, the decay of the pair

correlation function within a ferromagnet would be much slower than in the spin-singlet case. In

2010, the first convincing experimental evidence of these long-range spin-triplet pair correlations

was observed in a system of strong ferromagnets by the Birge group [15]. The experiment used

a geometry proposed by Houzet and Buzdin [16] which includes a system of three ferromagnetic

layers with the magnetizations of the outer ‘spin-mixing’ layers oriented perpendicular to that of

the central propagation layer [17]. Subsequently, additional work in the group fleshed out the effect

[18, 19, 20]. An alternate method of generating long-range spin-triplet supercurrent using interfa-

2

cial materials with a large spin-orbit coupling effect was investigated later in this group [21, 22],

and forms the basis of the work outlined in Appendix A.3.

1.4 Phase-Tunable Josephson Junctions

As the JMRAM project drew to a close, some of the later experiments investigating the use

of long-range spin-triplet generating systems [8, 10] led the group to explore similar materials for

use in the realization of a so-called ‘𝜑0-junction’. As discussed in greater detail in section 2.3.9,

this 𝜑0-junction had been predicted for some time [23, 24] and demonstrated only in some exotic

materials, but not using traditional ferromagnets. By design, the device allows for an arbitrary,

tunable phase, rather than the binary 0 or 𝜋 phase drop across its Josephson junction. This provided

the motivation for the work in the thesis of Victor Aguilar [25], and the work highlighted in Chapter

5. In many ways, the realization of such a device would be the culmination of over a decade of

work in the Birge group.

1.5 Chapters Overview

Chapter 2 will explore the fundamental science behind the research in this thesis. We will begin

with ferromagnetism, then move on to superconductivity, then explore the interplay between those

phenomena.

Chapter 3 covers the basics of sample fabrication in the Birge group, from wafer dicing to

methods of lithography to sputtering deposition and finally, sample measurement.

Chapter 4 describes work on the Intelligence Advanced Research Projects Activity (IARPA) C3

project in collaboration with Northrop Grumman Corporation toward optimization of a JMRAM

device [5, 6, 7].

In particular, it explores the use of an antiferromagentic layer used to pin the

fixed layer in the proposed device. This work is published in Institute of Electrical and Electronics

Engineers (IEEE) Transactions on Applied Superconductivity [26].

Chapter 5 explores progress toward the 𝜑0 junction – a proposed device with a tunable phase

rather than the binary 0 or 𝜋 phase seen in traditional superconductor/ferromagnet systems. This

includes evidence for the optimization of spin-triplet supercurrent generation from the addition of

a Nb/Au base layer, patterned and unpatterned candidate thin film characterization, and Josephson

3

junctions containing a full proposed stack.

Chapter 6 includes a brief summary of the work contained in this dissertation and a bit of

perspective.

Appendix A includes data collected on Ni73Fe18Cr9 films as part of a project exploring that

material’s viability for use in JMRAM, a study optimizing fabrication methods, specifically inves-

tigating whether a thin layer of Nb on the top of the bottom lead is necessary, and a summary of

work on a collaboration with a research group at Hebrew University in Jerusalem exploring the use

of chiral molecules as a generator of spin-triplet supercurrent.

Appendix B provides select laboratory notes including a calculation of the supercurrent through

a spin-triplet Josephson junction performed by Prof. Birge, a template for proper documentation

of a sputtering run in the logbook for maximum clarity and information density and contains a

procedure for dicing patterned magnetic array samples for measurement in the magnetometer.

4

CHAPTER 2

THEORETICAL BACKGROUND

...en matière scientifique, on a

souvent des prédécesseurs

beaucoup plus anciens qu’on ne

le pense a priori.

Louis Eugène Félix Néel

This chapter will focus on the phenomenological underpinnings of the experimental research in this

thesis. We will begin with ferromagnetism, then move on to superconductivity, the proximity effect,

ferromagnetic Josephson junctions, Superconducting QUantum Interference Devices (SQUIDs),

and finally spin-triplet superconductivity and the 𝜑0 junction. It is not intended to be comprehensive

by any means, but is meant to briefly discuss some of the history and relevant physics needed to

understand the projects discussed herein.

2.1 Ferromagnetism

Ferromagnetism was first discovered in lodestone in the 6th century BC [27]. Since then, it

has been an endless source of fascination among researchers and the general public alike. While a

basic understanding of the atomic origin of the phenomenon has been understood for some time,

its nuances continue to be a fertile ground for research. In the atomic case, one can think of the

absence or presence of unpaired spins dividing materials into either diamagnetic (where the orbital

magnetic moments weakly oppose an applied field) or paramagnetic (where the spin magnetic

moments weakly align with an applied field).

In atoms with multiple valence electrons in an

unfilled orbital, the exchange interaction leads to Hund’s second rule [28], which states that the

lowest energy state has the spins maximally aligned. The exchange interaction arises from the need

of the overall wavefunction of identical fermions to be antisymmetric under exchange. This causes

an antisymmetric spatial wavefunction to pair with symmetric spin states and vice versa. With

5

electrons in an antisymmetric spatial state, they are on average farther apart and therefore yield a

lower Coulomb repulsion energy.

When atoms are put together in insulating solids, similar arguments as above explain the

appearance of diamagnetism or paramagnetism. Metallic solids all exhibit Pauli paramagnetism,

which may or may not exceed the intrinsic atomic diamagnetism in strength. Far more interesting

is the case when there are strong exchange interactions between the electron magnetic moments

on neighboring atoms, which may give rise to ferromagnetism. Ferromagnetic materials may be

insulating, for example, Fe3O4, commonly known as magnetite, or metallic, for example, Fe, Ni,

or Co. In the latter case, the localized moments in the partially filled d bands interact with each

other via the conduction electrons, which are mostly the s electrons. The complete theory of

ferromagnetism is complicated and relies on a detailed understanding of the band structure. Stoner

introduced a simplified model where a threshold referred to as the Stoner criterion [29] determines

which materials exhibit this property. For a more complete picture, one should consult a magnetism

reference material such as [30, 31]. Some other types of magnetism include: antiferromagnetism

(where neighboring spins tend to align anti-parallel to one another) and ferrimagnetism, which

is akin to a special case of antiferromagnetism where the moments of the unpaired spins are

compensated in their direction, but not in their magnitude, so there is an overall moment.

2.1.1 Domains

While the local effect of the exchange interaction between neighboring atoms in a ferromagnet

will result in its spins aligning in a uniform direction, macroscopically, minimizing the magne-

tostatic energy dictates that regions of spins form whose overall moments will cancel each other.

This formation of domains is the reason that magnetic materials in nature are often found in a

demagnetized state.

6

Figure 2.1 Ferromagnetic domains. A representation of ferromagnetic domains where there are
sub-regions of uniform spin within a macroscopic shape.

Figure 2.1 shows a representation of this. It is only after application of a sufficient magnetic field

that the spins will align together on a macroscopic scale. Depending upon the material, this effect

will even impact devices on the sub-micron scale of those studied in this thesis. In particular, Ni

magnetic layers in our Josephson junctions will often break into domains and not switch uniformly,

wreaking havoc on the neat and tidy electron transport picture described later in this chapter.

2.1.2 Anisotropy

Magnetic anisotropy in general refers to the preference of a magnetic system to align in a

particular direction. Magnetocrystalline anisotropy is a special case of this effect where this

anisotropy is induced by the atomic structure of the crystal lattice due to the spin-orbit interaction.

By clever design, a preferred switching axis can be imparted to a magnetic system. In particular

in our research, while Ni81Fe19 (permalloy) is chosen for its low intrinsic magnetocrystalline

anisotropy, we can engineer this directional preference into the material by application of a magnetic

field during its growth. In a small enough system, the macroscopic shape of a magnetic structure

can also impart a preferred axis. For example, in an elliptical shape, the spins will preferentially

align along the long axis. Another useful anisotropy is perpendicular magnetic anisotropy (PMA),

where the spins of certain multilayers such as [Ni(0.4)/Co(0.2)]n will prefer to point perpendicular

7

to the plane of the interfaces of the materials, as explored in Chapter 5.

Figure 2.2 shows the ideal case of a single domain magnetic system with uniaxial anisotropy,

where its response to a magnetic field 𝐻 along one axis (the easy axis) behaves perfectly ferromag-

netically, i.e. it exhibits sharp switching at a coercive field 𝐻𝐶, and 100% remnance of the saturation

magnetization 𝑀𝑠𝑎𝑡 at zero field. Along the other axis (the hard axis), the behavior appears similar

to an antiferromagnet, i.e. the spins will be slowly pulled out of alignment with the easy axis up to

their 𝑀𝑠𝑎𝑡, and there is zero remnance of the magnetization at zero field.

Figure 2.2 Anisotropy. A representation of idealized easy and hard axis magnetization, 𝑀, vs.
applied field, 𝐻, in a magnetic system with uniaxial anisotropy. The easy axis exhibits idealized
ferromagnetic behavior, switching its magnetization abruptly and completely at its coercive field,
𝐻𝐶.

Figure 2.3 shows how these anisotropies can be ‘stacked’ together to create an even stronger

preferred switching axis. In the case of this graphic, the growth field and the shape of the ellipse

both impart a preferred axis along the long axis of the ellipse. This encourages uniform switching.

8

MH Easy Axis Hard AxisHCMSat00Figure 2.3 Addition of anisotropies. A graphic showing how anisotropies can be aligned to create
a dominant switching axis.

2.2 Superconductivity

Superconductivity is a phenomenon that is found at low temperatures in many materials and

was first discovered by Heike Kamerlingh Onnes in 1911 [32]. Onnes found the resistance of

mercury to abruptly drop to zero below a certain temperature. On the shoulders of pioneering

work by Meissner [33], the Londons [34], Ginzburg–Landau [35], and others, a microscopic theory

of superconductivity was posited by John Bardeen, Leon Cooper, and John Robert Schrieffer in

1957 [36, 37], which is now referred to as ‘BCS theory’. A full treatment of these theories could

not possibly be conquered in this humble thesis, but we will explore some key implications in the

following sections.

2.2.1 Meissner Effect

German physicists Walther Meissner and Robert Ochsenfeld performed an experiment in 1933

[33] by cooling tin and lead samples through their transition temperature in a magnetic field and

observed that the samples expelled all magnetic fields from the bulk of the materials. This expulsion

of magnetic field is referred to as the Meissner effect and was the first evidence that distinguished

superconductors from idealized perfect conductors. This effect is the basis of some of the flashiest

demonstrations of superconductivity such as passive magnetic levitation.

2.2.2 London Equations

In 1935, brothers Fritz and Heinz London devised a theory that was able to explain the Meissner

effect [34]. The London equations relate superconducting current density, 𝐽, to the electric (𝐸) and

9

Long Axis DirectionGrowth Field DirectionEasy Axis Directionmagnetic (𝐵) fields within a superconductor, and can be expressed as follows:

and

𝜕𝐽
𝜕𝑡

𝑛𝑠𝑒2
𝑚

𝐸

=

∇ × 𝐽 = −

𝑛𝑠𝑒2
𝑚

𝐵

(2.1)

(2.2)

where 𝑒 is the electron charge, 𝑚 is the electron mass, and 𝑛𝑠 is the number density of supercon-

ducting electrons. If the Maxwell relation ∇ × 𝐵 = 𝜇0𝐽 is applied to Eq. 2.2, the result can be

manipulated into the form:

∇2𝐵 =

𝐵

1
𝜆2
𝐿

which results in the definition of the phenomenological parameter:

𝜆𝐿 ≡

√︂ 𝑚

𝜇0𝑛𝑠𝑒2

(2.3)

(2.4)

the London penetration depth, which represents the characteristic length scale over which external

magnetic fields are suppressed exponentially within the superconductor.

2.2.3 Ginzburg–Landau theory

In 1950, Vitaly Ginzburg and Lev Landau posited a theory [35] to describe superconductivity

from a phenomenological perspective without a microscopic treatment. Their most salient inclusion

was the introduction of the complex psuedo-wavefunction 𝜓 which folded a quantum mechanical

understanding into superconducting theory. By treating the transition from resistive state to su-

perconducting state as a second-order phase transition, and minimizing the total free energy, they

derived the first Ginzburg–Landau equation:

𝛼𝜓 + 𝛽|𝜓|2𝜓 +

(cid:18)

1
2𝑚∗

−𝑖ℏ∇ −

(cid:19) 2

𝐴

𝑒∗
𝑐

𝜓 = 0

(2.5)

which is analogous to the time-independent Schrödinger equation. From this, they also derived an

equation for the current density, 𝐽𝑠:

𝐽𝑠 =

𝑖ℏ
2𝑚∗ (𝜓∗∇𝜓 − 𝜓∇𝜓∗) −

𝑒∗2
𝑚∗ |𝜓|2 𝐴

(2.6)

10

which comprises the second Ginzburg–Landau equation. The theory also introduces another

important characteristic length scale in superconductivity, the coherence length:

√︄

𝜉𝑆 =

ℏ2
2𝑚∗|𝛼|

(2.7)

which can be thought of as the Cooper pair size and, together with the London penetration depth,

𝜆𝐿, determine the parameter 𝜅:

𝜅 = 𝜆𝐿/𝜉𝑆

(2.8)

whose value determines whether a superconductor is Type I, where superconductivity is abruptly

destroyed above a critical field 𝐻𝑐, or Type II, where an intermediate vortex state is created between

critical fields 𝐻𝑐1 and 𝐻𝑐2.

2.2.4 BCS Theory

The key insight leading to the groundbreaking work of John Bardeen, Leon Cooper, and John

Robert Schrieffer in 1957 [36, 37] was that electrons in a superconductor form so-called Cooper

pairs that condense into a single coherent quantum state. The resulting theory was the first

microscopic understanding of superconductivity. At its core, BCS theory describes the interaction

between electrons and quantized lattice vibrations called phonons. Below a certain temperature, 𝑇𝑐,

the weakly attractive electron-phonon interaction compensates the repulsive Coloumb interaction

of the electrons and an energy gap, Δ, opens up, where 2Δ represents the energy required to break

up a Cooper pair into two quasiparticle excitations:

Δ(𝑇 = 0) = 1.764𝑘 𝐵𝑇𝑐

(2.9)

where 𝑇𝑐 is the critical temperature. The theory describes the aforementioned coherence length in

a more useful way:

𝜉ballistic
𝑆

=

ℏ𝑣𝐹
𝜋Δ

(2.10)

in the ballistic limit, where 𝑣𝐹 is the Fermi velocity. In the diffusive limit, where the mean free

path, ℓ, is smaller than the coherence length, then:

𝜉diffusive
𝑆

=

√︂ℏ𝐷 𝑆
Δ

11

(2.11)

where 𝐷 𝑆 is the electron diffusion constant.

BCS theory also helped shed light on many mysteries, such as the basis for what determines the

London penetration depth 𝜆𝐿, critical temperature 𝑇𝑐, and critical field 𝐻𝑐 for a particular material.

2.3

Josephson Junctions

2.3.1 The Josephson Effect

In 1962, Brian Josephson theorized what would happen when a superconductor was interrupted

by a thin insulating layer [38], now referred to as a Josephson junction (JJ). The insights from this

theory are at the heart of all of the research contained within this thesis. The theory builds on the

work of Ginzburg and Landau and was the first prediction of the tunneling of Cooper pairs through

such a barrier. It describes the current flowing across an insulating barrier as:

𝐼𝑠 = 𝐼𝑐 sin 𝜙

(2.12)

where 𝐼𝑐 is the critical current, the maximum allowable supercurrent through the junction, and 𝜙

is the phase difference from one side of the junction to the other. The phase evolution is described

by:

𝑑𝜙
𝑑𝑡

=

2𝑒𝑉
ℏ

=

2𝜋𝑉
Φ0

(2.13)

with Φ0 = 2𝜋ℏ

2𝑒 representing the magnetic flux quantum, discussed further in section 2.3.7. Equations

2.12 and 2.13 are referred to as the Josephson relations.

12

2.3.2 RCSJ Model

Figure 2.4 RCSJ Model. A diagram of the RCSJ model circuit showing the ideal Josephson
junction in the middle in parallel with a resistor and a capacitor.

As a way of understanding the behavior of a real Josephson junction, the resistively capacitively

shunted junction (RCSJ) model was developed. In this treatment, the junction is modeled as an

ideal Josephson junction in parallel with a resistor and a capacitor, as shown in Figure 2.4. This

accounts for the AC impedance of an actual junction. From this, we get an expression for the

current through the circuit:

𝐼 = 𝐼𝑐 sin 𝜙 +

𝑉
𝑅

+ 𝐶

𝑑𝑉
𝑑𝑡

combining this with 2.13 and defining the Josephson energy 𝐸𝐽 = ℏ𝐼𝑐0/2𝑒, we arrive at:

2(cid:19)

(cid:18) ℏ
2𝑒

𝐶

𝑑2𝜙
𝑑𝑡2

+

(cid:18) ℏ
2𝑒

(cid:19) 2 1
𝑅

𝑑𝜙
𝑑𝑡

= 𝐸𝐽

(cid:19)

− sin 𝜙

(cid:18) 𝐼
𝐼𝑐0

(2.14)

(2.15)

which gives us a second-order differential equation for the time dependence of the phase. This has

a classical analog to a particle of mass

(cid:17) 2

(cid:16) ℏ
2𝑒

𝐶 moving in a potential:

𝑈 = −𝐸𝐽

(cid:19)

𝜙 − cos 𝜙

(cid:18) 𝐼
𝐼𝑐0

(2.16)

with a linear drag force

(cid:17) 2

(cid:16) ℏ
2𝑒

𝑑𝜙
𝑑𝑡 . This implies a Stewart-McCumber damping parameter [39, 40]:

1
𝑅

𝛽𝑐 =

(𝐼𝑐0𝑅)2 𝐶
𝐸𝐽

13

(2.17)

CRWhen 𝛽𝑐 is small, this is the case of the overdamped junction, which simplifies equation 2.15

to a first-order differential equation of the form:

𝑑𝜙
𝑑𝑡

=

𝐼2
𝑅
𝑐0
𝐸𝐽

(cid:18) 𝐼
𝐼𝑐0

(cid:19)

− sin 𝜙

In this overdamped case, the time-averaged voltage becomes

√︃

|𝑉 | = 𝑅

𝐼2 − 𝐼2
𝑐0

.

(2.18)

(2.19)

All of the Josephson junctions studied in this thesis were in the overdamped limit as shown in

Figure 2.5, so Equation 2.19 was used to fit their current-voltage (I-V) curves.

Figure 2.5 Overdamped I-V Curve. Voltage vs. current (I-V) plot of an overdamped Josephson
junction, with the dashed line indicating the critical current, 𝐼𝑐.

14

VoltageCurrent2.3.3 Magnetic Field Effects in Josephson Junctions

Figure 2.6 Airy interference pattern. A representation of the magnetic field response of the
critical current of a circular Josephson junction.

An informative method of probing a Josephson junction is by application of an in-plane magnetic

field. The junctions discussed in this thesis are in the so-called small junction limit, such that the

Josephson penetration depth:

√︄

Φ0
2𝜋𝑑𝜇0𝐽𝑐
where 𝑤 is the width of the junction. In this regime, the critical current density can be treated

(2.20)

𝜆𝐽 =

≫ 𝑤

as uniform. Because of the gradient of the vector potential, the magnetic response function takes

a form analogous to that of optical interference, resulting in a Fraunhofer interference pattern for

rectangular junctions [41]. In circular junctions, or elliptical junctions with the field applied along

15

−4−20240.00.20.40.60.81.0IC/IC0F/F0the symmetry axis, the form is that of an Airy function, as shown in Figure 2.6, and described by:

𝐼𝑐 = 2𝐼𝑐0

𝐽1

(cid:12)
(cid:12)
(cid:12)
(cid:12)
(cid:12)
(cid:12)
(cid:12)

(cid:17)

(cid:16) 𝜋Φ
Φ0
𝜋Φ
Φ0

(cid:12)
(cid:12)
(cid:12)
(cid:12)
(cid:12)
(cid:12)
(cid:12)

(2.21)

with Φ = 𝐵𝑦2𝑅(𝜆𝐿 + 𝜆𝑅 + 𝑡) assuming 𝜆𝐿, 𝜆𝑅 ≫ 𝑡 where 𝜆𝐿 and 𝜆𝑅 are the London penetration

depths of the materials on each side of the barrier, 𝑡 is the barrier thickness, and 𝐽1 is a Bessel

function of the first kind. (This also assumes that the superconducting electrodes are much thicker

than their 𝜆’s.)

Figure 2.7 Airy interference pattern of a magnetic JJ. Magnetic field response of the critical
current of an elliptical, ferromagnetic Josephson junction showing a horizontal shift according to
the direction of its magnetization. In these data, which are taken from the study in Apendix A.2,
this magnetization switch occurs at a very low coercive field of ∼5 mT.

Together, these Airy patterns and Fraunhofer patterns are often colloquially referred to as

Fraunhofer patterns.

In a junction of known geometry, a fit using Equation 2.21 can give us

an estimate of 𝜆𝐿.

In very small junctions, where junction geometry may vary due to process

16

−80−60−40−200204060800.00.20.40.60.81.01.21.4 Upsweep DownsweepIC (mA)m0H (mT)variations, we can use known values of 𝜆𝐿 and 𝜆𝑅 to determine the junction width. Also, in such

cases where the central peak is shifted from zero field due to magnetization as shown in Figure

2.7, an extrapolation of the peak critical current and magnitude of the shift can also be made. Such

analysis was performed on the data in Chapter 5 and Appendix A.

2.3.4 S/N Proximity Effect

The Josephson junctions envisioned by Brian Josephson consisted of a very thin tunnel barrier

between the superconducting (S) electrodes. But one can imagine replacing the insulating barrier

with a normal (i.e. non-superconducting) metal (N) in which case this ‘barrier’ can be much thicker.

Later, we’ll see that the barrier can even be a ferromagnetic metal, but with only an intermediate

thickness. To begin to understand these situations, we must look at how electrons pass through an

S/N interface.

Figure 2.8 Andreev reflection. A depiction of Andreev reflection showing Cooper pair generation
at the N/S interface, adapted from [42].

17

xynormal cond.supercond.xynormal cond.supercond.eeehCooper pairExEFnormal cond.supercond.∆ExEFnormal cond.supercond.∆eeheNormal ReflectionAndreev ReflectionAndreev reflection [43] describes the scattering of electrons at the interface of a superconductor

and a normal metal. An incident electron from the normal metal may form a Cooper pair in the

superconductor while a hole is retroreflected back into the normal metal with opposite spin and

velocity, but equal momentum. Figure 2.8 shows a depiction of Andreev reflection compared to

normal reflection of an electron at the N/S interface. The inverse effect of a Cooper pair incident on

an S/N interface from the S side is also described in a symmetrical way. This process gives rise to

electron pair correlations in the normal metal near the S/N interface. Crucially, the phase coherence

of the electrons is preserved in this process. The length scale over which these correlations persist

is called the normal metal coherence length, 𝜉𝑁 and can again be calculated in either the ballistic

‘clean’ limit (where the mean free path is larger than the coherence length) or the diffusive ‘dirty’

limit (where the mean free path is smaller than the coherence length). In the ballistic limit, the

normal metal coherence length is described by:

𝜉ballistic
𝑁

=

ℏ𝑣𝐹
2𝜋𝑘 𝐵𝑇

(2.22)

where 𝑣𝐹 is the Fermi velocity, 𝑘 𝐵 is the Boltzmann constant, and 𝑇 is the temperature. In the

diffusive limit, we have

𝜉diffusive
𝑁

=

√︄

ℏ𝐷 𝑁
2𝜋𝑘 𝐵𝑇

(2.23)

where 𝐷 𝑁 is the electron diffusion constant. The value of 𝜉𝑁 is typically on the order of tens to

hundreds of nm at cryogenic temperatures.

18

2.3.5 S/F Proximity Effect

Figure 2.9 Spin bands. A toy model of spin bands within a ferromagnetic material, showing their
separation by twice the exchange energy, 𝐸𝑒𝑥, with the down spin electron (in red) and the up spin
electron (in blue) shown entering the different bands.

In proximity with a ferromagnet, the situation becomes more interesting. Whereas the spin

bands are degenerate within a normal metal, the spin bands in a ferromagnetic material are split

by twice the exchange energy, 𝐸𝑒𝑥. As depicted in Figure 2.9, when the two electrons from a spin-

singlet Cooper pair enter the ferromagnet, they must enter opposite spin bands, which results in the

pair acquiring a net center of mass momentum ℏ𝑄 =

(cid:16)

𝐹 − 𝑘↓
𝑘↑

𝐹

(cid:17)

= 2𝐸𝑒𝑥

𝑣𝐹 , assuming parabolic bands.

This, in turn, transforms the singlet wavefunction from the superconductor Ψ𝑆 = 1√
2

(| ↑↓⟩ − | ↓↑⟩)

into

which can be rewritten as

Ψ𝐹 =

1
√
2

Ψ𝐹 =

1
√
2

(cid:16)

| ↑↓⟩𝑒𝑖𝑄𝑥 − | ↓↑⟩𝑒−𝑖𝑄𝑥(cid:17)

(2.24)

[(| ↑↓⟩ − | ↓↑⟩) cos 𝑄𝑥 + 𝑖 (| ↑↓⟩ + | ↓↑⟩) sin 𝑄𝑥]

(2.25)

19

Ekk↑Fk↓F-k↓F-k↑F2Eexwhere 𝑥 is the center of mass coordinate of the pair measured from the S/F interface. This imparts

a spatial oscillation of the pair correlation function, which contains both a spin-singlet state (cosine

term) and the 𝑚 = 0 spin-triplet state (sine term).

Figure 2.10 Pair correlation graphic. A depiction of the pair correlation functions at S/N (left)
and S/F (right) interfaces indicating the steeper decay and oscillation within the ferromagnetic
layer. Note that 𝜉𝑁 ≫ 𝜉𝐹.

The characteristic length scale governing the oscillations of the pair correlations is sometimes

called the ferromagnetic coherence length or the ‘exchange length’, and is given by

𝜉ballistic
𝐹

= 𝑄−1 =

ℏ𝑣𝐹
2𝐸𝑒𝑥

(2.26)

In the ballistic limit, pair correlations decay algebraically due to angular averaging. In the diffu-

sive limit, in contrast, pair correlations decay exponentially, with both the oscillations and decay

characterized by

𝜉diffusive
𝐹

=

√︄

ℏ𝐷 𝐹
𝐸𝑒𝑥

(2.27)

where 𝐷 𝐹 is the diffusion constant in the ferromagnet. Figure 2.10 compares the pair correlation

function at the S/N interface to that at the S/F interface, where there is the oscillation and a much

steeper decay.

20

2.3.6 𝜋 Josephson Junctions

The oscillations in the S/F case of Figure 2.10 where the correlation function dips below zero

represent a situation where, if the width of a Josephson barrier is chosen to be in this region,

the energy is minimized when the phase drop across the junction is 𝜋 rather than 0. These are

referred to as 𝜋 junctions, and were first theorized by Bulaevskii et al. [44] in 1978, and observed

experimentally by Ryazanov et al. [3] and Kontos et al. [4] in 2001. A large amount of materials

work has been done exploring 𝜋 junctions in this group and others since then [45].

2.3.7 SQUIDs

Figure 2.11 SQUID. Diagram of a SQUID containing two Josephson junctions. Adapted from
[46].

First demonstrated in 1964, [47] Superconducting QUantum Interference Devices (SQUIDs)

comprise one or more Josephson junctions in a superconducting loop. A solid loop (without such

junctions), is subject to flux quantization, experimentally discovered in 1961 [48, 49]. This is a

result of the need for the superconducting wavefunction to be single-valued around a loop, and it

implies that the magnetic flux threading through a loop is quantized in multiples of the magnetic
flux quantum, Φ0 = ℎ

2𝑒 ≈ 2.068 × 10−15 Wb:
∬

Φ =

𝐵 · 𝑑𝜎 = 𝑛Φ0

21

(2.28)

Ic1sinϕ1Ic2sinϕ2IIBextA representation of a DC SQUID is shown in Figure 2.11 comprised of two Josephson junctions

in a superconducting loop. The current is clearly:

𝐼 = 𝐼𝑐1 sin 𝜙1 + 𝐼𝑐2 sin 𝜙2

(2.29)

If an external flux Φ𝑒𝑥𝑡 is applied to the loop (and the self-inductance of the loop is negligibly

small), the need for single-valuedness of the wavefunction (think of traveling around the SQUID

in Figure 2.11 clockwise from the top) implies:

𝜙2 − 𝜙1 − 2𝜋

Φ𝑒𝑥𝑡
Φ0

= 2𝜋𝑛

where 𝑛 is an integer. Plugging Eq. 2.30 into Eq. 2.29 gives:

𝐼 (Φ𝑒𝑥𝑡, 𝜙1) = 𝐼𝑐1 sin 𝜙1 + 𝐼𝑐2 sin

(cid:18)

𝜙1 + 2𝜋

(cid:19)

Φ𝑒𝑥𝑡
Φ0

(2.30)

(2.31)

If we consider a simple case of a symmetric SQUID and 𝐼𝑐1 = 𝐼𝑐2, we can find an expression

for 𝐼𝑐 by maximizing Equation 2.31 with respect to 𝜙1 and get:

𝐼𝑐 (Φ𝑒𝑥𝑡) = 2𝐼𝑐1

(cid:12)
(cid:12)
(cid:12)
(cid:12)

cos

(cid:18)

𝜋

Φ𝑒𝑥𝑡
Φ0

(cid:19)(cid:12)
(cid:12)
(cid:12)
(cid:12)

(2.32)

from which we see that the critical current of the SQUID oscillates periodically as a function of

the flux. Figure 2.12 shows this relation. Note that in the case where 𝐼𝑐1 ≠ 𝐼𝑐2, this plot would be

vertically offset by the difference in critical current.

22

Figure 2.12 SQUID IC vs. flux. Plot of critical current versus flux for a symmetric SQUID with
negligible self-inductance, showing sinusoidal oscillation.

2.3.8 Spin-Triplet Superconductivity

Figure 2.13 Triplet JJ design. Diagram of a trilayer spin-triplet Josephson junction with the outer
(𝐹1, 𝐹3) spin-mixing layers having magnetizations perpendicular to the central propagation layer
(𝐹2).

23

-1-1/201/2101IC/IC maxF/F0SF1F2F3SyzBeginning with the wavefunction of the supercurrent in a ferromagnetic Josephson junction

described earlier,

Ψ𝐹 =

1
√

2

[(| ↑↓⟩ − | ↓↑⟩) cos 𝑄𝑥 − 𝑖 (| ↑↓⟩ + | ↓↑⟩) sin 𝑄𝑥] ,

(2.33)

proper engineering can induce long-range spin-triplet superconducting pair correlations. As pre-

dicted by Bergeret et al. in 2001 [50], if a ferromagnetic propagation layer with a magnetization

(which sets the quantization axis) perpendicular to that of the first layer is introduced, as shown

if Figure 2.13, the short-range spin-triplet component is converted into long-range spin-triplet as

demonstrated in the basis transformation:

1
√

2

(| ↑↓⟩ + | ↓↑⟩) 𝑦 =

𝑖
√

2

(| ↑↑⟩ + | ↓↓⟩)𝑧

(2.34)

Figure 2.14 Triplet spin bands. Cartoon depiction of long-range triplet (like-paired) spins entering
the same spin bands within a ferromagnetic material.

The like-paired spins now enter the same spin bands within the propagation layer, as shown in

Figure 2.14. As a result, there is no longer a center-of-mass momentum, nor the spacial oscillation.

24

EkThis means there is a much longer coherence length analogous to the decay within a normal metal:

𝜉𝐹, long-range spin-triplet =

√︄

ℏ𝐷 𝐹
2𝜋𝑘 𝐵𝑇

(2.35)

in the diffusive limit. This generation of long-range spin-triplet supercurrent in ferromagnetic

layers was shown in the Birge group in 2010 [15], sparking even more experimental and theoretical

work since [51].

2.3.9 𝜑0 Junction

From the physics discussed in the previous sections, one might assume that a superconduc-

tor/ferromagnet system can only impart a phase drop of 0 or 𝜋 across a Josephson junction, but this

is not necessarily true. A JJ with a single ferromagnetic layer of varying thickness, where some

regions prefer the 0 state and some the 𝜋 state, can form ground states at ±𝜑, where 𝜑 can take any

value between 0 and 𝜋. These so-called ‘𝜑-junctions’ [52, 53, 54, 55, 56] still notably obey the

time-reversal symmetry relation 𝐼𝑐 (−𝜙) = −𝐼𝑐 (𝜙).

Alternatively, it has been theorized that a Josephson device could be created that imparts a

tunable, arbitrary phase drop of 𝜑0, which can take any value between 0 and 2𝜋, in an effect

referred to as the anomolous Josephson effect (AJE) [57, 58, 59, 60, 23, 61, 62, 63, 64, 65, 66,

67, 68, 69, 24, 70, 71, 72]. Crucially, such a device breaks the time-reversal symmetry relation

𝐼𝑐 (−𝜙) = −𝐼𝑐 (𝜙). This so-called 𝜑0-junction has been demonstrated in junctions containing exotic

materials with very strong spin-orbit coupling [73, 74, 75, 76, 77, 78, 79, 80]. A design realizing

this in traditional ferromagnetic materials using non-coplanar magnetizations was explored in this

research group by Victor Aguilar [25], but has yet to be fully demonstrated.

25

Figure 2.15 𝜑0 JJ design. Diagram of a 𝜑0 junction design with one fixed-magnetization spin-
mixing layer on the left, one variable-magnetization spin-mixing layer on the right, and a central
PMA propagation layer, along with a representation of the progression of the dominant spin pairing
within each layer (below), with 𝜑0 = 𝜋 + 𝜃.

In this ferromagnetic system, the proposed design is shown in Figure 2.15, with a fixed mag-

netization spin-mixing layer on the left (𝐹1), a central perpendicular magnetic anisotropy (PMA)

propagation layer (𝐹2), and a tunable magnetization mixing layer on the right (𝐹3). The progression

of the wavefunction through the junction is similar to that described in section 2.3.8, only, as it

moves from 𝐹2 to 𝐹3, it picks up a phase based on the relative orientation, 𝜃, of the magnetizations

of 𝐹1 and 𝐹3

1. This effect requires spin-triplet supercurrent and precise and individual control of

the magnetizations in each of the layers. The work shared in Chapter 5 is motivated by the hope of

realizing this goal.

1While the hand-waving explanation is given above, the calculation for supercurrent propagation through such a

system is quite involved and is given in truncated form in Appendix B.1.

26

|0,0⟩							→									|1,0⟩							→																			|1,1⟩															→					𝑒!"|1,0⟩					→					𝑒!#!|0,0⟩SF1F2F3θSCHAPTER 3

SAMPLE FABRICATION AND MEASUREMENT

Le savant digne de ce nom, le

géomètre surtout, éprouve en

face de son œuvre la même

impression que l’artiste; sa

jouissance est aussi grande et

de même nature.

Henri Poincaré

Figure 3.1 Fabrication overview. An overview of the sample fabrication process in a not-
representative-of-scale side view showing bottom lead patterning, sputtering deposition, junction
patterning, ion milling, SiOx deposition, lift-off, and top lead patterning and deposition.

So what does fabrication and measurement look like in the Birge group? Figure 3.1 shows a

graphical overview of the entire fabrication process. Let’s take a walk through, beginning with the

sample substrate. We choose a 3" silicon (100 orientation) prime wafer from PureWafer because it

has been shown to be exceptionally smooth and has proven itself through countless fabrication runs.

27

Bottom Lead PhotolithSputter DepositionJunction LithographyIon MillingSiOxDepositionLift-offTop Photo-lithTop Lead SputterJunctions can be patterned with EBL or image-reversal PL in ellipses or circles 𝑤=0.5	𝜇𝑚𝐴≈0.5	𝜇𝑚2𝑑=6	𝜇𝑚𝐴≈28	𝜇𝑚2A 3" diameter size is chosen because it can be subdivided into approximately 18 square chips of

side length 0.495" that fit within the existing sample holders used for deposition and measurement,

and there is room for 16 samples within the sputtering deposition system, leaving a couple of chips

for spares.

3.1 Wafer Dicing

To precisely dice the wafer, the Advanced Dicing Technologies 7122 automatic dicing saw is

used. Because it is housed outside of the clean room, and to protect the smooth silicon surface from

debris from the dicing saw, the wafer is first covered in photoresist. This mimics the later process as

a part of photolithography but is much more forgiving. The fresh wafer is unboxed within the clean

room and is immediately placed on the large diameter spinner chuck. Because the resist used for

photolithography (Microposit S1813 G2) must be freshly poured every 3 months, there is typically

some disused resist that is suitable only for protecting the wafers. To form a thick protective layer,

a spin rotation of 3,000 revolutions per minute (RPM) for a time of 50 seconds is used but care is

taken to begin the rotation at a minimum speed to first ensure the wafer is aligned correctly so it

does not wobble and shatter at the high rotation speed. Once the spin speed is ramped up safely to

3,000 RPM, the spinner can be stopped and a generous (nickel-sized) drop of resist can be placed

on the center of the wafer to spin for the 50 second recipe. Four wafers will fit on the ‘cookie sheet’

for the resist oven at a time, so the wafers can be easily baked in sets of four. The wafers are baked

at 90◦ C for 45 minutes. The protected wafers can then be transported outside the clean room to

the wafer dicer. The wafer dicing program is fully automated, so the main concern is aligning the

dicing grid pattern to maximize the number of useable pieces out of each wafer. The flat side of the

wafer is aligned with the first array of cut angles, then the first cut positions are indicated as a part

of the automatic alignment program. Note: for the nickel blade, a side length of 0.495" is used,

and for the resin blade, a side length of 0.485" is used to ensure that the chips will fit within the

holders due to the rougher cut edge of the resin blade. The cutting blade diameter is automatically

measured and calibrated every few cuts so the correct depth can be precisely made. The wafers are

15 mils thick, and an appropriate depth of cut is 8 mils to balance ease of dissecting yet transport

28

durability. Once the wafers are diced, they can be taken back in the clean room for separation and

cleaning.

3.2 Chip Cleaning

Within the protection of the class 100 portion of the clean room, the wafers can be separated

and immediately placed in individual test tubes containing acetone, which dissolves the photoresist.

Eight test tubes easily fit within a 250 mL beaker of water, which is heated for 5 minutes at 60◦

C to facilitate the dissolution of the resist. This containing beaker is then placed in an ultrasonic

bath for an additional 5 minutes. Then, each test tube has the acetone replaced with isopropyl

alcohol (IPA) and is sonicated for another 5 minutes. The chip will stick to the sides of the test tube,

so it can be inverted over a waste beaker and irrigated with the IPA to ensure all acetone is removed.

After sonication in IPA, the IPA is replaced with deionized (DI) water and again sonicated for 5

minutes. Then each chip is removed from the test tube with tweezers and laid flat upon a dust-free

clean room cloth and immediately blown dry from directly above with the wall-sourced compressed

nitrogen gas. The moisture on the backside of the chip will adhere it to the cloth and prevent it

from blowing away provided the airflow is from directly above and within ∼ 2" of the surface. To

ensure good adhesion of the photoresist and eventually the bottom lead material, the chips are then

plasma etched in an O2 plasma etcher. The etcher is first run empty at the maximum power of 300

W for a duration of 300 seconds, then the holder plate is cleaned with acetone and IPA to ensure

there is not contamination from previous users. After loading and pumping to a base pressure of

50 mTorr, the substrates are etched at 300 W for 300 seconds. After plasma etching, photoresist

can be applied.

29

3.3 Photolithography

Figure 3.2 Photomask pattern. Center of pattern for single junction photomask showing the
cut-outs for bottom lead exposure on the left and top lead exposure on the right, and alignment
marks in the corners of each section.

Photoresist is a chemical that is reactive to ultraviolet (UV) light and can either harden (negative

photoresist) or soften (positive photoresist) in reaction to a UV lamp shone through a chrome pattern

(mask) and be washed away with a specific chemical (developer) to create a precise pattern that can

be either deposited through or etched away before being removed itself. An example mask pattern

is shown in Figure 3.2. To create a pattern for sputter deposition of the bottom leads of our devices,

a positive photoresist from Microposit called S1813 G2 is used. In contrast to its use merely as a

protective layer (as discussed in the wafer dicing section above), spinning the resist for this purpose

is an extremely delicate process. By virtue of the nature of the exposure of positive photoresist to

a light source above the substrate, a very slight taper can form along the edges of the resist once

the softened resist washes away in the developer. This can make it difficult to lift-off the resist after

the deposition of material. To combat this effect, a layer of lift-off resist (LOR) can be spun on the

chips before the photoresist. Because this underlayer reacts differently to the UV exposure, using a

bilayer process creates a so-called ’undercut’ whereby the bottom LOR layer is recessed from the

top photoresist layer which mitigates this lift-off issue dramatically.

30

In this bilayer process, the first step is spinning the LOR, in particular LOR 5B. Because of

how important this layer is, it is imperative to start with fresh LOR that has been manufactured in

the last 2 years and properly stored at refrigerator temperatures. A small amount is poured out for

use 3 months at a time. FOR ALL RESISTS: The large, refrigerated bottle must be warmed to

room temperature for approximately 3 hours before opening to ensure there is no condensation

of water within the large resist bottle as this can ruin an entire batch of resist.

To begin spinning, the smallest spinner chuck should be used so there is no adhesion of resist

to the back of the chip. A clean substrate is then placed on the chuck and the spinner is calibrated

to the appropriate settings of 3,000 RPM and 45 seconds and blown with wall-sourced compressed

nitrogen gas. With the chuck stopped, a generous [∼5 drops] of LOR are placed in the center

of the chip and the spin is immediately started. Once completed, the chip can be moved to the

baking ‘cookie sheet’. A full run (16 chips) can be spun in this fashion before being placed in the

(preheated) baking oven for 45 minutes at 180◦ C. As a reference and sanity check, it is encouraged

to continually confirm the recipe with the resist guide document on the clean room computer at

each step.

Once the LOR baking is complete, the baking oven should be left off with the door wide open

whilst spinning the top layer of photoresist in order to cool to the appropriate temperature. The

chips, too, should be left to cool for a couple of minutes before spinning. The S1813 G2 photoresist

is dropped and spun in a similar fashion as the LOR only with a speed of 5,000 RPM and a time

of 50 seconds. These settings are crucial for a consistent thickness and UV response of the resist

(which is why it is good practice to double check them every time). Again, a full set can be

accumulated on the ‘cookie sheet’ before placing in the preheated oven for 45 minutes at 90◦ C.

Once the S1813 bake is complete, the chips are ready for exposure from the UV lamp. An ABM

mask aligner is used to allow for precise (X/Y-axis) alignment, (𝜃) rotation and (Z-axis) contact

with the chrome mask pattern. If proper care is taken to NEVER move the X/Y/𝜃 positioning

while under contact, the mask will stay clean for quite some time. But over time, some resist and

LOR will accumulate on the mask, and it should be delicately cleaned by warm PG remover and

31

gentle scrubbing with a cotton Q-tip or ideally professionally cleaned by the manufacturer.

The UV lamp should be switched on for ∼20 minutes to warm up before exposure to ensure a

consistent intensity. The intensity of UVA and UVB is measured after warming up and compared

to previous uses and the exposure time can be modified if it differs considerably. The small sample

holder stage is used, and the suction holes that extend beyond the 0.495" chip must be covered with

blue clean room tape so the substrate vacuum holds the chip securely in place. For the 5" masks,

the appropriate mask frame is installed, and the mask is secured by vacuum as well. For the bottom

lead pattern, precise (X/Y/𝜃) alignment is not crucial, but the pattern should be reasonably aligned

with the substrate below. What is crucial is the Z-axis contact. Good practice aligns the chip

reasonably well with the Z-axis set with a visible gap between the substrate and the mask. Then,

the substrate stage is raised until ideal contact is made. With the 5" masks, this requires a keen

eye because it is possible to force the substrate too far and bow the mask outward which results

in poorer contact for some distance before the mask pops off. As a result, one must rely on the

interference fringes— they will appear at some level of Z-axis adjustment and will move around

as contact is minimized until a point where they appear to stop moving. There should be some

resistance in the Z-axis adjustment knob, as well. This is the position of ideal contact.

Once the ideal alignment and contact have been dialed in, the UV lamp is brought over for

automatic exposure of 3.5 seconds. After exposure, the chips are immediately developed in

Microposit MF 319 tetramethyl ammonium hydroxide (TMAH)-based solution. The chips are

submerged in a small beaker of the developer while being held with tweezers and agitated for 45

seconds. The resist will visibly clear in the exposed regions in approximately half that time. Then

the chips are immediately rinsed similarly in a beaker of DI water for about 30 seconds. It is good

practice to let go of the chip and reposition the hold of the tweezers a few times to ensure all the

developer is rinsed off. Then the chips are dried again by laying flat upon a clean room cloth and

blown with compressed nitrogen. The small beaker of developer and the slightly larger beaker

of DI water should be refreshed every 4-5 uses. After each development, the chips are inspected

and photographed with the optical microscope for quality assurance. Finally, the chips undergo

32

a low-power plasma etch at 100W for 90 seconds to ‘descum’ the patterned photoresist before

loading into sample holders. Sample holders are prepped in the chemical room by soaking stainless

steel (shutter) parts in a 3:1 ratio solution of nitric acid and water followed by an intense scrubbing

with a wire brush. Afterward, both stainless steel shutters and aluminum holders are sonicated

sequentially in acetone, ethanol, and DI water for 5 minutes each and dried by heat gun. Samples

are placed at the bottom of the holders and secured by copper heatsinks and stainless-steel bridges.

Care should be taken particularly when tightening the bridge screws to not break the chips.

3.4 Sputtering Deposition

Bottom Nb leads, normal metal spacer layers, magnetic interlayers, and (in a separate run) top

Nb leads are deposited in a 7-gun DC high-vacuum sputtering chamber custom designed by Prof.

Bill Pratt and Prof. Jack Bass and maintained by Dr. Reza Loloee. Samples are placed face-down

on a precision motor-controlled plate that sits atop a two-position foil-wrapped shutter plate that

separates the sputtering targets from the samples and can be alternated between ‘open to large guns’

and ‘open to small guns and ion mill’ positions. There are 4 large (2.25" target) DC triode guns

and 3 small (1" target) DC magnetron guns and an ion mill for cleanup and adhesion before top

lead deposition. The large guns are ramped up slowly to operating voltage, which can be quite

high (∼500 V). The small guns are turned on and off as needed throughout the process. The entire

process of sputtering deposition is quite involved, and care should be taken to follow the procedure

in the instruction manual step by step as though an aeronautical pre-flight checklist in order to

neither damage the irreplaceable equipment nor deposit material other than intended. For this

reason, I will not reduplicate those instructions, but provide an overview of the process.

For loading, the top of the chamber is removed by chain hoist. This provides access to the gun

assemblies to install the appropriate targets and inspect and change the filaments as needed. The

targets must be electrically isolated from the housing when installed and this can be checked first

by visual inspection, then by use of a multimeter. A foil-wrapped chimney is placed atop each

assembly to direct the plasma up toward the samples and a shroud is placed around this to encourage

a smooth, consistent flow of argon gas. Once the samples are loaded into the top plate, all the targets

33

are installed and checked, and the two-position shutter plate is installed, the chamber can be closed.

A mechanical roughing pump is used to take the pressure from atmosphere (∼750 Torr) to about 5

× 10-2 Torr before switching over to a cryogenic pump, and it is advised to flush the chamber with

nitrogen gas and repump with the roughing pump 1 or 2 times before this as an extra attempt to

mitigate contamination from water vapor. Once switching to the cryopump (it is imperative that

the roughing pump and cryopump not be open to the chamber simultaneously), and a suitable

test pressure (∼5 × 10-6 Torr) is reached by reading of the ion gauge, the argon gas and cooling

water are switched on and the guns are tested by slowly ramping to an intermediate voltage and

checking for stable plasma. The guns are then ramped back down and turned off along with the

argon. From this point, the chamber is warmed by heating strips overnight (with the gate valve

partially open to protect the cryopump from warming). The cooling water is left on to protect the

gun assemblies.

The following day, when the heater is off and the chamber has cooled to room temperature, the

cryopump is fully opened to the chamber and it is pumped for an additional day to reach a base

pressure of ∼4 × 10-8 Torr. Once this pressure is reached, the deposition process can begin. First,

liquid nitrogen is flowed through the cold trap in the top of the chamber to condense any remaining

water and to cool the sample plate to ∼ -30◦ C to facilitate smooth deposition. This will cause

the base pressure to approach 3 × 10-8 Torr. The flow of liquid nitrogen is regulated by opening

and closing a supply of compressed nitrogen gas to maintain a stable temperature range. The

initial cooling takes approximately 1 hour, during which time the computer-controlled sputtering

sequences can be written and the shutter and sample plates are aligned. Once at temperature, a

supply of argon gas (purified by a gas purifier) is directed into each of the sputtering guns. Argon

is used because it is an inert gas. For the triode guns, current is run through each filament which

creates free electrons and ionizes the argon gas. The ionized argon is then directed toward each

target by a large voltage, which then frees and propels atoms of the target materials up toward the

samples. During this process, cooling water is run through the gun assemblies to keep them from

overheating. The large guns are ramped up to their appropriate voltages then pre-sputtered for some

34

time to remove oxidation and contamination from the surface.

Once the target voltages are achieved and the plasmas are stable, the deposition rates are

checked by film thickness monitor (FTM). The FTM is calibrated for each material by input of

reference parameters (such as density and Z-factor) and has been further verified by low angle

X-ray diffraction each time a new material is used. For normal deposition rates on the order of

angstroms per second, the rates are stable within 0.1 angstrom per second and can be read from the

FTM directly. However, for very thin layers where a slow deposition is desired, it is necessary to

average over a longer time to reduce the uncertainty. These rates are then entered into the Labview

computer program, which then can interpret a desired layer thickness and convert it to a deposition

time. The deposition sequence is manually generated, and care must be taken to avoid unwanted

deposition as the sample plate moves from position to position over the active plasma streams.

This often involves a delicate symphony of opening and closing the two-position shutter plate and

turning on and off the small guns. All information from the sputtering run must be dutifully

recorded in the logbook as outlined in Appendix B.2.

Each sample holder houses two samples, protected by a small rotating shutter designed to be

opened and closed by wobble stick while under vacuum. This means that only one sample is exposed

at a time. This allows for a unique recipe, if desired, for each of the 16 samples in a run. Once all

of this is orchestrated, the samples are deposited by running each recipe sequentially, with the user

manually opening and closing the sample shutters in between each deposition and remeasuring the

deposition rates every 2-4 samples. A typical stack (thicknesses in nm) for Josephson junctions

includes a bottom superconducting electrode of [Nb(25)/Al(2.4)]3/Nb(20), which has been found

to encourage smoother ferromagnetic growth. A normal metal spacer layer of fcc Cu(2) is used for

lattice matching between the bcc Nb and the fcc ferromagnet(s) and possibly better band matching

for supercurrent propagation. Then the ferromagnetic material(s) to be studied are deposited. A

symmetric Cu(2) spacer is added atop this, then a capping layer of Au(10) to protect the interlayers

from oxidation. A typical deposition recipe takes 5-10 minutes, so a full run of 16 chips will take

about 2 hours.

35

When the last deposition is finished, the target voltages and filament currents are gently ramped

down and turned off, the chamber is heated by heating strips to slightly above room temperature

to discourage condensation upon opening, and the chamber is filled with nitrogen gas back to

atmospheric pressure. The chamber can then be opened and samples retrieved. After transport

into the clean room, and removal from the holders, samples are soaked in individual beakers of PG

remover heated to 80◦ C to dissolve the photoresist and LOR and lift-off the excess metal deposited

atop unwanted areas. The metal will begin to visibly peel from these areas after 5-10 minutes. This

is followed by sonication for 30 seconds, then replacing the PG remover for IPA with another brief

sonication, then rinsing in DI water and blowing dry with nitrogen gas.

3.5 Electron Beam Lithography

The samples then must be patterned with lithography to define the junction areas (lovingly

referred to as ‘pillars’) with ion milling. Commonly, this is done by electron beam lithography (EBL)

for very small (∼0.5 𝜇m2 area) junctions, although photolithography can be used for larger areas.

Here I will only describe EBL for brevity. The Keck Microfabrication laboratory clean room

houses a Hitachi SU5000 field emission scanning electron microscope (SEM) for this use. First,

the samples are coated in EBL-responsive resist called Ma-N 2401 from Micro Resist Technology.

This is done by a similar process as described above for the photoresist, only with a spin speed of

3,000 RPM and a time of 40 seconds. The samples are then heated on a hotplate set to 90◦ C for 60

seconds. To make lift-off easier, in a process developed by Dr. Reza Loloee and Dr. Demet Korucu,

the samples are then coated, spun, and baked once more to form a thicker layer. The samples are

spun in batches of 5 to correspond to the number of sample slots in the ion mill chamber.

Once spun and baked, the samples are placed on a sample holder designed for the SU5000

along with a patterned chip used for stigmation and loaded into the SEM. The SEM chamber is

pumped out with an integrated vacuum system controlled by the software. The SEM software is

very intuitive and guides the user through the process of turning on and calibrating the electron

beam. Since the EBL patterning is carried out at 1000x magnification, the stigmation should be

done at many multiples of that (∼30-40k). Care is taken that the working distance is set to 15

36

mm and the beam current is measured by use of a small hole in the sample holder that acts as a

Faraday cup. This current measurement is used to calibrate the dwell time of the beam to deliver a

consistent exposure dosage. An alignment protocol is used to bring the beam writer directly over

the intended spot on the bottom lead. Then a computer-aided design (CAD)-drafted pattern is used

to direct the beam to expose only the small areas that will define the pillars and pinwheel designs

that give an impression of proper stigmation after development. The standard design incorporates

elliptical pillars of 0.5 𝜇m2 area, but can be easily modified for different shapes or sizes.

After exposure in the SEM, the samples are removed and developed by agitating in AZ 300 MIF

TMAH-based developer for 10 seconds, immediately rinsed in DI water (repositioning tweezers

to prevent streaking from residual developer) and blown dry with nitrogen gas. Since the e-beam

resist is a negative resist, the exposed portion is hardened and the unexposed portion washes away

in the developer. The samples are then imaged in the optical microscope to verify size, shape,

positioning, stigmation, and focusing before being loaded in holders for the ion mill chamber.

3.6

Ion Milling

Ion milling can be thought of as reverse sputtering. A filament is heated in a chamber of

argon gas, which ionizes the gas, then an accelerating voltage is applied which propels the ions

up toward a sample where their kinetic energy knocks off atoms of material layer by layer. In this

fabrication process, it is used to define the pillar of material that will become the Josephson junction

by removing all excess material. The samples are loaded into individual holders using a mask to

restrict the milling to the central area of the chip. Then a small amount of silver paste is used

to adhere the sample to the copper heatsink, which is then attached to a magnet for manipulation

in the load lock of the chamber and clearly labeled by sample number with a permanent marker.

Heatsinking is very important because the build-up of heat from the ion beam can be deleterious

to the E-beam resist. Loading of the sample holders is done in the clean room, then the samples

are transported out to the ion mill chamber.

The ion mill chamber is like a smaller version of the sputtering chamber described in the earlier

section, except it has only 4 locations for deposition and milling (ion mill, Au sputtering, SiOx

37

thermal evaporation, and null) and 5 sample holder slots plus an FTM. The Au sputtering gun

is used the deposit upon the FTM for calibration of the ion mill rate. The SiOx boat is used to

electrically insulate the top and bottom leads from each other after ion milling, and the ’null’

position is used as a safe position for the shutter opening during preparation for deposition and

milling. There is a rotating shutter plate and a rotating sample holder plate, both of which are

manually controlled. The chamber also incorporates a magnetic load lock which allows the main

chamber to remain under high vacuum except during maintenance and repair. As with the sputtering

deposition chamber, the instruction manual should be followed step by step to ensure protection

of the apparatus and samples, so this section will only provide an overview of the process and the

instructions will not be exhaustive.

The load lock incorporates a small loading chamber, a magnetic transport arm, a mechanical

roughing pump, a nitrogen gas port, a swinging access door, and a gate valve which separates the

main chamber. The loading chamber is first isolated by closing the gate valve (ensure the loading

arm is clear) then brought to atmospheric pressure by opening the nitrogen port. Then the access

door is opened whilst the nitrogen is flowing, and the first sample holder is attached to the magnetic

loading arm. The access door is held closed, while the nitrogen flow is shut off and the roughing

pump is immediately opened to the loading chamber. To keep the main chamber very clean, a

so-called ‘pump and flush’ routine is used where, upon reaching a pressure below 1 × 10-1 Torr as

read by the convection gauge, the roughing pump is closed, and the nitrogen port is opened until a

pressure of 1 × 10+2 Torr is reached. This can be repeated 2-3 times depending on the humidity

to minimize water vapor in the main chamber. The roughing pump is then again used to achieve a

pressure below 7 × 10-3 Torr which is suitable to hand-off to the turbo pump of the main chamber.

As with any vacuum system, only one pump should be open to a chamber at a time, so the load lock

gate valve is only opened after the roughing pump valve is closed. It should be opened slowly at

a rate that keeps the main chamber pressure (as read by the ion gauge) below 1 × 10-6 Torr at all

times to protect the turbo pump. Once the gate valve is opened fully, the loading arm is lowered

into the chamber and the sample plate is rotated to accept the sample holder. Once the holder is

38

seated, in a feat of coordination suitable for Cirque du Soleil, the sample plate is deftly twisted

whilst the magnetic arm is briefly held steady then abruptly removed to avoid reattaching to the

sample holder. The arm can then be fully extracted back into the load lock, which can then be

isolated again. This process is repeated for each sample until the chamber is fully loaded. The

chamber is left to pump for about 4 hours after loading to recover a base pressure of ∼3 × 10-8 Torr.

Upon reaching a suitable base pressure, argon is flowed into the chamber, the gate valve to the

turbo pump is closed to reach an Au sputtering pressure of 7 × 10-4 Torr, and the cooling water

is verified to be running. The Au gun is then turned on with the FTM positioned over it, and the

shutter plate is opened. The FTM display is zeroed, and Au is deposited upon the FTM until a

thickness of 2000 angstroms is reached (400 angstroms for each sample). The Au gun is then shut

off, and the FTM is positioned over the ion mill, and the pressure is reduced to 2.3 × 10-4 Torr by

opening the turbo pump valve. With the shutter plate closed, the ion mill beam is switched on and

warmed up and all posted parameters are verified to be within range (it will take about 10 minutes

for the beam to become stable). At this point, the ion mill rate is checked by opening the shutter to

mill away the some of Au deposited on the FTM. For the most reliable rate, a stopwatch is used to

determine how long it takes to mill 100 angstroms as read by the FTM display, and an Au mill rate

is then calculated in angstroms per second and should be about 5.5.

Since the nominal mill depth penetrates the top cap of Au, the top Cu spacer, all of the magnetic

layers, and halfway through the bottom Cu spacer, the thickness of each layer is multiplied by a

k-factor, which is the ratio of the mill rate through Au to the mill rate through each material, and

added together giving an overall ‘equivalent thickness’ to aid in calculating the mill time. These

k-factors have been experimentally determined by surface profiling before and after milling. To

keep these calculations straight by sample, a spreadsheet is made which can be quickly edited as

the mill rate is measured to calculate a mill time in seconds.

With the mill time calculated, the sample is moved over the ion mill, the shutter is opened, and

a stopwatch is used to precisely time the milling. The mill rate is verified between each sample

but should remain relatively stable throughout. Once all samples have been milled, the ion beam

39

is switched off, the FTM is moved over the SiOx boat (with the shutter closed), the argon is turned

off, and the SiOx boat is slowly warmed by increasing the voltage applied across it until reaching

the target setting. The deposition voltage will vary slightly as the Si is depleted from the boat, but

should be tuned for a deposition rate of about 7 angstroms per second as measured on the FTM

(ensure the display is set to the proper program). Then, similar to how the samples are exposed for

ion milling, each sample is held over the SiOx boat for the appropriate time to deposit 50 nm of

insulating SiOx. Then, the SiOx voltage is turned down slowly and the samples are unloaded via

the load lock.

3.7 Side Ion Milling and Lift-off

For such small features as the 0.5 𝜇m2 pillars, lift-off of the E-beam resist can be problematic.

To aid in lift-off, the samples are taken out of the ion mill holders (being careful to remove the silver

paste from the back with cotton-tipped swabs) and placed in holders that orient the chips at an 87◦

angle (with the ion beam parallel to the bottom lead) to break through any redeposited layers of

metal from the top-down mill or stray SiOx creeping up the sides of the pillars. The process from

loading to milling is identical as above, only the milling is done for 2 minutes, 2 times for each

sample in each orientation (top up and top down).

Figure 3.3 EBL lift-off. Before (left) and after (right) pictures of the lift-off process. The small
ellipses in the center and the pinwheel design have lifted off and appear brighter while the outer
L-shaped alignment marks have not.

After side milling, the samples are removed from the holders, imaged with the optical micro-

40

scope, and immediately placed in PG remover lift-off solution in individual beakers of a hot plate

set to 80◦ C for 10 minutes. They are then scrubbed (in the junction region) very gently with

cotton-tipped swabs and heated for an additional 20 minutes before being capped with aluminum

foil and left to soak overnight. Then the samples are swished in a beaker of IPA, a beaker of

DI water, and blown dry with nitrogen gas. The samples are imaged again, and the images are

compared before and after lift-off. As shown in Figure 3.3, properly lifted-off junctions will appear

noticeably brighter and larger than those capped in resist.

3.8 Top Lead Photolithography and Sputtering

After lift-off, the samples can be patterned for the final deposition of top leads. The recipe for

the bilayer resist spinning, baking, exposure, and development is identical as for the bottom leads,

with the crucial difference being that the X/Y/𝜃 alignment is now critical. The top lead pattern of

the photomask includes alignment marks that correspond to the alignment marks on the bottom

lead pattern which are now deposited material. There are four sets of alignment marks on the

four corners of the chip, and they each must be used to ensure that the top leads will overlap the

junction pillars. Again, the X/Y/𝜃 movements must be made when the mask is out of contact with

the resist to keep the mask clean. Once the exposure and development is complete and the samples

are again imaged on the optical microscope to verify the alignment, they undergo another 100W

for 90 second descum in the plasma etcher before being loaded in the sputtering sample holders.

The sputtering process for top leads is the same as above except for a few tweaks. First, the

base pressure does not need to be as low since the top leads need only to be superconducting and

not a base for ferromagnetic structures, so the additional day of pumping to reach 4 × 10-8 Torr

can be skipped if needed. And, to promote good adhesion of the top lead, 5 nm of the Au(10) top

cap is ion milled away in situ immediately before the Nb is deposited. Additionally, the smoothing

interlayers of Al used in the bottom lead are not needed, so simply 150 nm of Nb is deposited then

a final cap of Au(10). After top lead deposition, the resist is lifted off just as with the bottom leads,

and the samples are ready to measure.

41

3.9

Josephson Junction Measurement

Once completed, samples are measured by mounting on one of two dip probes designed by

Prof. Bill Pratt, then dipping in a dewar of liquid helium. Both probes employ flying leads attached

to the sample by pressed indium. Current is then driven through a junction and voltage is measured

across it in a 4-probe setup to collect I-V curves. The first probe, referred to as ‘quick dipper I’ or

QDI, includes a SQUID comparator circuit that amplifies the voltage measurement for low-noise

data collection [81] on samples with a very small critical current. QDI also includes an integrated

superconducting solenoid for application of a magnetic field. The second probe, QDVI, has all of

its electronics at room temperature, so it is not suitable for such a sensitive measurement. And it

must be dipped with a separate solenoid-containing sheath (which consumes addition He through

boil-off) in order to apply a magnetic field. However, it can connect up to 5 junctions at once to

allow for multiple measurements for each dip. Both systems can deliver a set of I-V curves across

a range of magnetic field steps for characterization of the junctions by their magnetic response.

3.10 SQUID Magnetometer Measurement

Samples deposited without patterning, thin films, are measured for magnetic characterization

in a Quantum Design MPMS3 SQUID-vibrating-sample magnetometer (VSM). As our deposition

equipment is set up for 12.7 mm × 12.7 mm samples (0.5" squares), this begins with careful

scoring and quartering (an alternate method is described in Appendix B.3). This results in ∼ 6.4

mm × 6.4 mm squares, which slide into measurement straws and secure with a friction fit. The

measurement straws are designed to slide onto the loading stick which places the sample in a

vacuum chamber. Once pumped out, the closed loop cryogenic system can be set to any desired

measurement temperature, down to about 2 K. S/F samples are typically measured above the 𝑇𝐶 of

Nb at 10 K. Once cooled to the desired temperature, the sample is aligned with a manual DC scan

(to account for thermal variations), then a custom sequence can be run to measure, for instance,

moment vs. field or moment vs. temperature. Geometrical measurements are taken with an optical

microscope once removed to normalize for area.

42

CHAPTER 4

NI-MN PROJECT

...ideoque memoriae infirmitati

continuo quodam cogitationis

motu succurrendum esse

dicimus.

René Descartes

One potential application of ferromagnetic Josephson junctions is within a superconducting com-

puter in the form of the switching part of a memory cell, in Josephson magnetic random-access

memory (JMRAM). The design, proposed by Anna Herr and colleagues [5] and implemented by

Northrop Grumman [7] involves a two-layer ferromagnetic junction within a SQUID loop whereby

the phase difference across the junction is switchable by changing the relative orientation of the

magnetizations of the two layers. One layer remains fixed in its magnetization, and one layer is

switchable (free) under a small magnetic field. The phase accumulation through the ferromagnetic

layers adds when the magnetizations are parallel and subtracts when they are antiparallel. This

effect was first demonstrated in the Birge group by Bethany Niedzielski and Eric Gingrich [6] as

a part of the collaboration with Northrop through the IARPA C3 program. Two key requirements

toward the scalability of this design were optimizing both the softness and coherent rotation of the

free layer and the robustness of the fixed layer. The original design used Ni81Fe19 (a.k.a. permalloy)

as the free layer and pure Ni as the fixed layer. Appendix A will briefly discuss the study of NiFeCr

for use as the free layer, and this chapter will discuss the exploration of antiferromagnetic (AF)

Ni-Mn used to pin the fixed layer through an effect called exchange bias. The text in this chapter

is adapted from this author’s work published in IEEE Transactions on Applied Superconductivity

[26] ©2023 IEEE.

43

4.1 Exchange Bias

Figure 4.1 Exchange bias. A visual interpretation of the exchange bias effect on the left, adapted
from O’Handley [82], and an idealized hysteresis curve on the right showing the characteristic shift
indicating a preferential direction of the magnetization.

In an antiferromagnetic material, electron spins of neighboring atoms tend to align into layers

with antiparallel orientation causing the material to have an overall net magnetization of zero. When

such an antiferromagnetic material is placed next to a ferromagnetic material, this tendency results

in an exchange coupling with the interfacial spins in the ferromagnetic layer which resists their

reorientation. The cartoon in Figure 4.1 shows a representation of this adapted from O’Handley

[82] and an idealized magnetic response plot (hysteresis curve) of this F/AF system. As shown by

the horizontal shift, this ‘exchange bias’ effect imparts a preferred direction of the magnetization

of the F-layer. This effect is used quite commonly in magnetoresistive random-access memory

(MRAM) [83, 84, 85] which relies on tunneling magnetoresistance, which is similar to the giant

magnetoresistance effect [86] whereby the resistance of a two-layer ferromagnetic system changes

based on the relative orientations of the magnetizations of the layers.

Another important characteristic to determine when considering applications of AF materials

is their so-called ‘blocking temperature’. This is the temperature below which the exchange bias is

maintained. In MRAM application, the layers are thick enough that this temperature is above room

temperature, so the materials must be heated above, then cooled through this critical temperature

whilst a magnetic field is applied to impart the exchange bias. In an F/AF system, the blocking

44

AFFHMHexxzyAFFxzyAFFH=0Htemperature can be determined by establishing the exchange bias, then warming in a small field in

the opposite direction. At the blocking temperature, the magnetization will switch sign as the AF

material ‘lets go’ of the ferromagnet and it is free to switch.

4.2 Past Work

Figure 4.2 FeMn/NiFe bilayer JJs. A graph of the critical current times normal state resistance
vs. thickness of FeMn/NiFe bilayers compared to NiFe alone showing a large suppression from the
additional AF layer.

Previously in the group, AF materials have been investigated for this purpose, namely FeMn

by Bethany Niedzielski [87] and IrMn during my time as an undergraduate [unpublished]. While

these materials are characterized quite well for MRAM application, two critical questions remain

when considering their usage in JMRAM: ‘is the exchange bias effect present in very thin (on

the order of nm) layers?’, and ‘is it possible to propagate supercurrent through the AF/F system?’.

Both materials indeed demonstrated the exchange bias effect in thin magnetic layers, but fell short

in the propagation of supercurrent, as seen in Figure 4.2, where there is a large suppression of the

supercurrent observed from the addition of the AF layer and which combines data from Bethany

Niedzielski [87], and Josh Willard and Swapna Sindhu Mishra [11]. Before abandoning this idea

entirely, we decided to investigate Ni-Mn due to the increased supercurrent transmission of Ni in

45

1.01.52.02.50.1110100IcRN (mV)NiFe Thickness (nm) NiFe/FeMn (BN) NiFe (JW) NiFe Fit (SSM)comparison to Fe and Ir.

4.3 Magnetic Characterization

We began by fabricating sheet films for characterization in the Quantum Design MPMS3 SQUID

VSM. Using sputtering deposition as described in Chapter 3, only without any patterning, thin films

were deposited on Si substrates. The 0.5" chips, when quartered, are the ideal size for measurement

in the VSM. Test samples were made both to calibrate the deposition rate and sample thicknesses

with low angle X-ray diffraction and their composition with energy dispersive X-ray analysis. The

analysis showed a composition of Ni41Mn59 as deposited. Samples were fabricated with the AF

NiMn atop both NiFe with a structure (thicknesses given in nm) of Ni81Fe19(dF)/Ni41Mn59(dAF)

with dF = 2 and dAF = 1.2, 1.8, 2.4 and pure Ni with a structure of Ni(dF)/Ni41Mn59(dAF) with dF

= 1.6, 2 and dAF = 1.2, 1.8, 2.4. In all samples, the F/AF layers were sandwiched between a seed

layer of Nb(5)/Cu(2) (for adhesion) and a symmetrical top cap of Cu(2)/Nb(5) to prevent oxidation.

The blocking temperatures of the samples were measured by establishing exchange bias in the

positive direction, then warming in a small negative applied field and plotting the magnetization

vs.

temperature. This is an important measurement for the proposed application.

It is ideal

that the blocking temperature be well above room temperature, because this allows the direction

of exchange bias and therefore pinned magnetization to be established once and endure many

cooling and warming cycles. It is notable that in MRAM application, thicker layers of AF and F

materials are used than in this study, and their blocking temperature is indeed often well above

room temperature. If the blocking temperature is below room temperature, a field must be applied

to re-establish the exchange bias effect each time the device is warmed to room temperature.

46

Figure 4.3 NiFe/NiMn thin films. Magnetic hysteresis curves (a)-(c) of NiFe/NiMn bilayer films of
thicknesses as labeled (in nm). All samples show characteristic horizontal shift indicating expected
pinning behavior of the AF layer placed adjacent to the F layer. The blocking temperature (d) was
measured by establishing exchange bias in the positive direction, then warming the samples in a
small negative applied field.

Figure 4.3 shows the magnetization vs. magnetic field for the NiFe/NiMn bilayer samples,

after cooling in a magnetic field of 0.1 T oriented in the positive direction. As expected from the

exchange bias effect, the curves are shifted toward negative fields indicating a pinning behavior

of the F/AF system. The magnitude of the exchange-bias shift increases with increasing NiMn

thickness, but is substantial even with a NiMn thickness of only 1.2 nm. All samples showed

blocking temperatures below 50 K.

47

050100150200-1000-50005001000Magnetization (kA/m)Temperature (K) NiFe(2)/NiMn(1.2) NiFe(2)/NiMn(1.8) NiFe(2)/NiMn(2.4)(d)-40-2002040-1000-50005001000Magnetization (kA/m)µ0H (mT) NiFe(2)/NiMn(1.8)(b)-40-2002040-600-3000300600Magnetization (kA/m)µ0H (mT) NiFe(2)/NiMn(2.4)(c)-40-2002040-1000-50005001000Magnetization (kA/m)µ0H (mT) NiFe(2)/NiMn(1.2)(a)Figure 4.4 Ni/NiMn thin films. Magnetic hysteresis curves (a)-(c) of Ni/NiMn bilayer films
of thicknesses as labeled. All samples show characteristic horizontal shift indicating expected
pinning behavior of the AF layer placed adjacent to the F layer. Panel (d) again shows the blocking
temperature measurement performed as described in Figure 4.3.

Figure 4.4 shows similar data for Ni/NiMn bilayers. The wide hysteresis loops are due to the

high coercive fields of the thin Ni layers [88], but again there is a noticeable exchange bias with a

NiMn layer of only 1.2 nm. An additional Ni sample was fabricated with a NiMn thickness of 0.6

nm, but it did not show exchange bias.

4.4

Josephson Junctions

Having demonstrated the desired exchange bias behavior with such thin Ni-Mn layers, we

then proceeded to fabricate and measure Josephson junctions. While the proposed application

in cryogenic memory would require an S/F/N/F/AF/N/S structure, our group’s previous attempts

to study such systems resulted in nearly immeasurably small critical currents. This informed

the decisions both to begin with the simpler S/N/AF/N/S structure as well as using larger area

48

050100150200-500-2500250500Magnetization (kA/m)Temperature (K) Ni(1.6)/NiMn(1.2)  Ni(1.6)/NiMn(1.8)  Ni(2)/NiMn(1.8) (d)-100-50050100-5000500Magnetization (kA/m)µ0H (mT) Ni(1.6)/NiMn(1.2)(a)-100-50050100-5000500Magnetization (kA/m)µ0H (mT) Ni(1.6)/NiMn(1.8)(b)-100-50050100-5000500Magnetization (kA/m)µ0H (mT) Ni(2)/NiMn(1.8)(c)junctions than are typical in our recent research. The thought behind this was that this would

allow extrapolation that would inform viability through critical current density JC. Fabrication was

similar to that described in Chapter 3, however junction patterning was done by photolithography in

an ‘image-reversal’ process using negative AZ 5214-E photoresist, which gives an undercut profile

for ease of lift-off.

Figure 4.5 NiMn Fraunhofer. Magnetic field dependence of critical current for most ideal dNiMn
= 4.8 nm sample with a junction diameter of 6 𝜇m. Upsweep data shown, with downsweep data
indistiguishable, showing no hysteresis. The solid line is a fit to the data of an Airy function, which
is appropriate for circular Josephson junctions [89].

Figure 4.5 shows the critical current plotted against magnetic field applied in-plane for a

circular Josephson junction of diameter 6 𝜇m containing a 4.8 nm NiMn layer. The data follow the

characteristic interference pattern of a non-magnetic Josephson junction [89]. We note that junctions

containing thinner NiMn layers (dNiMn ≤ 3.6 nm) produced less ideal interference patterns, possibly

due to magnetic disorder. In contrast to ferromagnetic junctions, whose interference patterns are

shifted and hysteretic due to the net magnetization of the interlayer, the AF samples in this study

show symmetry about zero field and no such hysteresis.

49

−8−40480.00.20.40.60.8IC (mA) Fit Upsweep Dataµ0H (mT)Figure 4.6 NiMn JC decay. Peak critical current density vs NiMn layer thickness. The line is a
least-squares fit to an exponential decay, and gives a decay length of 𝜉AF = 1.03 ± 0.05 nm.

Figure 4.6 compiles many such measurements and relates the peak, zero-field, critical current

density to the NiMn AF layer thickness. The plot shows a steep decay and was used to determine a

characteristic decay length, 𝜉AF, within the material, expecting that JC ∝ exp(-dAF/𝜉AF). The shown

fit gives us 𝜉AF = 1.03 ± 0.05 nm. That short decay length is very close to the one measured by

Bell et al. in junctions containing FeMn [90].

4.5 Discussion and Conclusion

The intended application of this work was to strengthen the fixed layer of an S/F/N/F’/S spin

valve inside a Josephson junction used in a superconducting memory cell. Given the strong

exchange bias exhibited in Figs. 4.3 and 4.4 for NiMn layers as thin as 1.2 nm, the steep decay

of JC shown in Figure 4.6 would not be a problem if the JC value of ∼ 109 A/m2 measured in the

junctions containing 1.2 nm of NiMn is sufficient for the intended application. In considering the

memory design discussed in [7], where the magnetic junction is placed in a SQUID loop that also

contains two S/I/S junctions as shown in Figure 4.7, the magnetic junction acts as a passive phase

shifter. This places a lower limit on the critical current of the spin valve to ensure that it is not

50

02461E71E81E9JC (A/m2)NiMn Thickness (nm)driven normal in the operation of the device. In the proposed device, this equates to a minimum IC

of about 200 𝜇A. That corresponds to a minimum JC of order 2 × 108 A/m2 given that the junction

area must remain small (area ∼ 1 𝜇m2) so that the free layer is magnetically single-domain and can

provide clean switching. Those with a keen eye may notice from Figure 4.6 that thinner layers of

NiMn alone meet this requirement, but a bit of extrapolation is needed to predict the value of 𝐽𝐶

upon adding the two F layers needed for operation of the device, each of which reduces the critical

current substantially.

Figure 4.7 Simplified JMRAM cell. Schematic of a simplified JMRAM unit cell showing the two
S/I/S junctions as X’s and the magnetic junction as an encircled ‘X’ as envisioned in the IARPA
C3 project, adapted from [7].

Baek observed values of the characteristic voltage VC = ICRN in junctions containing only

Ni of about 100 𝜇V, which corresponds to JC ∼ 1010 A/m2 using the approximate value for the

area-resistance product, ARN ∼ 10 fΩm2 [88]. Previous work in our group has shown that adding

the NiFe free layer to this system reduces this characteristic voltage to ∼ 5-10 𝜇V [6, 9] which

corresponds to a JC of ∼ 5 × 108 - 1 × 109 A/m2, this is a reduction by a factor of 10-20. Now,

more recent work has suggested that interface engineering can increase critical current transmission

51

MJJSIS JJSIS JJ0 or πthrough the free layer by a factor of about four [11]. Had the IARPA C3 project continued, an

obvious next step would have been to combine these findings in complete S/F/N/F/AF/S spin-valve

junctions and determine if the reduction in critical current from the additional NiMn in the fixed

layer can be compensated by the increase in critical current from interface engineering in the free

layer. Additionally, new work involving highly ordered AF materials [91] may have provided an

alternative path forward as long-range supercurrents have now been observed in novel devices

containing the chiral AF Mn3Ge, although this study involves epitaxial growth which complicates

the fabrication process.

52

CHAPTER 5

PROGRESS TOWARD PHASE-TUNABLE JJs

Un savant dans son laboratoire

n’est pas seulement un

technicien: c’est aussi un

enfant placé en face des

phénomènes naturels qui

l’impressionnent comme un

conte de fées.

Marie Skłodowska-Curie

Long range propagation of spin-triplet supercurrent through ferromagnetic layers is the subject of

intense study. Previous work involving trilayer magnetic systems with a central PMA layer has

demonstrated the generation of spin-triplet supercurrent [20, 92, 10]. Interfacial Ni layers have been

shown to enhance crtical current in permalloy (Ni81Fe19) Josephson junctions [11]. Here we present

progress toward optimizing and combining these effects. As discussed in section 2.3.9, the ‘holy

grail’ for this line of research is the so-called 𝜑0-junction, predicted theoretically by many research

groups [60, 23, 61, 62, 63, 64, 65, 66, 67, 68, 69, 24, 70, 71, 72], and demonstrated in some exotic

materials with very strong spin-orbit coupling [73, 74, 75, 76, 77, 78, 79, 80]. A design realizing this

in traditional ferromagnetic materials using non-coplanar magnetizations was progressed toward

previously in this research group by Victor Aguilar [25], but has yet to be fully demonstrated. Some

of the text in this chapter is adapted from our short paper in the 2024 IEEE International Magnetic

Conference proceedings [93] ©2024 IEEE. We begin here with a two-pronged investigation to both

increase critical current (to enable easier detection) and increase magnetization coherence of the

F-layers. As the device design requires non-coplanar magnetizations and spin-triplet supercurrent,

the central propagation layer needs to have a perpendicular magnetic anisotropy (PMA). Previously

in this research group, two main PMA systems have been investigated– [Ni(0.4)/Co(0.2)]n [20] and

53

[Pd(0.9)/Co(0.3)]n [92, 10] multilayers. In the Ni/Co system, the propagation of critical current

was strong, but the PMA effect of the magnetization was relatively weak. In the Pd/Co system,

the PMA effect was shown to be stronger, but the critical current transmission weaker. We first

present an attempt to bolster the PMA effect in the Ni/Co system. We then explore the magnetics of

elliptical arrays of ‘Ni dusting’ permalloy samples as an attempt to increase critical current based

on previous work in the group on such samples [11]. Josephson junctions of smaller area were also

tested as the previous work has suggested that Ni layers of 0.5 𝜇m2 size are not single domain.

5.1 Methods

Figure 5.1 Triplet JJ sizes. Diagram showing the relative sizes of Josephson junctions fabricated,
with the 0.5 𝜇m2 size on the left representing that used most commonly in the Birge group, and the
smaller sizes investigated for better control of magnetic behavior.

Data from three distinctly fabricated sets of samples are shared in this chapter– sheet films

of PMA Ni/Co multilayers, arrays of elliptical nanomagnets made from ’Ni dusting’ Ni/NiFe/Ni

trilayers (both for magnetic characterization), and spin-triplet Josephson junction samples for

electron transport measurement. The basics of the fabrication follow those outlined in Chapter

3, with deviations as discussed below. Thin magnetic sheet films were sputter deposited without

patterning for PMA characterization. Elliptical nanomagnets were patterned by electron beam

lithography in arrays of about 8 million and defined by ion milling. Josephson junction samples

were patterned by both photolithography (for top and bottom leads) and electron beam lithography

and ion milling again for junction definition. Junctions had nominal areas of 0.125, 0.25, or 0.5

𝜇m2, as shown in Figure 5.1. Junctions of different sizes were used to explore magnetic behavior

of smaller areas in hopes of encouraging single domain behavior of the Ni layers in particular.

Magnetic characterization measurements of moment vs. field were performed with the Quantum

54

𝑤=0.5	𝜇𝑚𝐴≈0.5	𝜇𝑚2𝑤=0.35	𝜇𝑚𝐴≈0.25	𝜇𝑚2𝑤=0.25	𝜇𝑚𝐴≈0.125	𝜇𝑚2Design MPMS3 SQUID-VSM at a temperature of 10 K with the field applied in and out of the

plane of the sample. Transport measurements were carried out using a probe with a built-in

superconducting magnet inserted in a liquid helium dewar at 4.2 K. Current-voltage (I-V) curves

were measured as a function of field, up to 10 mT in positive and negative directions applied along

the long-axis of the elliptical junctions.

5.2 Ni/Co Multilayer Sheet Films

Figure 5.2 Ni/Co n=6 thick base. Magnetization as a function of applied field for a
[Ni(0.4)/Co(0.2)]6 multilayer film grown on a [Nb(25)/Au(2.4)]3/Nb(20) seed layer, measured
both with the field in-plane and out-of-plane, demonstrating strong PMA.

Figure 5.2 shows the magnetic hysteresis loops for a [Ni(0.4)/Co(0.2)]6 multilayer sample

grown on a [Nb(25)/Au(2.4)]3/Nb(20) seed layer in both in-plane and out-of-plane orientations.

(All thicknesses are in nm.) These data suggest a substantial preference of the magnetization to

be oriented out-of-plane, with a near 100% remnance of the magnetization at zero field, and a

high coercivity of 57 mT, compared to negligible remnance in-plane. Further, Table 5.1 shows

the coercive field, 𝐻𝐶, and the ratio of remnant magnetization measured in-plane to the remnant

magetization measured out-of-plane (𝑀𝑅) of [Ni(0.4)/Co(0.2)]𝑛 samples with 𝑛 = 6, 10, 14 with and

55

−100−50050100−1500−1000−500050010001500 Out of Plane In Planem0H (mT)Magnetization (kA/m)−75−50−250255075Magnetization (kA/m)Table 5.1 Ni/Co magnetics summary. Coercive field (𝐻𝐶) and in-plane to out-of-plane remnant
magnetization ratio (𝑀𝑅 Ratio) for thin Nb seed layer and Nb/Au seed layer [Ni(0.4)/Co(0.2)]𝑛 with
𝑛 = 6, 10, 14.

Base

Nb(5)

Nb(5)

Nb(5)

[Nb/Au]3/Nb
[Nb/Au]3/Nb
[Nb/Au]3/Nb

𝑛 (layers)
6

10

14

6

10

14

𝑑 𝑓 (nm) 𝐻𝐶 (mT) 𝑀𝑅 Ratio (%)

3.6

6.0

8.4

3.6

6.0

8.4

33.5

45.5

30.8

56.8

55.0

48.5

7.8

12.

6.0

0.85

5.4

4.6

without a [Nb(25)/Au(2.4)]3/Nb(20) seed layer. This 𝑀𝑅 ratio should be very low for samples with

a strong PMA effect as it represents the percentage of the out-of-plane magnetization detectable at

zero field in-plane measurement. These data are consistent with a very strong PMA effect in the

Nb/Au seed layer samples, which compares favorably to the samples grown on Nb(5) seed layers

in this study and on Nb(50) seed layer used previously in this group [20].

Figure 5.3 Ni/Co n=10 thin base. Magnetization as a function of applied field for a
[Ni(0.4)/Co(0.2)]10 multilayer film grown on a Nb(5) seed layer, measured both with the field
in-plane and out-of-plane, demonstrating reasonably strong PMA.

56

−100−50050100−1500−1000−500050010001500 Out of Plane In Planem0H (mT)Magnetization (kA/m)−600−400−2000200400600 Magnetization (kA/m)Figure 5.3 shows the magnetic hysteresis loops for a [Ni(0.4)/Co(0.2)]10 multilayer sample

grown on a Nb(5) seed layer in both in-plane and out-of-plane orientations. Such a thin seed layer

of only a couple of atomic layers should propagate the smoothness of the Si substrate, and was

thought to be the ideal case for a base from a magnetics standpoint. As we see from comparison

to the [Ni(0.4)/Co(0.2)]10 grown on the [Nb(25)/Au(2.4)]3/Nb(20) seed layer shown in Figure 5.4,

this is clearly not the case. The out of plane loop is wider for the latter sample, indicating a higher

coercivity, and the in plane remnant magnetization is much smaller, both of which indicate a more

dramatic PMA effect.

Figure 5.4 Ni/Co n=10 thick base. Magnetization as a function of applied field for a
[Ni(0.4)/Co(0.2)]10 multilayer film grown on a [Nb(25)/Au(2.4)]3/Nb(20) seed layer, measured
both with the field in-plane and out-of-plane, demonstrating very strong PMA.

As the resilience of the PMA effect is crucial to the operation of the proposed device, the samples

were also measured out to very high in-plane field to ensure that the out-of-plane characteristic

would not be destroyed while initializing the in-plane Ni layer(s). Figure 5.5 shows one of these

measurements out to a field of 4T. The diamagnetic background signal from the Si substrate has

been subtracted from these data. Note that the PMA magnetization does not saturate until an

57

−100−50050100−1500−1000−500050010001500 Out of Plane In Planem0H (mT)Magnetization (kA/m)−300−200−1000100200300 Magnetization (kA/m)in-plane field of over 1 Tesla (10,000 G) is applied, and that the remnant magnetization behavior

(near zero field) is hardly altered from application of a field up to 4T. This means that the PMA

layer is quite robust, and will likely not be destroyed during in-plane initialization.

Figure 5.5 High in-plane field data. Magnetization as a function of applied field for a
[Ni(0.4)/Co(0.2)]6 multilayer film grown on a [Nb(25)/Au(2.4)]3/Nb(20) seed layer, measured
with an in-plane field. Note that the diamagnetic signal from the Si substrate is very strong at such
a high field and has been subtracted out.

58

−4−2024−1000−50005001000Magnetization (kA/m)m0H (T) In Plane5.3 Ni/NiFe/Ni Elliptical Arrays

Figure 5.6 Elliptical arrays. SEM images of Ni/NiFe/Ni elliptical arrays at 5k and 40k magnifica-
tion. The nominal size of each ellipse is 500 nm by 1.25 𝜇m.

In a previous study on so-called ‘Ni dusting’ Ni/NiFe/Ni samples, the addition of very thin Ni

layers of either 0.2 or 0.4 nm on either side resulted in increased supercurrent transmission through

permalloy (NiFe) Josephson junctions [11]. Also in that study, magnetic characterization of sheet

films was carried out, but not for the very thin layers that would be required to be useful as a

spin-mixing layer. Therefore, to characterize the magnetic behavior of elliptical pillars as would be

used in JJ, very thin arrays of this system were investigated. Thin films were deposited as described

in Chapter 3, then patterned with electron beam lithography in a very large array of approximately 8

million ellipses, each of size 500 nm by 1.25 𝜇m (this mimics the size of the Josephson junctions).

The process is similar to that for our Josephson junctions, but the pattern takes approximately 16

hours to write. The samples were then ion milled to define an array of magnetic pillars, as shown in

Figure 5.6 and diced as described in Appendix B.3 for characterization in the SQUID magnetometer.

Figure 5.7 shows the magnetic hysteresis curves of a Ni(0.4)/NiFe(0.4)/Ni(0.4) sample measured

parallel to and perpendicular to both the long axis of the ellipses and growth field. Note that,

as discussed in section 2.1.2 both the shape anisotropy of the ellipse and the magnetocrystaline

anisotropy from the growth field should add to make the parallel axis the preferred axis of the

magnetization. The opposite effect is observed in these data. That came as a total surprise. So we

59

10 µm1 µmconclude that the use of ’Ni dusting’ permalloy as a short-range triplet generating layer does not

appear to be promising, although our data showing the unexpected magnetization preferred-axis

are notable in their own right.

Figure 5.7 Ni dusting magnetics. Magnetization as a function of applied field for
Ni(0.4)/NiFe(0.4)/Ni(0.4) array sample measured in parallel and perpendicular to the long axis
and growth field of the ellipses. Surprisingly, the ‘easy axis’ preference of the magnetization is
oriented along the short axis of the ellipse.

5.4 Spin-Triplet Josephson Junctions

Figure 5.8 Ni/Co triplet JJ. Diagram of the trilayer spin-triplet Josephson junctions grown in this
study, where the outer Ni layers serve as spin-mixers that generate the triplet supercurrent that is
propagated through the central Ni/Co PMA layer.

60

−20−1001020−800−600−400−2000200400600800Magnetization (kA/m)m0H (mT) Long Axis Short AxisNb/AuNi[Ni/Co]nNiNbAs such a dramatic increase in the PMA effect was observed in sheet films of Ni/Co grown on

Nb/Au base layers, we next probed the effect of such base layers on critical current transmission

in Josephson junctions. Samples of the structure S/N/F1/N/F2/N/F3/S as shown in Figure 5.8

were measured with the central (F2) layer comprised of [Ni/Co]n multilayers with and without a

ruthenium coupling layer to create a synthetic antiferromagnet (SAF) [94]. Such SAF-containing

samples were used in previous triplet work in order to cancel flux from the magnetizations of the

PMA layers and were included for comparison.

Figure 5.9 Triplet critical current.
ICRN as a function of PMA [Ni/Co]n multilayer thickness
with and without Ru coupling layer to create a SAF. The plot also compares new junctions
containing [Nb(25)/Au(2.4)]3/Nb(20) base layers (green squares) to previously published [20]
junctions containing Nb(150) base layers (red circles).

Data from the transport measurements of the Josephson junctions grown on [Nb(25)/Au(2.4)]3

base layers are shown in Figure 5.9. Peak critical current is plotted against central ferromagnet

thickness. The very slow decay of the critical current with thickness for the non-SAF samples is the

61

5101520256.412.43.49.415.40.010.1110 Triplet - new Triplet - new w/ SAF Triplet - ECG paper Singlet - ECG paperThickness (nm)  ICRN (mV)Layers (n)signature of long-range triplet supercurrent propagation. The SAF samples show a much steeper

decay due to antiparallel magnetic layers having oppositely oriented majority spin bands therefore

reducing the long-range triplet propagation. Additionally, when compared to previous results on

Ni/Co junctions grown on Nb(150) base layers [20], there is a notable increase in the magnitude of

the critical current, likely due to more robust PMA layer.

The observed increase in critical current and dramatically better PMA effect in Ni/Co samples

grown on a Nb/Au multilayer base are notable and encouraging results toward the ultimate goal of

a 𝜑0-junction device, which relies on robust spin-triplet supercurrent propagation. Work carries

forward in the following section using Nb/Au-seeded Ni/Co PMA central ferromagetic layers with

alternate outer ferromagnetic layers.

5.5 Addition of Switchable Permalloy Layer

Figure 5.10 Permalloy triplet JJ. Diagram of the trilayer spin-triplet Josephson junctions as above,
but with one of the Ni outer spin-mixers replaced with permalloy (NiFe), which is shown in red.

In order to characterize critical current transmission through a trilayer ferromagnetic stack

that may actually provide phase-tunability, we next characterized junctions similar to those in the

section above, but replacing either the top or bottom Ni layer with permalloy (Ni81Fe19), as shown in

Figure 5.10. This is done because permalloy has a much lower coercivity than Ni (and PMA Ni/Co),

therefore it can theoretically have its magnetization tuned without disturbing the magnetizations

of the other layers, which is a key element of the proposed device. The previous assumption was

that placing the permalloy layer on the bottom of a trilayer stack (instead of the top) would result

in smoother deposition and therefore cleaner switching of its magnetization, but we decided to test

the veracity of this as well. Junctions were fabricated in the same manner as above, again in three

62

Nb/AuNi[Ni/Co]nNiFeNbdifferent junction areas per chip.

Figure 5.11 Permalloy triplet ICRN. Plot of peak critical current vs thickness of permalloy layer
in nm.

Figure 5.11 shows the peak critical current plotted against the thickness of the permalloy layer.

These data are consistent with previous results [18] and the prediction that the generation of short-

range triplet is at a maximum at the same thickness when the singlet term goes to zero (the 0-𝜋

transition), which for permalloy is around 1.6 nm [11]. Note that the overall pair correlation

function (with triplet and singlet components) decreases rapidly with thickness, which explains

why the samples with very thin permalloy may have similar critical current as the sample at the 0-𝜋

transition, rather than demonstrating a clear peak at such thickness. There is also no discernible

difference between samples with the permalloy on the top compared to those with permalloy on the

bottom in terms of critical current transmission.

In order to further characterize these samples, some of them were not only measured with a

varying magnetic field, but a varying initialization field, as shown in Figures 5.12 and 5.14. The

63

1.01.21.41.61.82.02.20.010.1110 Py Top Py BottomPeak ICRN (mV)Thickness (nm)magnetic field dependence of the critical current was taken from -500 to 500 Oe after initializing at

a negative field of 0, 1000, 1500, 2000, 2500, 3000, 3500, and 4000 Oe as displayed on the Z-axis

(going into the page). This was done in order to determine the minimum field to properly train

the (in-plane magnetization) Ni layers while not disturbing the central Ni/Co PMA layers. In the

‘medium area’ (0.25 𝜇m2) sample shown in Figure 5.12, it appears that an initialization of 2500 Oe

results in a decent Fraunhofer pattern, which begins to degrade with an initialization above 3000

Oe, likely from interfering with the perpendicular magnetization layer.

Figure 5.12 Permalloy triplet initialization, medium area JJ. Waterfall plot showing the field
dependence of the critical current vs. the magnitude of the initialization field in Oe for the 0.25
𝜇m2 area sample. Note that the Fraunhofers improve up to about 2500 Oe, after which point there
is no improvement by increasing the field.

64

Figure 5.13 Permalloy triplet initialization, medium area JJ breakout. Plot showing the field
dependence of the critical current at initializations of 0 and 2500 Oe for the 0.25 𝜇m2 area sample.
Note that after initialization, the critical current is higher at the peak, and the shape is more idealized.

Figure 5.13 shows a breakout of some of the data from the waterfall plot in Figure 5.12 for

easier comparison. The data after initialization at 2500 Oe shows a more idealized shape (akin to

the single magnetic layer JJ in section 2.3.3). The added complexity from the three layer magnetic

structure of course makes it much less straightforward to determine what is happening magnetically

from the Fraunhofer pattern. In the clear picture of the single magnetic layer, it can be interpreted

as jumping cleanly from one Fraunhofer pattern to a second Fraunhofer as the magnetization

coherently switches.

In the trilayer system, we would expect one ‘jump’ at relatively low field

that represents the permalloy (free) layer switching, and another at the switch of the nickel (fixed).

Although, as discussed in Chapter 4, nickel is notorious for switching non-coherently. This is all

said while disregarding the state of the magnetization of the PMA layer, which we assume to be

oriented perpendicular to the field and therefore ignorable. But we know that application of an

65

−400−20002004000.000.020.040.060.080.100.12IC (mA)H (Oe) 0 Init 2500 Initin-plane field will cant even a strong PMA system slightly into the plane and further complicate the

picture.

The data from the ‘large area’ (0.5 𝜇m2) sample shown in Figure 5.14 and the ‘small area’ (0.125

𝜇m2, not shown) follow a similar trend, only with the Fraunhofer patterns improving in quality up

to an initialization field of about 3000 Oe. This may indicate that the intermediate junction size

is in a sort of ‘Goldilocks’ zone exhibiting better switching behavior and Fraunhofer patterns than

either the larger sample or the smaller sample. This intermediate size may be explored in future

SQUID work.

Figure 5.14 Permalloy triplet initialization, large area JJ. Waterfall plot showing the field
dependence of the critical current vs. the magnitude of the initialization field in Oe for the 0.5 𝜇m2
area sample. Note that the Fraunhofers improve up to about 3000 Oe, after which point there is no
improvement by increasing the field.

66

5.6 Ni/[Ni/Co]/NiFe SQUIDs

Informed by the data from the previous sections, a set of SQUID samples with an identical

structure as shown in Figure 5.10 is being fabricated. The fabrication process is much the same as

described in Chapter 3, only each step is a bit more finicky, and a different photolithography mask

is used which allows for two EBL-defined junctions to be located in the same measurement loop,

for phase-sensitive measurement. Figure 5.15 shows an optical microscope image of the bottom

lead pattern used. In light of Alex Madden’s SQUID study [9] comparing the SQUID design used

in the original demonstration of phase control [6] to a new design intended to minimize inductance,

which showed it allows for more straight-forward fabrication and data analysis, we decided to use

this ultra-low inductance SQUID design. A total of eight Josephson junctions comprising four

SQUID devices can be fabricated per chip.

Figure 5.15 SQUID bottom lead pattern. Optical microscope image of the bottom lead pho-
tolithography pattern for the SQUID device samples.

This fabrication run will first test 0-𝜋 switching of these devices utilizing ellipses with different

aspect ratios as in the studies referenced above. And, if successful, will next include samples

67

with both a circular junction which can theoretically impart the mythical arbitrary phase drop in

accordance with the magnetization direction with the application of a small field, and an elliptical

junction that should maintain its magnetization direction along its long axis. The testing of such

a device requires a rotating magnetic field (or a rotating sample). Although a quick dipper in the

Birge group is physically capable of producing the required rotating magnetic field, the software is

not currently optimized for this type of measurement, therefore these samples may be measured in

a different system, such as that of Prof. Satchell’s group at Texas State University. The data will

not be taken in time to be included in this thesis, but may result in a future publication.

68

CHAPTER 6

CONCLUSIONS AND OUTLOOK

Ce que nous connaissons est

peu de chose, ce que nous

ignorons est immense.

Pierre-Simon Laplace

Bolstered by previous work in the group, the early work presented in this thesis is driven toward a

direct industrial application of ferromagnetic Josephson junctions in the form of a JMRAM memory

cell. I presented work investigating a method to make the fixed layer of the proposed device more

robust by pinning its magnetization with an adjactent AF layer. We found that the AF material

studied, NiMn, does indeed act as a pinning layer through the exchange bias effect in the very thin

layers that would be needed in JMRAM application. However, the reduction of critical current from

the addition of a NiMn layer observed in the data presented would seem to outweigh its benefit.

As the funding from the IARPA program ended shortly after this study, work evolved toward

pursuit of other potential collaborations. Highlighted in Appendix A.3, I will show work toward

the use of chiral molecules as the generators of spin-triplet supercurrent in ferromagnetic junctions.

This work was done in collaboration with the Hebrew University of Jerusalem. Another project

involving the investigation of intrinsic spin-triplet superconducting material NbRe was done in

collaboration with the University of Salerno, which is not covered in this thesis. Appendix A

also discusses a couple of side projects including preparing a study on NiFeCr for publication and

optimizing the fabrication process.

Not finding a source of funding during my time as a graduate student ultimately allowed for

flexibility in the direction of my thesis project.

I chose to focus on the 𝜑0-junction discussed

in Chapter 5, because, despite being quite ambitious for a research group with a single graduate

student, it offered the most interesting work, and work well-suited for the strengths of our fabrication

and measurement equipment. I discuss in this thesis my strides toward realization of this device,

69

including methods to increase the detectable critical current and shore up the PMA magnetization

of the propagation layer. I will also leave the group having fabricated devices that could result in

notable operation and future publication.

Now, insofar as the completion of a Ph.D. thesis is the culmination of a singular, cohesive

contribution to furthering the understanding and collective works of the human species, the efforts

contained herein could be seen as a failure. After all, where is the evidence of the namesake of this

work, the fabled 𝜑0 junction? And it is true, I do not claim nor present such evidence.

However, in this thesis, I have presented several unique and interesting results, and gently nudged

the boundary of known science, laying the groundwork for the next generation of researchers in

the boutique field of superconductor/ferromagnet systems. As this thesis has demonstrated, during

my time I fostered collaborations with many different research groups from around the world and

built a skill set with applications far beyond the confines of the Biomedical and Physical Sciences

building. These opportunities were thanks to the privilege of working at a phenomenal research

institution with such deep intellectual and unique equipment resources. Therefore, my time in the

graduate program at Michigan State University has been an unqualified success.

70

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78

APPENDIX A

ADDITIONAL WORK

A.1 NiFeCr Study

Figure A.1 NiFeCr magnetics. Magnetic hysteresis curves of Ni73Fe18Cr9 films of thicknesses in
nm as labeled.

Relating back to the superconducting memory cell project mentioned in Chapter 4, many other

materials were investigated for use in the free layer by Norman’s group such as Pd-Fe [95], Ni-Fe-

Mo [96], and Ni-Fe-Co [97]. Adding to this list, another particular material was an alloy of nickel,

iron, and chromium referred to as ‘chrome-doped permalloy’. The idea was to lower the switching

energy by reducing the magnetization, as permalloy (Ni80Fe20) has a rather large magnetization of

about 900 emu/cm3 [82]. Josephson junctions containing this material were characterized by my

former colleague Josh Willard, and the bulk of the data will appear in an upcoming publication

in the Journal of Applied Physics on which I am a coauthor. But I will mention a small study I

performed here to characterize sheet films of the material.

Samples of the structure Nb(5)/Cu(2)/Ni73Fe18Cr9(x)/Cu(2)/Nb(5) were fabricated on Si sub-

79

−50−2502550−300−200−1000100200300Moment/area (memu/cm2)Magnetic Field (Oe) NiFeCr(1.0) NiFeCr(1.5) NiFeCr(2.0) NiFeCr(2.5) NiFeCr(3.0) NiFeCr(3.5) NiFeCr(4.0) NiFeCr(4.5)strates by sputtering deposition as described in section 3.4 with x from 1.0 to 4.5 nm in steps of

0.5 nm. The samples were then quartered for measurement in the SQUID-VSM magnetometer.

The results are shown in Figure A.1. As the moments have been normalized by the areas of the

chips as measured by an optical microscope, the differences in saturation moment/area (as read

by the y-intercepts) are due to the increasing thicknesses of the samples. The coercivity (as read

by the x-intercepts) have an inverse relation to thickness as thinner samples are more resistive to

reorientation.

Figure A.2 Saturation magnetization. Saturation moment/area vs.
films.

thickness of Ni73Fe18Cr9

The saturation magnetization of Ni73Fe18Cr9 can be read off of the linear fit to the saturation

moment/area vs. thickness shown in Figure A.2. The slope is in 𝜇emu/(cm2*nm) which translates

with a factor of ten to emu/cm3 which gives a saturation magnetization of 560 ± 15 emu/cm2 at 10

K. This is notably lower than permalloy’s by about a third.

Also as a part of this study and in preparation for publication, the resistivities of permalloy

and chrome-doped permalloy were measured, as well as CoGd for another upcoming publciation.

Samples were sputter deposited in duplicate in thicknesses of 200 nm on Si substrates through

80

0.00.51.01.52.02.53.03.54.04.55.0050100150200250Sat. Moment/area (memu/cm2)NiFeCr Thickness (nm)Equationy = a + b*xIntercept-5.71611 ± 4.4793Slope56.16629 ± 1.5035Adj. R-Squar0.995Table A.1 NiFeCr resistivity. Resistivity measurements of 200nm NiFe, NiFeCr, and CoGd films.
Figures reported are the averages and standard deviations of two measurements per material.

Material
Ni81Fe19
Ni73Fe18Cr9
Co70Gd30

300 K Resistivity (𝜇Ω-cm)
22. ± 2
81. ± 4
337. ± 8

4 K Resistivity (𝜇Ω-cm)
13. ± 2
88. ± 1
364. ± 7

mechanical masks of known geometries in a contact pattern optimized for resistivity measurement.

The samples were then measured by four-terminal measurement at room temperature and 4.2 K

and the resulting I-V curves were fit to determine the resistance (slope). The samples were then

imaged and measured using an optical microscope to determine length and width, and divided out

to give resistivity. The results are shown in Table A.1.

81

A.2 Niobium Top Cap Study

Figure A.3 Nb top cap.
Cu(2)/Nb(5)/Au(5), Cu(2)/Au(5), and Au(5).

Graphic showing the three types of

top caps investigated:

For some time, sputtering of the bottom lead electrodes in the Birge group included a 20 nm

cap of Nb atop the ferromagnetic interlayers. This was because, as the superconducting coherence

length in Nb is about 14 nm, a layer of that thickness should be superconducting on its own. This

would ensure that an S/F/S Josephson junction is complete upon deposition of the top leads. But,

because Nb has such a high k-factor and ion mills very slowly, this means that milling through this

Nb layer takes a very long time. Ion milling for such a long time heats up the sample and resist,

which can make lift-off of the e-beam resist difficult. Therefore some time ago, it was decided to

reduce this layer to 5 nm. As lift-off becomes even more difficult for the very small area junctions

studied for the 𝜑0 junction project in Chapter 5, we investigated removing this superconducting

layer entirely and either capping our junctions with Cu and Au or just Au, as shown in Figure A.3.

As part of this study, we also tested the bilayer e-beam resist scheme devised by Reza Loloee

and Demet Korucu. In this elegant solution, they simply spun and baked our standard ma-N 2401

resist twice before writing with the SEM. While they had seen a dramatic improvement in lift-off

success anecdotally, we decided to test this more rigorously and perform a full characterization to

convince ourselves that other parameters of the junctions such as size and magnetization behavior

were unaffected.

As the critical current transmission of Josephson junctions containing permalloy has been

studied extensively in the Birge group, we fabricated a set of junctions nominally at the peak of

the 𝜋 state at a thickness of 2.2 nm. This meant that minor deviations from this thickness would

82

Au(5)Cu(2)Nb(5)Au(5)Cu(2)Au(5)vs.vs.not meaningfully affect the critical current and cloud our results. The wealth of previous data

also meant that overall parameters like 𝐼𝐶 𝑅𝑁 and switching field are known and easily compared.

Junctions were fabricated in 500 nm by 1.25 𝜇m ellipsoid sizes with either the single layer or bilayer

e-beam resist and with each of the three top caps as described above.

Figure A.4 Top cap ICRN. Plot of critical current vs. type for the junctions measured. Note that the
monolayer Au alone samples had an anomaly in bottom lead deposition that explains their higher
resistance. Some of the other characteristics should be unaffected by this anomaly, so the data are
included here.

The main data are shown in Figure A.4. There was a significant reduction of the resistance and

an even more significant increase in critical current from removing the Nb layer. The result is an

𝐼𝐶 𝑅𝑁 product that is increased by a factor of nearly two, as shown in Figure A.4. This is likely

because the non-superconducting Nb(5) layer acts as an insulating barrier, increasing the resistance

and decreasing the critical current.

83

Cu(2)/Nb(5)/Au(5)Au(5)Cu(2)/Au(5)05101520 Bilayer Ebeam Monolayer EbeamICRN (mV)Figure A.5 Top cap RN. Plot of normal state resistance vs. type for the junctions measured. Note
again that the monolayer Au alone samples had an anomaly in bottom lead deposition that explains
their higher resistance.

Figure A.5 shows the normal state resistance of the junctions measured, again with the mono-

layer Au(5) samples having a known anomaly during deposition of the bottom leads causing an

erroneously higher resistance. The overall trend, however, clearly shows that samples without the

Nb(5) top cap have a considerably lower normal state resistance, and there is consistency across

monolayer and bilayer ebeam samples.

84

Cu(2)/Nb(5)/Au(5)Au(5)Cu(2)/Au(5)05101520 Bilayer Ebeam Monolayer EbeamRN (mW)Figure A.6 Top cap width. Plot of junction width vs. type for the junctions measured. Junction
width is determined by an Airy function fit to the magnetic field dependence of the critical current
and extrapolation from known effective London penetration depth.

The data were further analyzed as discussed in section 2.3.3 by fit to an Airy function, and

extrapolation using the effective London penetration depth from previous studies [11] and the

relation Φ = 𝜇0𝐻𝑤(2𝜆𝑒 𝑓 𝑓 + 𝑑𝑁 + 𝑑𝐹) + 𝜇0𝑀𝑤𝑑𝐹. From this analysis, junction width, 𝑤, and field

shift, 𝐻𝑠ℎ𝑖 𝑓 𝑡, were determined and are shown in Figures A.6 and A.7 respectively. While there is

some scatter in the width data, this is consistent with previous results and is likely due to variations

in the SiOx deposition thickness during the fabrication process as discussed in [11].

85

Cu(2)/Nb(5)/Au(5)Au(5)Cu(2)/Au(5)300400500600700 Bilayer Ebeam Monolayer Ebeamw (nm)Figure A.7 Top cap Hshift. Plot of 𝐻𝑠ℎ𝑖 𝑓 𝑡 vs. type for the junctions measured. 𝐻𝑠ℎ𝑖 𝑓 𝑡 is determined
by an Airy function fit to the magnetic field dependence of the critical current and extrapolation
from known effective London penetration depth.

Our conclusions from all of this analysis is that the top cap of Nb is not necessary in future

fabrication runs, and the evidence shows its inclusion has a deleterious effect on critical current

transmission. Therefore, going forward, we plan to omit this layer. Further, the ‘bi-layer’ E-beam

procedure devised by Reza Loloee and Demet Korucu was found to increase lift-off yield (to 100%

from 93% in my testing) with no discernible negative impact on critical current, magnetic behavior,

junction width, or resistance.

86

Cu(2)/Nb(5)/Au(5)Au(5)Cu(2)/Au(5)050100150200 Bilayer Ebeam Monolayer EbeamHShift (Oe)A.3 Chiral Molecules Study

A project we embarked upon with collaborators at Hebrew University of Jerusalem (HUJI) was

motivated by the goal of inducing spin-triplet superconductivity, as discussed in section 2.3.8, but

using organic chiral molecules as the outer layers, instead of ferromagnets. This capability stems

from spin-orbit coupling. The use of spin-orbit coupling to impart long-range triplet supercurrent

has been suggested for some time [98, 99, 100, 101, 102, 103, 104, 105, 21]. The fact that organic

chiral molecules can impart a spin selectivity has also been known for some time, in an effect

called chiral-induced spin selectivity (CISS) [106, 107, 108, 109, 110]. Combining these effects,

one would expect a mixing layer of an organic chiral molecule such as alanine, shown in Figure

A.8 a), to also impart this long-range spin-triplet supercurrent.

Figure A.8 Chiral molecules. a) L-Alanine (left) and D-Alanine (right) chiral molecules. b)
Representation of proposed Josephson junction stack containing a layer of chiral molecules (Chiral),
a PMA propogation layer (F1), and a ferromagnetic spin-mixing layer (F2) sandwiched between
two superconducting layers (S).

The full triplet device would of course need to include a central ferromagnetic layer for propa-

gation of the triplet supercurrent, as represented in Figure A.8 b). However, to begin to characterize

the transmission of supercurrent through this chiral layer, samples were fabricated first as junctions

containing only these chiral molecules and a thin protective Al2O3 layer as the barrier. Ultimately

three batches of these samples were fabricated using different methods informed by the data, with

the following results.

87

ChiralF1F2SSOO-H3CNH3+OO-NH3+CH3a)b)A.3.1 Batch I

Figure A.9 Batch I data. a) SEM image of 2556-2B Pillar 6 after measurement. b) Magnetic field
dependence of the critical current of sample 2556-2B Pillar 6.

The first batch of samples was sputtered in October of 2021 (Run no. 2556) and was fabricated in

the traditional manner described in Chapter 3 by junction patterning and ion milling after deposition

of the chiral molecule layer. This involved patterning and deposition of the bottom lead electrodes

via sputtering at MSU, then shipping to Israel for deposition of the chiral molecule layer by wet

chemical process and atomic layer deposition (ALD) of the insulating Al2O3 barrier. Back at MSU,

the junctions were patterned by image reversal photolithography in 6 and 12 𝜇m diameter circular

shapes, ion milled, protected with SiOx, lifted-off and capped with top leads. Upon measurement,

the critical current vs field (IC vs B) plots displayed vertically shifted oscillation patterns suggesting

underlying shorting. One junction (2B-6, shown in Figure A.9) that had initially shown something

resembling a Fraunhofer pattern was remeasured out to a higher magnetic field and shows a

SQUID-like oscillation pattern similar to the other samples, see section A.3.4.3 for a more in-depth

explanation of this effect and its implications. [Fabrication at MSU was carried out by Josh Willard

and Swapna Sindhu Mishra and original measurement by Josh Willard. The remeasure and the

preponderance of fabrication and measurement of batches II and III were performed by myself.

Deposition at HUJI was carried out by Nir Sukenik with supervision from Oded Millo, Yossi Paltiel,

and Shira Yochelis.]

88

a)b)-100-500501000.000.050.100.150.200.250.30Ic (mA)Set Field (Oe) Upsweep DownsweepA.3.2 Batch II

Figure A.10 Batch II data. a) Optical microscope image of sample 2564-2B Pillar 2, of diameter
6 𝜇m, taken after return from Israel. b) Magnetic field dependence of critical current for sample
2564-2B Pillar 2, note that the period appears smaller than the ∼27 Oe that would correlate to
shorts spaced by the junction width, indicating a greater distance between the shorts.

Given the indications of shorting, the second batch of samples (Run no. 2564), which was

sputtered in April of 2022, was patterned before deposition of the chiral molecule layer. This was

done by depositing SiO over the junction photolithography then performing lift-off of the resist,

leaving holes in the SiO layer to define the pillars in 3 and 6 𝜇m diameter sizes prior to shipping

to Israel. During the fabrication for these samples we realized that two steps in the deposition of

top leads on the first batch of samples might have damaged the chiral molecule layer- the oxygen

plasma etch and the baking of the lift-off resist (LOR 5B) at 180◦ C. With the second batch, those

steps were bypassed by using chlorobenzene with S1813-G2 resist to provide an undercut profile,

or, on one sample (2B), using a mechanical mask instead of photolithography and foregoing the

plasma etch altogether. Some of the top leads showed poor adhesion (possibly from skipping the

plasma etch, see section A.3.4), but many junctions were measurable. Again, there was evidence

of shorting on most pillars (Figure A.10), but one small-area pillar (2B-1) showed a reasonable

resistance but an unmeasurably small critical current. The conclusion from this data was that larger

area junctions were needed to provide measurable supercurrent.

89

-100-500500.000.010.020.030.040.05Ic (mA)Set Field (Oe) Upsweepa)b)A.3.3 Batch III

Figure A.11 Batch III data. a) Optical microscope image of sample 2570-2B Junction 4 taken
after top lead deposition. b) Magnetic field dependence of critical current on sample 2570-2B
Junction 4.

The third batch of samples, which was sputtered in June of 2022 (Run no. 2570) skipped the

SiO layer entirely because we interpreted the previous Fraunhofer (SQUID-like) patterns as being

due to shorts at the edges of the junctions, so this set relied only on the overlap of the top and bottom

leads to define the Josephson junctions. To provide a wide range of areas in these samples, four

different geometries using a combination of photolithography and mechanical masks were grown.

This defined junction overlap areas ranging from 140 to nearly 80,000 𝜇m2. Upon measurement of

these junctions, we found relatively large values of critical current that could only be suppressed

by going to very high magnetic fields (Figure A.11). This likely indicates that the critical current

is again dominated by shorts, but likely more than just 2 shorts, as there is no discernible SQUID

oscillation pattern. This is not surprising given the much larger junction areas. A spreadsheet

summarizing the data from all junctions is included below in Table A.2.

A.3.4 Anomalies

Several anomalies arose during the fabrication and measurement of these samples, which are

enumerated below. Organic molecules are notoriously finicky to work with, so in that sense it is

not surprising to encounter many issues.

90

−4000−20000200040000.000.020.040.060.080.10Ic (mA)Set Field (Oe) Upsweep Downsweepa)b)A.3.4.1

‘Crinkling’ of the Top Leads

Figure A.12 Crinkling. a) Optical microscope image of sample 2570-6B taken after top lead
deposition at 1.25x magnification showing only minor crinkling. b) Optical microscope image of
sample 2570-6B taken after measurement at 4.2 K. The large dark nearly-circular blobs are pressed
Indium pads used for attaching wires to the sample.

Most samples from each batch showed a ‘crinkling’ effect of the top leads, as shown in Figures

A.12 and A.13. To eliminate the possibility that this is a thermal effect from sputtering the top leads

at -30 C, one sample (6B) was sputtered at room temperature and did not display this crinkling

effect initially. However, after dipping in liquid He for measurement, this sample also displayed

crinkling of the top leads.

Figure A.13 More crinkling. a) Optical microscope image of sample 2570-6B at 20x magnifi-
cation. b) Optical microscope image of sample 2570-1B taken after top lead deposition at 1.25x
magnification. Note that the crinkling is confined to the circular area, which defines the Au depo-
sition carried out at HUJI.

91

A.3.4.2 Contamination Within Chiral Molecule Layer

Figure A.14 Contamination. a) Optical image of sample 2570-7A (AlO only) taken after receiving
from Israel at 20x magnification. b) Optical image of sample 2570-4B taken after receiving from
Israel at 20x magnification.

The sample where only a layer of AlO was deposited (7A, Figure A.14 a) was visibly much

cleaner than the other samples (for example 4B, Figure A.14 b). This contamination did not wash

away in the acetone, IPA, DI water cleaning process, so our conclusion is that it must be embedded

in the chiral molecule layer.

A.3.4.3 Deviations from a Standard Fraunhofer Pattern

As discussed in section 2.3.3, if the supercurrent density is uniform, then plotting the magnetic

field dependence of a rectangular Josephson junction’s critical current produces an interference

pattern analogous to that of single slit diffraction (with circular junctions producing visually similar

Airy patterns). The oscillation period of the pattern is related to the London penetration depth of

the superconducting layers and the diameter of the junction and corresponds to the magnetic flux

quantum by the following formula:

Φ0 = 𝐵𝜔𝑑 (2𝜆𝐿 + 𝑡)

(A.1)

where Φ0 is the magnetic flux quantum, 𝐵𝜔 is the oscillation period, d is the diameter of the junction,

𝜆𝐿 is the effective London penetration depth, and t is the thickness of non-superconducting layers

inside the junction. In our junctions, the quantity 2𝜆𝐿 is close to 110 nm, and the thicknesses of the

92

various Au layers, chiral molecules and oxide add up to about 10 - 15 nm. This predicts a period

of about 27 Gauss for a typical 6 𝜇m diameter junction. (Recall that 𝐵 = 𝐻 in cgs units.) When

the critical current is dominated by two shorts, the pattern resembles that of a SQUID oscillation

without decay with a period related by the same formula above, only now the 𝑑 relates to the

distance between the shorts, which is how we interpret the data in Figures A.9 and A.10.

A.3.5 Conclusions

There are two things to consider when interpreting the data from this project: the fabrication

difficulties and the underlying science. It is important to parse those out in order to draw meaningful

conclusions. On one hand, there were clearly many challenges with fabricating devices containing

organic molecules, some of which are perhaps inherent [111], and some of which may be alleviated

by alternate deposition methods [112]. If we focus on the data of the few samples fabricated as

intended, with no apparent crinkling, shorting, or contamination, we find somewhat discouraging

results. For example, our best JJ, pillar 2564-2B-1, showed a very high normal state resistance of 48

ohms, and a immeasurably small critical current density (less than 1.4 × 10-4 mA/𝜇m2). The data

from the larger area junctions, which should exhibit measurable critical current, always showed

evidence of shorting. In other words, we either find very small critical current or shorting through

the chiral layer, with nothing in between. This indicates to us that the chiral organic molecule

alanine may not be practical in Josephson junctions as a generator of triplet supercurrent.

93

Table A.2 Chiral molecules JJ data. Summary table of Josephson junctions measured for Chiral
Molecules Project.

Pillar

Peak IC (mA) RN (Ohm)

ICRN (mV)

JC (mA/𝜇𝑚2) Area (𝜇𝑚2)

Run 2556 Sputtered 10/25/21 Measured March 2022

2B-1
2B-2
2B-5
2B-6

2B-0
2B-5
2B-1
2B-2
3A-6
3A-5
3A-3

113
113
28
28

-
0.15
1.5
1.1

-
0.87
0.435
0.517

7.07E-02
8
5.13E-02
5.8
1.03E-02
0.29
0.47
1.66E-02
Run 2564 Sputtered 4/13/22 Measured June 2022
2.47E-02
0.31
8.63E-03
0.244
<0.001
1.41E-04
1.59E-03
0.045
4.60E-02
1.3
>8
2.83E-01
<2
2.83E-01

1257
28
7
28
28
28
7
Run 2570 Sputtered 6/24/22 Measured August and September 2022

0.3875
0.2928
-
0.225
2.21
-
-

1.25
1.2
48
5
1.7
-
-

1B-1
1B-2
1B-3
1B-6
2B-1
2B-2
2B-2R
2B-3
2B-4
2B-5
2B-5R
2B-6
4B-2
4B-3
4B-4
4B-4R
6B-1
6B-4
6B-6
7A-3
7A-4
8A-1
8A-2
8A-3
8A-4
8A-5
8A-6

0.6
0.5
(discont.)
>5
1
0.175
0.07
0.01
0.09
0.006
0.003
0.075
19
100
1.2
0.7
16
>100
>100
>100
>100
>100
>100
80
70
>100
75

0.58
0.8
-
-
1.1
1.9
6.7
63
4.8
34
120
8.3
0.02
0.0014
0.8
0.5
0.019
-
5.30E-04
-
-
-
-
-
0.01
-
-

0.348
0.4
-
-
1.1
0.3325
0.469
0.63
0.432
0.204
0.36
0.6225
0.38
0.14
0.96
0.35
0.304
-
-
-
-
-
-
-
0.7
-
-

94

8.70E-04
4.42E-04
-
1.53E-03
3.03E-04
3.80E-04
1.52E-04
6.99E-05
3.75E-04
5.31E-06
2.65E-06
1.14E-04
7.60E-04
4.00E-03
4.80E-05
2.80E-05
4.00E-04
2.50E-03
2.50E-03
1.30E-03
1.30E-03
6.25E-03
6.67E-03
4.71E-03
4.67E-03
6.06E-03
4.69E-03

690
1130
255
3270
3300
460
460
143
240
1130
1130
660
25000
25000
25000
25000
40000
40000
40000
77000
77000
16000
15000
17000
15000
16500
16000

APPENDIX B

LABORATORY NOTES

B.1 Triplet Supercurrent Calculation

Adapted from unpublished work by Norman O. Birge and William P. Pratt, Jr., this section

provides a calculation for the propagation of supercurrent through a Josephson junction containing

three ferromagnetic layers, with a central PMA layer. This system is represented in Figure B.1.

Figure B.1 Triplet JJ. Representation of a Josephson junction which propagates long-range spin-
triplet supercurrent with three ferromagnetic layers– F1, F2, and F3– whose magnetizations are
indicated as M1, M2, and M3, respectively.

Using the formalism developed by Matthias Eschrig [17], what is calculated here is the quantum-

mechanical amplitude for a pair to propagate from SL to SR, remembering that the wave function

must begin and end as a spin-singlet state. The Josephson coupling amplitude, which we call 𝐶𝐽,

is proportional to this amplitude, and its starting formula is given by

𝐶𝐽 = ⟨𝑆𝑅 |𝑇3𝑇2𝑇1|𝑆𝐿⟩ = ⟨0, 0|𝑇3𝑇2𝑇1|0, 0⟩

(B.1)

where spin states are represented in the eigenstate basis of S2 and Sz with S being the total spin

of the pair Sz and its z-component. The ket |0, 0⟩ represents the singlet state and |1, 1⟩, |1, 0⟩, and

|1, −1⟩ represent the triplet states. The three 𝑇 operators describe propagation of the state through

the three ferromagnetic layers.

95

SLF1F2F3θSRzxyM1M2M3We know from section 2.3.5 that as SL propagates into F1 acquire opposite center-of-mass

momenta:

𝑇𝑥 |0, 0⟩ =

1
√
2

(cid:16)

| ↑↓⟩𝑒𝑖𝑄𝑥 − | ↓↑⟩𝑒−𝑖𝑄𝑥(cid:17)

= |0, 0⟩ cos(𝑄𝑥) − 𝑖|1, 0⟩𝑧 sin(𝑄𝑥)

(B.2)

where 𝑄 = 𝑘↑

𝐹 − 𝑘↓

𝐹 is the mismatch between majority and minority band Fermi wavevectors in F1

and 𝑥 is the center-of-mass coordinate of the electron pair. We also define the accumulated pair

phase shifts in the F layers as 𝜑1 = 𝑄1𝑑𝐹1, 𝜑2 = 𝑄2𝑑𝐹2, and 𝜑3 = 𝑄3𝑑𝐹3 where the 𝑑𝐹’s are the

thicknesses of the F layers. We also add a prefactor 𝑠1 to account for the decay of the short-range

pair correlations in F1. Putting this together, we write:

𝑇1|0, 0⟩ = 𝑠1 (|0, 0⟩ cos(𝜑1) − 𝑖|1, 0⟩𝑧 sin(𝜑1))

(B.3)

To calculate how this state propagates through F2, we must write it in the eigenstate basis of S2

and Sx, since the magnetization of F2 points in the x direction. The singlet is rotationally invariant,

so it does not change with the basis transformation. The result of the transformation is:

(cid:20)

𝑇1|0, 0⟩ = 𝑠1

|0, 0⟩ cos(𝜑1) − 𝑖 sin(𝜑1)

(|1, 1⟩𝑥 − |1, −1⟩𝑥)

(cid:21)

1
√

2

We next calculate how this state propagates through F2, we already know that:

𝑇2|0, 0⟩ = 𝑠2 (|0, 0⟩ cos(𝜑2) − 𝑖|1, 0⟩𝑥 sin(𝜑2))

(B.4)

(B.5)

The triplet components |1, 1⟩𝑥 and |1, −1⟩𝑥 do not acquire any phase shift, because they consist

of two electrons in the same spin band, with nearly zero center-of-mass momentum1. Electrons

propagating through a real ferromagnetic material are scattered at the interfaces and in the bulk.

The degree of scattering can be very different for majority and minority spin bandsa. So we define

transmission amplitudes 𝑡↑ and 𝑡↓ for the majority and minority electrons, respectively. Note that if

we replace F2 by a SAF, then we expect to have 𝑡↑ = 𝑡↓ for the whole SAF, since electrons that are

in the majority band in the first layer of the SAF will be in the minority band in the second layer,

and vice versa. But for a single-layer F2, we generally expect to find 𝑡↑ ≠ 𝑡↓. So we write:

𝑇2|1, 1⟩𝑥 = 𝑡↑|1, 1⟩𝑥 and 𝑇2|1, −1⟩𝑥 = 𝑡↓|1, −1⟩𝑥

(B.6)

1We say ‘nearly zero’ because there is a very small momentum in the direction of the supercurrent.

96

Putting together B.4, B.5, and B.6 we get:

𝑇2𝑇1|0, 0⟩ = 𝑠1

(cid:20)

𝑠2 cos(𝜑1) (|0, 0⟩ cos(𝜑2) + |1, 0⟩𝑥 sin(𝜑2)) + 𝑖 sin(𝜑1)

(cid:0)𝑡↑|1, 1⟩𝑥 − 𝑡↓|1, −1⟩𝑥(cid:1)

(cid:21)

1
√
2

(B.7)

To continue our calculation, it is convenient to express this result back in the z basis. The basis

transformation takes the form:

|1, 1⟩𝑥 =

|1, 0⟩𝑥 =

|1, −1⟩𝑥 =

1
2

Inserting those into B.7 gives:

(cid:16)

1
2
1
√

2
(cid:16)

|1, 1⟩𝑧 +

√

2|1, 0⟩𝑧 + |1, −1⟩𝑧

(−|1, 1⟩𝑧 + |1, −1⟩𝑧)

√

|1, 1⟩𝑧 −

2|1, 0⟩𝑧 + |1, −1⟩𝑧

(cid:17)

(cid:17)

(B.8)

𝑇2𝑇1|0, 0⟩ = 𝑠1𝑠2 cos(𝜑1) cos(𝜑2)|0, 0⟩ + 𝑠1𝑠2 cos(𝜑1) sin(𝜑2)

(−|1, 1⟩𝑧 + |1, −1⟩𝑧)+

1
√

2

(cid:20)

𝑠1

𝑖 sin(𝜑1)
2

(𝑡↑ − 𝑡↓)

1
√
2

(|1, 1⟩𝑧 + |1, −1⟩𝑧) + (𝑡↑ + 𝑡↓)|1, 0⟩𝑧

(B.9)

(cid:21)

Rather than continue propagating this state to the right through F3, it is easier to complete the

calculation by propagating this state from SL backward through F3. The center-of-mass coordinate

𝑥 will be negative in this case, which is equivalent to using the adjoint of the porpagation operator

𝑇3. So we have:

3 |𝑆𝑅⟩ = 𝑇 +
𝑇 +

3 |0, 0⟩ = 𝑠3 (|0, 0⟩ cos(𝜑3) − 𝑖|1, 0⟩𝜃 sin(𝜑3))

(B.10)

Now transform that state back to the 𝑧 basis:

(cid:18)

(cid:18)

𝑇 +
3 |0, 0⟩ = 𝑠3

= 𝑠3

|0, 0⟩ cos(𝜑3) − 𝑖 sin(𝜑3)

|1, 1⟩𝑧 + cos(𝜃)|1, 0⟩𝑧 +

|0, 0⟩ cos(𝜑3) − sin(𝜑3)

(|1, 1⟩𝑧 + |1, −1⟩𝑧) + 𝑖 cos(𝜃)|1, 0⟩𝑧

(cid:18) −𝑖 sin(𝜃)
√
2
(cid:18) sin(𝜃)
√
2

−𝑖 sin(𝜃)
√
2

(cid:19)(cid:19)

(cid:19)(cid:19)

|1, −1⟩𝑧

(B.11)

The adjoint of the previous expression is:

(cid:18)

⟨0, 0|𝑇3 = 𝑠3

⟨0, 0| cos(𝜑3) − sin(𝜑3)

(cid:18) sin(𝜃)
√
2

97

(⟨1, 1|𝑧 + ⟨1, −1|𝑧) − 𝑖 cos(𝜃)⟨1, 0|𝑧

(cid:19)(cid:19)

(B.12)

Our final amplitude is just the scalar product of B.12 with B.9. Note that the second term

in B.9 does not contribute because the combination of 𝑧 states in that term is orthogonal to the

combination in B.12.

𝐶𝐽 = 𝑠1𝑠2𝑠3 cos(𝜑1) cos(𝜑2) cos(𝜑3) −

1
2

𝑠1𝑠3 sin(𝜑1) sin(𝜑3) (cid:2)(𝑡↑ + 𝑡↓) cos(𝜃) + 𝑖(𝑡↑ − 𝑡↓) sin(𝜃)(cid:3)

(B.13)

Equation B.13 is our final result. If F2 is thick, then we expect that 𝑠2 ≪ 𝑡↑, 𝑡↓, namely the

Josephon coupling and supercurrent are entirely due to the long-range spin-triplet components in

F2. Furthermore, if 𝑡↑ ≪ 𝑡↓, then

𝐶𝐽 ≈ −

1
2

𝑠1𝑠3 sin(𝜑1) sin(𝜑3) (cid:2)𝑡↑ cos(𝜃) + 𝑖𝑡↑ sin(𝜃)(cid:3) = −

𝑠1𝑠3𝑡↑ sin(𝜑1) sin(𝜑3)𝑒𝑖𝜃.

(B.14)

1
2

This situation corresponds to a 𝜑-junction with 𝜑 = 𝜃 + 𝜋. For collinear alignments of the

magnetizations M1 and M3, the P state produces a 𝜋-junction while the AP state produces a 0-

junction. Intermediate angles produce intermediate phase couplings; the magnitude of the critical

current does not vary with 𝜃 in this limit.

If F2 consists of a SAF, however, the result is completely different.

In that case we expect

that 𝑡↑ = 𝑡↓ so that the imaginary term in B.12 vanishes. In that case the Josephson coupling is

purely real, meaning that one can only have a 0-junction or a 𝜋-junction. In that situation, 𝜃 = 𝜋/2

produces zero coupling as the junction transitions from the 𝜋-state to the 0-state.

Finally, consider the case where F2 is not very thick, which may be the case in Joseph Glick’s

study [8]. Then we cannot completely ignore the first term in B.13. That might explain why Joseph

observes slightly different critical currents in the 0-state and the 𝜋-state.

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B.2 Proper Documentation

As proper documentation is a critical part of scientific research, the following example is given

to aid in the clearest, densest representation of information from a sputtering run. Figure B.2 shows

the preferred format as it should be entered in the logbook. Things that should be clearly recorded

include:

run number, operator name(s), date, target materials and operating parameters, base

pressure, cold pressure, sputtering pressure, exact structure by sample, deposition time, deposition

temperature, deposition rate for each material (at every measurement), and ion mill settings (if

used).

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Figure B.2 Sputtering logbook format. Example of sputtering logbook documentation format for
maximum information density and clarity.

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Sputtering Logbook Record Format  xxxx (Run #) [Student Name]        xx/xx/xx (date)  A  [Material Name]  xxx/x.xx (V/I) 5  Cu  xx W     Pbase = x.x x 10-8 Torr B  [Material Name]  xxx/x.xx (V/I) 6  Ru  xx W     Pcool  = x.x x 10-8  C  [Material Name]  xxx/x.xx (V/I) 7  Au  xx W     Psputt = x.x x 10-3  D  [Material Name]  xxx/x.xx (V/I) IM  (settings below)   [Name of Study]  [Full stack #1 e.g. [Nb(25)/Al(2.4)]3/Nb(20)/Cu(2)/F1(dF1)/Cu(2)/Au(10)]      Deposition Rates (Å/s) (record only when measured) Sample dF1(nm) Time Temp [Mat A] [Mat B] [Mat C] [Mat D] Cu Ru Au IM 1A x.x 0:00 -xx  (°C) x.x x.x x.x x.x x.x x.x x.x x.x 1B x.x 0:00 -xx         2A x.x 0:00 -xx x.x x.x x.x x.x x.x x.x x.x x.x 2B x.x 0:00 -xx         3A x.x 0:00 -xx         3B x.x 0:00 -xx         4A x.x 0:00 -xx x.x x.x x.x x.x x.x x.x x.x x.x 4B x.x 0:00 -xx          [Full stack #2 e.g. [Nb(25)/Al(2.4)]3/Nb(20)/Cu(2)/F2(dF2)/Cu(2)/Au(10)]      Deposition Rates (Å/s) Sample dF2(nm) Time Temp [Mat A] [Mat B] [Mat C] [Mat D] Cu Ru Au IM 5A x.x 0:00 -xx x.x x.x x.x x.x x.x x.x x.x x.x 5B x.x 0:00 -xx         6A x.x 0:00 -xx x.x x.x x.x x.x x.x x.x x.x x.x 6B x.x 0:00 -xx         7A x.x 0:00 -xx         7B x.x 0:00 -xx         8A x.x 0:00 -xx x.x x.x x.x x.x x.x x.x x.x x.x 8B x.x 0:00 -xx           NOTES:  [SPACE TO RECORD ANYTHING THAT GOES WRONG]  IM Settings: (if used)  IB = x.x mA VB = xxx V VA = xx V VD = xx V IA = x.x mA IC = x.x A INE = x.x mA ID x.xx A INF = x.x A B.3 Array Dicing Procedure

Here I provide a guide for dicing large EBL array samples for characterization in the SQUID

magnetometer. This is necessary because the ion milling equipment requires larger samples than

will fit in the magnetometer, so they must be diced after patterning and definition.

1. Spin S1813 photoresist on donor 3” wafer. Use approx. 1-1.5k RPM for ∼30 seconds, and

enough resist to cover the entire wafer. (You want the resist to be slightly goopy to adhere

your sample.)

2. Quickly set array samples on 2 diagonal corners, in line such that the cut paths will not cross

each other.

3. Drop resist over each sample, and spin very cautiously (∼0.5k RPM) for 30 seconds, just

enough to coat. (Too long or too fast here will send your sample flying!)

4. Bake resist and wafer as usual in oven at 95◦ C for 45 minutes.

5. Inspect wafer with optical microscope and place delicate scratches at the corners surrounding

the array for location and orientation on the dicer.

6. Ensure dicer blade is non-ferrous. Warm up dicer. Select ‘Josh half inch’ dice program.

Change cut depth to 13 mil (this nominally cuts through the sample and 2 mil into the wafer

below). Load wafer into dicer.

7. Align (assuming Ebeam writing was aligned with edge of chip) using the auto align program,

first to the right side of the bottom of the chip edge, then the right. Note that leftmost arrow

buttons can be used to return to first alignment point as there is an automatic stage move

purely in X. The last two alignment (on-wafer) steps can be skipped.

8. Note: The wafer is rotated 90◦ during the alignment process. It is now time to use the Y-offset

feature to trick the dicer into doing our bidding.

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9. (Assumes 4.5 mm square array.) First, find the edge of the array in the dicer image. Use the

scratches to locate the area generally, then find the array itself. Note that the second leftmost

arrow buttons control the focus. From the bottom edge of the array, zero the Y and move

0.875 mm down.

10. Under spindle controls, select ‘Y-offset’. Perform a ‘test cut’, which will actually dice your

sample. The software warns you that the test cut is within the wafer area, this is okay.

11. Once the cut is complete, don’t forget to click ‘Finish’. If the stage is moved vertically before

you hit finish, this can misalign the cut target with the cut line; no bueno.

12. Next, move to the top cut target. The simplest way to do this is to re-zero the Y and move

-6.25 mm up. Perform another test cut.

13. Rotate the stage by pressing ‘A’ near the second leftmost arrow buttons, then pressing the

clockwise rotate button. Press ‘A’ again.

14. Find the array edge again, and repeat steps 10-12 to finish dicing the sample. Unload sample.

15. Repeat steps 7-14 for any other samples.

16. Gently rinse photoresist off of chips with acetone and place in sample holders. Note or create

visual elements to discern easy and hard axis for ellipses and/or growth field.

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