PHASE SENSITIVE MEASUREMENTS OF FERROMAGNETIC JOSEPHSON JUNCTIONS
FOR CRYOGENIC MEMORY APPLICATIONS
By
Bethany Maria Niedzielski

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Physics – Doctor of Philosophy
2017

ABSTRACT
PHASE SENSITIVE MEASUREMENTS OF FERROMAGNETIC JOSEPHSON JUNCTIONS
FOR CRYOGENIC MEMORY APPLICATIONS
By
Bethany Maria Niedzielski
A Josephson junction is made up of two superconducting layers separated by a barrier. The original
Josephson junctions, studied in the early 1960’s, contained an insulating barrier. Soon thereafter,
junctions with normal-metal barriers were also studied. Ferromagnetic materials were not even
theoretically considered as a barrier layer until around 1980, due to the competing order between
ferromagnetic and superconducting systems. However, many exciting physical phenomena arise
in hybrid superconductor/ferromagnetic devices, including devices where the ground state phase
difference between the two superconductors is shifted by π. Since their experimental debut in 2001,
so-called π junctions have been demonstrated by many groups, including my own, in systems with
a single ferromagnetic layer. In this type of system, the phase of the junction can be set to either 0
or π depending on the thickness of the ferromagnetic layer. Of interest, however, is the ability to
control the phase of a single junction between the 0 and π states. This was theoretically shown to
be possible in a system containing two ferromagnetic layers (spin-valve junctions). If the materials
and their thicknesses are properly chosen to manipulate the electron pair correlation function, then
the phase state of a spin-valve Josephson junction should be capable of switching between the 0
and π phase states when the magnetization directions of the two ferromagnetic layers are oriented
in the antiparallel and parallel configurations, respectively. Such a phase-controllable junction
would have immediate applications in cryogenic memory, which is a necessary component to an
ultra-low power superconducting computer. A fully superconducting computer is estimated to be
orders of magnitude more energy-efficient than current semiconductor-based supercomputers.
The goal of this work was to experimentally verify this prediction for a phase-controllable
ferromagnetic Josephson junction. To address this complicated system, first, studies of junctions
with only a single ferromagnetic junction were required to determine the 0-π transition thickness

of that material, the decay of the critical current through the junction with thickness, and the
switching field of the material. The materials studied included NiFeMo, NiFe, Ni, and NiFeCo.
Additionally, roughness studies of several different superconducting base electrodes and normal
metal buffer and spacer layers were performed to determine the optimum junction layers. The
ferromagnetic layers used were on the order of 1-2 nm thick, so a smooth growth template is
imperative to maintain continuous films with in-plane magnetizations. Lastly, single junction spinvalve samples were studied. We are not equipped to measure the phase of a single junction, but
series of samples where one ferromagnetic layer is systematically varied in thickness can inform
the proper thicknesses needed for 0-π switching based on relative critical current values between
the parallel and antiparallel magnetic configurations.
Utilizing this background information, two spin-valve samples were incorporated in a superconducting loop so that the relative phase of the two junctions could be investigated. Through
this process, the first phase-controllable ferromagnetic Josephson junctions were experimentally
demonstrated using phase-sensitive measurement techniques. This provided the proof of concept for the Josephson Magnetic Random Access Memory (JMRAM), a superconducting memory
system in development at Northrop Grumman, with whom we collaborate on this work. Phasecontrollable systems were successfully demonstrated using two different magnetic material stacks
and verified with several analysis techniques.

"For nothing is hidden except to be made manifest; nor is anything secret except to come to light."
Mark 4:22

iv

ACKNOWLEDGEMENTS

I have been truly blessed by the guidance and support of so many people through my time in this
program. First thanks must go to my adviser, Professor Norman Birge. Joining your group was
probably the best decision I made in graduate school. I appreciate all the opportunities you gave
me to present my work at conferences and collaboration meetings, prepare technical documents
for publications and conference calls, and network with academic and industry professionals. I
always feel that you respect and value my scientific opinion, giving me confidence in my abilities
as a researcher. It will be a difficult task to find a better boss.
Next, I must thank Professor William Pratt. In addition to your council on the direction of my
work and design and upkeep of much of the essential measurement equipment, you were a fount
of knowledge on topics from spin-flip scattering to boating knots. I hope to one day know as much
physics as you have forgotten.
The labs in the basement would all be in pieces without the care and dedication of Dr. Reza
Loloee. Thank you for all the maintenance procedures that keep our lab running smoothly, for
teaching me your sputtering and ion mill operational tips and tricks, and for being my lifeline
when something goes wrong. Besides the invaluable technical support, you encourage a friendly
and respectful work environment by taking the time to laugh and joke and engage with us lowly
graduate students. In the clean room, Dr. Baokang Bi similarly upkeeps the shared equipment
and is an invaluable technical resource. Thanks for your patient teachings on all the clean room
equipment and project counsel.
When I joined the Birge group, I had very little experience in condensed matter physics research. My success is largely due to the mentorship from my fellow group members, both past and
present. I need to thank by name Eric Gingrich, Yixing Wang, Bill Martinez, Joseph Glick, Alex
Cramer, Mazin Khasawneh, Victor Aguilar, and Josh Willard for their guidance and friendship.
Special thanks to Joseph Glick for invaluable Mathematica analysis software, most notably to fit
the SQUID oscillations, and Victor Aguilar for faster and better featured Labview measurement

v

software. I know I leave this group in capable hands and look forward to the great work to come.
My research was greatly aided from collaboration with Northrop Grumman and Arizona State
University. Special thanks go to Nick Rizzo, Don Miller, Anna Herr, and Ofer Namman. I am also
grateful to Northrop Grumman and IARPA for funding this work.
I have been able to fully focus on my research due to the excellent support staff in the P-A
department. Superstars like Debbie Barratt, Cathy Cords, Lisa Ruess, and especially Kim Crosslan
have made all the non-technical aspects of my MSU tenure incredibly smooth.
Outside of work, I need to thank my fellow classmates who pulled me through my first year
courses and even managed to make it a fun experience at times. Since then I have been lucky to
meet even more great friends here in Michigan, some who cared enough to drive to Connecticut
to help celebrate my wedding. The past and present members of the Grand Canonical Ensemble
gave me a fun and creative artistic outlet. All the students and faculty who supported my goals for
the Women and Minorities in the Physical Sciences (WaMPS) group have my sincere appreciation.
Especially my officers for the past three years have really helped me turn WaMPS into a strong and
impactful group.
Through it all, I have been blessed with the love and support of an incredible family. My
parents have always encouraged my scientific interests and pushed me to be my best. They are
my biggest champions when things are going well and a listening ear when they are not. I have
the best siblings in Amanda, Drew, and Luke who share my silly voice and remind me what is
important in life. Most of all, I must thank my husband, Andrew Huffman. You have continually
made sacrifices to enable my career goals and just been my rock through this whole crazy process.
I know we can do anything together. You truly are my favorite.
Lastly, I would like to thank my committee members, Professor Phil Duxbury, Professor Stuart
Tessmer, Professor Don Morelli, and Professor Brian O’Shea for their direction and guidance over
the years.
To all those named and unnamed, I greatly appreciate your impact on my success and I couldn’t
have done it without you.

vi

TABLE OF CONTENTS

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

ix

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

x

CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
3

CHAPTER 2 THEORETICAL BACKGROUND . . . . . . . . . . . . . .
2.1 Josephson Junctions . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Resistively and Capacitively Shunted Junction (RCSJ) Model
2.1.2 Overdamped Josephson Junction . . . . . . . . . . . . . . .
2.1.3 Short Circular Junction in a Magnetic Field . . . . . . . . .
2.2 S/N and S/F Proximity Effects . . . . . . . . . . . . . . . . . . . .
2.2.1 Phase of Ferromagnetic Josephson Junctions . . . . . . . . .
2.3 DC SQUIDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Asymmetric dc SQUID . . . . . . . . . . . . . . . . . . . .

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

5
5
7
11
12
15
20
23
27

CHAPTER 3 SAMPLE FABRICATION . . . . . . . . . . . . . . .
3.1 Fabrication Equipment . . . . . . . . . . . . . . . . . . . .
3.1.1 Sputtering System . . . . . . . . . . . . . . . . . . .
3.1.2 Electron-Beam Lithographer . . . . . . . . . . . . .
3.1.3 Ion-Mill and Thermal Evaporation . . . . . . . . . .
3.2 Fabrication Process . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Bottom Lead Photolithography . . . . . . . . . . . .
3.2.1.1 Small Feature Size Variant . . . . . . . . .
3.2.2 Bottom Lead Material Deposition . . . . . . . . . .
3.2.2.1 Tips and Tricks . . . . . . . . . . . . . . .
3.2.3 Pillar Definition . . . . . . . . . . . . . . . . . . . .
3.2.3.1 Electron-Beam Lithography . . . . . . . .
3.2.3.2 Ion Milling and SiO Deposition . . . . . .
3.2.3.3 Side-Milling and Pillar Lift-off . . . . . .
3.2.4 Top Lead Photolithography and Material Deposition
3.2.4.1 Small Feature Size Variant . . . . . . . . .

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

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

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

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

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

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

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

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

30
30
30
32
33
37
37
38
40
42
43
43
47
49
51
52

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

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

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

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

CHAPTER 4 NON-MAGNETIC MATERIAL OPTIMIZATION . . . . . . . . . . . . . . 53
4.1 Base Superconducting Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Normal Metal Buffer and Spacer Layers . . . . . . . . . . . . . . . . . . . . . . . 57
CHAPTER 5 MAGNETIC MATERIAL CHARACTERIZATION . . . . . . . . . . . . . 63
5.1 NiFe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

vii

5.3
5.4

NiFeCo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
NiFe/FeMn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

CHAPTER 6 SINGLE FERROMAGNETIC LAYER JOSEPHSON JUNCTIONS
6.1 NiFeMo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 NiFe/FeMn (pinned NiFe) . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 NiFe and NiFeCo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

73
74
79
82

CHAPTER 7 SINGLE JUNCTION SPIN VALVE DEVICES
7.1 NiFe(1)/NiFeCo(x) Spin Valves . . . . . . . . . . . .
7.2 NiFe(x)/Ni(2) Spin Valves . . . . . . . . . . . . . .
7.3 NiFe(x)/Ni(1.6) Spin Valves . . . . . . . . . . . . .

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

85
86
91
97

CHAPTER 8 SPIN VALVE SQUIDS .
8.1 NiFe(1.5)/Ni(1.2) SQUIDs . . .
8.1.1 SQUID Data Analysis .
8.2 NiFe(1.0)/NiFeCo(1.1) SQUIDs
8.3 NiFe(1.25)/Ni(2.0) SQUIDs . .

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

100
102
107
111
119

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

CHAPTER 9 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
9.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
9.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

viii

LIST OF TABLES

Table 3.1

Target voltage and filament current settings for large gun sputtered materials . . . 32

Table 3.2

Power settings for small gun sputtered materials . . . . . . . . . . . . . . . . . . 32

Table 3.3

Ion mill settings for the small and large milling chambers . . . . . . . . . . . . . 35

Table 4.1

RMS roughness values for superconducting base layers . . . . . . . . . . . . . . 55

Table 4.2

Coercive field values for six buffer and spacer layers . . . . . . . . . . . . . . . 60

Table 6.1

Average Ic RN values for NiFe/FeMn bilayer junctions . . . . . . . . . . . . . . 81

Table 6.2

Comparison of fit parameters from 0-π transition plots for NiFeMo, NiFe, and
NiFeCo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Table 8.1

NiFe(1.5)/Ni(1.2) SQUID and Junction Parameters . . . . . . . . . . . . . . . . 109

Table 8.2

Inductances of the Two SQUID Arms and Junction Critical Currents from Fit
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Table 8.3

Fit Results for NiFe(1.0)/NiFeCo(1.1) SQUID 2328 4A-4 . . . . . . . . . . . . 115

Table 8.4

NiFe(1.0)/NifeCo(1.1) SQUID 2336 5B-4 Fit Parameters . . . . . . . . . . . . . 118

ix

LIST OF FIGURES

Figure 1.1

Simplified Schematic of JMRAM Cell Layout . . . . . . . . . . . . . . . . . .

2

Figure 2.1

Cartoon of a Josephson junction . . . . . . . . . . . . . . . . . . . . . . . . .

6

Figure 2.2

Circuit equivalent of the RCSJ Model showing a capacitor and resistor in
parallel with the Josephson junction supercurrent . . . . . . . . . . . . . . . . .

7

Figure 2.3

Tilted Washboard Potential Analogy . . . . . . . . . . . . . . . . . . . . . . .

8

Figure 2.4

Pendulum Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Figure 2.5

IV characteristic for an overdamped Josephson junction . . . . . . . . . . . . . 12

Figure 2.6

Circular Josephson Junction in a Magnetic Field . . . . . . . . . . . . . . . . . 13

Figure 2.7

Airy Diffraction Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Figure 2.8

Schematic of Andreev Reflection . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 2.9

S/F Interface Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Figure 2.10 S/N and S/F Pair Correlation Functions . . . . . . . . . . . . . . . . . . . . . . 19
Figure 2.11 Critical Current Oscillations in S/F/S Junction . . . . . . . . . . . . . . . . . . 21
Figure 2.12 Critical Current Oscillations in S/F1/F2/S Junction . . . . . . . . . . . . . . . . 22
Figure 2.13 Schematic view of a dc SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Figure 2.14 Critical current vs applied flux for symmetric dc SQUID . . . . . . . . . . . . . 25
Figure 2.15 Schematic of an Asymmetric SQUID . . . . . . . . . . . . . . . . . . . . . . . 28
Figure 2.16 Theoretical Magnetic Flux Dependence of the Critical Current of an Asymmetric SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Figure 3.1

Top-down view of the sputtering system . . . . . . . . . . . . . . . . . . . . . 30

Figure 3.2

Schematic view of the Ion Mill . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 3.3

Schematic drawing of the sample fabrication process

Figure 3.4

Picture of Sputtering System Sample Holder . . . . . . . . . . . . . . . . . . . 40

x

. . . . . . . . . . . . . . 36

Figure 3.5

SEM image of patterned ma-N resist . . . . . . . . . . . . . . . . . . . . . . . 47

Figure 3.6

Vertical ion mill holders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Figure 3.7

SEM image comparison of write area before and after the lift-off process . . . . 50

Figure 4.1

AFM surface roughness comparison for nine base superconducting base layers . 54

Figure 4.2

TEM image of spin-valve Josephson junction with X-ray elemental analysis . . 56

Figure 4.3

Easy and Hard Axis Moment vs Applied Field Plots . . . . . . . . . . . . . . . 57

Figure 4.4

Moment vs Field measurement for thin spacer (buffer) layers . . . . . . . . . . 59

Figure 4.5

Moment vs Field measurement for thick spacer layers . . . . . . . . . . . . . . 59

Figure 4.6

Moment vs Field measurement for spin-valves with either Cu or Ru buffer layers 61

Figure 5.1

Moment vs Field measurement for NiFe films and arrays . . . . . . . . . . . . 64

Figure 5.2

Normalized moment vs applied field for spin valve NiFe/Ni samples . . . . . . 66

Figure 5.3

Moment vs applied field measurements of Ni array and extended film . . . . . . 67

Figure 5.4

Moment vs Field measurement for NiFeCo films . . . . . . . . . . . . . . . . . 68

Figure 5.5

NiFeCo thickness comparison of Moment vs Field measurements . . . . . . . . 69

Figure 5.6

Moment vs Field measurement of 2.5 nm NiFeCo films grown on 25 or 50
nm Nb base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 5.7

Moment vs Field measurements of NiFe/FeMn pinned bilayer samples . . . . . 71

Figure 5.8

Moment vs Temperature plot for the NiFe(1)/FeMn(1.5) bilayer sample . . . . . 72

Figure 6.1

Fraunhofer pattern for S/F/S Josephson junctions with 1 nm NiFeMo . . . . . . 75

Figure 6.2

Average Fraunhofer pattern shift vs NiFeMo thickness . . . . . . . . . . . . . . 77

Figure 6.3

Characteristic junction voltage,Ic RN , vs NiFeMo thickness . . . . . . . . . . . 78

Figure 6.4

Fraunhofer patterns for NiFe/FeMn Josephson junctions . . . . . . . . . . . . . 80

Figure 6.5

Ic RN comparison for Josephson junctions with NiFe and NiFe/FeMn . . . . . . 81

Figure 6.6

Ic RN vs material thickness for NiFe and NiFeCo . . . . . . . . . . . . . . . . . 83

Figure 7.1

Representative Zero-Field Measurements of NiFe(1)/NiFeCo(x) Spin Valve . . 87

xi

Figure 7.2

Representative Fraunhofer Patterns for NiFe(1)/NiFeCo(x) Spin Valve . . . . . 89

Figure 7.3

Zero-Field Ic RN in "P" vs AP State for NiFe(1)/NiFeCo(x) Spin Valves . . . . . 91

Figure 7.4

Representative Fraunhofer Pattern and Zero-Field Measurement for NiFe(x)/Ni(2)
Spin Valve Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figure 7.5

Zero-Field Ic RN in P vs AP State for NiFe(x)/Ni(2) Spin Valves . . . . . . . . . 95

Figure 7.6

AP
Theoretical Description of IP
c and Ic Trends for NiFe(x)/Ni(2) Spin Valves . . 96

Figure 7.7

Zero-Field Ic RN in P vs AP State for NiFe(x)/Ni(1.6) Spin Valves . . . . . . . . 98

Figure 8.1

Schematic Diagram of the Asymmetric SQUID Layout . . . . . . . . . . . . . 101

Figure 8.2

Three-Dimensional Plots of Positive SQUID Critical Current, Ic+ , vs FluxLine Current, Iφ , and In-Plane Set Field, Hin . . . . . . . . . . . . . . . . . . . 103

Figure 8.3

Ic+ , Ic− , and Iave
c Data with Fits for All Four Magnetic States for a SQUID
containing NiFe(1.5)/Ni(1.2) Free and Fixed Layers . . . . . . . . . . . . . . . 106

Figure 8.4

Cartoon of Symmetric SQUID Layout . . . . . . . . . . . . . . . . . . . . . . 112

Figure 8.5

Three-Dimensional Plots of Average SQUID Critical Current vs Flux-Line
Current and In-Plane Set Field, Hin for NiFe(1.0)/NiFeCo(1.1) SQUID . . . . . 113

Figure 8.6

Ic+ , Ic− , and Iave
c Data with Fits for All Four Magnetic States for a NiFe(1.0)/NiFeCo(1.1)
SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Figure 8.7

3D Plots of the average critical current, Iave
c , vs the flux-line current, Iφ , and
the ’set’ field, Hin for a NiFe(1.0)/NiFeCo(1.1) SQUID . . . . . . . . . . . . . 116

Figure 8.8

3D plot of average critical current vs flux current and applied ’set’ field for
NiFe(1.25)/Ni(2) SQUID 1A-2 . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Figure 8.9

Ambiguous Fits to NiFe(1.25)/Ni(2) SQUID Major Loop States . . . . . . . . . 121

Figure 8.10 SQUID Fit Data to All Major Loop States for a NiFe(1.25)/Ni(2) SQUID . . . . 122

xii

CHAPTER 1
INTRODUCTION

1.1

Motivation

The growth of Information Technology over the past several decades has been dramatic and impressive. But, this growth comes with a cost: supercomputer and data center facilities now use
a noticeable fraction of the world’s electrical power budget. There is a strong incentive to develop new computing technologies that are substantially more energy efficient than our existing
semiconductor-based technology. The development of a fully superconducting computer is one
approach being pursued. Such a computer would take advantage of energy efficiencies in three
major areas: logic, memory, and interconnects. Some workers believe that such a computer could
be up to 100 times more efficient than a semiconductor-based computer, even taking into account
the energy used to cool the entire system to liquid helium temperatures [38].
A superconducting supercomputer could have many potential advantages. Josephson junctions
switch on the picosecond time-scale and dissipate very little energy per switch. Single Flux Quantum logic circuits transmit small current pulses between neighboring loops that can travel at speeds
up to 1/3 of the speed of light [51]. Several energy-efficient variants of that logic have been developed over the past several years [51, 56, 43, 81, 37], but this technology has not yet become
competitive, in part due to the lack of a compatible superconducting memory [76].
Recently, Josephson junctions with ferromagnetic interlayers (SFS junctions) have attracted
interest for the role they can play in addressing this issue. The theory behind these devices will
be explained in Chapter 2. Proposals to use ferromagnetic Josephson junctions in memory applications come in several flavors, with some using the orbital or field effect [50, 34, 19, 5], and
others using the exchange field [35, 1, 10, 31]. Among those using the exchange field, the bit can
be controlled using either the amplitude of the critical current or the ground-state phase across the
junction [65, 4, 50]. In this work, we focus on the development of Josephson Magnetic Random

1

Figure 1.1 Simplified Schematic of JMRAM Cell Layout. The cell includes two SIS junctions
and the phase-controllable SFS junction together in a superconducting loop. As described in
Chapter 2, the critical current of the loop will oscillate with the applied flux through the loop.
This leads to the cell having a larger critical current when the SFS junction contributes 0
additional phase into the loop and a smaller critical current when the SFS junction contributes π
additional phase into the loop.
Access Memory (JMRAM) which uses the exchange field and phase control [35, 36]. We are
drawn to this approach due to its advantages in scaling and operational speed.
JMRAM is currently being developed by Northrop Grumman Corporation and draws inspirations from the field of spintronics, and specifically from commercial MRAM, which has been
designed and marketed by Everspin Technologies [64]. In JMRAM, the phase-switching element
would be a Josephson junction with two ferromagnetic layers. Changing the relative magnetization
directions of these two layers between the parallel and anitparallel configuration can change the
ground-state phase difference of the junction between π and 0. The mechanism for this is explained
in Chapter 2. The JMRAM design incorporates this phase-controllable Josephson junction into a
superconducting loop with two conventional SIS junctions (junctions with an insulating barrier)
which is shown schematically in Figure 1.1. This design uses the SFS junction only as a passive
phase shifter, either adding an additional 0 or π phase into the loop. Because the critical current
of the loop will naturally oscillate with phase, this results in the loop having a high critical current
when the SFS junction is in the 0 state and a low critical current when the SFS junction is in the π

2

state. These two states would act as the 0 and 1 of the memory system. You can imagine biasing
the loop at a current between the high and low value and if the cell is in the 0 state, its critical
current will be larger than this bias and nothing will happen, and if the cell is in the π state, its
critical current will be exceeded and it will emit a measurable voltage pulse. The speed of this
"read" operation is inversely proportional to the critical current times normal state resistance, or
Ic RN . In this case where the SFS junction is used as a passive phase shifter, the voltage pulse will
be produced by the SIS junctions, which is a major advantage of the JMRAM design since the SIS
junctions have a much larger Ic RN product than the SFS junctions. If the critical current of the
SFS junction is larger than that of the SIS junctions in the loop, then only the latter will switch into
the normal state when the critical current of the SQUID is exceeded. This leads to an extremely
energy efficient read operation for the memory cell. For more details, see [28, 35, 36]. In parallel,
Northrop Grumman is also developing logic that is compatible with this memory system. Together,
they form an important stepping stone towards a fully superconducting computer.

1.2

Thesis Structure

This thesis will detail my work on the phase-control and optimization of Josephson junctions with
ferromagnetic interlayers for use in memory applications. It is structured as follows: Chapter 2
will describe the theoretical background needed to understand this work, introducing the topics
of Josephson junctions, the proximity effect at superconductor/normal metal and superconductor/ferromagnet interfaces, phase effects in ferromagnetic Josephson junctions, and properties of
dc SQUIDs. Chapter 3 details the sample fabrication process used in this work including a discussion of the relevant equipment and detailed processing steps. Chapter 4 will share my results
from several studies aimed at reducing the roughness of the base superconducting electrode and
the normal metal spacer layers to enhance the properties of the junctions overall. In Chapter 5,
magnetometry measurements of blanket thin films of various magnetic materials are shown. All
these materials will be used later in this work in Josephson junctions. Chapters 6 and 7 show the

3

results of Josephson junction studies that include a single ferromagnetic layer or two ferromagnetic
layers respectively. Chapter 8 details the crowning achievement of this work, the demonstration of
a phase-controllable Josephson junction with two ferromagnetic layers. After the initial demonstration, several additional devices using different materials and design schemes were also tested to
optimize the phase control. Lastly, Chapter 9 will give a summary of the results and look forward
to future work that can build on this progress.

4

CHAPTER 2
THEORETICAL BACKGROUND

Since the discovery of superconductivity in 1911 [59], over 20 elemental superconductors have
been found and many useful devices have been developed. Below a critical temperature, these materials allow current to flow with no dissipation and completely eject magnetic field lines from their
interior. These phenomena are inherently quantum mechanical in nature, but manifest themselves
on a macroscopic scale. For conventional superconductors, including those studied in this work, a
full microscopic theory (called BCS theory) was developed by J. Bardeen, L.N. Cooper and J.R.
Schrieffer in 1957 [7, 8]. This theory identified that the dissipationless current flow of the superconducting state is due to electron pairs (called Cooper pairs) that have opposite spin and opposite
momenta. These Cooper pairs form a zero-spin state and act as a boson, which allows the entire
ensemble of pairs to condense to the lowest energy state characterized by a single phase-coherent
wavefunction. This leads to interesting effects in systems that combine superconductors with normal metals and especially ferromagnets. In this chapter, I will discuss the theory of the Josephson
equations, the RCSJ model for Josephson junction circuit elements, the effect of a magnetic field
on the critical current of a Josephson junction, the superconducting proximity effect in normal
metal and ferromagnetic materials, the phase properties of ferromagnetic Josephson junctions, and
Superconducting QUantum Interference Devices (SQUIDs).

2.1

Josephson Junctions

In 1962, Brian Josephson analyzed the behavior of the junction between two closely spaced superconductors separated by an insulating barrier. If this insulating barrier is thin enough, Josephson
postulated that electron pairs would be able to tunnel through the barrier [40, 41]. This type of
system with two superconductors separated by an insulating layer became known as a Josephson
junction, and the barrier material was later expanded to include normal metals and ferromagnets.

5

S1

S2

φ1

φ2

Figure 2.1 Cartoon of a Josephson junction. S1 and S2 are the two superconducting electrodes
which are separated by a non-superconducting barrier material. Each superconductor has its own
macroscopic phase. As defined in the text, the junction carries a positive supercurrent flowing for
S1 to S2 .
Each superconductor is characterized by a macroscopic phase φ as shown in Figure 2.1. Two equations, called the Josephson equations govern the flow of supercurrent (IS ) across the junction. The
first equation
IS = Ic sinφ

(2.1)

shows how the supercurrent varies with φ , the phase difference between the two superconducting
electrodes (φ2 - φ1 ). Ic is the maximum or critical current of the junction. If the critical current is
exceeded, a voltage will arise across the junction. This equation is also called the current-phase
relation. If a constant voltage V is applied to the Josephson junction, we obtain
2e
2π
δφ
= V=
V
δt
h¯
Φ0

(2.2)

h = 2.07*10−15 Wb. This second Josephson equawhere Φ0 is the flux quantum with a value of 2e

tion is also called the voltage-phase relation. Together, they describe the behavior of a Josephson
junction and lead to several interesting effects. The DC Josephson effect states that a DC current
can be drawn through the junction without any voltage drop as long as the current is smaller than
Ic and φ has a constant, nonzero value. When a constant voltage is applied to the junction, the
phase different between the two superconductors will vary linearly with time, causing the current
through the junction to oscillate with an amplitude of Ic and a frequency of 2e
h V. This is called the
AC Josephson effect.
These Josephson equations can be derived by following the arguments laid out by L.D. Landau and E.M. Lifschitz [48] or from the famous Feynman lectures [26]. The predictions from
6

JJ

C

R

Figure 2.2 Circuit equivalent of the RCSJ Model showing a capacitor and resistor in parallel
with the Josephson junction supercurrent
this formalism were experimentally validated only one year after Josephson’s paper by Philip W.
Anderson and John M. Rowell [2].

2.1.1

Resistively and Capacitively Shunted Junction (RCSJ) Model

The RCSJ model is used to gain some insight into the dynamics of a Josephson junction by describing the DC current-voltage characteristic. In this model, the Josephson junction has a critical
current Ic and is in parallel with its self-capacitance C and a resistance R [79, 73, 53]. The equivalent circuit is shown in Figure 2.2. This model assumes a linear resistance and neglects the current
noise from the resistor. Adding the current through these elements gives
I = Ic sinφ +

V
dV
+C .
R
dt

(2.3)

Combining this with the second Josephson relation, equation 2.2, we find that
Φ0 1 dφ Φ0 d 2 φ
I = Ic sinφ +
+
C
2π R dt
2π dt 2
Φ

(2.4)

Φ

If we multiply by 2π0 , use the Josephson coupling energy EJ0 = 2π0 Ic , normalize the current with
in = IIc , and re-arrange the terms, we find that
Φ0 2 d 2 φ
Φ0 2 1 dφ
d
C 2 +
+
(E [1 − cosφ − in φ ]) = 0
2π
2π
R dt dφ J0
dt
7

(2.5)

U
m
wp
I=0

0<I<Ic
I=Ic

I>Ic

φ

Figure 2.3 Tilted Washboard Potential Analogy Analogy between the motion of the phase
different of a Josephson junction and the damped motion of a particle of mass m in the tilted
washboard potential. When the current through the junction is low, the ’mass’ is trapped in one
well of the potential and can oscillate at the plasma frequency. The increase in current is modeled
as increasing the tilt of the potential. As the current is increased, the barrier height is reduced until
the applied current equals the critical current where any fluctuation can send the particle out of its
well. Above the critical current, there are no stable states and the particle will move freely along
the potential.

8

This equation describes the equation of motion for the phase difference across the junction and is
analogous to the equation of motion of a particle with mass m and damping η in a potential U:
m

dx2
dx
+
η
+ ∇U = 0.
dt
dt 2

(2.6)

Comparing these equations, we find that
m=

Φ0 2
C
2π

(2.7)

η=

Φ0 2 1
2π
R

(2.8)

U = EJ0 [1 − cosφ − in φ ]

(2.9)

Examining these relationships, we see that the mass of the particle is proportional to the capacitance C, the damping is inversely proportional to the resistance R, and the potential is that of a
tilted washboard. This description is visualized in Figure 2.3. When there is no current through the
junction, the particle is confined to a potential minimum. The time average of the phase difference,
and hence the time averaged dc voltage, is zero in this state. Increasing the current corresponds
to tilting the potential and lowering the barrier for the particle. If the current exceeds the critical
current, the washboard is tilted so far that the particle can’t stay in its well and it will slide down
the washboard. This dynamic case is associated with a finite dc voltage across the junction which
increases with increasing bias current.
cR
Equation 2.5 is commonly written in reduced units by using the normalized time τ = t 2πI
Φ
0

and the Stewart-McCumber parameter βc =

βc

2π
2
Φ0 Ic R C

[73, 53] to get

d 2 φ dφ
+
+ sinφ − in = 0.
dτ 2 dτ

(2.10)

If we neglect the damping and consider a horizontal potential (zero driving current) and small
amplitudes (so sinφ

φ ) then we can write equation 2.10 as
βc

d2φ
+ φ = 0.
dτ 2

9

(2.11)

Figure 2.4 Pendulum Analogy Analogy between the motion of the phase different of a Josephson
junction and the damped motion of a physical pendulum. The pendulum has mass m and length
deflected by angle θ due to a torque T that is represented by an unwinding mass.
The solution of that equation is
φ

i √τ
= Ae βc

= Aeiω pt .

where A is a constant and the plasma frequency ω p =

2πIc
Φ0C .

(2.12)
The plasma frequency represents

the oscillation frequency of the particle around the potential minimum at small amplitudes.
Another mechanical analogue that can be used to describe the dynamics of a Josephson junction
is a physical pendulum. The pendulum is defined by mass m and length

that is deflected from

normal by an angle θ inflicted by a torque T. This torque is directed parallel to the rotation axis and
has a magnitude of the product between the gravitational force mgsinθ and the pendulum length .
This system is shown in Figure 2.4 and is represented by the equation of motion
T = Θθ¨ + Γθ˙ + mg sinθ .

(2.13)

where Θ = m 2 is the moment of inertia of the pendulum and Γ is the damping coefficient. By
comparing with equation 2.4, we see that they are equivalent with I ↔ T, Ic ↔ mg , Φ0 /2πR
↔ Γ, CΦ0 /2π ↔ Θ, and φ ↔ θ . The dynamics of the Josephson junction correspond to the
10

dynamics of an oscillation or rotation of the pendulum. When the torque is zero, the pendulum
will oscillate around its equilibrium position with a frequency of

g/ which corresponds to the

plasma frequency of the Josephson junction. A finite torque that causes a constant deflection angle
of the pendulum corresponds to a finite current less than the critical current being applied to the
Josephson junction, causing a constant phase difference across the junction. A torque that deflects
the pendulum by 90° or more causing a rotation of the pendulum corresponds to a current above
the critical current and causes a changing phase difference in the Josephson junction, and therefore
a finite voltage.

2.1.2

Overdamped Josephson Junction

We will now consider the case of an overdamped Josephson junction, which corresponds to the type
that are measured in this work. In this case, βc = 2πIc R2C/Φ0

1, so the junction capacitance

and/or resistance are small, corresponding to a particle with a small mass and large damping in
the tilted washboard scheme. If you imagine this limiting case starting with a current larger than
the critical current and reducing to zero, the strong damping will cause the particle to become retrapped in a local minima as soon as the current is less than the critical current. This leads to a
non-hysteretic current-voltage characteristic for the overdamped Josephson junction. To derive the
current-voltage relationship, we can neglect the βc term from equation 2.10 to get
dφ
+ sinφ − in = 0.
dτ

(2.14)

At values less than the junction critical current, we expect all the current to flow as supercurrent.
The voltage phase relation implies that the junction is in the zero voltage state so there is no time
evolution of the phase. This leads to the relationship
φ = sin−1 in

f or

in ≤ 1.

(2.15)

Above the critical current, the full time dependence of the relationship must be taken into account.
Integrating equation 2.14, it can be shown that the time-averaged voltage has the following form
11

Figure 2.5 IV characteristic for an overdamped Josephson junction The black curve
represents equation 2.16 with zero voltage for currents below the critical current and voltages
approaching Ohm’s Law (shown in red) above the critical current.
[32]:
V (t) = Ic R i2n − 1 = Ic R

I 2
−1
Ic

f or

I > Ic

(2.16)

At current values much greater than the critical current, this equation approaches Ohm’s Law. The
full current-voltage characteristic for an overdamped Josephson junction is shown in Figure 2.5.

2.1.3

Short Circular Junction in a Magnetic Field

So far, we have only considered zero-dimensional Josephson junctions characterized by the Josephson current Is with maximum value Ic , and the phase difference φ across the junction. Now we
will allow for spatial variations in the supercurrent and phase difference and we will show that spatial interference in the Josephson junction can be observed if we apply an external magnetic field
[9, 32]. The observed interference effect is analogous to the single slit diffraction pattern in optics.
We will examine the short junction case, where the magnetic field generated by the Josephson
current itself is negligible compared to the externally applied magnetic field. Consider a circular
12

a)

X

By

S1
Z

2OL+t

I

Y

S2
2R
D

Figure 2.6 Circular Josephson Junction in a Magnetic Field Circular Josephson Junction with
radius R in a Magnetic Field Hy . The current flows through the junction in the x-direction, t is the
thickness of the junction barrier layer and λL is the London penetration depth.
Josephson junction with radius R in an external field H = (0, Hy , 0) as shown in Figure 2.6. When
a uniform external field is applied to the junction, the field will decay inside the superconductor as
e−|x|/λL where λL =

m .
µ0 ne2

The phase difference will have spatial dependence as
∇φ =

2π
d H × xˆ
Φ0

(2.17)

where d = 2λL + t, t is the barrier thickness, H is the magnetic field in the plane of the junction
(including both the externally applied magnetic field and the field generated by currents flowing in
the junction), and xˆ is the unit vector in the x direction. Integrating this equation for a field in the
y-direction, we find
φ (z) =

2πd
Hy z + φ0
Φ0

(2.18)

where φ0 is an integration constant. There is a linear spatial variation in the z-direction which is
proportional to the applied magnetic field. Plugging this result into the first Josephson relation, we
find that
J(z) = Jc sin

2πd
Hy z + φ0 .
Φ0
13

(2.19)

Figure 2.7 Airy Diffraction Pattern Maximum critical current vs normalized flux through the a
circular junction resulting in an Airy Pattern.
This indicates that the current density has a periodic nature inside the junction which will lead
to certain values of the external magnetic field that result in zero net current through the junction.
The total current in the junction is given by
I=

2πd
Hy z + φ0
Φ0

dydzJc sin

(2.20)

where integration is performed over the junction area. For the case of a circular junction with
radius R, this integral can be solved and maximized [52] to give
Ic = 2Ic0

J1 ( πΦ
Φ )
0
πΦ
Φ0

(2.21)

where the critical current with no external field Ic0 = πJc R2 , J1 is the Bessel function of first kind
and order, and the flux through the junction Φ = By 2R(2λL + t). This result is known as an Airy
pattern and it is plotted in Figure 2.7. Though calculated for a circular junction, the resulting
pattern is the same for the elliptical junctions studied in this work. If calculated for a rectangular
junction, the result is called a Fraunhofer pattern with a similar mathematical form to the optical
14

B)

A)
N

C)
N

S

S

Figure 2.8 Schematic of Andreev Reflection Schematic of Andreev Reflection using the
semiconductor model of a superconductor. The energy bands for the normal metal N and
superconductor S are shown filled up to the Fermi energy. Electrons are shown as red circles and
holes as white circles. For electrons to flow across this boundary, the process must exchange a
charge of -2e. In Andreev Reflection A) this is modeled as an electron in N traveling into S and
retroreflecting a hole back into N, thus creating a Cooper pair in S. In Inverse Andreev Reflection
B) a Cooper pair in S can travel into N as a hole incident on the interface and a retroreflected
electron.
Fraunhofer pattern. Throughout this thesis, the term "Fraunhofer pattern" is used in place of "Airy
pattern" due to colloquialism and the similar shape of the two functions.

2.2

S/N and S/F Proximity Effects

Thus far, all the properties that have been derived for Josephson junctions are general, and apply to
junctions of any barrier type. Now we will turn our attention to the specific effect that ferromagnetic materials have on the junction by comparing the effect of a superconductor (S)/normal metal
(N) interface with a superconductor (S)/ferromagnet (F) interface.

15

When a material becomes superconducting, the electrons at the Fermi level begin to pair up
into Cooper pairs. This leaves behind an energy gap in the single-electron density of states. The
electrons in a normal metal are nonlocalized with single-electron states filled up to the Fermi level.
You might then naively assume that these two materials could not exchange electrons, but this is
not the case. The microscopic model that describes how electrons can flow in this system is called
Andreev Reflection [3] and is shown schematically in Figure 2.8. Consider an electron in N with
spin ↑, momentum k, and energy above the Fermi level but below the superconductor energy gap.
There are no single-electron states in the superconductor, so the electron must find a partner in N
with opposite spin, momenta, and energy. Then these two electrons can fill a Cooper pair state in
S at the Fermi level, but must leave behind a hole in N with spin ↓ and momentum −k below the
Fermi level. The inverse of this process is also allowed to transmit Cooper pairs into the normal
metal. In all processes across this interface, an exchange of 2e is required.
In the case where Cooper paired electrons travel into the normal metal, those electrons are no
longer paired, but do retain a phase coherence with each other up to a certain length scale in N.
This length scale has a different functional form depending on if the electron transport in N is in
the diffusive or ballistic limit [21, 60, 23]. These limits depend on the relationship between the
pair coherence length in N, ξN , (defined momentarily), and the electronic mean free path, l. The
ballistic or clean limit is defined when the mean free path is much larger than ξN . In this case, the
electrons are moving at the Fermi velocity and travel in relatively straight paths without scattering
through N, leading to a coherence length through the normal metal of vF ∗ τ where vF is the Fermi
velocity of the electrons and τ = εh¯ is the coherence time. Taking the convolution of this length
scale with the Fermi-Dirac distribution with respect to energy, we find that only energies within
kB T of the Fermi energy have a significant contribution, so we can write ε ≈ 2πkB T . This leads to
a normal metal coherence length of
ξN =

h¯ vF
2πkB T

(2.22)

in this limit. The diffusive or dirty limit is characterized by a mean free path that is much shorter
than ξN , leading to multiple scatterings of the electrons as they travel through N according to the
16

A)

B)

EK

EK

EF

EF

-kF

kF

-kF -kF

k

2Eex

kF kF

k

Figure 2.9 S/F Interface Band Structure Toy band structure for S/F interface. The band
structure of the ferromagnet is modeled as a normal metal in a magnetic field with Zeeman
splitting equal to twice the exchange energy of the ferromagnet. Cooper pair electrons that enter
the ferromagnet must go into different spin-bands which have different potential energies leading
↓
↑
to |↑↓ pairs gaining a center of mass momentum of Q = kF − kF , and |↓↑ pair gaining a center of
mass momentum of -Q.
diffusion constant D. In this limit, the normal metal coherence length is
ξN =

h¯ D
.
2πkB T

(2.23)

For temperatures below 1 K, this length can be on the order of a micron and demonstrates how
far the once-superconducting electrons can remain coherent. This induces superconducting-like
properties in the normal metal corresponding to the Proximity Effect. Simultaneously, this leakage
of Cooper pairs weakens the superconductivity at this boundary, reducing the critical temperature
of the superconductor corresponding to the Inverse Proximity Effect.
In the case of a superconductor (S)/ Ferromagnet (F) interface, the exchange field and spinband splitting cause drastically different outcomes for the electron transport across the boundary
and coherence length in F. This topic has been treated extensively by Buzdin and Radovi´c [15, 16,
17, 62, 63] but here we will follow the qualitative picture set forth by Demler, Arnold, and Beasley
[22]. This is a hand-waving derivation but it gets across the key features of the S/F interface. In
this picture, we will model the band structure in the ferromagnet as that of a normal metal with
Zeeman splitting equal to twice the exchange energy of the ferromagnet, as shown in Figure 2.9.
17

In a conventional superconductor, the Cooper pairs form a spin singlet state given by
1
Ψ = √ (|↑↓ − |↓↑ )
2

(2.24)

where we are ignoring the spatial state of the Cooper pair in this simplified picture. Let us consider
the |↑↓ component with its momenta normal to the interface being transported across the S/F
interface. Because of the exchange field in F, the two electrons must enter different spin bands
leading to the up-spin electron lowering its potential energy by the exchange energy Eex while the
down-spin electron raises its potential energy by Eex . To conserve total energy, the electrons must
compensate for these changes by adjusting their kinetic energy. This leads to a non-zero center of
mass momentum between the two electrons of
↑

↓

h¯ Q = h¯ (kF − kF ).

(2.25)

If we assume that the bands are parabolic and that the Fermi velocity is the same in the two spinbands since Eex

EF , this can be reduced to
Q=

2Eex
.
h¯ vF

(2.26)

Because of the antisymmetric nature of the electron pair wavefunction, we must consider this case
together with the case in which the up and down spin electrons are exchanged, so a |↑↓ pair will
have a center of mass momentum of Q while a |↓↑ pair will have a center of mass momentum of
-Q. This can also be seen in Figure 2.9. Combining these pairs into the spin singlet configuration
given in equation 2.24, we see that the wavefunction is modified by the exchange field in the
ferromagnet to give
1
Ψ = √ (|↑↓ eiQX/¯h − |↓↑ e−iQX/¯h )
2

(2.27)

where X is the center of mass coordinate of the electron pair. Converting the exponentials into sine
and cosine terms and grouping those components, we find
1
Ψ = √ (|↑↓ − |↓↑ ) cos(Qx) + i (|↑↓ + |↓↑ ) sin(Qx).
2
18

(2.28)

ψ

ψ
N

Figure 2.10 S/N and S/F Pair Correlation Functions S/N and S/F pair correlation functions
highlighting the steep decay and oscillation of the function in the ferromagnetic case. The
horizontal scales are not the same in A) and B) with a much longer length scale in A) than in B).
The sine term represents a spin triplet component and can be neglected in this case with one
(or two) ferromagnetic layer(s) and S-wave superconductors. More generally, the pairs may not
have normal incidence with the interface but their momenta can make an angle θ with respect to
normal incidence. In this case, the pair momenta parallel to the interface must be conserved, so the
normal momenta are modified to Q/cosθ . After integrating over all angles, the total pair correlation
amplitude

sin ξx

ψ∝

x
ξF

F

(2.29)

in the clean limit, with the coherence length

ξF =

h¯ vF
.
2Eex

(2.30)

In the dirty limit, the pair correlation function becomes

ψ ∝e

−x
ξF

sin

x
ξF

(2.31)

with a coherence length of
ξF =

19

h¯ D
Eex

(2.32)

[14]. For elemental ferromagnets such as Fe, Ni, or Co, Eex is on the order of 1 eV [24, 25]. Hence,
this coherence length in the ferromagnet is on the order of 1 nm - about 1000 times smaller than
that of a normal metal at low temperature.
Figure 2.10 shows the comparison between the S/N and S/F pair correlation functions. In addition to having a much shorter decay length, the oscillations in the ferromagnetic case lead to several
other interesting features of this system including oscillations in the critical temperature [55, 75]
and density of states of S/F bilayers [47, 12] as a function of F-layer thickness. More relevant to
the remainder of this thesis will be the oscillation of the critical current with ferromagnetic layer
thickness in S/F/S Josephson junctions. This leads to the possibility of obtaining π phase coupling
between the two superconducting electrodes instead of the conventional 0 phase coupling. This
effect results in a π junction, which will be further detailed in the next section.

2.2.1

Phase of Ferromagnetic Josephson Junctions

A conventional Josephson junction will have a zero ground state phase difference between the two
superconductors. The energy stored in a so-called 0-junction is given by
EJ (φ ) =

Φ0 Ic
(1 − cosφ ) = EJ0 (1 − cosφ ).
2π

(2.33)

as was found in equation 2.9 and is clearly minimized when φ = 0. But, it was predicted that
negative critical current could be obtained in the case of tunneling through an insulator with enough
magnetic impurities [13]. This negative critical current leads to a ground state phase difference
of φ = π. This type of junction is called a π junction, as mentioned in the preivous section.
Buzdin showed that an S/F/S Josephson junction would be able to have either 0 or π coupling
depending on the thickness of the central ferromagnetic layer [15]. This is characterized by a
decay and oscillation of the junction’s critical current with F layer thickness. The thicknesses
where the critical current drops to zero indicate the phase changing from 0 to π or π to 0 since
only the absolute value of the critical current is measured in most experiments. This critical current

20

Ic/Ic0

dF/ξF
Figure 2.11 Critical Current Oscillations in S/F/S Junction The oscillation and decay of the
pair correlation function into the ferromagnet manifests itself in similar behavior of the critical
current. Regions where the current drops to zero indicates a phase transition of the ground state
by π.
oscillation can be modeled by
Ic = Ic0 e−dF ξF1 ∗ cos(dF /ξF2 − θ )

(2.34)

where ξF1 and ξF2 are the length scales governing the decay and oscillation of the critical current
respectively and θ is a phase shift [17]. This is plotted in Figure 2.11. These 0-π phase oscillations
has now been demonstrated by many groups, including my own, using both weak and strong
ferromagnetic materials including PdNi, Ni, CuNi, Co, Fe, NiFe, NiFeMo, PdFe, and NiFeCo
[68, 11, 46, 69, 58, 66, 70, 83, 67, 6, 1, 57, 30, 29].
With a single ferromagnetic layer, the ground state phase difference φ can be made either 0
or π depending on the choice of ferromagnetic layer thickness. In order to have a junction whose
phase can be controllably switched between 0 and π, a second ferromagnetic layer is required. In
this case, the ground state phase difference φ will depend on the phase accumulation φac of the
transport electrons that travel through the junction according to equations 2.30 and 2.32. The phase
accumulation through a single F layer φac = dF /ξF , so the phase accumulated across F1 is φ1 =
21

ac
Figure 2.12 Critical Current Oscillations in S/F1 /F2 /S Junction The phase accumulation of the
electrons across the junction determines whether the ground state phase difference of the
superconductors will be 0 or π. When the two F layers have parallel magnetization directions, the
total phase accumulation across the junction is the sum of the contribution from each layer.
Similarly, if the two F layers are antiparallel, the total phase accumulation will be the difference
of the contribution from each layer. So one scheme to produce a junction capable of switching it’s
ground state phase difference from 0 to π would be to have one F layer at it’s 0-π transition
thickness (indicated by the blue dotted line) and the other F layer thinner than it’s 0-π transition
thickness. Then when the contributions add in the parallel (P) state, the junction will be in the π
state and when the contributions subtract in the antiparallel (AP) state, the junction will be in the
0 state.
dF1 /ξF1 and the phase accumulated across F2 is φ2 = dF2 /ξF2 . In the case that the magnetization
directions of the two F layers are parallel (P), both layers will have the same minority and majority
spin-bands for the entire transport process, so the total phase accumulation will be φP = φ1 + φ2 .
Similarly, in the case that the two layers have magnetizations pointing antiparallel (AP) to each
other, the spin-bands will interchange relative to each other, so the total phase accumulation will
be φAP = φ1 − φ2 . If the F layer thicknesses are chosen correctly, this result can be used to create
a junction that can be switched between the 0 and π phase states. This is represented pictorially
in Figure 2.12. One F layer is chosen to be at its 0-π transition thickness, represented by the
blue dashed line in the figure. The other layer is chosen to be thinner than its 0-π transition

22

thickness. Then, when the two layers are parallel, the junction will be in the π state and when
the two layers are antiparallel, the junction will be in the 0 state. So, by changing the relative
magnetization direction of the F layers in a Josephson junction with two F layers between the
parallel and antiparallel configurations, the junction can be switched between the π and 0 phase
states [28].

2.3

DC SQUIDs

To measure the phase state of a junction, one must perform an interference experiment, e.g. by
using a "dc SQUID." The Supercondcutcing QUantum Interference Device or SQUID was first
invented in 1964 by Robert Jaklevic, John J. Lambe, James Mercereau, and Arnold Silver at Ford
Research Labs [39]. Since then, it has found many uses, including for magnetic measurements
and phase sensitive measurements, as in this work. A schematic configuration of a dc SQUID is
shown in Figure 2.13. It consists of a superconducting loop with a Josephson junction incorporated
into each arm. The ring is biased with a current I. The current in each arm of the loop can be
characterized by I1 = Ic1 sinφ1 and I2 = Ic2 sinφ2 from the Josephson relations where Ic1/2 are the
critical currents of the two junctions and φ1/2 are the phase differences across the junctions. The
two junctions limit the total current that can flow through the ring. To determine the behavior of a
dc SQUID, we will follow the framework of several references [9, 32, 18].
As we have seen, the Cooper pairs in the superconductor have a single wavefunction. In order
for the wavefunction to have physical meaning, it must be single-valued, implying that the phase
can only change by 2πn over a closed loop. This implies that
2πn =

∇ θ · dll = φab + φbc + φcd + φda

(2.35)

where the integral is divided up into four terms based on the phase difference across the paths
from Figure 2.13 as denoted in the subscripts. Using the relationship between the phase φ , the

23

Figure 2.13 Schematic view of a dc SQUID Schematic view of a dc SQUID formed by two
Josephson junctions in a superconducting loop driven by a current I. This current will split into I1
and I2 , or can equivalently be thought of as a circulating current around the loop J. The blue
dotted line indicates the closed contour integration path described in the text.
supercurrent densities J s , and the vector potential A ,
∇φ =

2π
Φ0

A+

1
Js ,
µ0 λL2

(2.36)

we find that
φab = φ1 +
c

φbc =

2π
b Φ0

2π b
A · dl
Φ0 a

(2.37)

1
J s + A · dl
µ0 λL2

(2.38)

φcd = −φ2 +
a

φda =

2π
d Φ0

2π d
A · dl
Φ0 c

1
J s + A · dl
µ0 λL2
24

(2.39)
(2.40)

Imax/Ic

Φext/Φ0
Figure 2.14 Critical current vs applied flux for symmetric dc SQUID Critical current vs
applied flux for symmetric dc SQUID shown for three values of βL . When βL 1, the SQUID
critical current oscillates between 2Ic and 0. This modulation depth decreases as βL increases in
value [18].
If the superconducting loop is wider than the London penetration depth, then the integration
path can be taken deep inside the superconductor where J s is zero, so those terms will not contribute to the final result. Additionally, the integral of the vector potential around a closed contour
will equal the total flux Φ enclosed by the contour. Using this with equation 2.35, we find that
2πn = φ1 − φ2 +

2π
A · dl
Φ0 C

(2.41)

or equivalently
φ2 − φ1 =

2πΦ
− 2πn
Φ0

(2.42)

In the case of a superconducting loop with no Josephson junctions, this formalism shows that the
flux enclosed by a superconducting loop in quantized. The total flux Φ in the loop is given as the
sum of the geometric flux inside the loop from an external field Φext and the contribution from the
screening currents J as
Φ = Φext + LJ

(2.43)

where L is the inductance of the loop and the screening current is given by
2J = I1 − I2 = Ic1 sinφ1 − Ic2 sinφ2 .
25

(2.44)

and
Φext = BAe f f

(2.45)

Ae f f is the effective area of the loop, including the penetration depth of the superconductors. The
total current flowing through the device is given by
I = I1 + I2 = Ic1 sinφ1 + Ic2 sinφ2 .

(2.46)

Theorists like to eliminate one of the variables above by inserting equation 2.42 into equations 2.43
and 2.46 to get
I = 2Ic cos

πΦ
πΦ
sin φ1 +
Φ0
Φ0

Φ = Φe − LIc sin

πΦ
πΦ
cos φ1 +
Φ0
Φ0

(2.47)
(2.48)

assuming that both junctions have the same critical current Ic . These two equations can be solved
self-consistently to determine the behavior of the dc SQUID. The maximum current allowed
through the SQUID for a given external flux can be found by maximizing 2.47 with respect to
φ1 with the constraint of equation 2.48, which was first solved by de Bruyn Ouboter and de Waele
[20].
c
Let us now introduce the screening parameter βL ≡ 2LI
Φ which is defined as the ratio between
0

Φ

the magnetic flux generated by the maximum circulating current Ic and half a flux quantum 20 .
In the case that βL

1, the flux produced by the screening currents is small compared to the flux

quantum so the maximum current through the SQUID is found to be
I = 2Ic |cos

πΦ
|
Φ0

(2.49)

from the method described above. So in this case of identical Ic junctions and low βL , the dc
SQUID modulates between 2Ic and 0. As βL increases, there is a reduction in the modulation
depth as shown in Figure 2.14.

26

2.3.1

Asymmetric dc SQUID

Since they will be experimentally measured in this work, we now turn our attention to the case
of the asymmetric dc SQUID. We will specifically consider SQUIDs with asymmetries in the
critical currents of the two Josephson junctions and in the inductance of each path. This is shown
schematically in Figure 2.15. In this case, the flux induced by the shielding current J is
LJ = L1 I1 − L2 I2 = L1 I1 sinφ1 − L2 I2 sinφ2

(2.50)

where the total inductance of the loop L = L1 + L2 [9, 27]. From equation 2.42 and using equations
2.50 and 2.43 we find that
2πn = φ1 − φ2 + 2π

L I
L I
Φext
+ 2π 1 c1 sinφ1 − 2π 2 c2 sinφ2 .
Φ0
Φ0
Φ0

(2.51)

L2 Ic2
L1 Ic1
, β2 = 2π Φ
, and φext = ΦΦext , the last equation can be
Using the parameters β1 = 2π Φ
0
0
0
re-written as

2πn = φ1 − φ2 + 2πφext + β1 sinφ1 − β2 sinφ2 .

(2.52)

The current flowing through the SQUID is the same as equation 2.46, rewritten here for convenience
I = Ic1 sinφ1 + Ic2 sinφ2 .

(2.53)

These two equations form a non-linear set in variables φ1 and φ2 with φext and I as external
parameters. We want to know the critical current of the loop as a function of the external flux
φext so we need to find the maximum value of I(φ1 , φ2 ) with φ1 and φ2 subject to the constraint
of equation 2.52. Several methods have been proposed to solve this problem, but we will follow
the method of Lagrange multipliers used by Tsang and Van Duzer [49, 80]. So, we introduce the
Lagrange multiplier λ and form the new function
I = I1 sinφ1 + I2 sinφ2 + λ (φ1 − φ2 + 2πφext + β1 sinφ1 − β2 sinφ2 − 2πn).

(2.54)

Then, finding the critical points of I as a function of φ1 , φ2 , and λ and eliminating λ gives these
two equations:
φext =

1
(φ − φc1 + β2 sinφc2 − β1 sinφc1 )
2π c2
27

(2.55)

Figure 2.15 Schematic of an Asymmetric SQUID In this case, the critical currents of the two
junctions and the inductances of each path can have different values.

φc2 = cos−1

−1
I2 /(I1 cosφc1 ) + βT

(2.56)

where the subscript ’c’ added to φ1 and φ2 indicate the phase values when the critical current
I

of the device is Ic (the maximized value of I ) and the parameter βT = β2 + β1 I2 . Now, we
1
can find all the pairs φc1 , φc2 that satisfy equation 2.56, which will form a locus in the φ1 , φ2
plane. Subsequently, each pair on that locus can be used in equation 2.53 to find I and in equation
2.55 to find φext . These can be used to find the Ic (φext ) dependence for all values of φext . Once
these relationships are known, the individual critical currents of the junctions can also be easily
calculated.
The Ic (Φext ) curve for the general case of I1 = I2 and L1 = L2 is shown in Figure 2.16. In this
case, the curves take on an asymmetric sawtooth shape with the peaks of the positive and negative
critical current polarities shifted off of zero along the flux axis by the same amount but in opposite
directions. At the peak positions, the current through each junction is the critical current so I1 = Ic1
and I2 = Ic2 . Comparing with equation 2.50, we find that φ1 = φ2 = π/2. Those currents induce a
flux through the SQUID loop, Φint = LJ = L1 Ic1 − L2 Ic2 , satisfying equation 2.42. That must be
balanced by the externally applied flux, so the peak in the critical current vs flux curve occurs at a
flux of Φ peak = −Φint = L2 Ic2 − L1 Ic1 . This can be re-arranged as 1/2βL (αI + αL ) where αI and

28

φ+ext, max
Ic(Φext)/I1I2

φ2

φ-ext, max

φ1

Φext/Φ0

Figure 2.16 Theoretical Magnetic Flux Dependence of the Critical Current of an
Asymmetric SQUID The device considered here has both Josephson junction critical current and
inductance asymmetries. The left-hand plot shows the locus of φ1 ,φ2 solutions described in the
text and the right-hand plot shows the resulting oscillation of the critical current of the device
with the applied external flux. The values of the characteristic parameters used are β1 = 0.5π, β2
= 0.1π, βT = 0.5π and I2 = 0.8I1 [9].
αL characterize the asymmetry of the junction critical currents and inductance as
I −I
αI = c2 c1
Ic1 + Ic2

(2.57)

L − L1
.
αL = 2
L1 + L2

(2.58)

This means that the difference between the peak locations of the positive and negative critical
current branches ∆Φ is given by
∆Φ = βL (αI + αL ).

(2.59)

Calculations for various values of αI and αL show that with increasing αI there is a reduction in
the modulation depth of the critical current. αL has no effect on the modulation depth but increases
the skewness of the curves. This framework will be used to analyze and and fit data collected from
asymmetric SQUID devices in Chapter 8.

29

CHAPTER 3
SAMPLE FABRICATION

Sample fabrication is an involved process with many steps. In this chapter, I will detail the main
equipment used in sample fabrication and the steps for the fabrication of sub-micron Josephson
junctions.

3.1
3.1.1

Fabrication Equipment
Sputtering System

All deposition of superconducting, magnetic, and normal metal materials is done by sputtering in
this work. The sputtering system can hold four 2.25-inch diameter triode sputtering guns, three 1inch diameter magnetron sputtering guns, and an ion mill. Each gun is topped with a foil-wrapped

Figure 3.1 Top-down view of the sputtering system Shown are the four triode sputtering guns,
three magnetron sputtering guns, ion-mill, and wobble stick on the far left. The large guns are
shown at various stages of installation. Starting in the northeast corner and rotating clockwise, the
four large guns are shown empty, with the target installed, with the gun housing installed, and
finally with the magnetic cover plate and chimney installed.

30

chimney to avoid cross contamination. A top-down view of the sputtering chamber can be seen in
Figure 3.1. Each gun will sputter a different material from the installed target. Up to 16 samples
are held on the sample positioning and masking (SPAMA) plate about four inches above the gun
targets. The samples are separated from the guns by the shutter plate, which has four equally
spaced openings that will either open the samples to the large or small diameter guns. Both the
SPAMA plate and shutter plate are automatically controlled by Labview computer software.
The deposition process occurs through momentum transfer between an argon plasma and the
target material. I will now describe the function of the triode gun. To start, argon gas is flowed
into the system. The guns produce a uniform magnetic field from a pair of magnets and an electric
field between the gun’s cathode and anode. The cathode is created by a hot filament that emits
electrons. The electric and magnetic fields intersect above the target and create a plasma of ionized
argon and electrons. The target is biased with a negative voltage, so this plasma interacts with the
target material and knocks off atoms which travel up towards the sample substrate. The deposition
rate of the material can be measured with a film thickness monitor (FTM) and is typically very
stable throughout a sputtering run if the target voltage and current are kept constant. The desired
sample deposition stack is entered into a sequence file by the user and the Labview software will
calculate how long the sample must remain over each gun using the measured deposition rate.
Then the sample will be fabricated through automatic movement of the SPAMA and shutter plates.
Up to 16 chips can be loaded into the sputtering chamber in each run. To protect the other chips
when one is being sputtered, each chip is loaded into a holder with a rotating window. There are
prongs on the bottom of this window that can be hooked with the wobble stick and rotated to reveal
a sample or shut it away. Proper alignment of this window is needed to ensure the whole chip area
will see the sputtered material if material deposition is desired, and that no additional material will
be deposited when subsequent chips are being sputtered.
The tables below shows the gun settings for each material used in this study.

31

Material
Nb
Al
Ni
NiFe
NiFeCo
NiFeMo
CoFeB

Voltage (V)
600
400
350
450-500
470-500
500
550

Current (A)
0.60
0.50
0.30
0.45 - 0.50
0.47 - 0.50
0.50
0.55

Rate (Å/s)
4.1 - 5.4
1.9 - 2.4
1.7 - 1.9
3.2 - 4.6
3.7 - 4.3
3.9 - 4.7
4.1 - 4.5

Table 3.1 Target voltage and filament current settings for large gun sputtered materials The
NiFe voltage and current values started at 500 V and 0.50 A and were gradually turned down as
the group started using thinner and thinner NiFe layers. Material deposition rates vary with
applied current/voltage, chamber pressure, and target thickness.
Material
Au
Cu
Ru
FeMn

Power (W)
17 - 20
19 - 30
18
37 - 44

Rate (Å/s)
4.5 - 5.5
2.6 - 4.5
0.9 - 1.3
2.3 - 2.7

Table 3.2 Power settings for small gun sputtered materials Power values are selected to obtain
the desired deposition rate based on the amount of material that will be deposited. Material
deposition rates vary with applied current/voltage, chamber pressure, and target thickness.
3.1.2

Electron-Beam Lithographer

Electron-beam lithography was used to pattern the submicron junctions. Much of this work was
done using the JEOL 840 Scanning Electron Microscope (SEM). Midway through 2016, we were
fortunate to be able to upgrade that piece of equipment to the Hitachi SU5000 Schottky FieldEmission SEM with Electron-beam Lithography (EBL) capabilities. Since this new system will
be the only one used by future students, I will detail it’s operation here and attempt to avoid
complaining about how much more user effort was required to use the JEOL.
Chips to be patterned with EBL must first be coated with a suitable resist. We use ma-N 2401
which is a negative-tone resist from Micro Resist Technology. After spinning and baking, about a
100 nm film rests on top of the chip. This resist is rated for pattern resolutions below 50 nm. After
development, we want a pillar of resist of the desired junction size to remain. Since the ma-N is
a negative resist, this means that the resist that is exposed to the electron beam will harden and

32

remain on the chip after development, so we want to expose only the pillar area. The write patterns
are drawn using designCAD software and converted to patterns that the SEM can recognize using
the Nanometer Pattern Generation System (NPGS) developed by Dr. Joe Nabity. It is convenient
to be able to draw your own patterns in the computer software so you can try out many different
junction sizes and shapes on a project-by-project basis without having to buy a new mask every
time, as is the case for photolithography. Based on dose tests, our patterns are written with an area
dose of 550 µC/cm2 .
The electron beam is created using a field emission gun of the Schottky type. The emitter tip
is made of tungsten coated with zirconium oxide. The purpose of this oxide is to reduce the work
function of the cathode. The Schottky effect, or field-enhanced thermionic emission is a process
in electron emission devices where the emitter is biased negatively, creating an electric field at the
surface of the emitter. This field reduces the electron barrier and increases the emission current
of the emitter. This process is maintained in the head of the SEM under high vacuum ( 7 ∗ 10−10
Torr) even when the system is not in use to ensure a stable beam current.
After a series of magnetic lenses focus and guide the beam down through the column, the
beam arrives at the sample surface. The electrons interact with the resist to harden the areas
that are exposed so that they will remain after development. The sample chamber has a variable
pressure option, but since our samples are conducting, the high vacuum option is used to enhance
the resolution.

3.1.3

Ion-Mill and Thermal Evaporation

Ion milling is a subtractive process used to pattern the bottom lead of the sample into a series
of junctions. The schematic layout can be seen in figure 3.2. In general, ionized argon gas is
accelerated towards the sample. When the gas collides with the sample, it chips away at the sample
surface, removing a relatively constant amount of material each second. The chamber contains a
3-inch Commonwealth Scientific Argon Ion beam source, a gold sputtering gun, SiO for thermal
evaporation, a sample plate containing slots for five samples and the FTM, and a separation plate
33

Figure 3.2 Schematic view of the Ion Mill The dashed lines represent the ion-mill grid while the
solid bold lines represent the ion-mill housing. The accelerating, beam, and discharge voltages
are labeled Va ,Vb , and Vd respectively, and the neutralizer current is labeled Ie .
with one opening between the samples and the deposition sources.
After loading the samples into the chamber and waiting for the excess water and gas to pump
out, Argon gas is introduced into the chamber. Then, a voltage difference is applied between the
cathode and anode of 39 V. Also, a current is applied to the cathode filament to generate an electron
beam and ionize the argon gas. Above the cathode and anode are two carbon grids. The first grid
is a screen that collimates the beam and acts to avoid direct collisions between the ionized gas and
the second grid. The second grid is the accelerator. While most of the acceleration comes from the
+300 V beam voltage, the accelerator grid receives a negative voltage of about -30 V to enhance
the acceleration of the positively charged argon ions up towards the sample. Last, the beam passes
by the neutralizer filament which adds electrons to the beam and acts to reduce the repulsion of the
like-charged argon ions. Typical ion mill settings can be seen in Table 3.3 below.
These ions then collide with the sample surface. These collisions cause atoms from the sample
surface to be knocked off and deposited elsewhere in the chamber. The rate of material removal is
measured with an FTM that is coated in gold. The milling rates of all other materials relative to the

34

Beam Voltage (V)
Beam Current (mA)
Discharge Voltage (V)
Accelerator Voltage (V)
Neutralizer Current (mA)

Figure Label
Vb
Ib
Vd
Va
Ie

Small Chamber Ion Mill
300
∼ 9.0
39
-30
∼ 0.5 higher than Ie

Large Chamber Ion Mill
175
∼ 1.0
40
-50
∼0.5 higher than Ie

Table 3.3 Ion mill settings for the small and large milling chambers The beam current values
shown are starting values. They will drift upwards during the milling process but the milling rate
remains constant if they are not adjusted.
gold milling rate is called the k factor. These multiplicative factors are measured for each material
by milling each material and measuring the milled depth in the atomic force microscope. The gold
milling rate can only be measured before and after a sample is milled, but luckily, this rate is quite
stable through the milling of all samples in the chamber. These values are used to calculate the
milling time needed for each sample, then the user must manually open and close the separation
plate with the sample positioned above the ion mill for the correct amount of time. This process
mills through the desired amount of material to define the size and shape of the junction which will
be the same as the size and shape of the electron-beam resist above.
Following ion-milling, the sample is coated in SiO in situ to electrically isolate the junction.
This is done by thermal evaporation. The SiO granules are placed in one side of a baffle boat in the
ion-milling chamber. The boat is heated by the application of a current to the resistive boat, which
heats the SiO. When the SiO is sufficiently heated, it will begin to evaporate SiO molecules. These
will be released from the other side of the boat, where they will travel up towards the sample and
adhere to the sample surface. A magnetic arm holds the sample above the evaporating SiO, which
can be spun to obtain a more uniform material distribution. The FTM in the chamber is used to
determine the SiO deposition rate.

35

(a)

(b)

(c)

(d)

(e)

(f)
Leads

Junction

(g)

(h)

(i)

Figure 3.3 Schematic drawing of the sample fabrication process The vertical scale is greatly
magnified and relative material thicknesses are altered to better show the process steps. Color
code: purple = resist, blue = superconductor, red = ferromagnetic material, orange = normal
metal,yellow = gold, brown = SiO, arrows show ion-milling direction a) Bottom lead
photolithography on cleaned Si substrate b) Material deposition through sputtering c) Bottom lead
lift-off and electron-beam lithography for junction definition d) Vertical ion-milling to define
pillar dimensions e) SiO thermal evapotation to electrically isolate the junction f) Horizontal side
ion-mill to break through SiO side-wall build-up to reveal resist g) Electron-beam resist lift-off h)
Top lead photolithography and top lead deposition through sputtering i) Top down view of final
junction

36

3.2

Fabrication Process

A cartoon of the entire process flow can be seen in figure 3.3. Starting with a blank silicon chip,
photolithography defines the bottom lead pattern which is filled with sputtered material. Josephson
junctions are patterned with electron-beam lithography, defined with ion milling, and electrically
isolated with SiO thermal evaporation. After lift-off, a second round of photolithography defines
the top leads which are also sputter deposited. This process has seen several variations in the past
few years and I will make note of past variants for completeness.

3.2.1

Bottom Lead Photolithography

Fabrication is performed on half-inch square silicon chips with native oxide. These chips were
diced from a wafer while protected with photoresist, so the first step is to clean these substrates. It
is important to start with a clean substrate surface to ensure good adhesion between the substrate
and subsequent sputtered materials. To clean the chips, place each chip in a test tube with acetone,
and the test tube in a beaker of water on a hot-plate set to 100°C for about five minutes. Then,
move beaker to the ultrasonic for 5-10 minutes. After this, replace the acetone in the test-tubes
with IPA and wait two minutes. Then, rinse the chip with IPA over the waste beaker and blow dry
with the nitrogen blower.
Now take your clean chips over to the spin-coater. For ease of clean-up, wrap the bottom of
the coater in aluminum foil. Choose an appropriate sized chuck based on your sample size. The
chuck should be slightly smaller than the substrate chip. After you make sure the chuck and pipette
are clean, apply four to five drops of S1813 photoresist to the center of the chip and spin for 50
seconds at 5,000 RPM. Then, bake the chips on the vacuum hot-plate on the PR-VAC program
(110°C for 120 seconds). We used to use this program for only 60 seconds but increased the time
as the heating surface became less effective with age and use.
S1813 is a positive resist, meaning when it is exposed to UV light, the parts that are exposed
become weakened and will be removed from the chip during development. So, the photomasks

37

we design are primarily chrome with openings that define the bottom leads of the pattern. The
bottom lead is typically a long wire from which the pillars will be defined as well as alignment
marks to properly line up subsequent masks. Alignment of the chip with the bottom-lead mask
does not need to be precise. Once the chip is roughly aligned with the mask, bring the chip into
contact with the mask and expose for ten seconds. For small scale features, you want the contact
to be as close as possible. For single pillars the "smalloverlapGMR" mask is primarily used and
the "BIRGE SQUID TRIPLET" mask is used for asymmetric SQUID samples. These masks are
four-inch square and were designed at MSU for measurement at MSU, meaning they have large
pads for pressed In wire connections. This process is slightly different for the symmetric SQUID
samples and will be discussed in the next subsection.
After exposure, the chips are soaked in chlorobenzene for five minutes, agitating the sample
for the first 10 seconds and the last 30 seconds of this time period. This creates an artificial bi-layer
where the top of the resist is harder to remove then the bottom. After the chip is developed in 352
developer for 45 seconds and rinsed in DI water for 30 seconds, the pattern created will have an
undercut profile, as shown in part (a) of figure 3.3. This profile aids in separating the deposited
material from the resist for an easier lift-off process. Always check each sample in the microscope
after development to ensure that all mask features were properly copied to the chip.

3.2.1.1

Small Feature Size Variant

When MSU fabricates chips for measurement at Northrop Grumman, there are several variants to
the above outlined photolithography process to ensure that the small features are properly replicated on the chip. This technique is also used on MSU chips with many small features or long,
straight, thin lines that don’t develop properly in the above outlined process. The NGC mask design has a two-by-two array of half-centimeter NGC chips that fit on our standard half inch square
substrate with a small amount of extra space on the edges for handling the chip with tweezers. The
contact pads are all located around the edges of the chip so it is important not to damage those
regions. The four NGC chips have similar layouts with an identifying mark in the center to break
38

the symmetry.
The substrate cleaning process is the same as above. Next place the chips in the oven set to
100°C for at least 10 minutes to remove any water residue from the chip surface. In this time, cut
out a circle the same size as the largest sized wafer chuck from the blue semiconductor processing
tape. Place the tape sticky-side up on the largest wafer chuck and center the baked chip on the
chuck, lightly tapping down the corners of the chip with the tweezers. When the chuck spins, the
vacuum will hold down the tape and the sticky side of the tape will hold on the chip.
First, use the pipette to load up the chip with an unreasonable amount of HMSD primer. The
primer should completely cover the chip and spill down over the entire perimeter of the chip making a large mound. By using this process, the surface tension of the primer is broken and the
edge-bead effect, where the material builds up around the edges of the chip, is highly reduced.
Additionally, the HMDS primer increases the adhesion of the subsequent S1813 resist to the chip.
This is important for patterns with stand-alone long, thin lines which can otherwise detach from
the chip during development or become wavy or broken. Then, spin the chip at 5,000 RPM for 50
seconds. Immediately after, cover the chip with S1813 photoresist using the same surface tension
reducing method and spin again at 5,000 RPM for 50 seconds. Now, carefully peel the chip off of
the semiconductor tape and bake it on the programmable hot-plate for 2 minutes at 110°C (also the
PR-VAC program).
The 5-inch "Anacostia" mask is used for symmetric SQUIDs. The chip is aligned in the maskaligner the same way as above, but because the edge-bead is much smaller, it should be possible to
make better contact between the chip and the mask. Once contact has been made, expose the chip
for 6 seconds and develop in cholorobenzene for 5 minutes (same as above), then 352 developer
for 35 seconds, followed by a rinse in DI water for 20 seconds. Carefully check the chip in the
microscope to make sure that all the pads and wires developed properly. Since there are so many
small, important features, it is helpful to have the mask coated in Teflon by the manufacturer to
reduce residue build-up which can cause pattern distortion.

39

Chip

Holder
Bridge
Figure 3.4 Picture of Sputtering System Sample Holder The sample chip is placed face-down
into the holder and is held in place with a heat sink and bridge with screws. The dashed black line
through the center of the chip represents the orientation of the bottom leads on the front side of
the chip. They are aligned parallel to the bridge orientation.
3.2.2

Bottom Lead Material Deposition

Once the chips are developed, they are ready to be loaded into the sputtering system for material
deposition. To prepare the sputtering system, both the sample holders and gun parts must be
properly cleaned and assembled. Clean the sample holders and cover plates in a 3:1 mixture of
Nitric Acid and DI water for 30-60 minutes. Leaving the parts in this mixture longer than 60
minutes can damage the screw holes in the holder so avoid doing that. Rinse the parts in DI water
and scrub each piece with a wire brush to remove any metal depositions from previous sputtering
runs. Put the parts in the ultrasonic bath in a glass beaker of acetone, then ethanol, then DI water
for 5 minutes each. After this, lay the parts out on a large kimwipe and blow them dry with the
heat gun set between 900 and 950°F until the parts are hot and the paper underneath them begins
to toast. Allow the parts to cool and bring them to the clean room to load the samples.
Load the samples into the holders with the long axis of the bottom leads oriented parallel to
the bridge that holds the heat sink against the sample as shown in Figure 3.4. This reduces non-

40

uniformity in sputtered material from rotating onto or away from active sputter guns. If in-plane
magnetic material is being deposited, it is important to grow the material in a magnetic field by
placing a half-inch square magnet directly behind the sample substrate. Typically, the magnetic
field is oriented parallel to the long axis of the bottom leads. Then, cover the sample with a copper
heat-sink and affix it with a bridge and screws. Do not over-tighten the center screw that pushes
down on the sample as it can cause the sample to crack. Up to sixteen samples in eight sample
holders can be loaded into the sputtering system each run.
The sputtering system can support the use of up to four 2.25-inch-diameter triode sputtering
guns and up to three 1-inch-diameter magnetron sputtering guns, and an ion mill. For proper use,
scrape all the gun parts and target bases with a razor blade to remove any metal flakes that can
cause electrical shorts. Their slots in the chamber must be vacuumed out and blown with nitrogen
gas for the same reason. Once the large guns have been installed, it can save a lot of heartache to
check the resistance between the target and base to make sure they are not shorting. Lastly, install
the chimneys and shutter plate into the system. They must be wrapped in aluminum foil that is
changed between runs to avoid contamination.
Once all the guns and samples are in the system, pump down below 8x10−6 Torr then test the
guns. If the testing goes well, close the gate valve so that it is only open 10 turns, then set it to bake
for eight hours with the small gun water running on a low setting. After the system has cooled
back down to room temperature, open the gate valve completely and wait until the pressure has
decreased to about 3x10−8 Torr before starting the sputtering run.
When ready to begin the run, cool down the system so that the substrate plate remains around
-30 to -20°C. Turn on all the guns and wait for a stable plasma. Each gun must be run at a specific
current and voltage setting based on the material. A list of materials used in this thesis work
along with their run values can be found in Tables 3.1 and 3.2. Once set, the deposition rates of
each gun are measured with the FTM. From there, a run file is made which details the materials
and deposition amounts desired by the user. The automated system will then move the sample
through the sequence to make the proper material stack. Josephson junction bottom leads include

41

deposition of a base Nb electrode, all magnetic layers with normal metal spacers, and a cap of Nb
and Au. Depositing all these materials in situ ensures clean interfaces between the layers. Several
base superconducting electrodes and spacer layers have been used in this group over the past few
years. The various options that we tried out are detailed in Chapter 5. The current "best" stack uses
a base electrode of [Nb(25)/Al(2.4)]3 /Nb(20), a thin spacer layer of Cu(2) and a thick spacer
layer of Cu(4). We also use Nb(5) for the capping layer while previously Nb(20) was used so that
this cap would be superconducting on its own instead of only by proximity. Part (b) of Figure 3.3
shows a cross section of the chip after material deposition.
After sputtering is completed, bring the samples in their holders into the clean room for lift-off
of the bottom-lead photolithography. This is done by putting each chip in a labeled test tube of
acetone, each placed in a beaker of water on a hot plate that is set to 100°C. Wait until the material
deposited over the resist regions begins to wrinkle and start to peel up. This should take about five
to ten minutes. Then place the beaker into the ultrasonic until all the excess material and resist
has been removed from the sample surface, revealing just the material in the bottom lead pattern.
This should take several minutes or less. Rinse each chip in acetone, IPA, and DI water, being
careful not to allow the lifted off material to redeposit onto the sample surface. Finally blow dry
with the nitrogen blower and inspect in the microscope to ensure that all the bottom lead features
are present on the chip.

3.2.2.1

Tips and Tricks

After thousands of sputtering runs, a user sees many failure mechanisms and learns a few tips and
tricks in troubleshooting. A common issue is failure for a sequence file to open in the sputtering
program. This is more frequent when creating the sequence using the set-up program since, if not
entered perfectly on the first try, many hidden errors can occur. These errors include hidden spaces
both at the start and end of a command line, extra carriage returns, and merged command lines.
If writing the sequence file from scratch or modifying an existing file, be sure to check for typos
and proper capitalization of commands. Even if the sequence file is written properly, attempting
42

to load the sequence file will give the same unhelpful error message if there are not deposition
rates measured for all the materials used in the sequence file. The program calculates the sequence
timing upon opening the file and has obvious issue calculating a deposition time for a material with
a rate of 0, which is the default value upon opening the program.
If a gun has a very large current (> 0.7 A) at usual voltage values, it probably has a short. If the
short is from a flake, it is possible to burn the flake off by leaving the gun on at low voltage values
for several minutes. If that does not work, you must open the system to clean off the flake.
If the motors will not connect when the sputtering program starts up, reset the motor controller
box located behind the computer screen.
Always check that the shutter plate is tightly screwed down when closing the system. This
can be checked by using the program to open and close the shutter several times and making sure
the positioning over the guns does not change. Also check this positioning after testing the guns
during the actual run.

3.2.3

Pillar Definition

Now that the bottom leads have been deposited, they must be shaped into a series of junctions.
This is done by patterning the desired junction shape onto the bottom lead using electron-beam
lithography, then milling away the unwanted material with a vertical ion mill, and electrically
isolating the junctions with a blanket SiO deposition. The SiO can block the electron-beam resist
removal, so a horizontal side-ion-mill is used to break through to the resist before lift-off. These
steps are shown in sections (c)-(g) of figure 3.3.

3.2.3.1

Electron-Beam Lithography

Pillar definition of the bottom lead is done by electron-beam lithography. First, the chip must be
coated in an appropriate electron-beam resist. We use the negative tone resist ma-N 2401. Spin
the resist onto the chip at 3,000 RPM for 40 seconds to produce a 100 nm layer on the chip. The

43

resist is very thin compared to the S1813 photoresist so only 2-3 drops are needed to completely
cover the chip. Then, bake the chip on the small hot plate in the fume hood for 120 seconds at 90
°C. Place the chip directly on the ceramic plate for the best heat exchange. After baking, the chip
should look blue in color.
Now, load the chips and stigmation sample into the SEM for writing. As mentioned above,
much of this work used a JEOL 840A SEM for writing, but since all future group members will
use the new Hitachi SU5000 SEM, I will focus on the use of this system. After logging into the
Hitachi system and opening the SEM software, choose the electron-beam lithography option and
vent the system. Choose a sample holder based on the number of samples you would like to load
at a time. The current maximum is a double-sided tray which can hold a total of eight half-inch
square chips. Enter the sample holder size and sample height into the SEM software. The doublesided tray size is not built into the software, so choose the 51 mm circular holder for the closest
size approximation. Our samples are also usually so flat that they measure less than 0 mm above
the height baseline. In this case, enter the height as 0 mm. You will then have the option to take a
picture of your samples in the holder with the external camera. This is helpful for quick movement
from chip to chip and keeping track of which samples you have already written when writing many
chips at a time.
When the main chamber is vented, pull the door open as far back as possible. Then, the ’move
stage’ button will become active. Pressing this button will raise the sample stage based on the
sample height you entered into the software. If you can close the door without your sample hitting
the height guard, then your sample will not be in the way of any microscope elements inside
the chamber. If your sample would hit the height guard, adjust the sample height setting in the
software.
After closing the door, click the button to evacuate the system on high-vacuum mode. Lowvacuum mode can be used for non-conducting samples, but gives worse image resolution. While
the system pumps down, open the NPGS software and prepare the pattern write files if needed.
This new SEM has been calibrated to write pillars with an area dose of 550 µC/cm2 and line-

44

based features, such as the stigmation pinwheels, with a line dose of 2.5 nC/cm. These values
should be reflected in the run file, as well as the beam current of 68 pA.
Now, turn on the beam with the default settings of spot size 1 and intensity 30. Move the field
of view to the stigmation sample and bring the center of the chip into focus. It is very important
to then change the z-height in order to obtain the desired working distance of 15 mm. The current
working distance is stamped on the bottom of the SEM image on the screen. Increasing the zheight will proportionally increase the working distance. When the image is perfectly in focus, the
working distance should read 15 mm. This must be done before stigmation or beam alignment as
the working distance has an effect on these properties.
Any small feature on the stigmation sample can be used for stigmation. Zoom in on the small
feature to about 200,000x magnification or more and quickly blur the feature in and out of focus.
If the beam is properly stigmated, you will see a the feature blur uniformly in all directions as the
focus is changed. Improper stigmation will lead to the feature stretching along a preferred axis as
the focus is changed. To correct this, adjust the two stigmation knobs while the feature is in focus.
The image will look sharper with more distinct features when the stigmation knobs are closer to
the ideal settings, so cycle through adjusting the focus and both stigmation knobs until the image
is as clear as possible and the feature blurs uniformly when the focus is changed.
Next, adjust the beam alignment by pressing the alignment button and working through several
phases of alignment. In each case, use the alignment knobs, which are the same ones previously
used for stigmation, to reduce the shaking of the image on the screen. It is easier to start this task
at low magnification and work your way higher if the alignment begins far off.
After stigmation and beam alignment, move to the first chip for pillar writing. Before writing
each chip, make sure that the chip is aligned vertically on the screen without any tilt. The tilt tool
can be used to draw a line along a known vertical surface, such as the edge of the bottom lead or
contact pad, and the software will automatically match that tilt. Then, move to the first write area
and focus on one of the outer alignment crosses. Typically, an extra feature can be found at the
inner corners of the crosses, which make an excellent feature to focus on. Focusing at 30,000x

45

magnification or greater is preferred. Then, zoom into the write area and center the inner L-shaped
alignment marks on the screen. Do not zoom to a magnification higher than 1000x or image the
write area for longer than needed as the electron-beam used to image can begin to develop the
resist in that area and lead to improper feature size after development. After centering, reduce the
magnification to 200x.
Switch the SEM to EBL mode in the NPGS software and run the alignment file. The alignment
mini-game consists of matching up the outlined alignment pattern with the scan of the chip, which
will show a similar pattern if the centering was done correctly. The outer alignment crosses are
aligned at a magnification of 200x and the inner alignment L’s are aligned at an increased magnification of 1000x. After alignment is complete, select the desired run file and run with alignment.
This will write the DesignCAD pattern from the run file onto the chip using the previous alignment
to determine where the center of the pattern should be placed on the chip. Continue to focus, align,
and write the pattern at each write area on the chip. It can be helpful to keep a list of write areas to
check off as they are completed if a large number will be written. Since the films are grown in field
pointing parallel to the bottom lead, ellipses tend to be written with the long axis of the ellipse
parallel to the bottom lead as well, so that this long axis is also the easy axis for any magnetic
layers.
Once all chips are written, shut off the beam and vent the sample chamber. Then, develop the
chips by wafting in AZ 300 MIF for 30 seconds followed by DI water for 20 seconds, and blowing
dry with the nitrogen gun. The ma-N is a single layer of resist so it will not have an undercut
profile. In fact, the resist profile has the opposite effect with broadening at the base of the resist.
This, as well as the fact that the resist hardens with heating, can cause the ma-N to be difficult to
remove in the later lift-off step.
Figure 3.5 shows two write areas on the same chip after development of the ma-N electron beam
resist. The right image shows a pinwheel with the proper circular shape and equal line weights,
indicating good focus and stigmation. Since the stigmation is set once while setting up the SEM
writing, all chips written in that batch should also have proper stigmation. As the pinwheel on the

46

Figure 3.5 SEM image of patterned ma-N resist These SEM images show the ma-N resist
patterned into the junction shape after electron-beam lithography and development. The small
ellipse centered on the vertical bottom lead is the ma-N pillar. The pinwheel marker can be seen
touching the lower left L shaped alignment mark. The left image shows a poorly formed pinwheel
while the right image shows a properly formed pinwheel. Only the overlap areas of the pinwheel
developed in the left image, indicating that the focus was off. The circular shape and equally
weighted lines in the right image indicate proper focus and stigmation.
left shows, if the focus is off, only the overlap regions of the pinwheel shape will develop. Since
the resist pillars are very small and difficult to see well in the optical microscope, the quality of the
pinwheel gives confidence in the focus and stigmation of the SEM, and hence size and shape of
the resist pillar.

3.2.3.2

Ion Milling and SiO Deposition

Next, the junction is defined by ion milling. To begin, place the chip in a vertical ion mill holder.
The face of the ion mill holder has a square opening to fit the 1/2 inch square chips with a smaller
circular opening through which the mill reaches the sample. Only the junctions need to be milled,
and they are clustered in the center of the chip, so, place a metal mask with a smaller 5 mm by 5
mm square opening in front of the chip to block the rest of the bottom leads from milling and SiO
deposition. Next, place a copper heat-sink behind the chip with silver paste in between. You should

47

Figure 3.6 Vertical ion mill holders The left image shows the individual ion mill holder parts.
The lower right corner is the holder face, and going clockwise are the metal mask, copper
heat-sink, and magnetic piece. The right image shows a fully assembled holder showcasing the
gap desired between the mask face and the copper heat sink.
see a gap between the holder face and the heat-sink indicating that the sink is in good contact with
the chip. This is especially important since heating of the ma-N resist makes it more difficult to
remove. Lastly, place a magnetic piece behind the heat sink and screw the three pieces together.
Make sure that the screws are not so long as to protrude out the back of the holder. The parts of the
ion mill holder and the desired gap between the holder face and heat-sink are shown in Figure 3.6.
Five samples can be loaded into the ion mill at one time. After loading the samples, wait for
the pressure in the chamber to drop below 3 ∗ 10− 8 torr before beginning the milling process.
The amount of material to be milled from the sample must first be converted into the equivalent
thickness of Au since that is the only milling rate that can be measured in the chamber. Do this by
adding up each material’s thickness multiplied by the k factor, which converts a material’s milling
rate to that of Au. These k factors are all determined experimentally. Then, calculate the milling
time by dividing the effective Au thickness by the measured Au milling rate in the chamber. To
reduce heating of the ma-N, milling processes that take more than three minutes are split into 2-3
minute sections. Run the mill with the settings specified in Table 3.3 for the small chamber. The

48

beam current value will drift with time, but the rate remains stable if you do not correct for this
drift. The cathode current will start around 5 mA when the filaments are freshly changed, and will
decrease with use until it eventually breaks. It would be a good idea to preemptively change the
filaments when the cathode current drops below 3 mA. The ma-N resist mills at a much slower rate
than the bottom lead material, so after milling is complete, the whole bottom lead that was exposed
has been milled down to the desired layer and the whole stack remains under the ma-N mimicking
its shape and size as seen in part (d) of Figure 3.3.
After milling, wait until the wall of the chamber is cool to the touch before moving on to
deposit the SiO. This will be used to electrically isolate the top and bottom leads as well as the
edges of the pillar. It is important to turn up the voltage on the SiO boat slowly to increase chances
of a stable deposition rate. 50 nm of SiO are deposited on each sample. The SiO deposition rate
is measured by the FTM in the chamber and the desired SiO thickness is divided by this value to
obtain the SiO deposition time required. During deposition, spin the sample with the chamber’s
magnetic arm to increase the uniformity of the layer and reduce the chance of pin-holes through
the SiO. If the correct thickness was deposited, the SiO should look a maroon/brown color.
The SiO deposition is somewhat collimated and forms a uniform layer on top of the milled
samples surfaces and the ma-N resist. Because of the sloped sidewall of the ma-N, it is possible
for the SiO on the sample surface to creep up the sides of the pillar and connect to the SiO on top
of the resist, forming a complete blanket on top of the chip. This is shown in part (e) of figure 3.3.
This would make lift-off impossible, so an additional side-mill step is needed.

3.2.3.3

Side-Milling and Pillar Lift-off

To break through the sidewall build-up, a side-mill is performed. Since the mill direction can’t
be changed in our chamber, place the sample in a holder that rotates it 87 °relative to the vertical
ion-mill holder, so that the pillar is sticking out horizontally from the substrate and rotated 3 °down
towards the ion mill. Perform a two minute mill on two sides of the pillar to break through the
SiO sidewall and allow a gap for remover to affect the ma-N resist. Choose the two short edges
49

Figure 3.7 SEM image comparison of write area before and after the lift-off process The left
hand image shows the sample before lift-off and the right hand image shows the sample after
lift-off.
of the pillars to prevent the edges of the bottom leads from poking through and shorting to the
subsequently sputtered top lead. This step is depicted in part (f) of figure 3.3.
Now, it is theoretically possible to lift-off the ma-N resist with its SiO cap to reveal a top
contact for the junction below. It can be difficult to tell if the junction has lifted off with just the
optical microscope. The best method is to directly compare the coloration of the pillar before and
after the lift-off process. The microscope current and voltage settings and picture exposure time
must remain the same in the before and after pictures for an accurate comparison.
After imaging the junctions, place each chip in a small beaker of Remover PG on a hot plate
set to 110 °C. Let the chip sit in the remover for 10 minutes, then gently scrub the junction region
of the chip with a q-tip from all angles and cover the beaker with an aluminum foil cap to better
hold in the heat of the hot plate. Let the chips sit on the hot plate for an additional 30 minutes, then
waft in DI water for 30 seconds and blow dry with the nitrogen blower. Image the junctions again
in the optical microscope and compare with the before pictures. It should be very obvious that the
L shaped inner alignment marks have lifted off and the junctions should look brighter in color. An
example of a set of two junctions before and after lift-off can be seen in figure 3.7. A cartoon of
successful liftoff is shown in part (g) of figure 3.3. If all junctions do not look lifted off, repeat the

50

whole lift-off process. Successful lift-off has taken as many as three full iterations of the process,
but usually works on the first try when the samples were properly heat sunk in the ion milling and
SiO deposition step.
Previous variants of this lift-off process included more vigorous scrubbing and 30 minutes in
the ultrasonic after being on the hot plate. These steps were found to be unnecessary after the
above heat sinking process was implemented. Previously, heat sinking was done with Santovac oil
instead of the silver paste and it was not required to have a gap between the holder face and the
heat sink. Either the Santovac oil or silver paste is probably a fine heat-sinking aid, but I prefer to
use the silver paste since the Santovac oil can squish around to the front side of the chip and cause
problems if too much is applied. The silver paste has more tolerance in the amount that can be
used since it is thicker. The ma-N sometimes became so difficult to remove that the ultrasonic and
q-tip scrubbing would remove the bottom leads from the substrate before the ma-N would lift off.
The heat-sinking method above has a higher success rate, but it would be preferable in the future
to have a process that does not require a side-mill step or q-tip assisted lift-off.

3.2.4

Top Lead Photolithography and Material Deposition

The last step in the fabrication process is to deposit the top lead superconductor material. First,
oxygen plasma etch the chips to clean the surface of any residual ma-N. Clean the system by
running at the resist stripping setting of 300 W and 500 mTorr for five minutes. Then, clean the
chips in the system at the residual resist clearing setting of 100 W and 500 mTorr for 90 seconds.
The top lead photolithography is very similar to the bottom lead process described in section
3.2.1. Spin and bake the S1813 resist in the same way. Now, however, the alignment process
is more involved since the 4 µm wide horizontal top lead must fully overlap the junction on the
vertical bottom lead as shown in part (i) of figure 3.3. To aid in this more complicated alignment
process, vernier alignment marks were implemented. The base set is included on the bottom lead
mask, and they can be lined up with the outline on the top lead mask. The single pillar and SQUID
masks use these same vernier alignment marks in three sizes. The alignment marks look like
51

fingers that become successively more spread out as they get farther from the center so that the
white space between the marks on the chip and on the mask increase farther from the center of
the marks. Several sets of these marks are stamped across the chip to more accurately align the
position and rotation of the chip relative to the top lead mask. After alignment, the exposure and
development process are the same as section 3.2.1.
In order to ensure a clean interface, oxygen plasma etch the developed chips again with the
same process described above. Then, load the samples into cleaned sputtering holders and place
them in the sputtering system. Bake the system for eight hours. The top leads require a less
stringent starting pressure of only 6 ∗ 10−8 Torr so they can usually be sputtered the day after
baking without requiring an additional full day of pumping.
As an extra precaution for a clean interface, first ion mill 2 nm of Au from the surface of the
chip. Run the mill at the large chamber settings from Table 3.3. Then, immediately sputter the
top lead of 150 nm Nb and a capping layer of 10 nm Au to prevent oxidation. In the past, all
samples were ion milled first, then all received the 150 nm Nb and 10 nm Au. This left the samples
sitting around in the chamber for quite a while between being milled and having the Nb deposited,
possibly leading to a less reliable interface.
After sputtering, the S1813 resist is lifted off in the same way as section 3.2.2. Now, fabrication
is complete, and it’s time to hope and pray that the samples are measurable.

3.2.4.1

Small Feature Size Variant

Patterns with small feature sizes use the same bilayer resist spinning method, and exposure and
development times as the bottom leads in section 3.2.2.1. As in the above top lead instructions,
the small feature top lead patterns will also have a more involved alignment process with vernier
alignment marks.

52

CHAPTER 4
NON-MAGNETIC MATERIAL OPTIMIZATION

The quality of data obtained from Josephson junctions depends on how the magnetic layers behave,
but all the layers and interfaces in the junction stack can affect these magnetic properties. In this
chapter, I will detail the characterization and optimization of the junctions’ base superconducting
electrode and normal metal spacer layers using Atomic Force Microscopy (AFM) to analyze surface roughness and SQUID Magnetometry to analyze the switching properties of a NiFe magnetic
layer grown between different spacers.

4.1

Base Superconducting Electrode

The Birge group has been concerned about the surface roughness of the base superconducting
electrode since before I joined the group. Any roughness introduced in this layer will be transmitted
to the whole stack, which adversely affects the magnetic layers, especially as they become thin.
The most common base layer for standard junction use was 150 nm of Nb. A previous student, Dr.
Yixing Wang, worked to improve the roughness of this layer by introducing thin Al spacers within
the Nb stack. He studied a base electrode with the structure [Nb(40)/Al(2.4)]3 /Nb(40), which he
found to have a surface roughness of 2.3 Å compared to 5.3 Å found for Nb(150) [82, 72, 78].
To further characterize the multilayer base electrodes, I grew several new multilayer stacks
and measured their surface roughness with AFM. The films were created by blanket sputtering
on a cleaned Si chip with no post-processing. The nine sample stacks measured were Nb(150),
Nb(100), [Nb(40)/Al(2.4)]3 /Nb(20)/Au(5), [Nb(25)/Al(2.4)]3 /Nb(20), [Nb(25)/Al(2.4)]4 /Nb(20),
[Nb(40)/Au(2.4)]3 /Nb(20)/Au(5), [Nb(25)/Au(2.4)]3 /Nb(20), [Nb(25)/Au(2.4)]4 /Nb(20), and
[Nb(40)/Ru(2.4)]3 /Nb(20)/Au(5). Figure 4.1 shows a representative AFM image of each sample type and Table 4.1 below summarizes the surface roughness results.
This study found [Nb(25)/Al(2.4)]3 /Nb(20) to be the smoothest layer for use in Josephson junc-

53

Nb(150)

Nb(100)

[Nb(40)/Ru]3

(a)

(b)

(c)

[Nb(25)/Al]4

[Nb(25)/Al]3

[Nb(40)/Al]3

(d)

(e)

(f)

[Nb(25)/Au]4

[Nb(25)/Au]3

[Nb(40)/Au]3

(g)

(h)

(i)

Figure 4.1 AFM surface roughness comparison for nine base superconducting base layers
All the AFM scans use the same scale bar shown on the right and are 1 µm by 1 µm in size. The
material stacks are (a) Nb(150), (b) Nb(100), (c) [Nb(40)/Ru(2.4)]3 /Nb(20)/Au(5), (d)
[Nb(25)/Al(2.4)]4 /Nb(20), (e) [Nb(25)/Al(2.4)]3 /Nb(20), (f) [Nb(40)/Al(2.4)]3 /Nb(20)/Au(5), (g)
[Nb(25)/Au(2.4)]4 /Nb(20), (h) [Nb(25)/Au(2.4)]3 /Nb(20), and (i)
[Nb(40)/Au(2.4)]3 /Nb(20)/Au(5).

54

Material Stack
[Nb(25)/Al(2.4)]3 /Nb(20)
[Nb(25)/Al(2.4)]4 /Nb(20)
[Nb(25)/Au(2.4)]3 /Nb(20)
[Nb(25)/Au(2.4)]4 /Nb(20)
[Nb(40)/Al(2.4)]3 /Nb(20)/Au(5)
Nb(100)
[Nb(40)/Au(2.4)]3 /Nb(20)/Au(5)
[Nb(40)/Ru(2.4)]3 /Nb(20)/Au(5)
Nb(150)

RMS Roughness (Å)
2.3
2.5
3.2
3.4
3.6
4.0
4.1
4.3
8.3

Figure Part
(e)
(d)
(h)
(g)
(f)
(b)
(i)
(c)
(a)

Table 4.1 RMS roughness values for superconducting base layers The table shows AFM
surface roughness values for the nine superconducting base layers listed in order of increasing
roughness. [Nb(25)/Al(2.4)]3 /Nb(20) has the smoothest surface with 2.3 Å of RMS roughness.
tions, showing about a 3.6 times reduction in RMS roughness compared to the standard Nb(150).
[Nb(25)/Au(2.4)]3 /Nb(20) would also be a good choice if the samples require more guns and there
is not room for the Al gun in the sputtering chamber. The frequency of the roughness is also important for the growth of subsequent magnetic layers. Ideally, we would like to have low frequency
roughness, but these nine base electrode options have little variation in the roughness frequency.
Plain Nb has a rice grain structure, while introducing the Al layers seems to round them out and
produce smaller grains. All the stacks with Nb(40) showed significantly increased roughness from
their Nb(25) counterparts, but it is also possible that the Au capping layer is playing a part. Going
from 3 to 4 repeats of the Nb(25)/Al(2.4) stack only affects the RMS roughness by a small fraction
of an angstrom. If thicker bottom leads were needed, attempting a larger number of these repeats
could provide a smoother solution. Judging by the highly improved RMS roughness of these layers
compared to Nb(150), all junctions made with sensitive magnetic layers should use one of those
smoother base electrodes.
An increased roughness was measured in the [Nb(40)/Al(2.4)]3 /Nb(20)/Au(5) compared to Dr.
Wang’s previous results. This could be due to the Au capping layer or just different AFM tip
morphology or instrument settings. The roughness of Nb(150) was also measured to be larger than
Dr. Wang’s.

55

Figure 4.2 TEM image of spin-valve Josephson junction with X-ray elemental analysis This
sample had the structure
Nb(40)/Al(2.4)]3 /Nb(20)/Cu(5)/NiFe(1.5)/Cu(10)/Ni(1.2)/Cu(5)/Nb(20)/Au(15)/Nb(150)/Au(10).
In the elemental analysis, red shows Nb, green shows Al, magenta shows Ni and NiFe, and yellow
shows Au. This analysis shows that the layers are well defined. These images were collected by
Nancy Missert and Paul Kotula at Sandia National Laboratory.
Our group was fortunate to be able to send several samples to Sandia National Laboratory to be
measured in their TEM to see sample cross-sections with elemental analysis. One of their images,
collected by Nancy Missert and Paul Kotula, is shown in Figure 4.2. The sample structure was
Nb(40)/Al(2.4)]3 /Nb(20)/Cu(5)/NiFe(1.5)/Cu(10)/Ni(1.2)/Cu(5)/Nb(20)/Au(15)/Nb(150)/Au(10).
In the elemental analysis, red shows Nb, green shows Al, blue shows Cu, magenta shows Ni and
NiFe, and yellow shows Au. From this scan, we saw that our Nb/Al multilayer is indeed quite
smooth and provides an ideal template for magnetic material growth. However, comparing the
roughness of the two magnetic layers, even over this short distance scale, it is clear that the upper
magnetic layer has increased roughness and lateral variation. This is likely due to the spacer and
buffer layers of Cu(10) and Cu(5), respectively. In the next section, I will discuss our work to
optimize the properties of these layers.

56

a)

b)
Mrem

Mrem

Figure 4.3 Easy and Hard Axis Moment vs Applied Field Plots Moment vs Field plots for a) an
ideal permanent magnet with the applied field aligned along either the easy or hard axis and b) a
typical real material. Msat represents the total or saturation magnetization of the material, Mrem is
the remanent magnetization that is left at zero applied field, and Hc is the coercive field or the
amount of field required to return the material’s magnetization to zero after being saturated.

4.2

Normal Metal Buffer and Spacer Layers

The TEM images in figure 4.2 opened our eyes to the detrimental effect that our Cu spacer and
buffer layers could have on the magnetics of a Josephson junction. It became obvious that we
needed to characterize our normal metal layers and compare with some alternatives. This comparison was done by measuring the switching properties of a 1.5 nm NiFe layer surrounded by
the various test spacer and buffer layers. Our general interest in NiFe will be discussed in the
next chapter. Here we focus on the infered properties of the normal metal materials determined by
changes in the switching properties of the NiFe. These switching properties were measured using a
SQUID magnetometer to plot the Magnetization vs Applied Field of the samples. At high applied
field values, the sample’s magnetization will be fully saturated in the direction of the applied field.
The direction that requires the least amount of applied field to saturate the magnetization is called
the easy axis of the material. This is the energetically favorable direction for the magnetization to
point. Typically perpendicular to this axis is the hard axis, which requires the most applied field
to saturate. In single-crystal ferromagnets, there will be well defined easy and hard axes that point
along certain crystallographic axes of the ferromagnet. The samples grown in this work are all
57

polycrystalline, so this magneto-crystalline anisotroly is washed out. In order to induce an easy
and hard axis in polycrystalline films, they can be grown in the presence of an external field, which
induces the easy axis parallel to the field direction. The expected response of the material’s magnetization will be different when an applied field is oriented along the easy or hard axis, as depicted
in Figure 4.3a. This ideal easy axis response has Mrem = Msat and perfect squareness. The values
of Hc will determine if the material is hard (high Hc ) or soft (low Hc ). A typical material, such as is
shown in Figure 4.3b, will have Mrem < Msat and lower squareness characterized by the material’s
magnetization switching over a range of fields surrounding Hc [71, 42].
Magnetization vs Applied Field plots were measured using SQUID magnetometry to compare
the effect on the NiFe switching field, squareness, and saturation magnetization when surrounded
by different normal metal materials. We tested the thin buffer layers Cu(2), Ru(2), and Cu(5),
and thick spacer layers of Cu(10), Ru(2)/Al(7)/Ru(2), and Cu(2)/Al(6)/Cu(2). The additional layers were chosen based on those being used by our collaborators at Arizona State University and
Northrop Grumman. All of the SQUID magnetometry measurements in this chapter were taken at
a temperature of 10 K.
These samples were sputtered as a blanket film over the whole Si chip. The sample structure
was [Nb(25)/Al(2.4)]3 /Nb(20)/Spacer/NiFe(1.5)/Spacer/Nb(5). The full base electrode was used
to simulate the structure of a real Josephson junction. A magnet was placed behind the sample
during deposition to create an easy axis in the NiFe switching along the field direction. The chips
were snapped in half along the easy axis and both halves were loaded into the measurement straw,
so the sample areas should be approximately the same for all samples. All measurements were
performed with the field oriented along the easy axis and at 10 K.
Figure 4.4 shows the comparison of the three thin buffer layers. Both alternative buffer layers
to the Cu(5) that has historically been used improved the magnetic properties of the NiFe, but the
Cu(2) buffer gave the NiFe the lowest switching field and the most squareness. Figure 4.5 shows a
similar comparison of the three thick spacer layers. Again, both alternatives to the conventionally
used Cu(10) spacer improved the NiFe’s magnetic properties. In fact, the multilayer spacers have

58

-4

2.0x10

Moment (emu)

-4

1.0x10

0.0

-4

-1.0x10

Ru(2)
Cu(2)
Cu(5)

-4

-2.0x10

-10

-5

0

5

10

Field (Oe)

Figure 4.4 Moment vs Field measurement for thin spacer (buffer) layers The samples consist
of NiFe(1.5) sandwiched by either Cu(2), Ru(2) or Cu(5). Based on this data, Cu(2) has the
lowest NiFe switching field and loop squareness.

-4

Moment (emu)

2.0x10

-4

1.0x10

0.0

-4

-1.0x10

-4

-2.0x10

-10

-5

0

5

10

Field (Oe)
Ru(2)/Al(7)/Ru(2)

Cu(10)

Cu(2)/Al(6)/Cu(2)

Figure 4.5 Moment vs Field measurement for thick spacer layers The samples consist of
NiFe(1.5) sandwiched by either Cu(10), Ru(2)/Al(7)/Ru(2) or Cu(2)/Al(6)/Cu(2). Based on this
data, both multilayer samples show highly reduced NiFe switching fields and improved
squareness over Cu(10).

59

similar properties to the Cu(2) despite being 5 times thicker. In both spacers with Ru, the total
moment was reduced in comparison with the Cu spacers. This suggests an increased dead layer at
the Ru/NiFe interface.
The table below shows the coercive field for the six spacer layers. Based on these results,
we planned to use Cu(2) as the buffer layer and Cu(2)/Al(6)/Cu(2) as the spacer layer in future
Josephson junction studies to improve the magnetic layer quality. However, as you will see in
later chapters, devices fabricated with this spacer, as well as the Ru(2)/Al(7)/Ru(2) spacer, showed
highly reduced critical current values. The effect was so large that we decided to explore other
spacer layer options of thinner Cu.
Spacer or Buffer
Cu(2)/Al(6)/Cu(2)
Ru(2)/Al(7)/Ru(2)
Cu(2)
Ru(2)
Cu(5)
Cu(10)

Coercive Field (Oe)
1.0
1.2
1.5
2.2
3
5

Table 4.2 Coercive field values for six buffer and spacer layers

The spacer layer is used to magnetically decouple the two ferromagnetic layers in the Josephson
junction. We are interested in pursuing thinner spacer layers to improve the surface roughness of
the spacer and subsequent magnetic layer, but if it is too thin, the magnetic layers in one device
will couple and we will not be able to independently switch the magnetization directions of the
individual layers. So, to fully test the effect of a spacer layer on the stack, a spin-valve structure
was needed.
The samples had the form [Nb(25)/Al(2.4)]3 /Nb(20)/Buffer1/NiFe(1.5)/Spacer/Ni(2)/ Buffer2/
Nb(5). Buffer1 was either Cu(2) or Ru(2), Spacer was Cu(2), Cu(3), Cu(4), or Cu(5), and Buffer2
was always Cu(2). The full Nb/Al base electrode was used to recreate real Josephson junction
conditions as far as roughness is concerned. The samples were sputtered as a blanket film on the
Si chips with magnets on the backs of the sample during growth. No post-processing was per-

60

-5

-5

4.0x10

-5

2.0x10

4.0x10

-5

Moment (emu)

Moment (emu)

2.0x10

0.0

Cu(2)

-5

-2.0x10

0.0

Cu(2)

-5

-2.0x10

Cu(3)

Cu(3)

Cu(4)

Cu(4)

Cu(5)

Cu(5)

-5

-5

-4.0x10

-600

-4.0x10
-400

-200

0

200

400

600

-30

-20

-10

Field (Oe)

0

10

20

30

Field (Oe)
-5

4.0x10

-5

4.0x10

Cu(2)
Cu(3)

2.0x10
Moment (emu)

2.0x10
Moment (emu)

Cu(4)

-5

-5

0.0

Cu(2)

-5

-2.0x10

Cu(3)

Cu(5)

0.0

-5

-2.0x10

Cu(4)
Cu(5)
-5

-4.0x10

-600

-5

-400

-200

0

200

400

600

Field (Oe)

-4.0x10

-40

-30

-20

-10

0

10

20

Field (Oe)

Figure 4.6 Moment vs Field measurement for spin-valves with either Cu or Ru buffer layers
Moment vs Field measurement for spin-valves with either Cu(2) (upper plots) or Ru(2) (lower
plots) as the bottom buffer layer and between 2 and 5 nm Cu for the central spacer layer. The
magnetic layers are NiFe(1.5) and Ni(2). All plots show major loop data of both magnetic layers
switching. The plots on the right side are zoomed in on the x-axis to show the NiFe switching.
Ignore the horizontal shift of the data in the lower plot. This is an artifact of the measurement
system.
formed. The samples were sent to Arizona State University where our collaborators measured
Moment vs Applied Field loops both in the hard and easy axis directions. Our chips were diced
to fit in their system and all chips were diced to the same size, so the total area should be comparable. The spin-valves were measured both along the easy and hard axis, though there was
almost negligible difference between these two loops in all samples except for the sample with
Cu(2)/NiFe(1/5)/Cu(2)/Ni(2)/Cu(2).
Figure 4.6 shows the results of these measurements. The upper plots have the Cu(2) bottom
buffer layer and the lower plots have the Ru(2) bottom buffer layer. The different colors in the plot

61

represent the four Cu spacer layers at 2, 3, 4, and 5 nm. Both plots on the left side show the major
loop of both the NiFe and Ni switching. All spacer thicknesses showed distinct switching between
the two magnetic layers, indicating that they are not coupled. The NiFe was soft and switched at
low field while the Ni switched slowly over a large field range from about 200 Oe to 500 Oe in
both directions. Ignore the overall slope of the saturation magnetization; that is an artifact of the
measurement apparatus. This slope could be subtracted, but we are not interested in a quantitative
analysis of the Ni switching as real devices will operate at low fields that will (hopefully) not affect
the Ni layer. Qualitatively, the Ni switching appears very similar as the spacer layer thickness is
changed.
Both plots on the right-hand side of figure 4.6 are zoomed-in to the low-field region of the
same major loop that is shown on the left. They are plotted over the same total field range for
direct comparison. While the Cu(2) buffer layer samples show slightly lower switching fields of
the NiFe, the samples with the Ru(2) buffer have increased squareness and a smaller switching
field range. Unlike the previous results, a decreased saturation magnetization is not seen in the
Ru(2) buffer layer samples. Later Josephson junction results revealed that even just one Ru buffer
layer, like in the structure here, has a large negative effect on the critical current of the sample.
So although the sharper switching of the NiFe is desirable, most future devices will rely on a Cu
buffer layer. From the samples with a Cu buffer, the optimal spacer layer thickness was chosen to
be 4 nm of Cu. Cu(2) was not a good choice due to it’s poor squareness and Cu(3), Cu(4), and
Cu(5) showed very similar behavior, so Cu(4) was chosen to be sufficiently far in thickness from
Cu(2). So, to optimize magnetic layer switching properties and critical current yield, we chose to
use the buffer layer Cu(2) and spacer layer Cu(4).

62

CHAPTER 5
MAGNETIC MATERIAL CHARACTERIZATION

The simplest phase-controllable memory device for JMRAM needs two magnetic layers, one free
and one fixed. The free layer should switch magnetization directions over a small field range and
require low switching fields. The fixed layer should be magnetically harder than the free layer and
experience little to no magnetic change at fields that would switch the free layer. The point is for
this layer not to switch magnetization directions, so it’s switching characteristics are not particularly important, but a relatively low initialization field is desirable. In this chapter, I will detail
SQUID magnetometry characterization measurements of free layer material NiFe and fixed layer
candidates NiFeCo, NiFe/FeMn (NiFe pinned with FeMn), and Ni. All these measurements were
performed on samples grown in our sputtering system and measured in the same SQUID magnetometer at a temperature of 10 K. Proper credit is given when samples were not grown/measured
by me.

5.1

NiFe

NiFe, known also as permalloy when in 80/20 ratio Ni to Fe, has long been used in the electronics
industry. It is desirable as a free layer because of its low coercivity and near zero magnetostriction.
It is currently used in commercial MRAM, on which this superconducting analog is loosely based.
Though our group has a permalloy target, the sputtered films show a Ni to Fe ratio of 84/16.
The one drawback of this material is its large magnetization. We have measured this value
to be on the order of 800 kA/m for bulk films. If all other forms of anisotropy are controlled,
the required switching field should be directly proportional to the material’s magnetization. The
group has investigated other free layer materials with lower magnetization values such as NiFeMo,
NiFeNb, NiFeCu, and PdFe, but despite the lower magnetization, many of these materials did
not show improved switching characteristics when compared to NiFe, while others require more

63

-5

-6

8.0x10
Moment (emu)

Moment (emu)

2.0x10

-5

1.5x10

-5

1.0x10

-6

5.0x10

0.0
-6

-6

6.0x10

-6

4.0x10

-6

2.0x10

0.0
-6

-5.0x10

-2.0x10

-5

-6

-1.0x10

-5

NiFe(1) on thick Nb

-1.5x10

NiFe(1.0) Array

-4.0x10

NiFe(1) Array

NiFe(1.2) Array

-6

-6.0x10

NiFe(1.4) Array

NiFe(1) on thin Nb
-5

-6

-2.0x10

-100

-8.0x10
-75

-50

-25

0

25

50

75

100

-100

External Field (Oe)

-75

-50

-25

0

25

50

75

100

External Field (Oe)

Figure 5.1 Moment vs Field measurement for NiFe films and arrays The left-hand plot shows
comparison between NiFe(1) patterned into an array of over 9,000,000 0.5 µm2 elliptical pillars
with aspect ratio 2.5 and bulk films grown on 5 nm Nb and 100 nm Nb. The right-hand plot shows
the NiFe switching behavior of three arrays with NiFe thickness 1.0, 1.2, and 1.4 nm. For both
plots, the in-plane magnetic field was applied along the easy axis of the samples, corresponding to
the major axis of the ellipses in the array. These data were measured by Joseph Glick.
evaluation. All the spin-valve devices featured in this work used NiFe as the free layer material.
Figure 5.1 shows 10 K SQUID magnetometry M vs H curves for NiFe thin films and arrays. All
these samples were fabricated and measured by Joseph Glick. The 1 nm NiFe films had structure
Nb(5)/Cu(5)/NiFe(1)/Cu(5)/Nb(5) for the sample grown on thin Nb. The thick Nb samples began
with 100 nm Nb instead of only 5 nm. Data for these samples are shown on the left-hand plot in
comparison to an array of 2.5 aspect ratio, 0.5 µm2 elliptical pillars. Shaping these polycrystalline
ferromagnetic films into small ellipses is done to induce the magnetic easy axis along the major
axis of the ellipse. The arrays were grown on the thin Nb(5) base layer to clearly see the magnetic
properties of the films unaltered by the roughness of a thicker Nb base layer. The pillars were
defined by electron-beam lithography which stamped rectangles of 99 x 39 bits onto the chip over
2,400 times to fill an area of about 0.45 cm by 0.55 cm with over 9,000,000 pillars. These are
then ion milled down through the ferromagnetic layer and halfway into the bottom Cu layer. The
total moment of the NiFe(1) array is reduced compared to the extended thin films since there is
proportionally less magnetic material in the arrays, but the switching fields and ranges can still be
compared. The NiFe(1) grown on thin Nb has the smallest coercive field, which increases by 5-10
64

Oe when grown on thick Nb. The NiFe(1) array shows an even larger increase in coercive field
from the extended film grown on the same thin Nb of about 15 Oe. The right-hand plot shows a
comparison of three NiFe arrays of differing NiFe thickness. It is unclear why the arrays with 1.2
nm NiFe and 1.4 nm NiFe have such a similar moment. Possibly there is some non-uniformity run
to run in the writing of the arrays that causes slight variation from the intended pillar size that is
compounded due to the large number of pillars in the array. The coercive field decreases for the
thicker samples, which has been observed in this and other materials at these low thickness values.
The decreased switching field is desirable, but thicker layers will also reduce the critical current in
Josephson junctions.
For JMRAM, we would prefer a free layer with a switching field below 10 Oe and with small
variations in this value pillar to pillar. So far, these results with NiFe have been about as good as
we can get with a switching field around 25 Oe. Ideally, a very soft material would be found for
the free layer and NiFe could possibly act as a fixed layer with low initialization field. But, for
now, it serves as our free layer in the thickness range from 1-2 nm.

5.2

Ni

Historically, Ni has seen a lot of use in the Birge group. It has been found to be quite hard in thin
films but allows the most critical current of any material tested to date [44]. For these reasons,
it makes a desirable hard layer. Originally, 1.2 nm Ni was used as a hard layer by several group
members. But, this layer required a very high initialization field of 2600 Oe in Josephson junctions
and did not always initialize into the same magnetic state, indicating non-uniform magnetization.
So later, thicker films of 1.6 and 2.0 nm Ni were investigated in search of favorable magnetic
characteristics and lower initialization field requirements.
Spin valve films were fabricated to determine the affect of changing Ni thickness in a full sample stack. The structure was [Nb(25)/Al(2.4)]3 /Nb(20)/Cu(2)/NiFe(1.5)/Cu(4)/Ni(x)/Cu(2)/Nb(5)
with x = 1.2, 1.6 and 2.0 nm. No post-processing was performed, and samples were sent to collab-

65

Figure 5.2 Normalized moment vs applied field for spin valve NiFe/Ni samples The samples
contain 1.5 nm NiFe and Ni varying between 1.2, 1.6, and 2.0 nm. The slight downward slope of
the 1.6 nm Ni data as it approaches saturation is an artifact of the measurement system and can be
ignored. All the samples show similar behavior in both magnetic layers. The right-hand plot
zooms in on the upper right quadrant of the left-hand plot to better show the Ni switching
comparison.
orators at Arizona State University for VSM measurement. Figure 5.2 shows the normalized moment vs applied field data comparison for the three samples. No change in the NiFe characteristics
were expected, but surprisingly, these thin films showed almost no change in the Ni characteristics
either. The left-hand plot shows the whole major loop with the NiFe switching very close to 0 field
and the Ni switches more gradually, saturating by 600 Oe in either direction. The right-hand plot
zooms in on the upper right quadrant of the left-hand plot, and shows that the switching range and
saturation field as well as qualitative shape are incredibly similar between the three samples.
To further investigate thicker Ni as a fixed layer candidate, an array was fabricated with the
structure Nb(5)/Cu(5)/Ni(2)/Cu(5)/Nb(5) with the same array fabrication process described above.
Figure 5.3 shows the normalized moment vs applied field for this sample compared to an extended
thin film of Ni(2) measured by Caroline Klose. The array data has more noise due to the low
total moment, but the comparison shows that while the coercive field remains relatively the same,
the array has a much longer tail before all the junctions are saturated into the same magnetization
direction. This is promising for a lower initialization field requirement for a 2.0 nm (compared to
66

1.0
0.8
0.6
0.4

M/Mo

0.2
0.0
-0.2
-0.4

Ni(2) Array

-0.6

Ni(2) Film

-0.8
-1.0
-1,000 -800

-600

-400

-200

0

200

400

600

800

1,000

External Field (Oe)

Figure 5.3 Moment vs applied field measurements of Ni array and extended film Normalized
moment vs applied field for Ni(2) comparing an extended thin film and an array of 0.5 µm2
elliptical pillars with aspect ratio 2.5.
a 1.2 nm) Ni fixed layer. Josephson junctions with 1.2, 1.6, and 2.0 nm Ni will be further explored
later in this work.

5.3

NiFeCo

Ni65 Fe15 Co20 was another material that I magnetically characterized and later used in SQUID
devices. This material was a fixed layer candidate with it’s high magnetization value of about
1000 kA/m. My first study of this material compared SQUID magnetometry measurements of
bulk NiFeCo (a 200 nm sample), and extended thin films with thicknesses of 2.5 nm, 5.0 nm,
and 7.5 nm NiFeCo. The bulk sample was grown directly on the Si substrate and the thin films
were sputtered with the structure Nb(25)/Cu(5)/NiFeCo(x)/Cu(5)/Nb(5) and were measured with
no post-processing. All measurements were performed with the applied field in the plane of the
film, but applied both in the easy and hard axis directions according to the growth field of the film.
These data are shown in Figure 5.4 with the easy axis data shown in black and the hard axis data
shown in red. The first obvious observation about these data is that there is a noticeable difference

67

NiFeCo(200)

NiFeCo(2.5)
-3

1.0x10

1.0x10

8.0x10-3

8.0x10-4

6.0x10-3

6.0x10-4

4.0x10-3

4.0x10-4

Moment (emu)

Moment (emu)

-2

2.0x10-3
0.0
-2.0x10-3

In-plane
Parallel
In-plane
Perpendicular

-4.0x10-3
-6.0x10-3
-8.0x10-3
-1.0x10-2
-40

-30

-20

-10

0

10

20

30

2.0x10-4
0.0
-2.0x10-4

In-plane
Parallel
In-plane
Perpendicular

-4.0x10-4
-6.0x10-4
-8.0x10-4
-1.0x10-3
-40

40

-30

-20

External Field (Oe)

NiFeCo(5)

10

20

30

40

-3

1.0x10

1.0x10

8.0x10-4

8.0x10-4

6.0x10-4

6.0x10-4

4.0x10-4

4.0x10-4

Moment (emu)

Moment (emu)

0

NiFeCo(7.5)

-3

2.0x10-4
0.0
-2.0x10-4

In-plane
Parallel
In-plane
Perpendicular

-4.0x10-4
-6.0x10-4
-8.0x10-4
-1.0x10-3
-40

-10

External Field (Oe)

-30

-20

-10

0

10

20

30

2.0x10-4
0.0
-2.0x10-4

In-plane
Parallel
In-plane
Perpendicular

-4.0x10-4
-6.0x10-4
-8.0x10-4
-1.0x10-3
-40

40

External Field (Oe)

-30

-20

-10

0

10

20

30

40

External Field (Oe)

Figure 5.4 Moment vs Field measurement for NiFeCo films Bulk (200 nm), 2.5 nm, 5.0 nm,
and 7.5 nm films were measured for comparison. The black data in each plot were measured with
the external field pointing along the easy axis of the film (in the direction of the magnetic field
applied to the film during growth), and the red data were measured with the external field pointing
in-plane along the hard axis of the film.
between the easy and hard axis data for all thicknesses measured, so growing this material in a
field does set a preferred magnetic direction in the film. The easy and hard axis behavior is more
idealized in the thicker films and deteriorates as the thickness decreases. In all samples, the hard
axis trend shows a mix of model hard and easy axis behavior.
These initial results showed low switching fields despite the large magnetization value of the
material. Joseph Glick made and measured thinner samples in order to compare more directly with
the switching properties of NiFe and to investigate material thicknesses closer to the expected range
for 0-π switching. Figure 5.5 shows the easy axis data above of the thin film samples with NiFeCo
thicknesses 2.5 nm, 5.0 nm, and 7.5 nm in comparison to a 1.0 nm sample measured by Joseph.

68

NiFeCo Thin Film Comparison
-3

1.0x10

-4

8.0x10

-4

Moment (emu)

6.0x10

-4

4.0x10

-4

2.0x10

0.0
-4

-2.0x10

-4

7.5 nm

-4

5 nm

-4.0x10
-6.0x10

2.5 nm

-4

-8.0x10

1 nm

-3

-1.0x10

-80 -70 -60 -50 -40 -30 -20 -10 0

10 20 30 40 50 60 70 80

External Field (Oe)

Figure 5.5 NiFeCo thickness comparison of Moment vs Field measurements All samples were
grown on the same base layer of Nb(25) and all data shown were measured with the field applied
in the plane of the film and along the easy axis. Thicknesses of 7.5 nm, 5 nm, 2.5 nm, and 1 nm
(fabricated and measured by Joseph Glick) NiFeCo are shown. The total moment decreases with
thickness and the film’s coercive field increases, with the field increasing by over two times going
from the 2.5 nm to 1 nm NiFeCo sample. The saturation moment of the 1 nm samples appears
larger than expected in comparison to the other data due to different amounts of the chip being
loaded into the system between Joseph and myself.
This new 1.0 nm sample was grown with the same structure as the thicker films. This figure shows
that there is a small increase in the coercive field of NiFeCo from 7.5 nm down to 2.5 nm, but the
1.0 nm samples shows a highly increased coercive field. The coercive field value increases by over
two times from 2.5 nm NiFeCo to 1.0 nm NiFeCo giving the 1.0 nm film a coercive field of over
50 Oe. This coercive field is large enough to use NiFeCo as a fixed layer in a junction with NiFe
as the free layer. NiFeCo’s coercive field will also increase when the film is patterned into small
junctions. We also want our fixed layer material to have a relatively low initialization field. This
plot shows that even the 1.0 nm film is fully saturated before 100 Oe. Though this value will also
increase when the film is patterned, it is significantly lower than the saturation field of Ni films, so
it will require a much lower initialization field in a spin-valve junction.

69

Magnetization (emu/cm^3)

1000
800
600
400
200
0
-200
-400
-600
Nb(50) base

-800

Nb(25) base

-1000
-40

-30

-20

-10

0

10

20

30

40

External Field (Oe)

Figure 5.6 Moment vs Field measurement of 2.5 nm NiFeCo films grown on 25 or 50 nm Nb
base This comparison shows how the magnetic properties of the film are altered because of the
surface roughness of the underlying layers.
Lastly, a comparison was made to see the effect of a thicker Nb base layer on the NiFeCo thin
film. Samples were fabricated with the structure Nb(25 or 50)/NiFeCo(2.5)/Au(2). The results
are shown in Figure 5.6. Comparing with the 2.5 nm data shown in the plots above, these films
do not have the Cu buffer layers surrounding the magnetic material. Looking at the NiFeCo 2.5
nm thin film grown on 25 nm Nb with and without the Cu buffers, the film without the buffers
shows a reduced coercive field. The switching range is more difficult to compare since the data
without the Cu buffer seem to have finer point spacing. The two curves in Figure 5.6 show that the
increased thickness (and therefore roughness) of the base Nb layer do have a significant effect on
the switching properties of the NiFeCo film.

5.4

NiFe/FeMn

The magnetics community has long known that the antiferromanget Fe50 Mn50 can be used to pin
another magnetic layer in a desired direction by "exchange bias" [54]. This trick is commonly used
to measure GMR samples but has not been used in Josephson junctions due to the large reduction in
critical current the FeMn was believed to cause. We decided that the desirable magnetic properties

70

Figure 5.7 Moment vs Field measurements of NiFe/FeMn pinned bilayer samples Samples
with NiFe(1)/FeMn(1), NiFe(1)/FeMn(1.5), and NiFe(2)/NiFe(1.5) are shown. The left-hand plot
shows the full loop. Very large fields are required to unpin the bilayer even at these small
thicknesses of FeMn. The right-hand plot zooms in on the field range from -1000 to 1000 Oe
where there is very little change in the magnetization in all thickness sets.
of a pinned fixed layer were too advantageous not to investigate. First, magnetometry studies were
performed to determine what thicknesses of FeMn and NiFe would produce good pinning and what
external field values would be needed to break this pinning. Later chapters will detail the results
of Josephson junctions made with these layers.
To reduce the loss of critical current through future Josephson junctions, very thin layers of
NiFe and FeMn were investigated. Samples were fabricated with structure Nb(5)/Cu(5)/NiFe(x)/
FeMn(y)/Cu(5)/Nb(5) with x/y combinations of 1.0/1.0, 1.0/1.5, and 2.0/1.5. Extended thin films
were grown in a magnetic field and measured after no post-processing. Figure 5.7 shows the
comparison of the moment vs applied field for these three combinations. Note that the x axis
values are much larger than any shown previously. Even at these very thin values of NiFe and
FeMn, the layers remain pinned for several thousand Oersted of field. The right-hand plot shows a
zoomed in view of the left-hand plot from -1000 to 1000 Oe. In this large field range, there is little
noticeable change in the magnetization of the pinned layers, showing that they would be robust
fixed layers at field values far larger than those needed to switch a free layer of NiFe.
Through these SQUID magnetometry measurements, we also learned that the blocking temperature for the thin FeMn system is below room temperature as seen in Figure 5.8. This sample with

71

-4

Moment (emu)

2.0x10

-4

1.0x10

0.0

-4

-1.0x10

0

50

100

150

200

250

300

Temperature (K)

Figure 5.8 Moment vs Temperature plot for the NiFe(1)/FeMn(1.5) bilayer sample At low
temperature, the sample is initialized with a negative magnetization. Then the temperature is
slowly increased with a +100 Oe field applied. The moment of the NiFe/FeMn bilayer transitions
from negative to positive between 100 and 200 K, indicating that the blocking temperature is
within this range. It is not ideal that this temperature is below room temperature.
NiFe(1)/FeMn(1.5) was initialized to have a negative moment by cooling from room temperature
to 10 K in the presence of a -100 field. Then a +100 Oe field was applied while the temperature
was slowly increased to 300 K in 20 K steps, while measuring the magnetization at every step.
Between 100 and 200 K, the pinning breaks down and the NiFe is able to switch to point its magnetization in the positive direction. This indicates a blocking temperature in this range. It is not
ideal that the blocking temperature is below room temperature since growth in a magnetic field will
not set an easy and hard axis directions and the sample must be cooled in a field to initialize the
magnetization direction. The samples with other thickness combinations showed similar results.

72

CHAPTER 6
SINGLE FERROMAGNETIC LAYER JOSEPHSON JUNCTIONS

SQUID magnetometry measurements give important information about the basic properties of
different magnetic materials and how those properties change when grown on different normal
metal and superconducting layers. But, there are many other parameters that can only be addressed
by transport measurements of Josephson junctions. In this chapter, I will discuss measurements of
Josephson junctions that contain a single ferromagnetic layer (or single pinned layer). This type of
measurement gives additional information about how a material will behave in a real sample that
undergoes all the same processing that will be needed for a JMRAM device.
Sets of samples were fabricated using the steps outlined in Chapter 3 to create chips with
micron-sized Josephson junctions containing a single ferromagnetic interlayer. Each chip had a
different ferromagnetic layer thickness to cover a range of thickness values. Fraunhofer patterns
were measured to learn about the transport properties of these junctions. The critical current and
phase state of the junctions depend on the F layer thickness, as discussed in Chapter 2. The
amount of critical current that can travel through the junction and how quickly that critical current
decays with F layer thickness are important parameters. The thickness where the critical current
is completely suppressed indicates the ground state phase of the junction changing between 0 and
π. This is called the 0-π transition thickness and tells how much a Cooper pair will dephase as
it travels across the junction. Knowing these values about a single magnetic layer is crucial to be
able to put together a viable two layer system. Magnetic changes in the junction will also manifest
themselves as changes in the shape of the Fraunhofer pattern, so magnetic switching and the fields
at which it occurs can be determined from these Fraunhofer patterns as well. These magnetic
switching values are more useful than SQUID magnetometry of extended thin films since they
include all the roughness and interlayer effects of the whole junction stack and the shape anisotropy
and switching mechanism of a patterned bit. They can also give more detailed information than
SQUID magnetometry of an array. In array measurements, you can’t tell the magnetic state of a

73

single bit, only the whole array of bits. So if a magnetization of 0 emu is measured, you can’t tell
if each bit has 0 magnetization or if half are fully magnetized in one direction and the rest are fully
magnetized in the opposite direction. By contrast, in single bit measurements, any deviations from
the typical Fraunhofer pattern must be directly due to the one magnetic layer in the junction. The
trade-off is that fabrication and measurement of a series of Josephson junctions is much more time
consuming than SQUID magnetometry.
This chapter will detail my work to measure single junctions with a thickness range of NiFeMo
and NiFe/FeMn (pinned NiFe). I will also show results from Joseph Glick’s measurements on
NiFe and NiFeCo since I used these materials in spin-valve devices.

6.1

NiFeMo

The first material that I investigated in single-layer Josephson junctions was Ni0.73 Fe0.21 Mo0.06 .
This alloy, near the concentration of commercial supermalloy, has low coercivity, like NiFe, but
a smaller moment. The Stoner-Wohlfarth model for magnetization switching by coherent rotation
of a uniform ellipsoid indicates that the switching field for that material is directly proportional to
the total moment of the material [74]. So, a material with good magnetic properties and a moment
lower than that of NiFe would likely require a lower switching field and switching energy in that
regime, and thus be a better free layer candidate for spin valve devices.
Single-layer junctions were fabricated with the structure Nb(150)/Cu(5)/NiFeMo(x)/Cu(5)/
Nb(20)/Au(20)/Nb(150)/Au(10) where x ranges from 1.0 to 2.7 nm in steps of 0.1 or 0.2 nm.
The junctions were patterned into elliptical pillars with nominal axis lengths of 1.26 x 0.5 µm2 ,
giving them an area of 0.5 µm2 and an aspect ratio of 2.5. The I-V characteristics of each junction
were measured using a four-terminal SQUID-based self-balancing potentiometer over a field range
of -60 to 60 mT (1 mT = 10 Oe), with the external field applied in the plane of the junctions and
parallel to its major axis. The standard I-V characteristic for an overdamped Josephson junction
(from equation 2.16) was used to fit the data and extract the critical current value for each field

74

(mA)

2.5

C

0.0

I

Voltage ( V)

2

0.3

-0.3

2.0
-30

0

30

-5

Current ( A)

0

5

H (mT)

I

c

(mA)

0

1

0
-60

-40

-20

0

20

40

60

H (mT)

Figure 6.1 Fraunhofer pattern for S/F/S Josephson junctions with 1 nm NiFeMo The blue
data show the field sweep in the positive direction and the red data show the field sweep in the
negative direction. In both cases, the Fraunhofer pattern is shifted horizontally in the opposite
direction of the NiFeMo magnetization. The left inset shows a typical I-V curve for the Josephson
junctions in this series. The right inset shows the low field behavior of the same junction by
taking smaller field steps of 0.5 mT between -8 and 8 mT to more clearly see the range of field
values over which the NiFeMo layer changes its magnetization direction. H is an in-plane field
pointing along the major axis of the elliptical junction. Figure was taken from [57].
and the normal state resistance of the junction. The latter quantity is determined by the slope of
the I–V relation at currents much larger than the critical current, and preferably where the critical
current value is as small as possible.
A Fraunhofer pattern was then created by plotting the critical current vs the applied external
field. The Fraunhofer pattern and its accompanying equations are more fully described in Chapter
2. For an elliptical junction, the patterns are technically Airy patterns, but I will continue to call
them Fraunhofer patterns out of habit. The junctions in this series had thin enough ferromagnetic
layers to reproduce the theoretical Fraunhofer patterns, so they could be fit with the functional
form Ic = Ic0 * [2J1 (πΦ/Φ0 )/ (πΦ/Φ0 ) where J1 is a Bessel function of the first kind, Φ = µ0 (H-

75

Hshi f t )w(2λL +2dN +dF ) is the flux through the junction, and Φ0 =h/2e is the flux quantum. H,
w, λL , dN , and dF are the applied field, width of the minor axis of the elliptical pillar, London
penetration depth of the Nb electrodes (measured to be 85 nm in our samples), and the thickness
of the N and F layers, respectively.

[9]. The field shift, y-intercept current Ic0 , and junction

width were allowed to vary while the other parameters were set to their nominal values. One
Fraunhofer pattern is shown in Figure 6.1 for NiFeMo = 1 nm. The pattern was collected by
sweeping the applied field first from -60 mT to 60 mT then back again. The blue data show the
positive sweep direction and the red data show the negative sweep direction. A typical Fraunhofer
pattern is centered on zero field, but this pattern shows a shift in the central peak position opposite
to the NiFeMo magnetization direction, and a sharp transition to a Fraunhofer pattern shifted in the
reversed direction. The change from a positively-shifted Fraunhofer pattern to a negatively-shifted
Fraunhofer pattern signals the reversal of the NiFeMo magnetization direction which occurs in
the field range of 1–6 mT. In Figure 6.1, the solid symbols were fit to the theoretical pattern,
while the hollow symbols indicate where the magnetization of the NiFeMo changes direction. The
hollow symbols of the positive (negative) sweep direction line up with the solid symbols of the
negative (positive) sweep direction showing that the magnetization direction is fully switching. The
excellent quality of the Fraunhofer patterns with nodes approaching zero critical current indicate
that the current density is uniform at the central peak of the pattern, there are no short circuits in the
surrounding oxide, and there is no flux trapped in the junction electrodes. The fact that the data at
H = 0 lie on the fitted curve indicates that the remanent magnetic state of the NiFeMo nanomagnet
is probably single domain.
The right inset of Figure 6.1 shows the peak of the pattern measured again with finer field point
spacing of 0.5 mT over the field range from -8 to 8 mT. This inset shows that the NiFeMo layer
does not switch its magnetization direction instantly in one field step, but more slowly over a range
of about 5 mT. This doesn’t mean that the bit is multidomain. This effect could be due to a curling
of the magnetization at the ends of the bit. But either way, it is not a preferable characteristic for a
free layer material in JMRAM.

76

16

Fraunhofer Shift (mT)

14

12

10

8

6

4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

NiFeMo Thickness (nm)

Figure 6.2 Average Fraunhofer pattern shift vs NiFeMo thickness The blue and red data
represent junctions that were fabricated in two different sputtering runs. The linear fit to the data
was used to calculate a magnetization value for NiFeMo of 710 ± 140 kA/m (1kA/m = 1
emu/cm3 ) and the dead layer thickness to be 0.14 ± 0.42 nm.
Figure 6.2 shows the horizontal shift in the Fraunhofer pattern as a function of NiFeMo thickness. The shift value plotted is the average between the positive and negative sweep directions.
The amount of shift in each pattern should be proportional to the F-layer magnetization M and
should increase with the F layer thickness since the flux in the junction from a uniform magnetization M is equal to ΦM = µ0 MwdF . There is significant scatter in the data, but they show a
roughly linear trend. The slope and x-intercept of the linear fit was used to calculate the NiFeMo
magnetization and dead layer thickness. The magnetization was found to be 710 ± 140 kA/m
(1kA/m = 1 emu/cm3 ) and the dead layer thickness was 0.14 ± 0.42 nm. This is consistent with
previous SQUID magnetometry measurements indicating a bulk saturation magnetization of 590
± 60 kA/m.
Figure 6.3 shows the culmination of this measurement series, the critical current times normal

77

100

1

c

I R

N

( V)

10

0.1

0.01
0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

NiFeMo Thickness (nm)

Figure 6.3 Characteristic junction voltage,Ic RN , vs NiFeMo thickness The blue and red
symbols represent junctions that were fabricated in two separate sputtering runs. The solid line is
a fit to the data (further explained in the text) and indicates that the 0-π transition for NiFeMo
occurs at 2.25 ± 0.01 nm.
state resistance product (Ic RN ) vs the NiFeMo junction thickness. The critical current values used
came from the maximum of the Fraunhofer pattern for each thickness. The data was fit with
the equation Ic RN = V0 *e−dF /ξF1 *cos(dF /ξF2 − φ ) where ξF1 and ξF2 are the length scales
governing the decay and oscillation of the critical current, respectively, and φ is a phase shift [17].
From the fit, we obtained V0 = 150 ± 50 µV and ξF1 = 0.48 ± 0.04 nm. The values for φ and
ξF2 can only be determined unambiguously if more than one 0-π transition is observed. That was
not possible in this work due to the steep decay of the critical current with NiFeMo thickness. But,
if the value of φ is fixed to the value π/4, as is suggested for this type of junction in the literature
[33], then we obtain ξF2 = 0.955 ± 0.004 nm, although the true uncertainty is much larger due
to our inability to determine the value of φ . Lastly, the fit shows the 0-π transition thickness for
NiFeMo to be 2.25 ± 0.1 nm. A more detailed analysis of this sample series and data can be found
in [57].

78

All these properties are informative to determine whether this material should be further pursued for JMRAM devices. The total critical current that can get through the junction must be above
100 µA. So the "starting height" of the critical current, V0 , and the steepness of its decay, 1/ξF1 ,
are desired to be large and small respectively. You don’t want the 0-π transitions to be too close
together, which is related to ξF2 , or small variation in the material thickness will cause drastic
changes in the critical current. The exact value of the 0-π transition is also important. If it is too
thin, the magnetic properties of the material will likely degrade, but if it’s too thick, it might suppress the critical current. It is a hard game to play to try and find materials that fit all these criteria.
After careful consideration of NiFeMo, we decided that it’s magnetic and superconducting properties were inferior to plain NiFe despite our hopes that the lower magnetization would give NiFeMo
the advantage. Table 6.2 presented later in this chapter shows the fit parameter comparisons for
these materials.

6.2

NiFe/FeMn (pinned NiFe)

Based on the positive SQUID magnetometry results for the NiFe/FeMn (pinned NiFe) discussed
in the previous chapter, we decided to investigate this material stack in Josephson junctions to determine how much critical current is lost due to the FeMn layer. Though there are two magnetic
layers in this system, I chose to report them here in the single F layer chapter since in a JMRAM device, they would act together as the fixed layer. This junction series had the structure
[Nb(25)/Al(2.4)]3 /Nb(20)/Cu(5)/NiFe(x)/ FeMn(y)/Cu(5)/Nb(20)/Au(15)/Nb(150)/Au(10). The
x/y thickness pairs examined were 2.0/1.0, 1.5/1.0, 1.0/1.5, and 1.5/1.5 with all thicknesses in
nm. The junctions were patterned into ellipses with an aspect ratio of 2.5 and an area of 0.5, 1, or
2 µm2 .
Fraunhofer patterns were measured for at least two junctions on each chip in the series with no
initialization. Figure 6.4 shows three of these Fraunhofer patterns for junctions with 2.0 nm NiFe
and 1.0 nm FeMn. The top left pattern is a 2 µm2 area junction, the top right pattern is a 1 µm2 area

79

(Oe)

(Oe)

(Oe)

Figure 6.4 Fraunhofer patterns for NiFe/FeMn Josephson junctions All three patterns were
measured from the same chip which had 2.0 nm NiFe and 1.0 nm FeMn. The upper left pattern is
from a junction with 2 µm2 area, the upper right pattern is from a junction with 1 µm2 area, and
the lower pattern is from a junction with 0.5 µm2 area. The blue data were collected by sweeping
the field in the positive direction and the red data by sweeping in the negative direction. Unlike
the NiFeMo Fraunhofer patterns, these show no hysteresis with field sweep direction and the
horizontal shift is not consistent from junction to junction in direction or magnitude.
junction, and the lower pattern is a 0.5 µm2 area junction. In all plots, the blue data is sweeping
the field in the positive direction and the red data is sweeping the field in the negative direction.
Compared to the Fraunhofer patterns for NiFeMo, there are some clear differences. First, there
is no hysteresis in the pattern with sweep direction. The positive and negative sweep Fraunhofer
patterns essentially line up with each other. This indicates that there is no magnetic switching of
the layers in the junction even up to ± 1000 Oe. There also seems to be no systematic pattern
to the horizontal shift in the Fraunhofer patterns. Though the junction area is changing for each
pattern, you would expect at least the sign of the shift to be the same between these three junctions,
but because the blocking temperature is below room temperature, this is not the case. Since these
junctions were not cooled in a field, the virgin magnetic state was ’frozen’ into place when the
sample was dipped into the measurement dewar. Hopefully, shape anisotropy would cause the
80

100

NiFe/FeMn
NiFe

c

I R

N

(

V)

10

1

0.1
1.0

1.5

2.0

2.5

NiFe Thickness (nm)

Figure 6.5 Ic RN comparison for Josephson junctions with NiFe and NiFe/FeMn
magnetization to be primarily along the ellipse long axis, but the direction is seemingly arbitrary.
The possibility of non-uniform magnetization could also be artificially lowering the peak critical
current value in the Fraunhofer pattern, so these values can only be taken as a lower limit.
❛❛

❛ NiFe
FeMn❛❛❛
❛

1.0 nm
1.5 nm

1.0 nm

1.5 nm

2.0 nm

xx
1130 nV

680 nV
460 nV

240 nV
xx

Table 6.1 Average Ic RN values for NiFe/FeMn bilayer junctions This table shows the average
Ic RN values (in nV) for samples with NiFe/FeMn thicknesses of 1.0/1.5, 1.5/1.0, 1.5/1.5, and
2.0/1.0 with all thicknesses reported in nm.

Table 6.1 shows the average Ic RN values for the different NiFe/FeMn thickness combinations
tested. Interestingly, changing the NiFe thickness by 0.5 nm seems to have a larger impact on the
total Ic RN than changing the FeMn thickness by 0.5 nm. But either way, the total Ic RN for this
fixed layer is significantly smaller than that of junctions with only a NiFe layer. Figure 6.5 shows
that the separation between the Ic RN values is over an order of magnitude. Though the NiFe/FeMn

81

Material
NiFeMo
NiFe
NiFeCo

V0 (µV)
150 ± 50
70 ± 20
30 ± 6

ξF1 (nm)
0.48 ± 0.04
1.50 ± 0.38
1.10 ± 0.16

ξF2 (nm)
0.955 ± 0.01
0.58 ± 0.10
0.48 ± 0.03

0-π Thickness (nm)
2.25 ± 0.1
1.76 ± 0.05
1.16 ± 0.02

Ic RN π peak (µV)
0.25
16.5
5.9

Table 6.2 Comparison of fit parameters from 0-π transition plots for NiFeMo, NiFe, and
NiFeCo Additionally, the last column shows the Ic RN value for the peak of the π state for each
material. This serves as a rough comparison of the materials taking into account all three fit
parameters. For JMRAM devices, we generally want this value to be maximized.
has great magnetic properties as a fixed layer, this drastic reduction in critical current makes it of
little use for the JMRAM project. S/F/S junctions with only NiFe will be further discussed in the
next section.

6.3

NiFe and NiFeCo

Similar sample fabrication and measurements to those done for NiFeMo and NiFe/FeMn were carried out by Joseph Glick on free layer NiFe and fixed layer NiFeCo (with help from Dr. Mazin
Khasawneh, Dr. Eric Gingirch, and myself on the NiFe data). Thicknesses ranging from about 1 3.5 nm were explored for both materials. I will not go into detail on the single junction measurements of these materials, but I would like to share a summary plot of the Ic RN vs thickness for
each material as well as a chart of the fit parameters for a comparison of these materials.
Figure 6.6 shows the Ic RN vs F layer thickness for NiFe and NiFeCo. There is significantly
more scatter in the NiFe data, probably due to the fact that many different people were involved
in the fabrication and measurement of those samples which spanned several sputtering runs. Nevertheless, fits were performed to both sets of data to determine the 0-π transition thicknesses, V0 ,
ξF1 , and ξF2 values. These fit parameters are summarized and compared with those from NiFeMo
in Table 6.2. Though NiFeMo has the highest V0 , it also has the steepest exponential decay, characterized by the lowest ξF1 value, which quickly decreases the critical current through the junction
as the NiFeMo thickness increases. NiFeCo shows nicer magnetic properties, but compared with
Ni, which has been used historically in many junction stacks measured by the group, it highly

82

IcMax*Rn vs. F Layer Thickness
100
IC, Max*Rn( V)

50
●●

●●

●●
●●
●●

●●
●●

10
●●

5

●●

●●

●●

●● ●●
●●

●●

●●

●●
●●
●●

1
1.5

.0

2.0

2.5

3.0

3.5

NiFe Thickness(nm)

IcMax*Rn vs. F Layer Thickness

IC, Max*Rn( V)

10

 ✁✁
 

 ✁

✁
 
 ✁

 ✁

 ✁

 ✁
 
 ✁✁  ✁

 ✁✁
 

 ✁
 ✁

 ✁
 ✁

1

 ✁
 ✁
 ✁
 ✁
 ✁✁
 

0.10

0.01
0.0

 ✁
 ✁

 ✁

0.5

1.0

1.5

2.0

2.5

3.0

3.5

NiCoFe Thickness(nm)
Figure 6.6 Ic RN vs material thickness for NiFe and NiFeCo This plot shows the Ic RN vs
material thickness for NiFe and NiFeCo, primarily measured by Joseph Glick. The Ic RN values
are taken from the peak of the Fraunhofer pattern as extrapolated from fits. The whole plot is fit in
red with the same equation as the NiFeMo data in the previous section.

83

suppresses the critical current with a low V0 value and a relatively steep critical current decay. The
fit parameters for these materials can be roughly combined by comparing the Ic RN value of each
material at the peak of the π state. For JMRAM devices, we generally want this value to be maximized. By this comparison, you can see that NiFe is highly advantageous compared to the other
two materials. Spin-valve junctions using free layers of NiFe and fixed layers of Ni and NiFeCo
will be discussed in the next chapter.

84

CHAPTER 7
SINGLE JUNCTION SPIN VALVE DEVICES

This chapter will detail measurements of single pillar Josephson junctions that contain two ferromagnetic layers, making them spin valve devices. A junction such as this will ultimately serve as
the phase controllable S/F/S junction in the JMRAM memory cell, but though a single junction is
all that is needed to create a phase change, we are not set up to measure phase changes in a single
junction. For that, we need to measure the relative phase between two spin valve junctions in a
SQUID, which will be discussed in Chapter 8. Many other useful pieces of information can be
obtained from transport measurements of single junction spin valves, such as switching field values for the two layers, the amount of critical current that can travel through the junction when the
magnetizations of the two layers are oriented parallel and antiparallel, and the field values required
to saturate each magnetic layer. Also, since there is only one junction being measured, the results
are easier to interpret than those comparing two junctions with a more complex circuit design.
If a series of layer thicknesses is considered, these measurements can also be used to inform
future devices on the F layer thickness range that will show 0-π phase switching. As is shown in
Figure 2.12, we are attempting to control the thicknesses of our F layer materials such that one
layer is at its 0-π transition thickness and the other is thinner than its 0-π transition thickness,
leading to a junction whose phase can be changed between 0 and π when the magnetizations of the
two F layers are oriented antiparallel (AP) or parallel (P) to each other. As the figure shows, this
is characterized by equal critical current through the junction in the P vs AP states. Technically,
it is the peak critical current of the junction (from the peak of the Fraunhofer pattern) that should
be equal, but because of the shifts in the Fraunhofer pattern due to the magnetic material in the
junctions, the peak value will be shifted away from zero field in the opposite direction as the net
junction magnetization. We hoped that the small size of these junctions, which increases the width
of the Fraunhofer pattern, would cause the zero-field and peak critical current values to be similar.
This chapter will detail several series of spin valve measurements where one of the F layers is

85

held at a constant thickness and the other is systematically varied. When the critical current of the
junction in the P or AP state dips to zero, this indicates crossing into a new phase lobe on the Ic vs
AP
thickness plot, so the thickness region between the two zeros of IP
c and Ic and will support 0-π

phase transitions. The same types of measurements were performed for all series, but they will
only be described in detail in the first section. Systems with NiFe/NiFeCo and NiFe/Ni will be
discussed.

7.1

NiFe(1)/NiFeCo(x) Spin Valves

The first set of spin valve samples that I studied contained NiFe as the free layer and NiFeCo
as the fixed layer. SQUID devices for phase sensitive measurements had already been made and
measured using these materials, but nominally the same samples made in different sputtering runs
showed different results, as will be discussed in Chapter 8. We decided that our chosen thicknesses
must put one of the states very close to a 0-π phase transition. This study varying the NiFeCo
thickness was intended to determine a better thickness range to use in future SQUID devices.
These samples had the following structure: [Nb(25)/Al(2.4)]3 /Nb(20)/Cu(5)/NiFe(1)/Cu(10)/
NiFeCo(x)/Cu(5)/Nb(5)/Au(15)/Nb(150)/Au(10) where x = 0.9 - 1.5 nm in 0.1 nm steps. The
samples were grown in a field with a square magnet placed in the center of the sputtering holder,
and processed as described in Chapter 3 into ellipses with 0.5 µm2 area and an aspect ratio of either
2.2 or 2.8. Major and minor loop zero-field measurements were taken of all samples. In a major
loop, both magnetic layers switch (both the NiFe and the NiFeCo) back and forth, whereas in a
minor loop only the free layer (NiFe) switches back and forth. To perform these measurements,
first the magnetizations of the two layers must be initialized in one direction. I chose to initialize
in the negative direction with a -400 to -600 Oe field. The major loop was collected by measuring
IV curves starting at zero field, then slowly stepping up this ’set’ field and returning to zero field
to measure the next IV curve. The IV curves were fit with the standard overdamped relation given
in equation 2.16 and the resulting critical current was plotted vs the set field. The goal of these

86

Figure 7.1 Representative Zero-Field Measurements of NiFe(1)/NiFeCo(x) Spin Valve Here, x
= 0.9 nm NiFeCo. All points are the critical current fit from an IV curve measured at 0 field after
the appropriate ’set’ field was applied. The black arrows indicate the magnetization direction of
the NiFe (lower arrow) and NiFeCo (upper arrow).
measurements was to determine the critical current of the junction at zero field in the P and AP
states and to compare their values as the thickness changes and also to see the switching and
saturation fields for both F layers. The maximum magnitude of the ’set’ field before measuring in
the opposite field direction determines whether a major or minor loop is collected. A typical minor
loop extended to ± 50 Oe taking 5 Oe steps, and a typical major loop continued until the hard
magnetic layer was fully saturated (up to about ± 200 Oe for this NiFeCo series). After measuring
several of the thinner NiFeCo samples which showed very low critical current in the P state, I
started to also measure the Fraunhofer pattern for each sample to get a better feel for the shift of
the central peak and to observe any deviations in its shape from what was expected.
Figure 7.1 shows a representative zero-Field measurement. The upper plots show the major
loop and the lower plots show the minor loop. In the two right hand plots, labeled as the ’up’
87

sweep, the sample was initialized fully in the negative direction and the field was swept in the
positive (right) direction. In the right hand plots, the field sweeps in the negative (left) direction
and follows directly after the ’up’ sweep. These are labeled as ’down’ sweeps. The black arrows
indicate the magnetization direction of the NiFe (lower arrow) and NiFeCo (upper arrow). The
major loop data indicate the switching of both magnetic layers. The "Major Loop Up" plot shows
the NiFe switching from a low critical current in the P state to a higher critical current in the AP
state in the field range of 20-30 Oe. The critical current and therefore the magnetic configuration
remain stable until 100 Oe when we see the NiFeCo begin to switch over a range of field values
ending at 185 Oe and including several intermediate switching states. Continuing this major loop
by sweeping the field in the negative direction, as shown in the "Major Loop Down" plot, we see
that the NiFe switching is now less abrupt and settles to a stable AP state with a lower critical
current then seen during the ’up’ sweep. The NiFeCo still switches over a wide range of fields
including many intermediate states.
The minor loop plots on the lower half of the figure show that the NiFe switches over a small
field range with asymmetry in the switching field with the field sweep direction. Features from
these zero-field measurements that repeated themselves sample to sample include the presence of
intermediate switching states, switching fields for the NiFe below 50 Oe, saturation of the NiFeCo
by around 200 Oe, and larger critical current values when the sample was in the AP state vs the
P state. This last point may be due to magnetic changes suppressing the critical current near
zero field and will be discussed momentarily. There was also no discernible difference between
measurements of junctions with an aspect ratio of 2.2 compared with those with an aspect ratio of
2.8. It was expected that the lower aspect ratio junction would show lower NiFe switching fields
but the data showed no clear trend between aspect ratio and switching field.
The low critical current values observed in several P state zero-field measurements led to additionally measuring the Fraunhofer patterns for subsequent junctions. We expect some horizontal
shift in the Frauhnofer pattern due to the magnetization of the F layers themselves, and this effect
will cause larger shift amounts in the P state. However, given the small size of these junctions and

88

Figure 7.2 Representative Fraunhofer Patterns for NiFe(1)/NiFeCo(x) Spin Valve The blue
data sweep from negative to positive field values and the orange data sweep from positive to
negative field values. The circled regions indicate where the junction is switching into and out of
the antiparallel magnetic configuration. The black arrows indicate the magnetization direction of
the NiFe (lower arrow) and NiFeCo (upper arrow).
taking into account the shift amounts observed in single F layer junctions, we thought that even
in the P state, the zero-field measurement would be close to the Fraunhofer pattern’s central peak
value. As can be seen in Figure 7.2, this is not always the case. This figure shows two Fraunhofer
patterns collected from samples with NiFeCo thicknesses of 1.1 and 1.3 nm. The blue data is collected by sweeping the external ’set’ field from negative to positive values and the orange data is
collected subsequently by sweeping the magnetic field from positive to negative field values. The
black arrows indicate the magnetization direction of the NiFe (lower arrow) and NiFeCo (upper
arrow). The circled part of the pattern indicates the portion where the junction is suspected to be in
the AP state. The data here are measured in the presence of the ’set’ field. The ending field values
of ±400 Oe are sufficient to saturate the NiFe and NiFeCo layers as can be seen from the zero-field
measurements. Because of this, we expect the Fraunhofer shift to always be larger in the P vs AP
state and for the P state pattern to always have its central peak occur at a field opposite in sign from
the layers’ magnetization direction. It is, therefore, curious to see that the blue (orange) data, which
should have initially negatively (positively) magnetized layers, appears to have a peak Fraunhofer
pattern value also at negative (positive) field. This indicates that there is some magnetic change

89

in the junctions before zero field is reached that causes a downturn in the junction critical current
and a dramatic suppression of the critical current for the "P" state from zero-field measurements
(P is now in quotes because if there is a magnetic change, the magnetizations of the two layers are
no longer parallel). This critical current suppression of the "P" state is observed in all Fraunhofer
pattern measurements and means that our zero-field measurements of the "P" state do not convey
information about the peak Fraunhofer pattern value. A possible culprit is magnetostatic coupling
between the two magnetic layers which favors the AP state and could cause the magnetic state to
begin to change before zero field is reached. Some patterns also showed strange rapid oscillations
of the critical current with H near zero field indicating magnetic instability within the junction. If
the downward turn of the critical current is neglected and the peak of the Fraunhofer is projected
to the proper side of zero field, it appears that the P state has a lower maximum critical current
than the AP state in the 1.1 nm NiFeCo sample where as the opposite is seen in the 1.3 nm NiFeCo
sample. Though some Fraunhofer patterns are difficult to interpret, overall this switch in P vs
AP critical current ratio occurs nominally at 1.3 nm NiFeCo indicating a 0-π transition thickness
around this value.
The summary plot of zero-field Ic RN values in the "P" and AP state vs NiFeCo thickness is
shown in Figure 7.3. As stated previously, the "P" state values represent a suppressed critical
current, not the peak value, so solid conclusions cannot be drawn from this plot. However, even
looking at the AP state Ic RN values, they are significantly lower than those needed for JMRAM
applications, which on top of the other magnetic issues make this system undesirable for future
study. Additionally, these samples used rougher spacer and buffer layers of Cu(5) and Cu(10).
If this system was transitioned to use smoother normal metal layers, the switching field of the
NiFeCo might begin to overlap with that of the NiFe. A fixed layer with a larger switching field
and lower magnetization are desired to give tolerance to the allowed switching fields and reduce
low field magnetic issues caused by dipolar coupling. This led us back to studying the NiFe/Ni
system further, now utilizing smoother spacer and buffer layers and investigating thicker Ni layers
than used in previous studies.

90

Figure 7.3 Zero-Field Ic RN in "P" vs AP State for NiFe(1)/NiFeCo(x) Spin Valves The AP
state data somewhat follow the expected trend, but in comparison, the "P" state has a considerable
smaller critical current and is possibly being artificially reduced at zero field as discussed in the
text.

7.2

NiFe(x)/Ni(2) Spin Valves

Our group has historically used Ni in Josephson junctions due to the high critical current obtained
through junctions containing this material compared with all other materials that have been investigated by the group. Ni layers between 1.0 and 1.5 nm thickness were found to require 1000 - 2000
Oe switching fields, making it a hard layer candidate [45]. In Chapter 8, phase-sensitive measurements will be discussed from a system using NiFe(1.5)/Ni(1.2). To improve that system we wanted
to investigate thicker Ni layers in hopes of improving the Ni magnetic properties. Since we were
unable to measure the 0-π transition thickness of Ni, this spin valve study with NiFe(x)/Ni(2) was
carried out to determine the range of thicknesses that should give 0-π phase transitions.
The first version of this study used a Cu(2)/Al(7)/Cu(2) spacer layer between the NiFe and
Ni layers. SQUID magnetometry results showed that this spacer layer was very smooth, as seen
in Figure 4.5. Unfortunately, transport measurements revealed that the critical current is highly
suppressed through this spacer layer and the majority of spin valve samples showed almost zero

91

critical current in either the P or AP states (depending on the NiFe thickness). In order to view
systematic trends, a new set of samples was fabricated using our current "best" buffer and spacer
layers of Cu(2) and Cu(4) respectively. These layers were found to show the best magnetometry
results of spin valve samples.
The spin valve samples in this series had the following structure: [Nb(25)/Al(2.4)]3 /Nb(20)/
Cu(2)/NiFe(x)/Cu(4)/Ni(2)/Cu(2)/Nb(5)/Au(15)/Nb(150)/Au(10) where x = 1.1 - 1.8 nm in 0.1 nm
steps. Three additional samples were also made with the bottom Cu(2) replaced with Ru(2) and
NiFe thicknesses of 1.3, 1.5, and 1.7 nm. The samples were patterned into ellipses with a 0.5 µm2
area and an aspect ratio of 2.5. Fraunhofer patterns and zero-field measurements were performed to
determine the relative P vs AP critical currents for this series, to investigate the switching properties
of the thicker Ni and NiFe, and to compare the results for the Cu vs Ru seed samples.
Figure 7.4 shows a representative Fraunhofer pattern and set of zero-field measurements for
a sample with 1.3 nm NiFe. This junction was intialized with a positive field. Part a) shows the
Fraunhofer pattern, b) and c) show the major loop zero-field measurements, and d) and e) show
the minor loop zero-field measurements. The black arrows indicate the magnetization direction of
the NiFe (lower arrow) and Ni (upper arrow). The blue data in the Fraunhofer pattern sweep in the
positive direction and the orange data sweep in the negative direction, as indicated by the blue and
orange arrows. The black circles enclose the data where the junction is assumed to be in the AP
state. In parts b) and d) the field sweeps in the negative direction and in parts c) and e) the field
sweeps in the positive direction. Looking at all the minor loop data, the NiFe was found to switch
its magnetization direction over a range of fields about 5 - 10 Oe wide, typically completing the
switching process before 50 Oe. We would expect the NiFe to have a lower switching field when
switching from the P to AP state than when switching from the AP to P state since the dipolar
coupling should make the AP state more stable. However, while this set of samples did show
some switching field asymmetry between the two switching directions, the AP to P switch did not
show systematically lower switching fields for all samples. The major loop data show that the
Ni switches over a much larger field range starting between 300 and 400 Oersted and completely

92

Figure 7.4 Representative Fraunhofer Pattern and Zero-Field Measurement for
NiFe(x)/Ni(2) Spin Valve Series The black arrows indicate the magnetization direction of the
NiFe (lower arrow) and Ni (upper arrow). This sample was initialized with a positive field. Part a)
shows the Fraunhofer pattern with blue data advancing in the positive field direction and orange
data advancing in the negative field direction, as indicated by the blue and orange arrows. The
black circled regions indicate where the junction is believed to be in the AP state. Previous to this
region, the junction was in the P state, and after, the Ni is switching over a large field range. Parts
b) and c) show a major loop zero-field measurement with both magnetic layers switching and
parts d) and e) show a minor loop zero-field measurement where only the NiFe layer switches
back and forth.
93

saturating by 1000 - 1500 Oe. This saturation field is much lower than the ±2600 Oe that we used
to initialize the 1.2 nm Ni layers in the past, which is an advantage of this 2.0 nm Ni layer.
The Fraunhofer pattern in Figure 7.4 part a) shows several distinctive features. These features
appear symmetrically in both sweep directions. The P state part of the pattern should have its
peak value at a field with the opposite sign as the layers’ magnetizations. Similarly to the NiFeCo
samples, this is not the case and there is a premature downturn of the junction critical current when
approaching zero field. Additionally, many patterns measured in this series showed one point with
a significantly lower critical current while the NiFe was switching. This feature is occasionally
captured in the zero field measurements, such as in the P state minor loop critical current shown
in Figure 7.4 part e). Here, a critical current of about 0.12 mA is expected from the Fraunhoffer
pattern but the junction locks into a state with much lower critical current. The Ni was not fully
saturated by the ±600 Oe used to measure the Fraunhofer pattern, so the sample needed to be
initialized with a ±1500 Oe field before each sweep.
The Ic RN values in the P vs AP states for NiFe(x)/Ni(2) series are shown in Figure 7.5. These
values are taken from the zero-field measurements and cross-checked with the Fraunhofer pattern
data. The blue data show the AP state zero-field values for the Cu seed samples, the red data show
the P state zero-field values for the Cu seed samples, the purple data show the P state zero-field
values for the Ru seed samples, and the black data show the AP state zero-field values for the Ru
seed samples. Two samples were measured for each thickness with the P and AP state data from
the same junction sharing the same symbol (either circles or triangles). There is no significance to
which junctions were assigned to be circles vs triangles. There is a clear systematic trend in the
Ic RN values with the changing NiFe thickness. The Cu seed data show that IAP
c was continually
rising while IP
c decreased to a minimum at 1.5 nm NiFe before rising again. These follow the
expected trends given the simplified picture in Figure 2.12 where the pair phase accumulation
d
d
φ P = φ1 + φ2 = ξF1 + ξF2 , φ AP = φ1 − φ2 =
F1
F2

dF1
ξF1

d

− ξF2 , dF is the ferromagnetic layer thickness
F2

and ξF is the coherence length in the ferromagnetic material. The theory of this system was
further detailed in Chapter 2, but the case describing this data shown pictorially in Figure 7.6.

94

a)

b)

Figure 7.5 Zero-Field Ic RN in P vs AP State for NiFe(x)/Ni(2) Spin Valves Part a) shows only
the samples with all Cu spacer and buffer layers while part b) includes the data from the samples
with the Ru seed layer. The blue data show the AP state zero-field values for the Cu seed samples,
the red data show the P state zero-field values for the Cu seed samples, the purple data show the P
state zero-field values for the Ru seed samples, and the black data show the AP state zero-field
values for the Ru seed samples. Red and blue circles or triangles of the same thickness represent
the P and AP state data from the same junction. Two junctions were measured for each thickness.
AP
The data show a clear trend with the changing NiFe thickness. IP
c and Ic are closest to being
equal between 1.2 and 1.3 nm NiFe indicating the optimal thickness for 0-π switching, though
AP
anywhere between the minimum of IP
c and Ic should also produce a 0-π phase change. Part b)
shows that the Ru seed layer causes a drastic reduction of the P state critical currents as well as a
difference in trend compared to the Cu seed samples.

95

AP
Figure 7.6 Theoretical Description of IP
c and Ic Trends for NiFe(x)/Ni(2) Spin Valves The
P
AP
P
data show that at low NiFe thicknesses IAP
c < Ic and at larger NiFe thicknesses Ic > Ic . As
shown in the figure, this picture is consistent with the case where the pair phase accumulation
across the Ni, φ2 = dF2 /ξF2 is greater than half of the oscillation period.

In this figure, φ1 and φ2 represents the pair phase accumulation through the NiFe and Ni layers,
respectively. In Figure 7.6, the location of φ1 is denoted by the unlabeled central dotted line and
φ2 is the distance between this line and and the outer dashed lines, labeled P and AP. The data
d
are explained by this picture where ξF2 > π2 or the Ni thickness is greater than its 0-π transition
F2
AP
AP
P
AP
P
thickness. This gives IP
c > Ic for smaller dF values and Ic > Ic for larger dF values. Ic = Ic

around 1.25 nm NiFe so that is the desired thickness to use in 0-π switching experiments, but
samples with 1.1 -1.5 nm NiFe and 2.0 nm Ni should show 0-π phase switching between the P and
AP magnetic configurations. However, the theory is based on the maximum Fraunhofer pattern

96

values. The AP state data seems to have a small enough horizontal shift for the zero-field value
to be a good estimate of the peak value, but this is not always the case for the P state data, so this
analysis must be taken with a grain of salt. SQUID measurements are taken at zero field, so it is
still very useful to know what kinds of critical currents we will see and balanced critical currents in
the P and AP state will reduce asymmetries in the system. Part b) of Figure 7.5 includes the three
sample thicknesses with the Ru seed on plotted together with the full series of Cu seed data. There
was a dramatic reduction of the P state critical currents as well as a difference in trend compared
to the Cu seed samples. To understand the full trend, more samples of different thicknesses would
be needed, but since the critical current is so reduced, it is unlikely that this spacer layer will be
pursued further.

7.3

NiFe(x)/Ni(1.6) Spin Valves

The analysis of the pair phase accumulation pointed to the Ni(2) layer being thicker than its 0π transition thickness. Thinner Ni would then increase the critical current at the crossover point
AP
where IP
c = Ic since positioning on the theoretical curves shown in Figure 7.6 would be closer to

the peaks. Having less ferromagnetic material in the junction should increase the critical current as
well. To test this theory, and additional set of spin valve samples were fabricated and measured with
NiFe(x)/Ni(1.6) where x = 1.1 - 1.8 nm. These samples had the same structure as those in the previous section, except Ni(1.6) instead of Ni(2.0): [Nb(25)/Al(2.4)]3 /Nb(20)/Cu(2)/NiFe(x)/Cu(4)/
Ni(1.6)/Cu(2)/Nb(5)/Au(15)/Nb(150)/Au(10) where x = 1.1 - 1.8 nm in 0.1 nm steps. The sample
with 1.2 nm NiFe had fabrication issues and was not able to be measured. Like the Ni(2) series,
these junctions were patterned into ellipses with an area of 0.5 µm2 and an aspect ratio of 2.5.
Fraunhofer patterns and zero-field measurements were performed on two junctions of every
NiFe thickness. The overall shapes and features were very similar to those of the Ni(2) series.
zero-field measurements showed NiFe switching below 50 Oe but with a bit more symmetry in
minor loop switching fields from one sweep direction to the other. This thinner Ni did require a

97

Figure 7.7 Zero-Field Ic RN in P vs AP State for NiFe(x)/Ni(1.6) Spin Valves The pink data
show the AP state zero-field values and the black data show the P state zero-field values. Two
junctions were measured for each thickness. Circles or triangles of the same thickness represent
the P and AP state data from the same junction. Compared with the Ni(2) series, the critical
AP
current values are generally quite similar. Above 1.3 nm NiFe, the trend of IP
c < Ic matches with
the Ni(2) data, but both P and AP states have low critical current for the 1.1 nm sample. The 1.2
nm NiFe sample did not survive the fabrication process.
larger saturation field. The majority of the samples were saturated between 1300 and 1700 Oe
but a couple samples took as much as 2500 Oe or as little as 1000 Oe to fully saturate. The
Fraunhofer patterns were all of good quality with symmetric behavior with field sweep direction.
They continued to exhibit the behavior of critical current reduction when approaching zero field
during the NiFe switching process.
Figure 7.7 shows the summary for this series with the zero-field values of the Ic RN for the P
and AP state vs the NiFe thickness. The pink data show the AP state zero-field values and the
black data show the P state zero-field values. Two junctions were measured for each thickness.
Circles or triangles of the same thickness represent the P and AP state data from the same junction.
The trend of the data where the AP state has a higher critical current than the P state is reproduced

98

between the two series above 1.3 nm NiFe, though the trend is not as smooth in this Ni(1.6) series.
Below 1.3 nm NiFe, it is difficult to tell what is happening since the 1.2 nm NiFe sample could not
AP
be measured and the 1.1 nm sample does not meet our expected values for IP
c and Ic . From the
AP
Ni(2) series, we would expect that IP
c > Ic at these low NiFe thicknesses. But in this series, they

show very similar critical current values between the P and AP states with satisfactory Fraunhofer
patterns and zero-field measurements indicating no issues with the junction.
Generally, the critical currents were not much higher than those in the Ni(2) series. There, the
maximum Ic RN is about 6 µV and here it only gets up to about 8 µV. Additionally, though it is
AP
unclear exactly where IP
c = Ic , the Ic RN appears to be similar in value at this crossover point
AP
in both series. This means that if this system was used in SQUID devices where IP
c = Ic for

optimum 0-π phase switching measurements, then there would not be an appreciable gain in the
critical current of the devices. Since the saturation field for Ni(1.6) is also larger and the trend of
the data for this series is not as nice as the Ni(2) series, SQUID devices were subsequently made
with NiFe(1.25)/Ni(2). All SQUID device data will be detailed in the following chapter.

99

CHAPTER 8
SPIN VALVE SQUIDS

The ultimate goal of this work was to create a spin valve Josephson junction with two magnetic
layers where the phase across the junction could be controllably changed between 0 and π by
changing the relative magnetization directions of the two magnetic layers from the antiparallel
(AP) to parallel (P) state. Only a single junction is needed for this effect, but in order to make
a phase-sensitive measurement to experimentally verify the phase change, we utilized a Superconducting QUantum Interference Device (SQUID) to measure the relative phase between two
such junctions in a superconducting loop. In order to obtain a phase change in a single junction,
the magnetic material switching fields and thicknesses must be carefully chosen. As described in
Chapter 2, a free layer with a low switching field and a fixed layer with a larger switching field
are needed. After initializing both magnetic layers in the same direction, only the free layer will
switch its magnetization direction back and forth by 180° to put the junction in the P or AP state.
These magnetic configurations alone, however, are not sufficient to produce phase switching. The
magnetic materials must have the proper thicknesses relative to their 0-π transition thicknesses. In
our design, we wanted one layer close to its 0-π transition thickness and the other layer thinner
than its 0-π transition thickness. Our initial results yielded from devices with NiFe(1.5)/Ni(1.2)
and much of the discussion of that result in the following section comes from our publication
of that work [28]. The experimental design and data analysis discussed in the following section
will be applicable to all the devices detailed in this chapter. After incorporating optimization in
base electrode and normal metal layer roughness, magnetic material properties, and device design,
systems with NiFe(1.0)/NiFeCo(1.1) and NiFe(1.25)/Ni(2) were also investigated.

100

(b)

Is

BΦ

Is

IΦ
Hin

Ni
“Fixed”

#1

NiFe
“Free”

#2

Cu

#3

#4

B
JJ-2

A
JJ-1

Figure 8.1 Schematic Diagram of the Asymmetric SQUID Layout Cartoons show the
magnetization directions of the free and fixed layers for the four magnetic states discussed in this
experiment. The colored arrows show positive directions of the measurement current, Is , the
applied in-plane magnetic field, Hin , the flux-line current, Iφ and the magnetic field produced by
the flux line, Bφ . The more circular junction is labeled as ‘JJ-1’ whereas the more eccentric
elliptical junction is labeled as ‘JJ-2.’ The sizes of the four arrows in the four magnetic states
depict the magnitude and direction of Hin required to reach each state.

101

8.1

NiFe(1.5)/Ni(1.2) SQUIDs

The samples in this study had the following structure: [Nb(40)/Al(2.4)]3 /Nb(20)/Cu(5)/NiFe(1.5)/
Cu(10)/Ni(1.2)/Cu(5)/Nb(20)/Au(15)/Nb(150)/Au(10). From the magnetic data shown in Chapter
6, the NiFe was the free layer with a thickness close to its 0-π transition thickness and the Ni
was the fixed layer with a thickness less than its 0-π transition thickness. The SQUID design
and layout are shown in Figure 8.1. The design includes two spin-valve junctions with the same
material composition together in a superconducting loop. The junctions are patterned into ellipses
with different aspect ratios to induce a difference in the free layer switching field and to provide a
preferred easy axis magnetization direction along the long axis of the ellipse [74, 71]. The ellipses
both had an area of 0.5 µm2 and aspect ratios of 2.2 or 2.8 with the 2.2 aspect ratio junction
corresponding to a lower switching field for the free layer than the 2.8 aspect ratio junction. The
straight bottom lead and pitchfork-shaped top lead make up the SQUID and were both 5 µm wide.
The inner dimensions of the resulting loop were 10 µm by 10 µm. The adjacent straight, long wire
is 10 µm wide. In this measurement technique, sample current, Is is driven down the pitchfork top
lead where it must split, with some current traveling down each leg of the loop, through a junction,
and recombining through the straight bottom lead. The adjacent flux-line wire is driven with a
current, Iφ , which creates a magnetic field, Bφ , that injects magnetic flux into the SQUID loop.
As described in Chapter 2, the critical current of a SQUID loop will oscillate with the flux
through the loop. The junctions are labeled JJ-1 and JJ-2 for the more circular and more elliptical
junctions, respectively. If both junctions are in the 0 phase state, this oscillation will be unaltered.
If one junction is in the π state and the other is in the 0 state, then the oscillation will be horizontally
shifted by a phase of π or equivalently, an extra flux of Φ0 /2. If both junctions are in the π state,
the two additional phase shifts cancel out and the oscillation is unaltered. These phase states are
achieved by manipulating the magnetization directions of the two F layers in the spin valve into the
parallel or antiparallel configuration using an external in-plane magnetic field, labeled Hin in Figure
8.1. This figure also shows the positive directions for Is , Iφ , Bφ , and Hin with the corresponding

102

9
0.

I c+ (mA

8
0.
7
0.
6
0.

10
0
75

I

(a)

(m

.4
0

A)

25
.8
0

0

e

.0
0

)

50

(O

.4
-0

in

5
0.
4
0.
.8
-0

H

)

0
1.

0.4
0.6
0.8

0
1.

1

7
0.
6
0.

0
-25

I

.0
0

(m

.4
0

A)

-75
.8
0

-10
0

)

-50

e

.4
-0

(O

5
0.
4
0. .8
-0

in

(b)

1

8
0.

H

I c+ (mA

)

9
0.

Figure 8.2 Three-Dimensional Plots of Positive SQUID Critical Current, Ic+ , vs Flux-Line
Current, Iφ , and In-Plane Set Field, Hin After each value of Hin is applied, the field is returned
to zero and a scan of Ic+ vs Iφ is measured. Cross-sections at a fixed Hin value show clear
SQUID oscillations in Ic+ (Iφ ) with a period of about 1.1 mA, corresponding to one flux quantum,
Φ0 . Sudden jumps in the magnitude and phase of Ic+ indicate changes in the magnetic state of
one of the Josephson junctions in the SQUID. The four total jumps correspond to the four
magnetic states shown in the cartoons in Figure 8.1. a) shows the data for Hin > 0 and b) shows
the data for Hin < 0. In both cases the data are taken with |Hin | increasing in time.

103

arrows. Four distinct magnetic states can be accessed combining the P and AP states of the two
junctions in the loop. They are shown in the cartoon below the SQUID layout in the figure with
labels indicating the magnetization direction of the Ni and NiFe layers with black or red arrows
and the expected phase state of the junctions with the P state corresponding to the π phase state
and the AP state corresponding to the 0 phase state.
These devices are mounted onto a quick dipper probe with a surrounding solenoid magnet and
submerged in liquid helium for measurements. To start, we initialize the junctions into the (π − π)
state by applying a large in-plane field of Hin = -2,600 Oe, which sets all four magnetic layers in
the negative direction. The sample is then warmed above 10 K by raising the sample up out of the
liquid helium to remove any trapped flux from the initialization process. We then measure, at zero
field, a set of IV curves while varying the current, Iφ , through the flux line to observe oscillations
in the SQUID critical current as a function of applied flux. Critical currents are obtained by fitting
the IV curves to the standard form for an overdamped Josephson junction given in equation 2.16.
Note that the critical currents for the two polarities of applied current, Ic+ and Ic−, need not be the
same. Next we apply a small ’set’ field of Hin = 5 Oe, return the field to zero, and repeat the scan
of IV curves versus flux. We continue taking small steps in Hin , each time setting the field back to
zero and repeating a full flux scan.
Figure 8.2 shows three-dimensional plots of Ic+ versus Hin and Iφ as Hin is stepped from 0 to
100 Oe. Cross-sections of the plot at fixed values of Hin exhibit clear oscillations in Ic+ (Iφ ). As
Hin is varied, those cross-sections exhibit two large jumps, the first at Hin = 30 Oe and the second at
Hin = 50 Oe. At each jump, the overall magnitude of the critical current changes, and the peaks in
Ic+ shift along the flux axis. We identify the first jump with the NiFe free layer in the more circular
JJ-1 switching its magnetization direction, so that the phase state of JJ-1 switches from π to 0, thus
changing the SQUID from the (π − π) to the (0-π) state. The second jump signifies that the NiFe
layer in the more elliptical JJ-2 has switched its magnetization direction, and is now also in the
0-state, so the SQUID is now in the (0–0) state. Figure 8.2 part b) shows similar data acquired for
Hin < 0. Again, there are two jumps in the plot, the first occurring at Hin = -35 Oe, putting the
104

SQUID in the (π-0) state, and the second at Hin = -100 Oe, returning the SQUID to the (π − π)
state as at initialization. Taken together, Fig. 2a, b corresponds to a major loop through all four
accessible magnetic states of the system, where only the NiFe layer of each junction switches and
the Ni in both junctions remains always in the initialization direction. The fact that the magnitudes
of the switching fields for Hin < 0 are generally larger than for Hin > 0 is consistent with the effect
of dipolar coupling between the fixed Ni layer and the free NiFe layer in each junction.
Figure 8.3 shows more detailed data of Ic+ and Ic− versus Iφ for four selected values of Hin
taken just after each phase jump. Several features are immediately apparent in the data. First, Ic+
and Ic− never approach zero, but rather oscillate with an amplitude of approximately 85 µA in all
four magnetic states. Second, the oscillations of Ic+ and Ic− are not sinusoidal, but rather have an
asymmetric saw tooth or ratchet shape. Third, the maxima in the Ic+ and Ic− data do not line up
with each other, so in general Ic− (φ ) = −Ic+ (φ ). All three of these features are well understood
[9, 18]; the first is due to the finite geometrical inductance of the SQUID loop, whereas the second
and third are due to asymmetries in the inductances of the two arms of the loop and in the critical
currents of the two junctions. The four magnetic states were fit independently, as described below.
They properly take these asymmetries into account and show not only excellent agreement with
the data but confirm π phase shifts between successive magnetic states. These are most obviously
observed in Figure 8.3 part b) which shows the average critical current, Iave
c = (Ic+ − Ic− )/2, vs Iφ .
Though the offsets in Ic+ and Ic− cause these curves to have an atypical shape, the black dashed
line guides the eye to see the π phase shifts between each state. The NiFe switching fields are also
labeled for each state.
The results represented in Figure 8.3 were reproducible upon repeating the whole major loop
several times. In addition, we obtained ‘minor loop’ data after initialization by keeping Hin between +30 Oe and -35 Oe, so that only the free layer of JJ-1 switches its state back and forth. We
have obtained similar minor loop data from several different nominally identical devices; the best
major loop data were obtained in the device shown here.

105

(a)
(a)

(b)
0.50
0.45

I

10

-100 Oe

0.48

-0.45
-0.50

0.50

C+

I

8

0.46

C-

0.78

0.75

I

0.70

+30 Oe

C+

C-

1.00
0.95
0.90

I

4

(mA)

I

-0.75

ave

6

Ic

Ic+, Ic-

(mA)

0.74

-0.70

0.70

+50 Oe

0.95

C+

-0.90

I

-0.95
-1.00
0.70

2

I

0.65

0.94
C-

-35 Oe

0.72
C+

0.68

-0.65
-0.70

0
-2

I

0

-1

0

I

2

1

C-

4

0.64

6

2

(mA)

-2

8
-1

0

I

(mA)

10
1

2

Figure 8.3 Ic+ , Ic− , and Iave
c Data with Fits for All Four Magnetic States for a SQUID
containing NiFe(1.5)/Ni(1.2) Free and Fixed Layers a) Positive and negative critical current
values vs flux-line current, Iφ for the four magnetic states of the major loop. The state labels of
’π − π,’ ’0 - π,’ etc, refer to the phase states of JJ-1 and JJ-2, respectively. The ratchet shapes of
the curves are due to asymmetries in the critical currents of the two junctions and the path
inductance of the two arms of the loop. For each magnetic state, the Ic+ and Ic− curves are
shifted with respect to each other in opposite directions and by amounts that depend on the
individual critical currents, Ic1 and Ic2 , of the two Josephson junctions. The solid lines are the
result of least-squares fits to the data using the asymmetric SQUID model described in Chapter 2.
b) Plot of average critical current, Iave
c = (Ic+ − Ic− )/2 versus Iφ , for the same four magnetic
states represented in a) including the switching field for each state. The colored solid lines are
derived from the fits in a). Whereas the shapes of the Iave
c curves depend on the alignment
between the Ic+ and Ic− curves, the positions of the maximum and minima in Iave
c are immune to
the shifts in Ic+ and Ic− . This figure shows schematically the π phase shifts in the (0 - π) and (π
– 0) states relative to the (π − π) and (0 – 0) states, though the full fit analysis is required to verify
the 0 - π switching of the junctions.

106

8.1.1

SQUID Data Analysis

Several complementary methods were used to fit this asymmetric SQUID data to confirm a π phase
shift between successive magnetic states. The theory of an asymmetric SQUID was discussed in
Chapter 2. The SQUID is characterized by the four parameters L1 , L2 , Ic1 and Ic2 , which are the
effective inductances of the two arms and the critical currents of the two Josephson junctions. L1
and L2 are simply related to the geometric inductances of the two arms if the mutual inductance
between them is properly taken into account [77]. On the basis of the geometry shown in Figure
8.1, we expect that L2 > L1 . In our samples L1 and L2 are fixed to the same value in all four
magnetic states, whereas Ic1 and Ic2 change depending on whether the corresponding junction is
in the 0 or π state. The phase shifts seen in part b) of Figure 8.3 are not sufficient to verify real
phase changes within the junctions because apparent π shifts in the Iave
c (Iφ ) curves can arise purely
from changes in Ic1 or Ic2 . One can detect the presence of π phase shifts by analyzing the shifts
in the peak positions of the Ic+ and Ic− curves when the SQUID transitions from state to state, as
shown by the following argument.
The current reaches its maximum value, Ic = Ic1 + Ic2 , when the phase drop across each junction
is π/2, so that the currents I1 and I2 through the two arms of the SQUID equal Ic1 and Ic2 , respectively. Those currents induce a flux through the SQUID loop, Φint = L1 Ic1 − L2 Ic2 . That must be
balanced by the externally applied flux, so the peak in Ic+ occurs at a flux of Φ peak+ = −Φint+ =
L2 Ic2 −L1 Ic1 . The maximum negative critical current occurs at flux Φ peak− = −Φ peak+ , hence the
peaks in Ic+ (φ ) and Ic− (φ ) are shifted with respect to each other by ∆Φ peak ≡ Φ peak+ −Φ peak− =
2(L2 Ic2 − L1 Ic1 ). Because the Ic (φ ) curves are periodic, ∆Φ peak can be determined only modulo
Φ0 . That means that the center of the pattern, that is the point half-way between an Ic+ peak
and its corresponding Ic− peak, can be determined only modulo Φ0 /2. Fortunately, you can determine which of the possible values for ∆Φ peak is the physical value by analyzing the changes
in ∆Φ peak when the critical current of only one of the junctions changes. If JJ-1 changes its critical current by an amount ∆ Ic1 whereas Ic2 remains unchanged, then the peak separation will

107

change by δ (∆Φ peak ) = −2L1 δ Ic1 . Turning the argument around, one can extract the inductance
L1 from the transition using L1 = −δ (∆Φ peak )/2δ Ic1 . Similarly, if JJ-2 changes its critical current by an amount δ Ic2 whereas Ic1 remains unchanged, then the peak separation will change by
δ (∆Φ peak ) = +2L2 δ Ic2 . What one finds is that, if one takes the wrong value of δ (∆Φ peak ) for
a transition, then the value of L1 or L2 extracted from the transition is unphysical. Our data set
provides four transitions; the transitions from the (π − π) state to the (0-π) state and from the (0-0)
state to the (π-0) state allow us to extract L1 , because only Ic1 changes, whereas the transitions
from the (0-π) state to the (0-0) state and from the (π-0) state to the (π − π) state allow us to
extract L2 , because only Ic2 changes. Only when π phase shifts are included between successive
staes can a consistent set of inductance values be obtained with L1 = 6.0 ± 0.5 pH and L2 = 11.7
± 0.1 pH. These values are in agreement with the results of simulations of our SQUID geometry
using the FastHenry software, which produced values in the range of 6–7 pH for L1 and 13 pH for
L2 , with variations of about 1 pH for each depending on the type of mesh used in the simulation.
The inductance and junction critical current values obtained from this method are summarized in
the first data row of Table 8.1. Different choices of δ (∆Φ peak ) that do not include the π shifts
yield values of L1 and L2 that differ in either direction by about 5 pH; those values are not only
inconsistent with simulations of our geometry, but more importantly they are inconsistent with the
observed depth of the Ic (φ ) oscillations, which must be approximately equal to Φ0 /L [18]. The
phase shifts deduced from this analysis confirm that the SQUID does indeed acquire a phase shift
of π each time the system transitions between successive states in the sequence. Analyzing the
four SQUID transitions in this manner also provides us with values for δ Ic1 and δ Ic2 , but not
values of the individual critical currents for each junction in each magnetic state. To estimate the
latter, one can assume that the ratios of critical current densities between the 0 and π states in both
junctions are equal. That assumption implies that Ic10 /Ic1π = Ic20 /Ic2π , but allows the areas of the
two junctions to differ. That analysis leads to the approximate critical current values listed in the
top data row of Table 8.1.
To obtain more accurate values of the SQUID parameters, we performed a nonlinear least-

108

Preliminary
Analysis
Leastsquares fits

I0c1 (µA)

L1 (pH)

L2 (pH)

6.0 ± 0.5

11.7 ± 0.1

5.68 ± 0.1

11.46 ± 0.12

Iπc1 (µA)

I0c2 (µA)

Iπc2 (µA)

560 ± 10

290 ± 10

420 ± 10

220 ± 10

565.9 ± 1.4

292.8 ± 1.2

419.5 ± 0.2

210 ± 7

Table 8.1 NiFe(1.5)/Ni(1.2) SQUID and Junction Parameters The inductances of the two arms
of the SQUID and the critical currents of each junction in each of its two possible magnetic states
are estimated from a simple analysis described in the text (top data row), or by least-squares
fitting of the data shown in Figure 8.3 by numerical analysis.

State

L1 (pH)

L2 (pH)

Ic1 (µA)

(π-π)
(0-π)
(0-0)
(π-0)

5.73±0.05
5.64±0.04
5.63±0.03
5.71±0.03

11.38±0.08
11.33±0.07
11.56±0.06
11.56±0.05

291.6±1.5
564.5±1.8
567.3±2.0
294.0±1.3

Ic2 (µA)

φshi f t

216.8±1.5
202.5±1.8
419.3±2.0
419.7±1.3

-0.1195±7E-4
+0.3517±6E-4
-0.1360±5E-4
+0.3955±4E-4

φshi f t φglobal
0.0076
0.4788
-0.0089
0.5226

Table 8.2 Inductances of the Two SQUID Arms and Junction Critical Currents from Fit
Parameters These inductance values were obtained from the fits to the data for the four SQUID
states listed in column 1. The uncertainties are given by the Nonlinear Least Squares fitting
routine in Mathematica, and do not account for correlations between the fitting parameters [61].
φglobal = -0.1271 and is the average of the φshi f t values after subtracting 0.5 from the values of
the (0-π) and (π-0) states.
squares fit to the data of a numerical analysis of the asymmetric SQUID using the Mathematica
software. This fitting software was almost exclusively coded and executed by my coworker Joseph
Glick. The asymmetric SQUID model used for this analysis was fully described in Chapter 2. To
reduce the number of free parameters in the fits, we first determined the conversion from Iφ to φ
by fitting the Iave
c (φ ) curves shown in Figure 8.3 part b) with a simple Fourier series. For the (0-π)
and (π–0) states, a single cosine wave fits the data well, whereas for the (0–0) and (π–π) states
we used a cosine wave plus its second harmonic. From the Fourier series fits to the four data sets,
we determined that Iφ = (1.115 ± 2)µA * φ /Φ0 . That conversion factor was then kept fixed in
all the ensuing fits. The fitting procedure was as follows. For each magnetic state, the data for
Ic+ (Iφ ) and Ic− (Iφ ) were fitted simultaneously. The free parameters in each fit were Ic+ , |Ic− |, βL ,
αL , αI and φshi f t . The dimensionless parameters βL , αL , and αI were discussed in Chapter 2 and

109

can be easily manipulated to determine the physical parameters L1 , L2 , Ic1 , and Ic2 . Although we
expected Ic+ and |Ic− | to be equal to each other, the data exhibited small differences between Ic+
and |Ic− |, of order a few µA. The last parameter, φshi f t , is the dimensionless shift of the center
of the pattern relative to zero flux. The values of the physical SQUID parameters extracted from
the fits to all four magnetic states are shown in Table 8.2 with the average values of L1 , L2 , I0c1 ,
Iπc1 , I0c2 , and Iπc2 listed in the bottom row of Table 8.1 for comparison with the phase-shift method
values. The independent fits to the four magnetic states produce remarkably consistent results
for the values of the two SQUID inductances and the critical currents of the two junctions, each
in two magnetic states. Those values are very close to the preliminary values extracted from the
analysis of the peak positions described above. The junction critical current values in each state
confirm that between each successive magnetic state, primarily, one junction was switching. There
is about an 8% change in the critical current of JJ-2 when JJ-1 was primarily switching from the
(π − π) state to the (0-π) state, but this change is required to obtain consistent inductance values
so we believe this is a real effect caused by a slight magnetic change to JJ-2 during this switching
process. Also, all these critical current values are large enough for JMRAM applications. Most
importantly, the values of φshi f t confirm the additional phase shifts of π that occur at each magnetic
transition which is most obvious from the last column of Table 8.2 where φshi f t values of 0 and 0.5
correspond to phase shifts of 0 and π, respectively.
The data did include a global phase shift, φglobal = 0.1271 that is the average of the φshi f t
values after subtracting 0.5 from the values of the (0-π) and (π-0) states. Despite our best efforts,
we were not able to pin down the origin of this global shift. The data in the last column of Table
8.2 also show that, after subtracting φglobal from φshi f t , the values of φshi f t are not exactly equal
to 0 or 0.5 but include extra small shifts of about 0.022 in the (0-π) and (π-0) states and less
than 0.01 in the (0-0) and (π-π) states. These small changes in φshi f t are consistent in relative
magnitude and sign with what one would expect from the flux coupled into the SQUID by the
NiFe layer magnetizations as they change direction. For example, the (0-π) state has both NiFe
magnetizations pointing inward so they induce positive flux into the SQUID loop, thereby causing

110

the peaks in Ic+ and Ic− to shift toward smaller flux. We have calculated the magnitude of these
flux changes and find values several times larger than what is observed in the experiment; we
believe that most of the flux is shielded by the wide superconducting electrodes placed directly
above and below the junctions, which were not taken into account in the calculations. The major
change in φshi f t is the addition of 0.5 in the (0-π) and (π-0) states relative to the (0,0) and (π-π)
states, which is the major result of this work. This is clear from the last column of Table 8.2. This
experiment and these results are similarly explained in reference [28].

8.2

NiFe(1.0)/NiFeCo(1.1) SQUIDs

After successfully demonstrating 0-π phase switching in the NiFe(1.5)/Ni(1.2) system, we turned
our attention to working towards optimizing these devices. Now that the proof of concept for JMRAM was complete, we needed to work towards creating many such phase controllable junctions
with similar properties for use in a memory array and unit cell demonstration. We believed that
the Ni fixed layer had poor magnetic properties and wanted to replace it with a better behaved
magnetic material. Preliminary work measuring the 0-π transition thickness for NiFeCo led us
to believe that it would make a better choice. NiFeCo requires a lower initialization field of only
several hundred Oersted, it was found to have single domain properties at the 0.5 µm2 size, its
switching field was sufficiently larger than that of the free layer, NiFe, and its magnetic switching
showed more ideal behavior both directly from magnetometry measurements and indirectly from
Fraunhofer pattern measurements.
The fixed layer NiFeCo was chosen to be a thickness of 1.1 nm to be close to its 0-π transition
thickness and the free layer NiFe was chosen to be a thickness of 1.0 nm to be below its 0-π transition thickness. Additional improvements of the smoother base Nb electrode [Nb(25)/Al(2.4)]3 /
(Nb(20) and a switch to a symmetric SQUID design, as shown in Figure 8.4, were implemented.
The smoother electrode should improve the surface morphology and hence the magnetic properties
of the two F layers. The symmetric design will reduce the inductance asymmetry since now L1

111

Figure 8.4 Cartoon of Symmetric SQUID Layout The SQUID device is made up of the blue
pitchfork bottom lead which has a 3 µm width and the green T-shaped top lead with a 4 µm
width. The inner dimensions of the loop are 6 µm by 6 µm. Sample current, Is , travels up
through the pitchfork and recombines in the green top lead. The nearby 3 µm wide purple flux
line is driven with a current, Iφ , to inject magnetic flux into the loop. An external in-plane field,
Hin , is used to manipulate the magnetic layers in the junctions. The red and blue solid lines show
the equal sample current paths through this symmetric SQUID design.
= L2 which will reduce the shift in the Ic+ and Ic− curves. This design also features smaller line
widths. The blue bottom lead and purple flux line are 3 µm wide, the green top lead is 4 µm wide,
and the inner dimension of the SQUID loop is 6 µm by 6 µm. The device functions in the same
way as the asymmetric design described in Figure 2.15, but now the red and blue lines depicting
the sample current path should have the same length. This new layout required slightly more fluxline current to complete one SQUID oscillation, with Fourier fits giving 1.382 mA of current for
each flux quantum induced in the loop.
Since the NiFeCo has a lower saturation field, initializations were performed at -600 Oe before
removing trapped flux from the device. In the same way as with the NiFe(1.5)/Ni(1.2) SQUID,
oscillations of the critical current with applied flux were measured (at zero field) after an in-plane
’set’ field was slowly stepped from 0 to +100 Oe and 0 to -100 Oe. The results from one such
measurement are shown in the 3D plot of Figure 8.5. Here, the average critical current, Iave
c , was

112

Figure 8.5 Three-Dimensional Plots of Average SQUID Critical Current vs Flux-Line
Current and In-Plane Set Field, Hin for NiFe(1.0)/NiFeCo(1.1) SQUID The Iave
c vs Iφ
oscillations have much more sinusoidal shape due to the reduced asymmetry of these junctions
and the low critical current values. These plots show evidence of 0-π switching between
successive states, but also several intermediate states. The ’up’ sweep shows data for Hin > 0 and
the ’down’ sweep show data for Hin < 0.
plotted against the flux-line current and the ’set’ field. While 0-π switching is visually observed between several states, with a total of two phase switches in each field sweep direction, as expected,
now we see the presence of intermediate switching states as well. The first oscillation at zero field,
colored in light and dark blue, shows a maximum at zero flux-line current and is characterized
as the (π-π) state. At around 5 Oe, the device exhibits a shift in phase with little change in the
critical current total height before increasing drastically in critical current while maintaining the
same phase shift by around 14 Oe. This lower critical current state at 5 Oe was characterized as
an intermediate state with the full (0-π) state occurring at 14 Oe. This state is maintained until the
’set’ field reaches 28 Oe when the device cleanly switches into the (0-0) state. Continuing with the
’set’ field in the negative direction, the device transitions into a second intermediate state before
switching to the (π-0) state at -44 Oe, and a third intermediate state before returning to the (π-π)
initialization state at -70 Oe. These three intermediate states and the features of the 3D plot in general were reproducible over several major loop iterations and cooling cycles. Robust minor loops

113

Figure 8.6 Ic+ , Ic− , and Iave
c Data with Fits for All Four Magnetic States for a
NiFe(1.0)/NiFeCo(1.1) SQUID The left-hand plot shows positive and negative critical current
values vs flux-line current, Iφ for the four magnetic states of the major loop. These oscillations
show a much more sinusoidal shape due to the reduced asymmetry and lower critical current
values compared to the data in Figure 8.3. The solid lines are the result of least-squares fits to the
data using the asymmetric SQUID model described in Chapter 2. The right-hand plot shows the
average critical current, Iave
c versus Iφ , for the same four magnetic states represented in a)
including the switching field for each state. The colored solid lines are derived from the fits in a).
This figure shows the π phase shifts in the (0 - π) and (π – 0) states relative to the (π − π) and (0
– 0) states, though the full fit analysis is required to verify the 0 - π switching of the junctions.
with only the NiFe layer of one junction switching back and forth were also reproducibly collected.
The intermediate switching states are not ideal, as they indicate some kind of magnetic change to
the junctions before the full switch is realized. This could indicate a magnetic layer breaking into
magnetic domains, remaining a single domain but with a a non-uniform magnetization direction,
or another magnetic change that is stable over a small field range. However, intermediate states of
this type do not pose a problem for JMRAM elements as long as a consistent field value can be
used to change the junction phase by π.
Figure 8.6 shows these four magnetic states in terms of the Ic+ , Ic− , and Iave
c oscillations with
114

State
(π − π)
(0-π)
(0-0)
(π-0)
Average
Standard
Deviation

L1 and L2 (pH)
5.9
12.1
7.9
6.1
8.0

Ic1 (µA)
16
15
37
42

Ic2 (µA)
7
23
27
6

φshi f t
0.024
0.541
0.035
0.513

2.9

Table 8.3 Fit Results for NiFe(1.0)/NiFeCo(1.1) SQUID 2328 4A-4 Since the symmetric design
was used, the fits assumed that L1 = L2 . There is a larger spread in the fitted inductance values
compared to the NiFe(1.5)/Ni(1.2) SQUID and that is not well understood. The φshi f t values
changing between around 0 and 0.5 represent the successive π phase changes to the junctions
between magnetic states.
flux-line current, Iφ . It is immediately obvious that all of these oscillations are considerably more
sinusoidal in shape than those from the NiFe(1.5)/Ni(1.2) SQUID since here the inductances are
symmetric and the critical current is much lower. The solid lines represent least-squared fits to the
data described in the analysis section above. Again, the theory is aptly able to match the data in all
four states. The right-hand plot of Iave
c vs Iφ shows the 0-π phase shifts between each state with
the black dashed line guiding the eye. The switching fields obtained for this sample are somewhat
lower than those from the NiFe(1.5)/Ni(1.2) SQUID, possibly due to the thinner NiFe or smoother
base electrode used in this case. We also see that the switching fields are asymmetric, with larger
values in the negative direction. This is again consistent with the effect of dipolar coupling which
will favor a junction switching into the AP state.
The numerical results of the fits were used to calculate the physical parameters of the device,
L1 , L2 , Ic1 , Ic2 , and φshi f t . These values are summarized in Table 8.3. Since the symmetric SQUID
design was used, L1 and L2 were constrained to have the same value. There is more variability
in the value state to state, but the average of 8.0 pH is consistent with the expected value of 8.5
pH from our device geometry. The junction critical currents show that while primarily only one
junction critical current changes between phase states, JJ-2 actually switches first instead of JJ-1 as
expected from the junction shapes. Luckily, there was still a switching field difference between the

115

Figure 8.7 3D Plots of the average critical current, Iave
c , vs the flux-line current, Iφ , and the
’set’ field, Hin for a NiFe(1.0)/NiFeCo(1.1) SQUID These curves are also primarily sinusoidal in
shape but the critical currents are significantly higher than those seen in the previous nominally
identical SQUID. There are still some intermediate states but they persist over a much narrower
field range. Below the 3D plots, four slices at each magnetic state are plotted together and labeled
with their switching field values.
two junctions, but clearly the aspect ratio is not sufficient to control which junction will switch at
a lower field value. There are some small critical current changes in the presumed non-switching
junction which are not ideal and the magnitude of all these critical currents are too low for JRMAM
applications. The φshi f t values, though, convincingly display 0-π switching between the magnetic
states making this system the second to demonstrate the effect.

116

The point of this second 0-π demonstration was to show the π phase switching in a more
reproducible system, so another batch of nominally identical SQUIDs were fabricated in an attempt
to observe the same effect in several additional samples. Unfortunately, that desire was not realized.
Several samples showed reproducible minor loops, but the one sample which appeared to have 0-π
switching in a reproducible major loop showed its true behavior through the fit parameters and
peak-shift analysis. Figure 8.7 shows the 3D plot for this second NiFe(1.0)/NiFeCo(1.1) SQUID.
There are two apparent π phase changes in each direction with less glaring intermediate states.
The presumed ’(π-0)’ state, colored dark blue, has a very small oscillation amplitude, but does
also show an apparent π phase shift. This is a little easier to see in the lower plot showing the four
magnetic states of the major loop where the ’(π-0)’ state is colored yellow. Some key differences
between this sample measurement and the previous NiFe(1.0)/NiFeCo(1.1) SQUID are apparent.
First, the maximum total critical current here is about four times larger. Second, the switching
fields for the NiFe in this sample are also significantly larger. Third, the intermediate states are
still occasionally present, but they persist for a much shorter field range. Lastly, even looking at
the Iave
c data, the successive states do not show perfect π phase shifts between all four states. This
is most obviously seen in the lower plot.
Fits were only obtained for the first three magnetic states, with the ’(π-0)’ state showing too
small of an oscillation amplitude for a reliable fit to be found. A summary of the fit result parameters are shown in Table 8.3 where the fit starting values were chosen to encourage a π phase shift
in the ’(0-π)’ state. You can see that the first fit to this state has highly irregular L1 and L2 values. Additionally, the critical current values show that both junctions change their critical currents
between successive states. Also, when the peak shift analysis is considered between the ’(π-π)’
and ’(0-π)’ state and between the ’(0-π)’ and ’(0-0)’ state a value for L1 and L2 can be obtained.
Using this process gives L1 = 0.45 pH and L2 = 3.25 pH. These values are clearly too small for the
physical device layout.
When the π phase shift is not encouraged in the starting fit values, a different local minima
is chosen by the fit which gives more reasonable L1 and L2 values from the fits. This is shown
117

State
(’π − π’)
(’0-π’ (1))
(’0-π’ (2))
(’0-0’)
Average (1)
Standard
Deviation (1)
Average (2)
Standard
Deviation (2)

L1 (pH)
8.24
9.90
10.13
7.65
8.59

L2 (pH)
7.63
16.99
12.81
7.59
10.74

1.17

5.42

8.67

9.35

1.30

3.01

Ic1 (µA)
27
101
133
151

Ic2 (µA)
51
67
35
138

φshi f t
0.00
0.524
0.024
-0.075

Table 8.4 NiFe(1.0)/NifeCo(1.1) SQUID 2336 5B-4 Fit Parameters Fit Parameters giving initial
conditions to encourage the appearance of 0-π switching in the φshi f t value for
NiFe(1.0)/NiFeCo(1.1) SQUID 2336 5B-4. Only the first three magnetic states could be
successfully fit. The forced state, ’(π-0)(1)’, shows an unphysically large asymmetry in L1 and
L2 . State ’(π-0)(2),’ which does not include the π phase shift, still shows some inductance
asymmetry but has much more reasonable values for L2 . This feature leads us to believe that the
junction is not showing 0-π phase changes. Both fits show some degree of critical current change
in both junctions, though only one is presumed to switch between each magnetic state. Primarily,
JJ-1 switches first and JJ-2 second, but the other junction is somewhat affected.
in Table 8.3 as state ’(0-π) (2).’ The peak-shift analysis inductances are also much closer to the
expected values with L1 = 10.08 pH and L2 = 7.70 pH. However, even this fit with no 0-π phase
changes shows that both junctions change critical current in each state change. This analysis
indicates that the second NiFe(1.0)/NiFeCo(1.1) SQUID did not show phase switching despite
being nominally identical in material stack and fabrication to the first sample which did show phase
switching. This unfortunate result led us to believe that even though these material thicknesses
were chosen based on single layer S/F/S studies of the two individual materials, perhaps that is
not sufficient to predict how the junction will behave in a spin-valve stack. Perhaps this set of
thicknesses puts either the P or AP state very close to a phase transition so that small variations in
material thickness from sputtering run to sputtering run could cause one sample to show 0-π phase
switching while another does not. This result led to the first of the single junction spin-valve series
studies described in Chapter 7 used to pin down the range of thicknesses that would produce phase
switching in several systems.

118

Figure 8.8 3D plot of average critical current vs flux current and applied ’set’ field for
NiFe(1.25)/Ni(2) SQUID 1A-2 The ’up sweep’ shows positive set field values and the ’down
sweep’ shows negative field values. The first measured oscillation at zero field had the largest
critical current, so the ’up sweep’ data is rotated with zero field in the back of the plot working
forward to positive field values so the data can be better seen. The ’real’ phase states and
intermediate phase states are labeled in the plots with black arrows.

8.3

NiFe(1.25)/Ni(2.0) SQUIDs

Continuing the quest for reproducible phase switching samples, we returned to the NiFe/Ni system.
A smoother base electrode and normal metal buffer and spacer layers were developed, as discussed
in Chapter 4, which were expected to reduce sample roughness and improve magnetic behavior.
Thicker Ni was investigated as a fixed layer in a single junction spin-valve study which showed
acceptable magnetic results as well as determined the optimum NiFe thickness to use with Ni(2).
This thickness was shown to be 1.25 nm based on where 0-π switching was expected to occur
and where the critical currents of the junction was most similar in the P and AP state at zero field.
We believed that this would highly reduce the critical current asymmetry in the SQUID devices.
Paired with the symmetric SQUID design which reduces the inductance asymmetry, we expected
very little shift in the Ic+ and Ic− curves for these samples.
The final structure of these samples was [Nb(25)/Al(2.4)]3 /Nb(20)/Cu(2)/NiFe(1.25)/Cu(4)/
Ni(2.0)/Cu(2)/Nb(5)/Au(15)/Nb(150)/Au(10). A handful of SQUIDs were measured from this
batch. Samples were initialized with a -1500 Oe field and trapped flux was removed. Many
119

samples showed minor loop behavior and apparent π phase switching. The best major loop data
is shown in Figure 8.8. This 3D plot shows the average critical current vs flux-line current and
applied ’set’ field for an ’up’ and ’down’ sweep of positive and negative field values, respectively.
The ’real’ and ’intermediate’ states are labeled in the plot with black arrows. In addition to the four
expected magnetic states, three intermediate states were observed for this sample. The intermediate
states all show a dip in critical current reminiscent of the dips in critical current of the Fraunhofer
patterns near zero field in the spin-valve series studies. Switches occurred at +25 Oe, +60 Oe, -25
Oe, and -45 Oe. For the first time, the asymmetry in these switching fields does not favor the AP
magnetic state.
Both the presumed ’real’ phase states and intermediate states were fit to determine the physical
parameters of the SQUID and to see if 0-π switching occurred in this sample. Figure 8.9 shows the
results of these fits for the four main phase states. Each row represents one of the four magnetic
states and each column represents a starting horizontal shift (φshi f t ) value for the fit of either 0
or 0.5. A shift of 0 indicates both junctions are in the 0 or π phase states and a shift of 0.5 indicates that one junction is the the 0 state and the other is in the π state. Both versions of the fit for
each magnetic state not only have excellent agreement with the data, but the other fit parameters,
shown in Figure 8.10, have physically reasonable values. For past samples, fit ambiguity was distinguished by unphysical inductance values obtained either directly from the fit parameters or from
the peak-shift analysis. Figure 8.10 shows that the SQUID parameters obtained from the two fits
for each of the expected and intermediate states have reasonable inductance values. Intermediate
states 2 and 3 were only able to be fit with one set of parameters and the black arrows on the
left-hand side of the table indicate where the intermediate states fall into the ordering of the major
loop. The set of states colored either light or dark blue run through a full major loop of states and
exhibit π phase switching between successive state. The light blue data begin assuming the correct
(π-π) state has φshi f t = 0 while the dark blue data begin assuming the correct (π-π) state has φshi f t
= 0.5. Both states tell the same story with one junction switching between each magnetic state
except for the (π-0) to (π-π) state change where both stories require that both junctions change

120

Figure 8.9 Ambiguous Fits to NiFe(1.25)/Ni(2) SQUID Major Loop States Each row
represents one of the four magnetic states. Depending on the starting values given to the fitting
software, fits with shift values of approximately 0 (both junctions are in the same phase state) or
0.5 (only one junction is in the π phase state) could be obtained. In previous cases, the fit
inductance values or peak-shift analysis inductance values could be used to distinguish the
physically relevant state. Unfortunately, for this data, both fits for each state give nearly identical
inductance values by both analysis methods, so the results are ambiguous.

121

Figure 8.10 SQUID Fit Data to All Major Loop States for a NiFe(1.25)/Ni(2) SQUID Each of
the four expected magnetic states and three intermediate states were fit with starting parameters to
encourage either a φshi f t of 0 or 0.5. Intermediate states 2 and 3 only converged into one fit. State
sets marked in either light or dark blue represent a complete set of major loop states that include
π phase shifts between successive states. The inductance values obtained from the fits can’t be
used to distinguish between physcial and unphysical fits since the values are very similar whether
the phase shift is 0 or 0.5.
critical current.
The peak-shift analysis requires looking at the changes between two different magnetic states.
This was used to investigate whether the light or dark blue data sets gave physically relevant inductance values. Unfortunately, both sets gave almost identical inductance values, so that method
could not be used to eliminate one set of fits. Mixing states from the light and dark blue sets so that
no phase switching is assumed sometimes gives identical inductance parameters and sometimes
values that differ by 3-4 pH. So while it is likely that this sample and others in this set are showing
0-π phase switching, we cannot reliably distinguish the physical SQUID parameters that describe
the sample.
To overcome this issue, it would be helpful if it were only possible to fit each magnetic state
with one set of parameters. This can be achieved with a low inductance SQUID design. Generally,
122

the peak position of one state is given by φ peak = (L2 Ic2 −L1 Ic1 )/Φ0 = βL (αL +αI )/2. (Reminder
that αL = (L2 − L1 )/(L1 + L2 ), αI = (Ic2 − Ic1 )/(Ic1 + Ic2 ), and βL = Ic L/Φ0 ). The peak shift
when a magnetic state changes from one state to the next is given by ∆φ peak = βL ∗ ∆αI /2. Since
max =
αI is constrained to have values between -1 and 1, we find the maximum peak shift ∆φ peak

βL . If ∆φ peak < 1/2 then only one set of fit parameters will match the data, so if we design our
SQUIDs so that βL < 0.5 we will be able to avoid ambiguity regarding π phase shifts in our
fits. Assuming SQUID critical currents of 0.5 mA, total SQUID inductance of 2 pH or less will
meet this criteria. This criteria is very strict since we use ∆αI = 2 indicating that in one state all
the critical current passes through JJ-1 with none passing through JJ-2 and in the next state all
the critical current passes through JJ-2 with none passing through JJ-1. Since this is unlikely to
happen in our samples, slightly larger L values would likely still produce unambiguous fits. The
group is currently working towards fabricating SQUIDs with much lower inductances to continue
the search for reproducible phase switching junctions.

123

CHAPTER 9
CONCLUSIONS

9.1

Summary of Results

Throughout this work, an extensive study of ferromagnetic Josephson junctions was performed
with the hopes to experimentally realize the first phase-controllable junctions. Theories predicted
that a phase-controllable junction could be realized if the junction contained two ferromagnetic layers (a spin valve) with properly chosen thicknesses. Then, when the magnetizations of these two
layers are manipulated between the parallel and antiparallel configurations, the junctions would
change its ground state phase between π and 0. Such a phase-controllable junction has immediate applications as the switching element in a superconducting memory to serve ultra-low power
computing efforts.
To experimentally verify phase switching, interference measurements were needed. This required complicated measurements with two spin-valve junctions together in a superconducting
loop so that the relative phase between the two junctions could be probed. The results from such an
experiment are difficult to interpret without adequate background information about the magnetic
and superconducting properties of the ferromagnetic materials used as well as interface effects and
roughness induced from the base superconducting electrode and normal metal spacer layers.
Preliminary work was completed to address these issues. Prior to my time in the group, samples
were fabricated with one of two base superconducting layers. One was a slab of Nb and the other
interleaved Al with that Nb for smoother surface morphology. My AFM study of seven additional
base electrode candidates varying Nb thickness, interleave material, and number of base structure
repeats was able to identify a base electrode with 35% lower RMS roughness than the previous
best structure. Subsequently, the surface roughness of the normal metal layers used in the full
spin-valve stack were also evaluated. Historically, Cu(5) was used as a magnetic seed layer and
Cu(10) was used to magnetically decouple two ferromagnetic layers. TEM images revealed that

124

these layers were introducing roughness to the thin ferromagnetic layer, which can have adverse
effects on their magnetic properties. Indirect roughness measurements were taken by sandwiching
a NiFe layer between a spacer layer of interest and comparing the magnetic properties of that
NiFe with magnetometry measurements. Many normal metal spacer layers were identified that
produced better NiFe magnetic properties than Cu(5) and Cu(10). However, some of these layers,
namely Ru(2)/Al(7)/Ru(2) and Cu(2)/Al(6)/Cu(2) produced excellent NiFe magnetic properties,
but later were found to cripple the critical current through a Josephson junction. The struggle to
obtain both adequate superconducting properties (sufficient critical current through the junction)
and adequate magnetic properties (low switching field for free layer, single domain reproducible
magnetic behavior) within a single Josephson junction was the main goal of these background
studies. Cu(2) and Cu(4) spacers were decided to have the most advantages for both properties.
Magnetometry is a valuable tool to determine the magnetic properties of potential materials
for spin-valve devices. Measurements of extended thin films gave information about the switching
field range of the material, dead layer effects at interfaces, saturation magnetization, and the fields
required to obtain this saturation. Data from studies of free layer candidate NiFe and fixed layer
candidates Ni, NiFeCo, and NiFe/FeMn were showcased to support their inclusion in subsequent
junction studies.
Next, ferromagnetic materials of interest for the spin-valve stack were first classified alone in
S/F/S Josephson junctions while varying the F layer thickness. This crucial study informed the 0-π
transition thickness of the material, the switching field range to change the material magnetization
direction by 180°, the magnitude of the critical current that can traverse the junction, and the
decay in that critical current as the F layer thickness increases. After these studies, NiFeMo and
NiFe/FeMn were found to have undesirable properties and were not further studied. Free layer
material NiFe and fixed layer materials Ni and NiFeCo were the focus of spin valve and SQUID
devices.
Independently studying materials in S/F/S junctions gave us much information about the superconducting and magnetic properties of our materials of interest. However, we learned that when

125

putting two such materials together in a spin valve, you don’t have sufficient predictive power from
only these single F layer studies. To bridge this gap, studies of several series of spin-valves varying
the thickness of one F layer were performed. These valuable studies shed light on the proper thickness combinations for the F layers that produce phase switching, the total critical currents obtained
when the junction is in the parallel and antiparallel configurations, switching field ranges for the
two F layers, fields required to saturate the magnetization of the two F layers, and the stability of
the magnetic state at and around zero external applied field. Series with NiFe/NiFeCo and NiFe/Ni
were studied to inform SQUID device reproduciblity and F layer thickness choices.
The culmination of this work came from the successful demonstration of phase-controllable
SQUID devices in both the NiFe/NiFeCo and NiFe/Ni magnetic systems. Major loop measurements where both junctions’ free layers switched back and forth, and minor loop measurements
where only one junction’s free layer switched back and forth were shown in both cases. Independent fits to the four accessible magnetic configurations in the major loop were performed to verify
the presence of successive π phase shifts between states. This marked the first phase-sensitive
demonstration of phase-controllable ferromagnetic Josephson junctions.

9.2

Future Work

Though great progress has been made in this work to demonstrate phase-controllable ferromagnetic
Josephson junctions, for memory application, large numbers of junctions with the same properties
are required for memory arrays. This will require much additional investigation. First, the magnetic
materials used in the spin-valve junctions could be improved. A free layer with lower switching
fields and a fixed layer with more reliable magnetic properties are desired. We are constrained,
however, by the need to obtain at least 100 µA of critical current through the stack, limiting our
options. Future free layer material studies will include PdFe alloys and fixed layer material studies
will include attempting to pin Ni with IrMn. PdFe is a weak ferromagnet, so its 0-π transition
thickness can be many times larger than that of NiFe depending on the Fe concentration. This

126

gives larger margins on the layer thickness and could improve magnetic properties. We know
from our studies of Ni that it shows non-reproducible magnetic behavior. Perhaps this could be
controlled by pinning the Ni with IrMn. In contrast to the FeMn pinning used previously, IrMn
could allow more critical current through the junction. Additionally, the Ni is known to have
significantly higher critical current values than NiFe, so a spin-valve stack with this fixed layer
could possibly meet the 100 µA desired value.
To address SQUID fitting ambiguity issues, low inductance SQUID layouts have already been
designed by the group recently. If the inductance of the design is sufficiently low, such that only one
set of fit parameters can describe the data, it will greatly simplify the SQUID analysis procedure.
With this advantage, minor loops alone could be used to verify phase switching in the devices. This
opens up new experimental designs where one bit is patterned into a specific shape to increase its
switching fields, such as a high aspect ratio diamond or hexagon, while the other remains an easy to
switch elliptical bit. Then measurements would only switch the elliptical bit back and forth while
the higher switching field bit would remain always in the same initialized state. This would speed
up the measurement and analysis process as well as restrict measurements to lower field ranges,
decreasing the possibility of altering unstable magnetic states.
Lastly, our collaborators at Northrop Grumman have been developing read and write architecture to use our phase-controllable junction in a real memory scheme. They recently realized a
functional unit cell demonstration using the magnetic stack developed by our group at Michigan
State, but hopefully the future will hold larger array demonstrations and eventually a commercially
available memory system. In time, this, or a similar memory system could be integrated into a
fully superconducting supercomputer, able to solve interesting problems at a fraction of the energy
cost needed for conventional technology.

127

BIBLIOGRAPHY

128

BIBLIOGRAPHY

[1] Makram Abd El Qader, R. K. Singh, Sarah N. Galvin, L. Yu, J. M. Rowell, and N. Newman.
Switching at small magnetic fields in Josephson junctions fabricated with ferromagnetic barrier layers. Appl. Phys. Lett., 104(2), 2014.
[2] P. W. Anderson and J. M. Rowell. Probable observation of the Josephson superconducting
tunneling effect. Phys. Rev. Lett., 10:230–232, Mar 1963.
[3] A. F. Andreev. The thermal conductivity of the intermediate state in superconductors. J.
Exptl. Theoret. Phys. (U.S.S.R.), 46(5):1823–1828, 1964.
[4] B. Baek, W. H. Rippard, S. P. Benz, S. E. Russek, and P. D. Dresselhaus. Hybrid
superconducting-magnetic memory device using competing order parameters. Nature Commun., 5:3888, 2014.
[5] S. V. Bakurskiy, N. V. Klenov, I. I. Soloviev, V. V. Bol’ginov, V. V. Ryazanov, I. V. Vernik,
O. A. Mukhanov, M. Yu. Kupriyanov, and A. A. Golubov. Theoretical model of superconducting spintronic SIsFS devices. App. Phys. Lett., 102(19), 2013.
[6] A. A. Bannykh, J. Pfeiffer, V. S. Stolyarov, I. E. Batov, V. V. Ryazanov, and M. Weides.
Josephson tunnel junctions with a strong ferromagnetic interlayer. Phys. Rev. B, 79:054501,
Feb 2009.
[7] J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Microscopic theory of superconductivity.
Phys. Rev., 106:162–164, Apr 1957.
[8] J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Theory of superconductivity. Phys. Rev.,
108:1175–1204, Dec 1957.
[9] A. Barone and G. Paternò. Physics and applications of the Josephson effect. Wiley, 1982.
[10] C. Bell, G. Burnell, C. W. Leung, E. J. Tarte, D.-J. Kang, and M. G. Blamire. Controllable
Josephson current through a pseudospin-valve structure. Appl. Phys. Lett., 84:1153–1155,
2004.
[11] Y. Blum, A. Tsukernik, M. Karpovski, and A. Palevski. Oscillations of the superconducting
critical current in Nb-Cu-Ni-Cu-Nb junctions. Phys. Rev. Lett., 89:187004, 2002.
[12] Kurt M. Boden, W. P. Pratt, and Norman O. Birge. Proximity-induced density-of-states oscillations in a superconductor/strong-ferromagnet system. Phys. Rev. B, 84:020510, Jul 2011.
[13] L. N. Bulaevskii, V. V. Kuzzii, and A. A. Sobyanin. Superconducting system with weak
coupling to the current in the ground state. JETP Lett., 25:290, 1977.
[14] A. I. Buzdin. Proximity effects in superconductor-ferromagnet heterostructures. Rev. Mod.
Phys., 77:935–976, Sep 2005.

129

[15] A. I. Buzdin, L. N. Bulaevski, and S. V. Panyukov. Critical-current oscillations as a function
of the exchange field and thickness of the ferromagnetic metal (F) in an S-F-S Josephson
junction. JETP Lett., 35:179, 1982.
[16] A. I. Buzdin and M. Yu. Kupriyanov. Transition temperature of a superconductor-ferromagnet
superlattice. JETP Lett., 52:488, 1990.
[17] A. I. Buzdin and M. Yu. Kupriyanov. Josephson junction with a ferromagnetic layer. JETP
Lett., 53:321, 1991.
[18] Boris Chesca, Reinhold Kleiner, and Dieter Koelle. The SQUID Handbook, Volume 1. WileyVCH Verlag GmbH & Co. KGaA, 2005.
[19] T. W. Clinton and Mark Johnson. Nonvolatile switchable Josephson junctions. Journal of
Applied Physics, 85(3):1637–1643, 1999.
[20] R. de Bruyn Ouboter and A. Th. A. M. de Waele. Superconducting point contacts weakly
connecting two superconductors. Rev. Phys. Appl. (Paris), 5:25, 1970.
[21] P. G. de Gennes. Boundary effects in superconductors. Rev. Mod. Phys., 36:225–237, Jan
1964.
[22] E. A. Demler, G. B. Arnold, and M. R. Beasley. Superconducting proximity effects in magnetic metals. Phys. Rev. B, 55:15174–15182, Jun 1997.
[23] G. Deutscher and P. G. de Gennes. Superconductivity, Vol. II. edited by R. D. Parks, Marcel
Dekker, New York, NY, USA, 1969.
[24] D. E. Eastman, F. J. Himpse, and J. A. Knapp. Experimental band structure and temperaturedependent magnetic exchange splitting of nickel using angle-resolved photoemission. Phys.
Rev. Lett., 40:1514–1517, Jun 1978.
[25] D. E. Eastman, F. J. Himpse, and J. A. Knapp. Experimental exchange-split energy-band
dispersions for Fe, Co, and Ni. Phys. Rev. Lett., 44:95–98, Jan 1980.
[26] R. P. Feynman, R. B. Leighton, and M. Sands. The Feynman Lectures on Physics, Vol III.
Addison-Wesley Publishing Company, Massachusetts, 1965.
[27] T. A. Fulton, L. N. Dunkleberger, and R. C. Dynes. Quantum interference properties of
double Josephson junctions. Phys. Rev. B, 6:855–875, Aug 1972.
[28] E. C. Gingrich, Bethany M. Niedzielski, Joseph A. Glick, Yixing Wang, D. L. Miller, Reza
Loloee, W. P. Pratt Jr, and Norman O. Birge. Controllable 0-π Josephson junctions containing
a ferromagnetic spin valve. Nat. Phys., 12(6):564–567, Jun 2016.
[29] J. A. Glick, M. A. Khasawneh, B. M. Niedzielski, E. C. Gingrich, P. G. Kotula, N. Missert, R. Loloee, W. P. Jr. Pratt, and N. O. Birge. Critical Current Oscillations of Elliptical
Josephson Junctions with Single-Domain Ferromagnetic Layers. arXiv:1608.08998, August
2016.
130

[30] J. A. Glick, R. Loloee, W. P. Pratt, and N. O. Birge. Critical current oscillations of Josephson
junctions containing PdFe nanomagnets. IEEE Transactions on Applied Superconductivity,
27(4):1–5, June 2017.
[31] E. Goldobin, H. Sickinger, M. Weides, N. Ruppelt, H. Kohlstedt, R. Kleiner, and D. Koelle.
Memory cell based on a φ Josephson junction. App. Phys. Lett., 102(24), 2013.
[32] R. Gross and A. Marx. Applied Superconductivity: Josephson Effect and Superconducting
Electronics. Walther-Meissner-Institute, 2005.
[33] D. M. Heim, N. G. Pugach, M. Yu Kupriyanov, E. Goldobin, D. Koelle, R. Kleiner, N. Ruppelt, M. Weides, and H. Kohlstedt. The effect of normal and insulating layers on 0-π transitions in Josephson junctions with a ferromagnetic barrier. New J. Phys., 17(11):113022,
2015.
[34] R. Held, J. Xu, A. Schmehl, C. W. Schneider, J. Mannhart, and M. R. Beasley. Superconducting memory based on ferromagnetism. Applied Physics Letters, 89(16):163509, 2006.
[35] A. Y. Herr and Q. P. Herr. Josephson magnetic random access memory system and method,,
September 18 2012. US Patent 8,270,209.
[36] A.Y. Herr, Q.P. Herr, and O. Naaman. Phase hysteretic magnetic Josephson junction memory
cell,, March 8 2016. US Patent 9,281,057.
[37] Quentin P. Herr, Anna Y. Herr, Oliver T. Oberg, and Alexander G. Ioannidis. Ultra-low-power
superconductor logic. Journal of Applied Physics, 109(10):103903, 2011.
[38] D. S. Holmes, A. L. Ripple, and M. A. Manheimer. Energy-efficient superconducting computing[mdash]power budgets and requirements. IEEE Trans. Appl. Supercond., 23:1701610,
2013.
[39] R. C. Jaklevic, John Lambe, A. H. Silver, and J. E. Mercereau. Quantum interference effects
in Josephson tunneling. Phys. Rev. Lett., 12:159–160, Feb 1964.
[40] B.D. Josephson. Possible new effects in superconductive tunnelling. Physics Letters, 1(7):251
– 253, 1962.
[41] B.D. Josephson. Supercurrents through barriers. Advances in Physics, 14(56):419–451, 1965.
[42] S. O. Kasap. Principles of Electronic Materials and Devices, Third Edition. McGraw-Hill
Education, 2005.
[43] D. E. Kirichenko, S. Sarwana, and A. F. Kirichenko. Zero static power dissipation biasing of
RSFQ circuits. IEEE Transactions on Applied Superconductivity, 21(3):776–779, June 2011.
[44] C. Klose. Spin Triplet Superconductivity in Conventional Superconductor/Ferromagnetic
Hybrid Systems. Bachelor’s Thesis, Michigan State University, 2010.

131

[45] Carolin Klose, Trupti S. Khaire, Yixing Wang, W. P. Pratt, Norman O. Birge, B. J. McMorran,
T. P. Ginley, J. A. Borchers, B. J. Kirby, B. B. Maranville, and J. Unguris. Optimization of
spin-triplet supercurrent in ferromagnetic Josephson junctions. Phys. Rev. Lett., 108:127002,
2012.
[46] T. Kontos, M. Aprili, J. Lesueur, F. Genêt, B. Stephanidis, and R. Boursier. Josephson Junction through a Thin Ferromagnetic Layer: Negative Coupling. Phys. Rev. Lett., 89:137007,
Sep 2002.
[47] T. Kontos, M. Aprili, J. Lesueur, and X. Grison. Inhomogeneous superconductivity induced
in a ferromagnet by proximity effect. Phys. Rev. Lett., 86:304–307, Jan 2001.
[48] L. D. Landau and E. M. Lifschitz. Lehrbuch der Theoretischen Physik. Bd. IX, AkademieVerlag, Berlin, 1980.
[49] B. Landman. Calculation of threshold curves for Josephson quantum interference devices.
IEEE Transactions on Magnetics, 13(1):871–874, Jan 1977.
[50] Timofei I. Larkin, Vitaly V. Bol’ginov, Vasily S. Stolyarov, Valery V. Ryazanov, Igor V.
Vernik, Sergey K. Tolpygo, and Oleg A. Mukhanov. Ferromagnetic Josephson switching
device with high characteristic voltage. Applied Physics Letters, 100(22), 2012.
[51] K. K. Likharev and V. K. Semenov. RSFQ logic/memory family: a new Josephson-junction
technology for sub-terahertz-clock-frequency digital systems. IEEE Transactions on Applied
Superconductivity, 1(1):3–28, March 1991.
[52] J. Matisoo. Critical currents and current distributions in Josephson junctions. Journal of
Applied Physics, 40(4):1813–1820, 1969.
[53] D. E. McCumber. Effect of ac impedance on dc voltage-current characteristics of superconductor weak-link junctions. Journal of Applied Physics, 39(7):3113–3118, 1968.
[54] W. H. Meiklejohn and C. P. Bean. New magnetic anisotropy. Phys. Rev., 105:904–913, Feb
1957.
[55] Th. Mühge, N. N. Garif’yanov, Yu. V. Goryunov, G. G. Khaliullin, L. R. Tagirov, K. Westerholt, I. A. Garifullin, and H. Zabel. Possible origin for oscillatory superconducting transition
temperature in superconductor/ferromagnet multilayers. Phys. Rev. Lett., 77:1857–1860, Aug
1996.
[56] O. A. Mukhanov. Energy-efficient single flux quantum technology. IEEE Transactions on
Applied Superconductivity, 21(3):760–769, June 2011.
[57] Bethany M Niedzielski, E. C. Gingrich, Reza Loloee, W. P. Pratt, and Norman O. Birge. S/F/S
Josephson junctions with single-domain ferromagnets for memory applications. Supercond.
Sci Technol., 28(8):085012, 2015.

132

[58] V. A. Oboznov, V. V. Bol’ginov, A. K. Feofanov, V. V. Ryazanov, and A. I. Buzdin.
Thickness Dependence of the Josephson Ground States of Superconductor-FerromagnetSuperconductor Junctions. Phys. Rev. Lett., 96:197003, 2006.
[59] H. Kammerling Onnes. The resistance of pure mercury at helium temperatures. Leiden
Comm., 120b, 122b, 124c, Sep 1911.
[60] R. D. Parks. Superconductivity, Vol 2. Marcel Dekker, New York, NY, USA, 1969.
[61] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes.
Cambridge Univ. Press, Cambridge, 1988.
[62] Z. Radovi´c, L. Dobrosavljevi´c-Gruji´c, A. I. Buzdin, and John R. Clem. Upper critical fields
of superconductor-ferromagnet multilayers. Phys. Rev. B, 38:2388–2393, Aug 1988.
[63] Zoran Radovi´c, Marko Ledvij, Ljiljana Dobrosavljevi´c-Gruji´c, A. I. Buzdin, and John R.
Clem. Transition temperatures of superconductor-ferromagnet superlattices. Phys. Rev. B,
44:759–764, Jul 1991.
[64] N. D. Rizzo, D. Houssameddine, J. Janesky, R. Whig, F. B. Mancoff, M. L. Schneider, M. DeHerrera, J. J. Sun, K. Nagel, S. Deshpande, H. J. Chia, S. M. Alam, T. Andre, S. Aggarwal,
and J. M. Slaughter. A fully functional 64 Mb DDR3 ST-MRAM built on 90 nm CMOS
technology. IEEE Transactions on Magnetics, 49(7):4441–4446, July 2013.
[65] J. W. A. Robinson, Gábor B. Halász, A. I. Buzdin, and M. G. Blamire. Enhanced Supercurrents in Josephson Junctions Containing Nonparallel Ferromagnetic Domains. Phys. Rev.
Lett., 104:207001, May 2010.
[66] J. W. A. Robinson, S. Piano, G. Burnell, C. Bell, and M. G. Blamire. Critical current oscillations in strong ferromagnetic π junctions. Phys. Rev. Lett., 97:177003, 2006.
[67] J. W. A. Robinson, S. Piano, G. Burnell, C. Bell, and M. G. Blamire. Zero to π transition in
superconductor-ferromagnet-superconductor junctions. Phys. Rev. B, 76:094522, Sep 2007.
[68] V. V. Ryazanov. Coupling of two superconductors through a ferromagnet: evidence for a π
junction. Phys. Rev. Lett., 86:2427–2430, 2001.
[69] Hermann Sellier, Claire Baraduc, Francois Lefloch, and Roberto Calemczuk. Temperatureinduced crossover between 0 and π states in S/F/S junctions. Phys. Rev. B, 68:054531, Aug
2003.
[70] V. Shelukhin, A. Tsukernik, M. Karpovski, Y. Blum, K. B. Efetov, A. F. Volkov, T. Champel,
M. Eschrig, T. Löfwander, G. Schön, and A. Palevski. Observation of periodic π-phase shifts
in ferromagnet-superconductor multilayers. Phys. Rev. B, 73:174506, May 2006.
[71] Nicola A. Spaldin. Magnetic Materials, Fundamentals and Applications. Cambridge University Press, Cambridge, 2011.

133

[72] D Sprungmann, K Westerholt, H Zabel, M Weides, and H Kohlstedt. Josephson tunnel junctions with ferromagnetic Fe 0.75 Co 0.25 barriers. Journal of Physics D: Applied Physics,
42(7):075005, 2009.
[73] W. C. Stewart. Current-voltage characteristics of Josephson junctions. Applied Physics Letters, 12(8):277–280, 1968.
[74] E. C. Stoner and E. P. Wohlfarth. A mechanism of magnetic hysteresis in heterogeneous
alloys. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical
and Engineering Sciences, 240(826):599–642, 1948.
[75] C. Strunk, C. Sürgers, U. Paschen, and H. v. Löhneysen. Superconductivity in layered Nb/Gd
films. Phys. Rev. B, 49:4053–4063, Feb 1994.
[76] National Security Agency Superconducting Technology Assessment.
https://www.nitrd.gov/pubs/nsa/sta.pdf, 2005.

Available at.

[77] Claudia D. Tesche and John Clarke. dc SQUID: Noise and optimization. Journal of Low
Temperature Physics, 29(3):301–331, 1977.
[78] C. D. Thomas, M. P. Ulmer, and J. B. Ketterson. Superconducting tunnel junction base
electrode planarization. J. App. Phys., 84(1):364–367, 1998.
[79] Michael Tinkham. Introduction to Superconductivity, Second Edition. Dover Publications,
Inc., New York, 1996.
[80] Won-Tien Tsang and T. Van Duzer. dc analysis of parallel arrays of two and three Josephson
junctions. Journal of Applied Physics, 46(10):4573–4580, 1975.
[81] M. H. Volkmann, A. Sahu, C. J. Fourie, and O. A. Mukhanov. Implementation of energy efficient single flux quantum digital circuits with sub-aj/bit operation. Superconductor Science
and Technology, 26(1):015002, 2013.
[82] Y. Wang, W. P. Pratt Jr, and N. O. Birge. Area-dependence of spin-triplet supercurrent in
ferromagnetic Josephson junctions. Phys. Rev. B, 85:214522, 2012.
[83] M. Weides, M. Kemmler, E. Goldobin, D. Koelle, R. Kleiner, H. Kohlstedt, and A. Buzdin.
High quality ferromagnetic 0 and π Josephson tunnel junctions. Appl. Phys. Lett., 89:122511,
2006.

134