FERROMAGNETIC JOSEPHSON JUNCTIONS WITH BOTH IN AND

OUT OF PLANE MAGNETIC ANISOTROPY

By

Victor Aguilar

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics—Doctor of Philosophy

2021

ABSTRACT

FERROMAGNETIC JOSEPHSON JUNCTIONS WITH BOTH IN AND OUT OF

PLANE MAGNETIC ANISOTROPY

By

Victor Aguilar

In this thesis we present experimental data showing enhancements of critical current

through ferromagnetic Josephson junctions. Previous work in our group has shown promising

results using ferromagnets with perpendicular magnetic anisotropy (PMA) as one of the

magnetic layers in Josephson junctions. Magnetic characterization has shown that these

PMA layers have strong out of plane magnetization.

In this work we use a multilayer

of palladium and cobalt as the PMA layer. By depositing the PMA layer as the central

ferromagnet in between two other ferromagnets we are able to generate long range spin triplet

supercurrent. There are both benefits and drawbacks with spin triplet supercurrent when

compared to spin singlet supercurrent. We present a method used to confirm the presence

of spin-triplet supercurrent generation from an S-type superconductor. We also compare the

magnitude of the spin-triplet supercurrent in our junctions with the supercurrent in similar

junctions where the central PMA layer is configured as a synthetic antiferromagnet. Finally

we show data from phase sensitive measurements where we have fabricated a device with

two Josephson junctions that can each be in one of two phases, either a 0 or π state. This

last set of data shows switches of phase in Josephson junctions that are controlled by an

external magnetic field, which can have applications in cryogenic memory.

For my mom and dad, who showed me the meaning of hard work and dedication.

“Con valor para adelante” – Gerardo Aguilar

iii

ACKNOWLEDGMENTS

To reach this milestone has been a long journey with many obstacles along the way.

Obstacles overcome with the help of many that I will thank. First, I would like to thank my

advisor, Norman Birge, for his guidance and support even if he seemed overwhelmed with

his own work, he always made time for me. My time at the Birge group has been incredible

and I believe this was largely in part because of having Norman as my advisor. Thank you

to Reza Loloee for all the times he rescued me from problems during a sputtering run or

needing to do some complicated fabrication tasks. Without his quick thinking and expertise

many of my samples would have never been measured. Thank you to Bill Pratt for all the

clever ideas he has had which guided some of my experiments leading to very interesting

results. To Bethany Niedzielski, William Martinez, Eric Gingrich and Alex Kramer, thank

you for teaching me the fabrication processes that were crucial to my work. Thank you to

Alex Madden, Swapna Mishra, Bob Klaes for your help and ideas in many experiments. To

Anna Osella and Benjamin Byrd thank you for all your hard work in developing both fitting

programs and characterizing materials making my work easier. I thank Nathan Satchell for

the discussions about my work and ideas to try out for my experiments. To Joshua Willard,

thank you for all the hard work you have done testing, measuring and developing new

processes for our work. To Joseph Glick thank you for the many discussions we had where

we would work out issues in the fabrication process and the specifics about measurements.

I would like to thank Baokang Bi for teaching me how to work in the cleanroom as well as

giving me the freedom to develop new processes. I would like to thank the Physics Machine

Shop, Tom Palazzolo, Tom Hudson, Jim Muns and Rob Bennett, for letting me have a

creative outlet and guiding me through some tough projects. The help they provided was

iv

vital in making my project easier and successful. I would like to thank Kim Crosslan for her

kind words and for always being there when I needed someone to talk to.

Thank you for the financial support from the MSU physics department and Northrop

Grumman Corporation giving me the freedom to work on the physics free from worry or

distractions. I am grateful for the funding from the Intelligence Advanced Research Projects

Activity that gave me the opportunity to work on several projects during my time at MSU.

Additionally, I would like to thank Scott Holmes and Marc Manheimer for their tireless work

in bringing all these experts into this field to work on such a difficult and ambitious goal. I

would like to thank Tyler Cocker, Artemisia Spyrou, Mohammad Maghrebi as my committee

members during meetings they always had great discussions about our work as well as my

goals. I would like to thank Scott Pratt especially for setting time aside in the Summer to

help me study for my exams.

A mis padres Blanca y Gerardo, gracias por dejarme siempre perseguir mis sue˜nos. Por

amarme incondicionalmente y estar siempre ah´ı incluso cuando estaba tan lejos. If not for

their courage and strength to strive for a better life I would never have had the opportunity

to accomplish this goal. To my siblings, Jeannette, Benjamin and Juan thank you for putting

up with me and this dream of mine even though it took longer than we would have wanted.

v

TABLE OF CONTENTS

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

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

ix

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Superconducting computing, energy efficiency and cryogenic memory . . . .
1.1.1 Background: energy use in large-scale computing systems . . . . . . .
Superconducting computing . . . . . . . . . . . . . . . . . . . . . . .
1.1.2
1.1.3
Spin-triplet supercurrent . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Chapters overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2

Superconductivity and Magnetism . . . . . . . . . . . . . . . . . . . .
2.1 The Meissner-Ochsenfeld Effect . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The Josephson Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Magnetic Domains
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . .
S/N proximity effect
S/F proximity effect
. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2.1 Current-phase relation of ferromagnetic Josephson junctions
2.5 Long range spin-triplet supercurrent in S/F’/F/F”/S Josephson junctions . .
2.6 SQUIDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4 Proximity effects in Josephson junctions

2.4.1
2.4.2

Chapter 3

Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Microfabrication Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Photolithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Electron Beam Lithography . . . . . . . . . . . . . . . . . . . . . . .
Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3
3.1.4
Ion Milling
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Magnetic characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Josephson Junction Fabrication Procedure . . . . . . . . . . . . . . . . . . .
3.3.1
Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Photolithography: setup and bottom lead deposition . . . . . . . . .
3.3.3
. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Electron beam lithography-EBL . . . . . . . . . . . . . . . . . . . . .
3.3.5
Junction definition by ion milling . . . . . . . . . . . . . . . . . . . .
3.3.6 Top lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Setup and mounting . . . . . . . . . . . . . . . . . . . . . . . . . . .
Single junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Sputtering Chamber

3.4 Measurement

3.4.1
3.4.2

vi

1
1
1
3
6
7

9
10
12
14
14
15
16
16
19
23
25
28

33
33
33
34
34
35
35
37
37
38
40
42
43
47
47
47
48

3.5

3.4.3 Phase Sensitive Measurements-Superconducting Quantum Interference
Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Improvements to measurement and fabrication systems . . . . . . . . . . . .
3.5.1 Room temperature electronics: . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Low temperature electronics: . . . . . . . . . . . . . . . . . . . . . . .
3.5.3 Rezanator and sputtering chamber:
. . . . . . . . . . . . . . . . . . .

Chapter 4

Shuffled and Triplet Josephson junctions . . . . . . . . . . . . . . . .
4.1 Magnetic characterization of Pd/Co multilayers
. . . . . . . . . . . . . . . .
4.2 Fabrication of junctions containing Pd/Co . . . . . . . . . . . . . . . . . . .
4.3 Measurement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5

PMA-SAF and PMA Josephson junctions

. . . . . . . . . . . . . . .
5.1 Magnetic Properties
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Fabrication of spin triplet PMA and PMA-SAF junctions . . . . . . . . . . .
5.3 Measurement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49
50
50
50
51

52
55
59
62
65
66

69
70
71
73
74
81

Chapter 6

Phase Controllable SQUIDS . . . . . . . . . . . . . . . . . . . . . . .
83
84
6.1 Magnetic characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
6.2 SQUID fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
6.3 Measurement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Chapter 7

Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . 104

APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

vii

LIST OF TABLES

Table 6.1: Sample parameters for each ferromagnetic layer . . . . . . . . . . . . . . . 101

Table 6.2: Maximum measured critical current for each sample . . . . . . . . . . . . 101

Table 6.3: Sample Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

viii

LIST OF FIGURES

Figure 1.1: Memory Cell

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

Figure 2.1: Meissner Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.2: Josephson Effect

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

Figure 2.3: Magnetic Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.4: Schematic of Andreev Reflection . . . . . . . . . . . . . . . . . . . . . .

Figure 2.5: Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.6: S/N and S/F Pair Correlation Functions . . . . . . . . . . . . . . . . . .

Figure 2.7: S/F/S Junctions Critical Current vs. Thickness . . . . . . . . . . . . . .

Figure 2.8: Schematic of a Spin-triplets Josephson junction . . . . . . . . . . . . . .

Figure 2.9: Schematic view of a dc SQUID . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.10: Critical current vs. applied flux dc SQUID . . . . . . . . . . . . . . . . .

Figure 3.1: Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.2: Junction Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.1: Singlet and Triplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.2: PMA-SAF and Shuffled junctions . . . . . . . . . . . . . . . . . . . . . .

Figure 4.3: Magnetic force microscopy of Pd/Co multilayers . . . . . . . . . . . . . .

Figure 4.4: Hysteresis Curve of Pd/Co multilayers: Out-of-plane . . . . . . . . . . .

Figure 4.5: Hysteresis Curve of Pd/Co multilayers: In-plane . . . . . . . . . . . . . .

Figure 4.6: Photolithography bottom Lead . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.7: Sample mounted on QDI . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.8: Bottom Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

10

13

15

17

20

22

24

26

29

32

39

46

53

54

56

58

59

61

62

63

ix

Figure 4.9: V vs. I of a Josephson junction . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.10: Ic vs. H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.11: IcRn vs. Ni Thickness

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

Figure 5.1: PMA-SAF and PMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.2: PMA-SAF and PMA schematic diagram . . . . . . . . . . . . . . . . . .

Figure 5.3: PMA Triplet Fraunhofer pattern . . . . . . . . . . . . . . . . . . . . . .

Figure 5.4: PMA-SAF Ic vs. Thickness

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

Figure 5.5: PMA-SAF Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.6: PMA Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.1: Triplet PMA Josephson Junction . . . . . . . . . . . . . . . . . . . . . .

Figure 6.2: Easy axis magnetometer of elliptical and hex arrays: major loops

. . . .

Figure 6.3: Easy axis magnetometer of elliptical and hex arrays: minor loops

. . . .

Figure 6.4: Photolithography SQUID mask design . . . . . . . . . . . . . . . . . . .

Figure 6.5: Top and orthographic view of ULI SQUID design . . . . . . . . . . . . .

Figure 6.6: Wiring diagram for SQUID using QDI

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

Figure 6.7: Measurement Flow Diagram . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.8:

Initial measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.9: Sample 1a SQUID 3 before training . . . . . . . . . . . . . . . . . . . . .

Figure 6.10: Sample 1a SQUID 3 after training

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

Figure 6.11: Sample 1a SQUID 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.12: Sample 1a SQUID 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.13: Sample 4a SQUID 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.14: Sample 4a SQUID 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

66

67

71

72

74

75

80

80

84

85

86

87

88

89

90

91

94

95

96

97

98

99

x

Figure 6.15: Sample 6a SQUID 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 7.1: φ0 junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure 7.2: φ0 phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 1:

NPGS array run file

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Figure 2:

Labview front panel: Top . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Figure 3:

LabVIEW front panel: Bottom . . . . . . . . . . . . . . . . . . . . . . . 114

xi

Chapter 1

Introduction

1.1 Superconducting computing, energy efficiency and cryogenic memory

1.1.1 Background: energy use in large-scale computing systems

With the emergence of new technologies and the ability to have so much information

stored and accessed by simply having access to a computer and internet we continue to see a

rise in computer storage and the need for larger and larger data centers. When first joining

this group, in 2014, energy usage for these data centers in the U.S. was projected to go

from 72 TWh in 2009 to 176 TWh in 2020 [1], which was one of the key motivators for this

research. Reducing energy consumption in technology was then and is now a major driving

force since estimates said that reducing the data center energy consumption by a factor of 10

could potentially save the United States about $15 billion dollars by the year 2020 assuming

an energy cost of 0.1 $/kWh. Another study published a couple of years later showed that

globally electricity demands of data centers would be about 700 TWh in the year 2020 [2].

This study also showed that by the year 2030 the global electricity demand of data centers

will be in the best case about 1137 TWh and up to 7933 TWh in the worst-case scenario

meaning data centers could use around 3–13% of global electricity in 2030 compared to 1%

in 2010.

Data centers are not the only increasing consumers of energy; supercomputers are getting

larger, faster, and more power hungry. The projected computing power of up to 1018 cal-

1

culations per second at the Exascale Computing Project at Los Alamos, faster than current

supercomputers at about 1015 calculations per second, indicates an even greater need for

energy efficiency to deal with these advancements in technologies. Supercomputers play a

large role in the solving new and more complex problems. They are being used in many

fields including quantum mechanics, weather forecasting, climate research and physical sim-

ulations to name a few examples. Breakthroughs in these fields are fueling new and more

exciting discoveries. Although we have seen a steady rise in computing power ever since

the introduction of this technology, it is limited by a few key factors. Processor manufac-

tures face many challenges, one of which is the limit in size, more computing power in a

smaller area. Some talks in International Electron Devices Meeting hint at possibly pushing

towards sub nanometer processors which would require a different type of processing using

2D self-assembly materials [3]. Cooling is another factor that must be looked at carefully

when producing smaller and more powerful processors. Power dissipation in smaller areas

is limited by surface area, meaning these smaller chips will be running faster but also much

hotter.

Energy efficiency is also an important obstacle at large scale. The power consumption of

one of the most powerful modern supercomputers, the Sunway TaihuLight [4] with over 10.5

million cores, can be as high as 15MW at a peak performance of 93 petaFLOPS. The power

consumption of next generation computers, exaFLOPS supercomputers, is predicted to be

in the sub-gigawatts level [5]. This is similar to the power generated by a small powerplant,

which can cost hundreds of millions of dollars per year. Considering all the factors that can

lead to an increase in energy usage is difficult, but the overall trend leads to a need for a more

energy efficient solution when compared to the Complementary Metal Oxide Semiconductor

(CMOS) technology we have all grown accustomed to using.

2

1.1.2 Superconducting computing

To try to alleviate this inevitable rise in power consumption when considering large scale

computing and data centers, one proposal is to develop superconducting computers, which

are expected to have orders of magnitude better energy efficiency over conventional CMOS

technology [1]. The reasoning behind the energy efficiency comes from superconducting ma-

terials having the ability to carry current with zero energy loss due to Joule heating.

In

a system with Very-Large-Scale integration combining thousands of circuits, having super-

conducting components closely packed to each other without the worry of heat generation

decreases time delays in interchip communications. To attain these superconducting states,

we must use materials that superconduct and cool them down to temperatures below their

“critical temperature”, or Tc. For Niobium, the most commonly used superconducting ma-

terial, Tc is just above 9 K. To reach temperatures below 9K we use liquid helium at about

4.2 K. Although it does cost a significant amount for cooling the circuits to liquid helium

temperatures, this is taken into account when comparing superconducting computers over

CMOS systems.

An important milestone in superconducting devices was discovered in the 1962 by Brian

David Josephson, the Josephson effect, where you can have supercurrent flow across a thin,

non-superconducting, barrier that is sandwiched by two superconductors [6,7]. This discovery

paved the way for new types of logic circuits that were based on what is known as a Josephson

junction. A Josephson junction is based on the Josephson effect and is fabricated with

different layers as you would imagine stacking coins on top of each other where each coin is

a different material. One of these logic circuits is known as Resistive Single-Flux Quantum

(RSFQ) logic. RSFQ was proposed by Konstantin Likharev, Oleg Mukhanov, and Vasili

3

Semenov in 1985 at Moscow State University as a Josephson junction based logic that was

able to achieve fast switching at picosecond time scales [8]. The RSFQ logic uses pico-

second SFQ voltage pulses that can encode, process, and transport digital information as

opposed to voltage levels produced by transistors in semiconductor technology. There have

been many more superconducting logic families based on Josephson junctions that have

been developed.

In one variant, reducing the resistor and adding an inductor in parallel

to the RSFQ (LR-RSFQ) made a more energy efficient circuit. [9]. By reducing the bias

voltage in a RSFQ circuit you can also increase the energy efficiency giving a Low Voltage

RSFQ (LV-RSFQ) [10]. As the name suggests the energy efficient RSFQ (eeRSFQ) [11] helps

eliminate the static power losses of the RSFQ by replacing bias resistors with sets of inductors

and current-limiting Josephson junctions. More closely related to our work, the Reciprocal

Quantum Logic (RQL) [12] was developed by Northrop Grumman Corporation and uses

reciprocal pairs of SFQ pulses to encode a logical ‘1’ and works with alternating current.

Finally, I will just mention the Adiabatic Quantum flux parametron (AQFP) logic [13],

which uses alternating current and was developed to be extremely energy efficient, but in

comparison remains slower compared to SFQ-based logic.

There are many components needed to have a working superconducting computer, but

our work focuses on the memory element of a superconducting computer. There are many

researchers along with our group working on Josephson junctions containing ferromagnetic

layers that can be used in a superconducting memory circuit [14–24]. Such a memory must

be capable of switching quickly, have random access, and be non-volatile, similar to magnetic

random-access memory (MRAM). The benefit, as mentioned previously, over conventional

logic circuits would be the gain in energy efficiency in the superconducting circuits.

An important step for this work is the proposed memory architecture from Northrop

4

Figure 1.1: Memory Cell : Circuit diagram of a superconducting memory cell by Northrop
Grumman. a) A single memory cell where the X’s indicate Josephson junctions and the X
inside a circle indicates the magnetic Josephson junction. The right diagram is an array of
memory cells. Taken from [25].

known as Josephson magnetic random-access memory (JMRAM). The JMRAM memory

cell is composed of several elements, one of which is a ferromagnetic or magnetic Josephson

junction (MJJ) with a controllable ground-state phase shift. The readout of the memory is

accomplished by applying flux to a selected memory cell so that the bit-read current exceeds

the readout SQUID critical current in one memory state, but not the other [25]. The MJJ

is what our work focuses on [26–28].

The Northrop JMRAM memory cell is shown in Figure 1.1 where (a) is the memory cell

and (b) is an array of memory cells showing the read and write lines [25]. In this circuit

the magnetic Josephson junction plays the role as a bit by adding a variable phase to the

SQUID loop [20, 26, 29]. Simply put the junction would serve as the “0” or “1” for the binary

memory.

The idea for JMRAM was clearly influenced by MRAM. They are similar in that informa-

tion is stored in the relative orientations of the magnetizations of two or more ferromagnetic

layers. But they are different because the property of the junction that reflects the memory

5

state is the resistance in the case of MRAM whereas it is the ground-state phase difference

across the Josephson junction in the case of JMRAM.

1.1.3 Spin-triplet supercurrent

The work in this thesis focusses on a special type of ferromagnetic Josephson junction

in which the supercurrent is carried by spin-triplet electron pairs rather than the usual

spin-singlet pairs found in conventional superconductors such as Niobium. The spin triplet

supercurrent is fundamental to the following work. Spin triplet supercurrent has the unique

property that it can travel significantly further than the spin singlet supercurrent in ferro-

magnets – almost as if they were normal metals. Our group has done extensive work on

spin singlet ferromagnetic junctions and in some cases shown phase control of these types

of junctions [20–22, 26–28]. Our group has also demonstrated the generation and control of

spin triplet supercurrent [30–33]. The culmination of that work was Joseph Glick’s demon-

stration of phase control with spin triplet supercurrent [29]. The limitation of that work was

that the critical current in those junctions was too small for applications to the cryogenic

memory discussed previously. The work we present here is specifically done to address that

point of being able to have higher critical current with spin triplet supercurrent while still

maintaining phase control. The spin triplet supercurrent is of particular interest because of

its forgiving nature when considering how robust it is in terms of thickness variations of the

central ferromagnetic layer. This may allow the triplet junctions to be easier to fabricate

compared to spin singlet junctions. In this work we plan to answer the question whether it

is possible to improve the critical current in spin-triplet Josephson junctions and then show

phase control. This is done by characterizing, fabricating and measuring both spin triplet

and control, spin singlet, Josephson junctions [24]. Since the interplay of ferromagnetism and

6

superconductivity are thought to counteract each other, it is fascinating to see the interesting

physics we have that could not exist without their coexistence.

1.2 Chapters overview

Chapter 2 give a brief discussion of superconductivity and magnetism starting with the

Meissner-Ochsenfeld effect and Josephson effect. We then give a brief overview of ferro-

magnetism where we discuss magnetic domains and magnetic anisotropy. Superconducting

Quantum Interference Devices (SQUIDs) are briefly covered, as the main part of the work

requires them as a measurement tool. We then introduce the physics of S/N and S/F inter-

faces, discussing supercurrent generation and propagation.

Chapter 3 gives a very detailed step-by-step explanation of experimental techniques used

in nanofabrication. Topics include fabrication techniques such as photolithography, elec-

tron beam lithography, sputtering and ion milling. There is a discussion of magnetic mea-

surements using a SQUID magnetometer. Finally, there is a section that deals with the

measurement of samples as well as improvements made to various fabrication systems.

Chapter 4 provides the motivation behind the use of spin-triplet junctions as possible

memory bits. Since spin-triplet Josephson junctions are more forgiving in terms of thickness

variations that can happen during the fabrication process, when compared to singlet junc-

tions, they may be easier to fabricate in large quantities. The main point of this chapter

is to show that the main contribution to the supercurrent in these types of junctions are

spin-triplet pairs. This work lays the groundwork for Chapters 5 and 6.

Chapter 5 provides a comparison of spin-triplet junctions containing a multilayer with

perpendicular magnetic anisotropy arranged as a synthetic antiferromagnet (PMA-SAF),

7

and junctions that contain only the perpendicular magnetic anisotropy (PMA) multilayer.

There is an interpretation of what may cause the PMA junctions to have a shallower decay

of critical current with increasing the number of bilayers in the multilayer, when compared

to the PMA-SAF junctions.

Chapter 6 will show how we fabricate the on-chip SQUIDs used in conjunctions with our

junctions to make our phase-sensitive measurements. We show some magnetic measurements

used to characterize the junctions as arrays before fabrication of SQUIDs. We also show some

measurement procedures as well and wiring steps for these samples. Finally, we show data

on the SQUIDs in what we refer to as “waterfall plots” in which we plot critical current as a

function of external field and flux line current.

Chapter 7 is the summary chapter where we discuss results and possible outlooks for

future experiments.

8

Chapter 2

Superconductivity and Magnetism

Superconductivity was first discovered in 1911 by Dutch physicist Heike Kamerlingh

Onnes of Leiden University. A sample of mercury was cooled down to 4 degrees Kelvin,

below its transition temperature, Tc, where the electrical resistance of this sample dropped

to zero [34]. The remarkably discovery dawned the age of superconductivity. Onnes won the

Nobel Prize for research in the field in 1913. Another related discovery was made in 1933

by German researchers Walther Meissner and Robert Ochsenfeld. They found that when

a material is superconducting that it has the peculiar ability to expel magnetic fields [35].

This phenomenon is known as the Meissner effect. The field of superconductivity contains

many materials than can superconduct from elements such as mercury, lead and niobium

known as conventional superconductors, to more complicated materials such as yttrium

barium copper oxide which has a much higher superconducting temperature of about 92 K.

Conventional superconductors, the superconductors used in this work, have a full microscopic

theory know as BCS theory. BCS theory was developed by J. Bardeen, L.N. Cooper and

J.R. Schrieffer in 1957, who showed that dissipationless current flow in the superconducting

state is caused by electron pairs [36, 37]. In this theory the electron pairs, known as Cooper

pairs, behave as bosons, with zero total spin and momentum. The Cooper pairs condense to

the lowest energy state characterized by a single phase-coherent wavefunction. This chapter

will discuss the Meissner effect, the Josephson effect, SQUIDs, magnetic domains and the

physics of superconducting/ferromagnetic (S/F) hybrid systems including the properties of

9

Figure 2.1: Meissner Effect: Cartoon representation of a Meissner Effect. The left image
shows the superconductor above Tc where the magnetic field B penetrates the material.
The right side image shows the same superconductor below Tc where the magnetic field is
expelled, we see there is zero net field inside the superconductor. Taken from [38].

S/F/S Josephson junctions.

2.1 The Meissner-Ochsenfeld Effect

For simplicity we will look at the main points of the Meissner effect. When superconduct-

ing metals are cooled below their Tc they can expel magnetic flux from their interior [35].

The cause of this effect is that the superconductor generates surface currents that produce

a field that exactly cancels the external field inside of the material. Interestingly this effect

causes the superconductor to behave as a perfect diamagnet in the presence of an external

magnetic field.

The Meissner Effect is a telltale sign of superconductivity. The brothers F. and H. London

wrote down a pair of simple equations which incorporate the electrodynamic response of a

superconductor. These equations describe the microscopic electric and magnetic fields inside

a superconductor. Start with Newton’s second law (F = ma) applied to the electrons in a

10

superconductor:

The current density is

−eE = m

dv
dt

,

J = n(−e)v,

(2.1)

(2.2)

Combining the previous two equations and assuming that superconducting electrons do not

have their velocities reduced to zero by means of scattering, we have:

∂J/∂t = E/Λ,

(2.3)

where the time derivative of the current density, J, is proportional to E, and Λ ≡ m/(e2ns).

The factor e is the magnitude of the electron charge and m its mass, and ns is the density
of superconducting electrons. Applying Maxwell equation ∇× E = −∂B/∂t, where B is the

magnetic field and taking the curl of 2.3, we get

(cid:104)∇ × J +

(cid:105)

B
Λ

∂
∂t

= 0.

(2.4)

which shows that the quantity inside the brackets is conserved. Given that deep inside a

bulk superconductor, J = 0 and B = 0, we now have the London equation,

Using the Maxwell relation,

∇ × J +

B
Λ

= 0.

∇ × B = µ0J + µ0
0(∂E/∂t)

11

(2.5)

(2.6)

taking the curl of both sides, assuming that the electric field E is constant in time we have,

which gives

∇ × (∇ × B) = µ0∇ × J

∇(∇ · B) − ∇2B = −µ0
Λ

B

now using ∇ · B = 0 in the previous equation we get,

∇2B =
∇2J =

µ0
Λ
µ0
Λ

B

J.

(2.7)

(2.8)

(2.9)

(2.10)

The µ0/Λ is related to the length scale that fields can penetrate into the superconductor,

which is known as the London penetration depth:

λL ≡(cid:112)Λ/µ0 =

(cid:113)

m/(µ0e2ns).

(2.11)

2.2 The Josephson Effect

The Josephson effect is a macroscopic quantum phenomenon. In 1962 British physicist

Brian Josephson predicted that supercurrent could flow between two superconductors that

are separated by a thin barrier, without any external bias voltage applied. For that work he

won the Nobel prize in Physics in 1973.

In this system we can write supercurrent Is as a function of the critical current Ic,

the maximum supercurrent that can flow through the Josephson junction, and the phase

12

Figure 2.2: Josephson Effect: Cartoon representation of a Josephson junction that contains
two superconductors separated by a thin barrier. Each of the superconductors has its own
intrinsic phase.

difference φ across the junction:

Is = Ic sin φ,

(2.12)

where φ = φ2 − φ1. The equation is known as the current-phase relation.

If the current is larger than the critical current, there will be a measurable voltage across

the junction. In that case the phase acquires a time dependence,

dφ
dt

=

2eV
 =

2π
Φ0

V,

(2.13)

where Φ0 = 2π/(2e) is the magnetic flux quantum. As a result, the supercurrent Eq. (2.12)

oscillates at a frequency ν = 2eV /h and the energy of a Cooper pair traversing the junction

changes by an amount hν.

By integrating the work done by the current to change the phase we get the Josephson

energy stored in the junction.

E =

IsV dt =

(cid:90)

(cid:90)


2e

Ic sin φ dφ = EJ

13

(cid:0)1 − cos φ(cid:1),

(2.14)

where we used Eq. (2.13) to change the energy integral from time to phase. The Josephson

coupling energy is

EJ =

Ic
2e

.

(2.15)

2.3 Ferromagnetism

Like superconductivity, ferromagnetism is also a quantum phenomena that is observable

macroscopically. In the following we discuss a brief description of what leads to ferromag-

netism. Since spin is the dominant source to ferromagnetism, we will try to give some

understanding of this mechanism. We start by viewing the electron’s magnetic moments

as tiny magnets. In a ferromagnetic material, the exchange interaction causes neighboring

spins to align parallel to each other. The exchange interaction is a consequence of Coulomb

repulsion and the antisymmetry of the two-electron wavefunctions under particle exchange.

Once the spins, and hence the magnetic moments, are aligned, we see their effect on a much

larger scale, causing the ferromagnetism that can be observed.

2.3.1 Magnetic Domains

Considering a system that contains many dipoles that make up some material we know

that the exchange energy is the leading term in how they behave microscopically. Figure 2.3

shows a series of systems that start with a single domain on the left and gradually increase in

domains as you move to the right. We can see from the first image on the left we have a single

domain ferromagnet with the lowest exchange energy but with large magnetostatic energy

due to the large magnetic field created outside of the material. As we move to the right the

number of domains increases, lowering the magnetostatic energy, and increasing the number

14

Figure 2.3: Magnetic Domains: Cartoon representation of magnetic domains, starting from
a single domain (left image) to increasing the number of domains moving right. The single-
domain configuration has the smallest exchange energy but large magnetostatic energy. As
you move to the right the exchange energy is increased due to the additions of domain walls,
but the magnetostatic energy is lowered. Taken from [39].

of domain walls. Domain walls are very narrow surfaces which are continuous transitions

between adjoining domains. The more domain walls we have the larger the exchange energy.

The system is trying to decrease its energy so there is a point where breaking up into smaller

domains is no longer favorable because of increasing exchange energy due to creating more

domain walls.

2.3.2 Magnetic Anisotropy

Our work takes advantage of many types of magnetic anisotropy that can occur in met-

als. Magnetic anisotropy occurs when a ferromagnet has a preferred direction to have its

spins pointing along. The preferred direction is called the easy axis while the perpendicular

direction is called the hard axis. In our work we make use of what is called shape anisotropy

where we purposely grow magnetic materials in elliptical shapes causing them to have their

easy axis pointing along the long axis of the ellipse. This shape is chosen because the mag-

netization direction can be switched between the two opposite directions using an external

magnetic field. We can also have materials that have magnetocrystalline anisotropy where

15

the combination of crystal structure and spin-orbit coupling causes the magnetization to

preferentially point along certain crystallographic directions. Specifically for our work we

use materials with low magnetocrystalline anisotropy, such as NiFe (Permalloy), to easily

switch the direction of magnetization with an external magnetic field. We also use materials

with higher magnetocrystalline anisotropy, such as nickel, to have their magnetization set in

a certain direction and not change during a measurement. Finally, we use materials that are

fabricated so they have an out-of-plane magnetization, called perpendicular magnetocrys-

talline anisotropy (PMA), driven by strong spin-orbit coupling at the interface between Pd

and Co.

2.4 Proximity effects in Josephson junctions

2.4.1 S/N proximity effect

The previous sections discussed traditional Josephson junctions that contain a thin insu-

lating tunnel barrier. Now we focus our discussion on situations that more closely represent

our experiment. The work described in this thesis involves Josephson junctions that contain

normal metals as well as ferromagnets. Since the following experiments use several metals

such as Cu, Pd, Ru among others, we will present a simple mechanism behind charge transfer

in a S/N system. Andreev reflection, named after Russian physicist Alexander F. Andreev,

was discovered in 1964 and describes the scattering process that occurs when an electron in a

normal metal approaches a superconductor [40]. During the process, each Andreev reflection

transfers a charge of 2e across the S/N interface.

Before we discuss Andreev reflection, we must understand the energy level structure of

electrons in a superconductor. As a superconductor cools below its critical temperature the

16

Figure 2.4: Schematic of Andreev Reflection: Schematic of Andreev Reflection. a) Normal
reflection shows an electron reflecting at the interface with the superconductor and scattered
back into the normal metal. b) Andreev reflection shows an electron incident on the interface
and a hole scattering back into the normal metal. Inside the superconductor a Cooper pair
is created causing a -2e transfer of charge into the superconductor. Taken from [41].

17

electrons at the Fermi level form Cooper pairs. As we recall Cooper pairs behave like bosons

with zero spin and a single phase-coherent wavefunction. When these Cooper pairs form

they have a lower energy than the original two electrons in single electron states. This lower

energy causes an energy gap ∆ to form in the single electron density of states, as shown

in the right side of Figure 2.4. The metal that is next to the superconductor has electrons

filled up to the Fermi level. It appears that electrons can pass from the normal metal to the

superconductor only if their energy exceeds ∆ above the Fermi level. But there is another

way.

Figure 2.4 shows cartoon diagrams of normal reflection and Andreev reflection. An

electron propagating through a normal metal is incident at the interface where the metal

meets the superconductor. Assume that the energy of the electron is less than ∆, so there

are no single-particle states in the superconductor for the electron to occupy. We have

two possible results. The not-so-interesting result is when the electron hits this surface and

reflects back into the normal metal as seen in the image on the left in Figure 2.4(a). The more

interesting result is when the electron performs an Andreev reflection, as shown in Figure

2.4(b). In this process the incident electron reflects as a hole back into the normal metal,

which transfers a Cooper pair into the superconductor. The electron needed for this process

comes from below the Fermi level in the normal metal, and has opposite spin, momentum

and energy compared to the incident electron.

The reverse of this process is when a Cooper pair in the superconductor enters the normal

metal producing two electrons that are no longer bound as a pair. The electrons do retain

some phase coherence up to a certain length, known as ξN , which depends on the material

and temperature. The length scale of the coherence depends on whether one considers the

ballistic or diffusive limit, i.e. whether the mean free path is larger or smaller than ξN [42,43].

18

One can estimate ξN using an Uncertainty Principle argument, where the energy uncertainty
comes from the thermal energy 2πkBT , causing a coherence time of order /2πkBT . During

that time, an electron propagates a distance

ξN =

vF
2πkBT

(2.16)

In the other limit where the mean free path is much shorter than ξN , the diffusive limit,

the electron motion is diffusive with diffusion constant D, and we have

(cid:115) D

2πkBT

ξN =

.

(2.17)

This coherence causes the normal metal to acquire some properties that appear to be

superconducting. At low temperatures, the normal metal coherence length can be as long

as a micron. The inverse effect also occurs, whereby ”leakage” of Cooper pairs from the

superconductor weakens the superconductivity near the boundary.

2.4.2 S/F proximity effect

We now consider the more interesting case where we have a superconductor next to a

ferromagnet. Since we have an exchange field and different spin bands in the ferromagnet

we have more interesting physics. Here we provide a qualitative explanation of the physics

behind the S/F system. For a more in-depth understanding we can look at the work done

by Buzdin and Radovi´c [44–47]. For simplicity we will look at the description by Demler,

Arnold and Beasley, who modeled the ferromagnet as a normal metal with a Zeeman-like

energy splitting between the majority and minority spin bands [48]. They assumed that spin

is a good quantum number and Cooper pairs are being adiabatically transported across the

19

Figure 2.5: Band Structure: A) Nickel band structure [49] showing energy bands for majority
spins (solid lines) and minority spins (dashed lines). B) An idealized band structure for a
ferromagnet contains a single parabolic band with spin splitting equal to twice the exchange
energy. When a Cooper pair enters the ferromagnet the electrons go into different spin-bands
causing the pair to acquire a non-zero center of mass momentum.

SF interface.

First, we will look at the band structure of a typical strong ferromagnet. Figure 2.5a

shows the band structure for Ni. We notice several energy bands near the Fermi surface.

This band structure is very complex. To simplify this, theorists working in the field of

superconductivity use a simplified model of a ferromagnet as shown in figure 2.5b. In this

model the ferromagnet has a parabolic band that is spin-split by twice the exchange energy,
Eex. They assume that the Fermi velocity is the same in both since Eex (cid:28) EF .

Since we are studying S/F/S Josephson junctions, we want to know what happens to a

Cooper pair that starts in one of the superconducting electrodes and enters a ferromagnet.

Considering only the spin and center-of-mass components of the wavefunction, in S we have

the usual spin-singlet wavefunction:

Ψ =

1√
2

(|↑↓(cid:105) − |↓↑(cid:105))

20

(2.18)

As the Cooper pair crosses the interface into the ferromagnet the two electrons are no

longer in an eigenstate and enter different spin bands. The up-spin electron lowers its poten-

tial energy by Eex while the down-spin electron increases its potential energy by Eex. Since

the electrons must conserve total energy, their kinetic energies must change respectively

leading to a non-zero center of mass momentum

Q = (k

↑
F − k

↓
F ).

Since Eex (cid:28) EF , we can approximate that as

Q =

2Eex
vF

.

(2.19)

(2.20)

The two terms in the spin-singlet wavefunction acquire opposite momenta: |↑↓(cid:105) has Q

and |↓↑(cid:105) has -Q center of mass momentum respectively, so we get:

Ψ =

1√
2

(|↑↓(cid:105) eiQX − |↓↑(cid:105) e−iQX )

(2.21)

where X is the center of mass coordinate. Rewriting this equation in terms of sine and cosine

we get

Ψ =

1√
2

[(|↑↓(cid:105) − |↓↑(cid:105)) cos(QX) + i (|↑↓(cid:105) + |↓↑(cid:105)) sin(QX)].

(2.22)

Now we can see the two components of the pair correlation function inside the ferromag-

net. The cosine term is dominant at the origin while the sine term starts from zero and

grows larger from there. The cosine term is the spin-singlet term of the function while the

21

Figure 2.6: S/N and S/F Pair Correlation Functions: Figure showing the S/N and S/F pair
correlation functions. Both have a decay, but the S/F system has steeper decay and has an
oscillation.

sine term is the short-range spin-triplet term.

A more general case is when the electron pairs have their momentum at an angle θ with

respect to the interface normal, i.e., ∆px = h/vF cosΘ and ∆py = ∆pz = 0. Momentum is

conserved in the direction parallel to the interface, allowing the momentum to only change

in the x direction. Integrating over all possible angles of incidence gives the overall Cooper

pair distribution as

ψ ∝ sin x

ξF
x
ξF

where the clean-limit coherence length is given by

ξF = Q−1 =

vF
2Eex

.

and we used Q from Eq 2.20. The dirty limit pair correlation function behaves as

(cid:18)−x

(cid:19)

ξF

ψ ∝ e

(cid:18) x

(cid:19)

ξF

sin

22

(2.23)

(2.24)

(2.25)

Nψψwith a coherence length of [50]

(cid:114) D

Eex

ξF =

(2.26)

For strong ferromagnets like Ni and Fe the exchange energy is on the order of 1eV [51, 52]

giving a coherence length ξF on the order of a nanometer, whereas normal metals can have

coherence lengths ξN about 1000 times longer.

Figure 2.6 shows a comparison between the S/N and S/F pair correlation functions. The

normal metal shows a decay as a function of thickness while the ferromagnet has an oscillation

in addition to this decay. The oscillation of the wavefunction in the ferromagnets gives the

ability to have π phase coupling between the two superconducting electrodes of a Josephson

junction, giving what is known as π junction which will be discussed in the following section.

2.4.2.1 Current-phase relation of ferromagnetic Josephson junctions

The energy stored in a conventional Josephson junction was found previously in Eq. 2.14

as

E(φ) =

Ic
2e

(1 − cosφ).

(2.27)

The energy is minimized when φ = 0. In 1977 Bulaevskii predicted that two superconductors

sandwiching an insulator containing magnetic impurities could have a π phase shift (i.e., a

sign change) in their Josephson coupling [53]. We saw this type of behavior in fig. 2.6b where

the pair correlation function oscillates between positive and negative values as a function of

thickness of a ferromagnet. Indeed, Buzdin showed that an S/F/S junction could have either

0 or π coupling depending on the thickness of the F layer. The 0-π oscillations of many

ferromagnets have been mapped out by many groups including ours [18, 21, 22, 28, 54–63].

23

Figure 2.7: S/F/S Junctions Critical Current vs. Thickness: Plot of π junctions for S/F/S
junction plotting critical current as a function of ferromagnet thickness. The minima delin-
eates separations between standard junctions and π junctions.

24

0π0IcdFThe energy stored in a π junction is

E(φ) =

Ic
2e

(1 − cos(φ − π))

(2.28)

making the first minima of the energy occur at φ = ±π.

Since the pair correlation function oscillates with ferromagnet thickness, the critical cur-

rent does, too. In the diffusive limit, the oscillation of the critical current as a function of

ferromagnet thickness can be modeled as

Ic = Ic0e−dF /ξF 1 ∗ cos(dF /ξF 2 − θ)

(2.29)

where ξF 1 and ξF 2 are the decay and oscillation length scales of the critical current re-

spectively and θ is a phase shift [45]. Ic0 is the maximum critical current and dF is the

thickness of the ferromagnet. The point where the critical current drops to zero and rises

again indicates a change in ground-state phase going from either 0 to π or π to 0 since we

can only measure the absolute value of the critical current in most experiments. Figure 2.7

shows critical current with varying F layer thickness which gives us the ability to map out

the phase relation and extract many important features such as coherence length, period of

oscillation and the critical current phase relation for a particular F layer.

2.5 Long range spin-triplet supercurrent in S/F’/F/F”/S Josephson junc-

tions

We will now talk about a more complex situation that can occur in S/F systems.

In

2001 Bergeret et. al. predicted that it was possible to generate spin triplet pairs from spin

25

Figure 2.8: Schematic of a Spin-triplets Josephson junction: Schematic drawing of a ferro-
magnetic tri-layer that has noncolinear magnetizations of adjacent ferromagnetic layers. S
are superconductors, N are normal metals and F, F’ and F” are the ferromagnets. In this
case the F’ layer is the soft ferromagnet.

singlet pairs by using ferromagnetic layers with non-collinear magnetizations [64]. They

and others then predicted several ways that spin triplet pair correlations can be generated

in systems containing multiple ferromagnetic layers with magnetic inhomogeneity [64–68].

Those predictions have been verified experimentally by many different techniques [30,31,69–

88]. In this thesis we will focus on the generation and propagation of spin triplet supercurrent

in Josephson junctions containing multiple ferromagnetic layers.

Figure 2.8 is a schematic diagram of a proposal by M. Houzet and A. I. Buzdin in 2007 [89].

This figure shows a S/F’/F/F”/S Josephson junction composed of a ferromagnetic trilayer

whereby having ferromagnets with non-collinear magnetizations the Josephson current will

be dominated by spin-triplet, long-range triplet proximity effect, pairs. If any two adjacent

magnetizations are collinear, then only spin-singlet supercurrent is produced. In the work

performed in this thesis, F’ and F” are in-plane ferromagnets. The F layer is a ferromagnet

that has an out-of-plane magnetization.

Starting with a hand-waving argument, we know from the S/F system we have Cooper

pairs entering the ferromagnet expressed as a pair correlation function [90]. We can write

26

equation 2.22 as

|Ψ(cid:105) = |0, 0(cid:105) cos(QX) + i|1, 0(cid:105) sin(QX).

(2.30)

where we have the pair correlation function in terms of the states |s, m(cid:105) labeled according

to their total spin quantum number s and projection m. Eq. 2.30 has both the spin singlet
|0, 0(cid:105) and the short-range spin triplet |1, 0(cid:105) components in this representation. The s = 0 and

s = 1 terms both enter the ferromagnetic layer but begin to decay rapidly as a function of

F’ thickness. The pairs now enter the second F layer that has a non-collinear magnetization

with the first F’ layer. The m = 1 spin triplet component undergoes a basis rotation set

by the direction of the magnetization M in F. The spin singlet component where m = 0 is

rotationally invariant and does not change in the F layer. In the rotated basis we generate

the other two spin triplet components,

|1, 0(cid:105) = cos(θ)|1, 0(cid:105)θ +

sin(θ)√
2

|1, 1(cid:105)θ − sin(θ)√

2

|1,−1(cid:105)θ

(2.31)

The angle made between the F’ and F layer is θ where |s, m(cid:105)θ is expressed in the rotated

basis. We have now converted from the short-range triplet to the long-range spin triplet
where we have |1, 1(cid:105) and |1,−1(cid:105) as the newly generated long range triplet components. Both

do not acquire any phase shift since they consist of two electrons in the same spin band. Since

we want to have the maximum conversion from the F’ to the F layers we use a ferromagnet

with out-of-plane magnetization or perpendicular magnetic anisotropy (PMA). The PMA

layer gives θ = π/2 or 3π/2 which maximizes the triplet supercurrent conversion. The spin

singlet and m = 0 spin triplet pair correlations decay rapidly in the PMA layer as we have
discussed previously. The m = ±1 components can propagate further in the F layer, like

in a normal metal, so they are less dependent on thickness than the other pair correlations.

27

The third ferromagnetic layer (F”) is used to convert back into the spin-singlet state since

the superconductor only accepts spin-singlet states. The conversion back into spin singlet is

done by another basis rotation perpendicular to the F layer.

The ground-state phase of the spin triplet Josephson junctions depends on the relative

direction of magnetizations of all three ferromagnets. In our experiments we want to keep the

F’ and F” layers in plane and the F layer out-of-plane to maximize the spin triplet conversion.

The phase of such a junction, assuming the central PMA layer is not changing, depends on

the F’ and F” layers magnetization being either parallel or antiparallel to each other. Having

all three layers in plane would also generate spin triplet supercurrent if all three layers have

non-collinear magnetizations. The problem with this type of junction is that controlling one

layer out of three is extremely difficult. We are using shape anisotropy and an out of plane

central ferromagnet to get around this issue. Ideally you want one of the layers to switch at

a smaller field than the other one. In our experiments we choose the F’ layer to be Permalloy

(Py) which has a small switching field while the F” layer is nickel which has a larger switching

field. Although, in theory these junctions are great for generating spin triplet supercurrent,

in practice the fabrication is much more difficult and is discussed in the later chapters.

2.6 SQUIDs

The goal of this work is to fabricate phase controllable 0-π junctions. This means we

need to control the magnetics of individual layers within each of our Josephson junctions.

The magnetics of the junctions are studied extensively, and to verify that we are changing

the phase of one of the junctions we must perform an interference measurement by using

a Superconducting QUantum Interference Device (SQUID). SQUIDs were first made by

28

Figure 2.9: 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 including a circulating current around
the loop J. The blue dotted line indicates the closed contour integration path described in
the text.

Robert Jaklevic, John J. Lambe, James Mercereau, and Arnold Silver at Ford Research

Labs in 1964 [91]. SQUIDs can detect magnetic fields as small as a millionth as strong as
those produced by the human brain or less than 5×10−18 T. They can also be used to detect

things such as the cosmic microwave background radiation and nondestructive materials

testing and are able to work in temperatures less than 10 K.

Figure 2.9 shows a schematic view of a DC SQUID, which we will use as a model following

work done previously [92, 93]. The SQUID is made up a superconducting loop that has two

Josephson junctions labeled 1 and 2 in the diagram. The SQUID has a current flowing

through it with breaks up into two currents I1 and I2. Applying what we know from the

Josephson effect we can write these currents as I1 = Ic1sinφ1 and I2 = Ic2sinφ2, where Ic1

and Ic2 are the critical currents of the junctions and φ1 and φ2 are their phase differences,

respectively.

29

Cooper pairs inside of a superconductor are represented by single-phased wavefunctions

and because of this their phase can only change by 2πn around a closed loop. Using this

starting point, we have

(cid:73)

2πn =

∇θ · dl = φab + φbc + φcd + φda

(2.32)

where we are summing up over each piece of the loop. The superconducting parts of the loop

contribute two parts to the sum while the Josephson junctions give the other two parts to

our sum. The relation between the phase and supercurrent density Js as well as the vector

potential A is,

We have the following,

(cid:32)

A +

∇φ =

2π
Φ0

(cid:33)

Js

1
µ0λ2
L

(cid:90) b

a

(cid:90) d

c

A · dl

(cid:33)

Js + A

(2.33)

(2.34)

(2.35)

(2.36)

(2.37)

· dl

· dl

φab = φ1 +

2π
Φ0

(cid:32)

A · dl

(cid:33)

φbc =

2π
Φ0

1
µ0λ2
L

Js + A

(cid:90) c

b

φcd = −φ2 +
(cid:32)
(cid:90) a

2π
Φ0

2π
Φ0

d

1
µ0λ2
L

φda =

If we consider the case where the arms of the loop are wider and thicker than the London

penetration depth, and if we choose an integration path deep inside the superconductor,

then the Js term is zero and the integral of the vector potential is equal to the total flux Φ

enclosed.

30

or

2πn = φ1 − φ2 +

(cid:73)

C

2π
Φ0

A · dl

φ2 − φ1 =

− 2πn

2πΦ
Φ0

(2.38)

(2.39)

The total flux Φ = Φext + Φint in the loop is the sum of the flux from an external field

Φext and the flux from the circulating current J and loop inductance L: Φint = LJ.

Φ = Φext + LJ

(2.40)

The circulating supercurrent is given by

2J = I1 − I2 = Ic1 sin φ1 − Ic2 sin φ2.

(2.41)

while the total current through the loop is

I = I1 + I2 = Ic1 sin φ1 + Ic2 sin φ2.

(2.42)

Combining eqs. 2.39, 2.40, 2.41 and 2.42 we have

(cid:19)
(cid:18) πΦ
(cid:18)πΦ

(cid:18)
(cid:19)

sin

Φ0

I = 2Iccos

Φ0
Φ = Φext − LIcsin

(cid:19)

πΦ
Φ0

πΦ
Φ0

φ1 +

(cid:18)

cos

φ1 +

(cid:19)

(2.43)

(2.44)

where we assume both junctions have the same critical current. The maximum critical

current can be found by maximizing eq. 2.43 with respect to φ1 and using eq. 2.44 for

31

Figure 2.10: Critical current vs. applied flux for dc SQUID: Plot of critical current vs applied
flux for symmetric dc SQUID. For βL (cid:28) 1 we see an oscillation between 2Ic and 0. The
oscillation decreases in amplitude for larger values of βL.

φ1 [94]. We now introduce the screening parameter βL ≡ 2LIc
as the ratio of the maximum
Φ0
circulating current to half a flux quantum Φ0/2. For cases where βL (cid:28) 1 the circulating

current can be ignored giving a maximum current through the device as,

(cid:18) πΦext

(cid:19)

|

(2.45)

I = 2Ic|cos

Φ0

Figure 2.10 shows a SQUID oscillation in a plot of Imax/Ic as a function of Φext/Φ0. This
figure assumes that βL (cid:28) 1 which gives the characteristic SQUID oscillation we have in our

experiments.

32

Chapter 3

Experimental Techniques

3.1 Microfabrication Techniques

3.1.1 Photolithography

Photolithography (PL) in its simplest form is copying a pattern from a mask onto a

substrate using an ultraviolet light. The reason we use photolithography in our design is to

pattern top and bottom leads of our junction designs on silicon substrates. Since the design

of the leads doesn’t have to change, this step of the process is very reproducible. PL cannot

be used to make features that are the size of our junctions so most of the features on the mask

are relatively large. The process involves spinning a coating of a photoresist on top of the

substrate and exposing the then baked photoresist to a UV light. There are different types

of photoresist and all have specific purposes. The resist used in our fabrication process for

Josephson junctions is a bi-layer (S1813/LOR5B). The bi-layer has been developed to help

with the lift-off and definition of features because it can produce an undercut in the resist

profile. The undercut is basically a shadow caused by a step where no deposited material

can build up. For positive resist, exposure to UV light causes the photoresist to become

more soluble in the developer. We also use negative resist that when is exposed causes the

resist to cross-link to form a hard plastic. In either case the developer removes soluble resist

defining the features from the lithography step. For our case, the positive resist is the first

lithography step where we use the resist to define a pattern and the metal is sputtered into

33

the pattern. After metal deposition, the remaining resist is removed, which takes some of

the metal along with it but leaves metal where no resist was present. That step is called

“lift-off”.

We use negative resist in our process for defining our junctions. The negative resist

creates a hard plastic on top of the already deposited metal to protect it from chemical

etching or ion milling. The negative resist protects the metal underneath it, so the ion mill

etches away any metal not covered by the resist. Once the pattern is etched away the resist

left on top of the remaining metal is removed.

3.1.2 Electron Beam Lithography

Electron beam lithography(EBL) is used as a small feature writing process. The features

we write are on the order of a few tenths of a micron. Similarly, to the PL the EBL uses resist

to form patterns over a substrate. The difference here is that we can change the pattern

anytime we write. The shape of the junctions can be altered from sample to sample to change

their characteristic behavior. The EBL exposes the resist to highly energized electrons that

causes the same cross-linking of the resist to form a plastic. The development process then

follows to define the pattern written with the electron beam.

3.1.3 Sputtering

Sputtering involves highly energized atoms hitting a target surface and causing the target

atoms to be knocked off and deposited on a substrate. First, we need to create a plasma

from argon atoms. To create a plasma the neutral argon atoms are bombarded with electrons

emitted from a tungsten filament, which knock off an outer electron, causing the argon atom

to carry a net positive charge. There is an electric field applied in the plane of the target,

34

which will be called axis one for reference. A magnetic field generated by two permanent

magnets points in the plane of the target but perpendicular to the electric field. The magnetic

field causes the electrons to spiral according to their cyclotron frequency, making electron-

argon collisions more probable. The ionized atoms are now attracted to the cathode that is

held at a negative potential. The target is mounted on the cathode and the ions bombard

the target surface knocking off (sputtering) atoms from the target, some of which land on

the sample substrate. The target voltage is kept constant during the sputtering run and is

unique for each target.

3.1.4

Ion Milling

To ion mill, first we need to create a plasma. The plasma is created in a manner similar to

what happens in the triode sputtering guns above. A magnetic field is applied perpendicular

to the electric field, which applies a Lorentz force on the moving electrons causing them

to spiral according to their cyclotron frequency, making the electron-argon collisions more

probable. The ionized atoms are now accelerated to the grid (cathode) and out towards the

sample. Before they reach the sample, the ionized atoms pass through a neutralizer. The

neutral argon atoms slam into the sample colliding with and knocking off atoms from the

sample.

3.2 Magnetic characterization

An important first step in our research is to characterize the magnetic behavior of our sam-

ples since the relative orientation of the magnetic layers dictates the results of our electronic

transport measurements. There are two measurements that we perform using a Quantum

Design MPMS3 SQUID Magnetometer, magnetization vs. temperature and magnetization

35

vs. field, to characterize our samples. The first measurement is used when we want to find

the transition (Curie) temperature of a given sample/material. The second measurement

can probe information like switching behavior and saturation magnetization. Initial mea-

surements are performed on films to get a general idea. If further investigation is needed

the films can be patterned into arrays of nanomagnets with the same dimensions as our

junctions. The sputtering of the films follows the same steps as the sputtering of the bottom

leads. The only difference in the sputtering is that the photolithography step is not present

for the magnetic films. After sputtering, the samples are brought out of the clean room and

cut into four pieces taking care that they are not near anything magnetic. Sample are loaded

into plastic straws and placed into the MPMS3 for measurement.

Arrays: The arrays are needed when we want to determine the switching behavior that

will occur for the magnetic layers in our Josephson junctions. Starting with the magnetic

films we must now pattern an array of pillars using EBL. Like the EBL procedure with our

samples, starting with samples coated with e-beam resist, we use a diamond scribe to make

a scratch mark near the corner of the substrate though the magnetic film. This scratch mark

is used for focus and stigmation in the SEM. The writing script starts from the scratch mark

and the stage moves away from the mark to the center of the array. The move places the

mark outside of the writing area. Our standard array dimensions are 4.5mm in height and

width. The array is developed using AZ-300MIF then rinsed with deionized water. The next

step is to ion mill the array. We load the samples into ion mill holders using masks that have

the largest cutout to mill as much of the film as possible. The less film left after ion milling

the less magnetic residue will be left after processing. The ion mill is directed perpendicular

to the surface. After ion milling, we must prepare the array for dicing by spinning and baking

photoresist on the array, for protection during dicing, and the chip must also be glued to a

36

sacrificial wafer. A few drops of photoresist are placed and spread thinly on the wafer where

we plan to place the substrate making sure to press down on the corners of the sample. The

wafer is then placed on a hot plate at 110 Celsius for an hour. The wafer is then brought

out to the dicer and aligned, and the arrays are diced into 6x6mm squares. For dicing we

use the diamond blade to minimize magnetic contaminants left over from the blade. The

arrays are diced completely through since they are attached to the wafer. We now take the

wafer back into the cleanroom in preparation for removal of the resist. Acetone in a wafer

beaker is warmed to 110 Celsius and the wafer is placed into a beaker for 20 minutes. We

rinse off the acetone residue with IPA followed by DI water. For our measurements we want

to look at the switching characteristics in both the easy and hard axis of the array. Using

a diamond scribe, we label the easy axis on the back of the samples for orientation during

measurement.

3.3 Josephson Junction Fabrication Procedure

3.3.1 Sample Preparation

Starting with a three-inch single-side polished silicon wafer in a class 100 cleanroom we

spin photoresist in preparation for dicing. The resist protects the substrate during the dicing

process and keeps the surface clean from contaminants since the dicing is done outside of the

cleanroom. After placing the wafer onto a Headway resist spinner, we dispense S1813 pho-

toresist from a disposable pipet onto it. The wafer is then spun at five thousand revolutions

per minute for fifty seconds to create a uniform layer of photoresist. The wafer is then placed

on a hot plate for two minutes at ninety degrees Celsius. The wafer is now brought out of

the cleanroom and diced into 0.495 inch squares (chips) using an ADT wafer dicing saw.

37

Approximately eighteen chips can be diced out of one wafer. The dicing saw is programmed

to cut into the wafer leaving only five thousandths of an inch of the wafer remaining. After

dicing we take the wafer back into the cleanroom and label each individual chip using a

diamond scribe with a distinct number according to the location in the sputtering chamber.

The chips are held by the corners to prevent scratches near the areas of interest. The chips

are cleaned by first holding them over a waste beaker with tweezers and rinsing the bulk of

the resist using a wash bottle filled with acetone. The chips are then placed into individual

test tubes that are half filled with acetone that has been warmed to 70 Celsius using a beaker

water bath. The chips stay in the warm acetone for ten minutes with ultrasonic agitation

on high. The chips are now rinsed with Isopropanol (IPA) to remove any acetone residue.

The IPA is followed by a rinse in deionized water (DI) which is blown dry using nitrogen

and wicked from the edge of the chip by cleanroom wipes. The chips are now placed into an

oxygen plasma etcher for ten minutes at 300 watts after the plasma etcher was pre-cleaned

by running empty at 300 watts for ten minutes.

Figure 3.1 shows a cartoon representation of the Josephson junction fabrication process.

Each step is discussed in the following sections in detail. The layers in this representation

correspond to materials that we can sputter in our chamber. These materials are named in

the sputtering chamber section below.

3.3.2 Photolithography: setup and bottom lead deposition

Starting with the previously cleaned chips we first bake them at 110C to remove any

residual water. After letting the substrates cool, one at a time, they are placed on a Headway

resist spinner that is set to 3000 RPM and 45 seconds spin duration. After setting the correct

spin speed we place the chip on the spinner and use a nitrogen gun to blow off the surface of

38

Figure 3.1: Fabrication Process: Diagram of fabrication process: A. Bottom lead lithography
and deposition of metallic multilayer. PR is the bi-layer photo resist. B. Bottom lead
liftoff C. Sample coated with electron beam lithography resist. D. Ion milling E. Patterned
junction. F. Silicon Oxide deposition G. Side mill of silicon oxide H. Junction liftoff I. Top
lead photolithography J. Top lead metal deposition K. Top lead liftoff

the chip. Using a disposable pipette, we fill from the center of the resist bottle to avoid any

possible contaminants from the surface. For our bottom lead we use a bi-layer to provide an

adequate undercut. The first photoresist we spin is LOR5A, followed by S1813-G2. Holding

the pipette directly above the center of the chip, we dispense enough resist to cover the

center while avoiding air bubbles from forming. We start to spin immediately after the resist

settles. Next, the chips are placed on an aluminum foil tray and into an oven for 45 minutes

at 180C. After allowing the chips to cool we repeat this process for S1813-G2 changing the

39

spin speed to 5000 rpm for 50 seconds. To remove the solvent from the photoresist we bake

the samples in an oven for 45 minutes at 110 Celsius. Before alignment, the underside of

the samples must be clean. A swab with acetone can be used to remove any baked-on resist

from the back of the chip. This step is done to ensure a clean surface for the vacuum chuck

in the ABM mask aligner to securely hold the substrate in place during alignment. Since the

sample is held at the center of the chuck, rotation adjustments are about the center of the

sample. Alignment is done using the edges of the chip. We expose the chips for 4.5 seconds.

The developer used is MF 319 and is done for 45 seconds followed by a rinse with deionized

water. The last step of the process is a plasma descum at 100 watts for 2 minutes right

before loading the samples into holders.

3.3.3 Sputtering Chamber

Once the substrates have gone through the photo-lithography process we load them into

aluminum sample holders. The holder has a stainless steel shutter with a single square cut-

out that allows one sample to be exposed to sputtering at a time. The holders are cleaned

before each sputtering run. Cleaning involves placing the shutters into a solution of one

part deionized water to three parts nitric acid for thirty minutes and rinsing thoroughly

with DI water. The shutters and aluminum parts are scrubbed to remove any residual metal

with wire brushes and DI water. All parts are then placed into a beaker that is filled with

acetone and placed in a sonication bath for five minutes. The sonication steps are repeated

for ethanol and DI water. The parts are dried with a heat gun and placed into resealable

zipper bags.

Each holder has openings for two substrates and each substrate is held in place by a

copper heatsink. The samples are loaded into the holders in a class 100 room. Each holder

40

is labeled as “1” through “8” and individual samples are marked as “A” or “B” for sample

identification. Samples are placed into holders while keeping the shutter opening always

oriented towards the top of the holder relative to labeling. While loading the samples and

to measure their temperature a thermocouple is mounted directly on a heatsink holding a

sample using a screw as a mechanical anchor to keep it in place. Each sputtering run can

have up to seven different sputtering guns, four 2 1/4 inch triode guns and three 1 inch

magnetron guns. For the triode guns, ferromagnetic targets are soldered to a copper base

using indium to prevent them from moving due to permanent magnets near them. The

magnetron targets have silver paste on them and are held down with the gun parts. To

avoid cross contamination each of the sputtering targets has its own parts that are kept

with their corresponding targets. The sputtering chamber usually reaches a base pressure
of 2x10−8 torr after baking the chamber for eight hours and after opening it to a cryopump

for the following day. During the sputtering run, to further help lower the base pressure,

we use a cold trap to freeze any possible water still in the chamber. Passing argon through

a purifier introduces the gas into the chamber. We control the pressure by adjusting the
gate valve to the cryopump to maintain a pressure of 2.3x10−3 Torr for sputtering. The

targets are water-cooled throughout the run and have interlocks that prevent switching on

the targets without proper cooling. The plasma power supply is switched on followed by the

target power supply and target controllers. For magnetic targets, the voltage and current

values are much higher when compared to non-magnetic targets. The voltage and current are

slowly increased, fifty volts every thirty seconds, to avoid damaging the gun filament. Once

the voltages are set, we begin to measure sputtering rates using a film thickness monitor.

When sputtering niobium, we have the target on for thirty minutes prior to sputtering to

coat the walls and act as a getter.

41

When we are done depositing the niobium, we shut down the sputtering system according

to the shutdown procedure. The chamber can be left to warm up slowly overnight. If the

samples are needed quickly, we can warm up the chamber to room temperature using the

heat strips to have the samples ready for liftoff in about 2 hours. The samples are removed

from the sputtering chamber and placed into a resealable plastic zipper bag. The samples

are taken into the cleanroom to begin the lift-off process. To lift-off the photoresist we first

remove most of it by rinsing the sample with Remover PG over a waste beaker. The sample

is then placed in test tubes partial filled with Remover PG that have been warmed to 90

Celsius for 30 minutes and are sonicated for 2 minutes. The chips are then rinsed with IPA

followed by a rinse with DI water. Verification of the lift-off process is done with an optical

microscope.

3.3.4 Electron beam lithography-EBL

Once the bottom lead has been sputtered and we have processed the sample through

lift-off we can now move on to the EBL process. In this step of the fabrication process, we

are defining the shape of the junctions using a negative electron beam resist (ma-N 2401).

This resist acts as a mask protecting everything that is underneath it. In the class 100 room

the samples that have bottom leads are placed into the oxygen plasma etcher for a de-scum

process at 100 Watts for 2 minutes. Once the samples are cool, they are placed on the

resist spinner that has been set to 3000 rpm for 40 seconds. The e-beam resist is dispensed

from a disposable pipette onto the sample at the center of the chip avoiding any formation

of bubbles. The samples are then baked on a hotplate for 60 seconds at 90 Celsius. The

samples are now placed on the holder along with a stigmation sample. In preparation for ion

milling, we load five samples at a time for e-beam lithography to avoid having samples with

42

e-beam resist on them for an extended period of time. Remembering to place the samples

in the correct orientation for writing, we take an optical image for ease of alignment using

the SEM software. The height adjustment for both holders is 2mm. Following standard

loading procedure, the samples are loaded into the SEM. After turning on the beam, we

move towards the center of the stigmation sample to begin our calibration procedure. The

focus and stigmation is done on small circular gold features found on the alignment marks

of the stigmation sample. The initial alignment is done at high magnification at a working

distance of 15 mm. The following steps should be done with care not to expose the region

of interest. Once we are done with the stigmation sample we go to the lowest magnification

and move towards one of the pads of the bottom lead of our first chip. Using the vertical

alignment tool on the SEM toolbar we align to the edge of the pad for writing (a slow, high

resolution scan is useful for this step). Now we move near the area of interest and focus

on one of the alignment marks next to the writing area at 60x magnification. Zooming out

completely we move over the writing area then switch to EBL mode and align the sample

using an alignment script in NPGS. Writing is done at 1000x magnification. Our current

samples have three writing areas so focusing is done three times per sample. For development

we use AZ300MIF developer for 30 seconds followed by a rinse in DI water. Verification of

the lithography is done with an optical microscope.

3.3.5 Junction definition by ion milling

After writing features with EBL, we are ready to pattern using the ion milling process.

This step involves the use of two different holders during this process. The first sample

holder allows the milling to occur perpendicular to the plane of the sample. This step etches

the features from the bottom lead removing all but what is underneath the e-beam resist.

43

We first place a stainless steel mask that covers part of the sample, exposing only the area

near the e-beam resist to the mill. Stainless steel is used for the mask because of its low

etch rate. The sample is placed face down, directly on the mask. We apply a thin layer of

silver paste to the back of the sample to provide good thermal conductivity aiding in keeping

the sample from getting overheated during the milling process. The silver paste layer must

be thin enough so as not to spill out onto the edge or face of the sample. Following the

silver paste is a brass or copper heatsink. Some samples need a copper spacer to fill in the

space between them and the heatsink. The parts are held together with bolts and a metal

plate sandwiching all the parts together. The plates are labeled for identification during the

milling process. The holders are loaded into the milling chamber, one at a time through

a loadlock, purging with nitrogen between each opening and keeping track of the order of

the holders for identification during the process. Pumping down the chamber for one day
gives a base pressure of about 3x10−8 Torr. In preparation for milling, we turn on power

supplies for ten minutes prior. To calibrate the mill rate we must first deposit gold on a film

thickness monitor (FTM). Argon is allowed to enter the chamber and using a turbo pump

we tune to a pressure of 0.7 mTorr . To measure the mill rate, we place the FTM over the

ion mill before each sample is milled keeping track of how much gold is left after each for the

rest of the samples. Most samples need different mill times since the thicknesses of layers

vary from sample to sample. Now we are ready to start milling and the chamber pressure

is set to 0.19 mTorr using the turbo pump. Once the power supply is stable, we open the

shutter to the FTM and begin to measure a milling rate. The milling value is recorded

and using the thickness for each material along with the k-factor we calculate the mill time

for the corresponding sample. The k-factor corresponds to the ratio of milling rate of gold

compared to the material of interest. The sample is now placed over the ion mill for the

44

appropriate amount of time then the shutter is closed off once the time has elapsed. The

steps are repeated for all samples and once completed we shut off the ion mill power supply

and argon gas. If the mill time exceeds 2 minutes, we break it into parts.

The silicon oxide power supply is turned on and slowly brought up to the optimal voltage

in 5 mV steps. The preferred deposition rate is near 7 angstroms per second. We want to

protect the exposed areas with silicon oxide to prevent shorts from overlapping areas between

the top and bottom superconducting electrodes. The rate is measured with the FTM making

sure the value is set for silicon oxide. The sample is placed over the silicon oxide and spun

continuously in order to have a uniform insulating layer. After milling the samples, we take

them back into the cleanroom and clean off the silver paste using a cotton swab and acetone.

The samples are then placed into side mill holders making sure to have the bottom lead

directed along the opening of the holder. Following the same steps as before we measure

the rate of the ion mill and mill each side of the sample for four minutes on each side. The

samples are rotated by 180 degrees to mill both sides of the sample. The side mill step is

in place to help with the liftoff of the e-beam resist. Images before liftoff are taken with an

optical microscope using manual settings for comparison. Samples are placed in Remover

PG that has been warmed to 90C, for 10 minutes followed by a mechanically-assisted liftoff

with a Q-tip. The samples are placed in the warmed Remover PG for 1 hour. After an hour

we rinse the samples with DI water and verify that the pillars have had a successful lift off

using an optical microscope. Once the steps are completed, we are ready for the top lead

lithography.

Arrays: For fabrication of arrays some different steps need to be taken. The arrays are

written on unpatterned magnetic films. The film must be marked first in order to align,

focus and stigmate. The mark is done near a corner with a diamond scribe. The EBL array

45

Figure 3.2: Junction Array: Optical microscope view of array of elliptical nanomagnets pat-
terned with electron beam lithography. Each nanomagnet measures 0.5µm by 1.25µm. The
pattern shown contains 99 x 39 nanomagnets, and measures 100 microns in both directions.
The pattern is repeated 45 x 55 times to form the entire array.

writing file will include an offset for centering the array. Once the ion milling is done the

liftoff procedure may leave some resist on the tops of the pillars. The substrate must be

attached to a large wafer for dicing out the array. The attaching of the substrate is done by

wetting the back of the sample with photoresist and baking at 90C for 1 hour. The wafer

with the sample is then spun to coat completely with photoresist and baked at 110C for 2

hours. The dicing is done by aligning to the edges of the array, which should be visible in

the dicing saw.

Figure 3.2 is an optical image of one of our lithography patterns of arrays. The bits seen

in the image are the same size as the junctions patterned in our samples. The pattern is 99 x

39 bits repeated 45 x 55 times. The arrays give us approximately 9.5 million bits. The write

time for a whole array is 12 hours. The reasoning for having so many bits is to produce a

46

signal strong enough to be measurable by the SQUID magnetometer.

3.3.6 Top lead

For the top lead photolithography, we follow the same steps as before, but the alignment is

done using the markers from the bottom lead. The initial vertical, horizontal and rotational

alignment is done using the marker near the center of the sample. The rotational alignment

is done using the outer markers. As the mask is brought into contact the tilt adjustment

must be held down to ensure full contact with the sample. We check the alignment once

again to make sure nothing has shifted after full contact. The alignment must be checked

after the development step to check for the correct overlapping of the leads. Two sputtering

targets are used for the top lead sputtering process, niobium and gold. Before depositing the

top leads, we use a small ion mill to clean off the capping layer of gold covering the niobium

from the bottom lead. Each sample is milled just before the top lead niobium is deposited

to minimize any possible oxidation of the niobium. The top lead is 150 nm of niobium which

is once again capped with gold.

3.4 Measurement

3.4.1 Setup and mounting

Once we have completed the fabrication of our samples and have taken images of them

using the optical microscope, we take them into our measurement room. The first step is to

check resistance values of the junctions using a two terminal measurement using a standard

voltmeter. The sample is placed on a copper base, for stability, with a vacuum to hold it in

place. Our typical resistance values for junctions are on the order of tens of mOhms when

47

cooled but at room temperature using a two wire terminal measurement, we get resistance

values on the order of hundreds of kOhms due to the long Nb leads. We also check the

resistance along the top and bottom lead. We prepare the sample for mounting on a quick

dipper by pressing indium on each pad to be used as a mechanical anchor for electrical

connections. The indium should be higher towards the center of the pad to give a place for

the wire to be pressed into. The wire is placed on the center of the indium and a stub point

is used to press the wire into the indium. The sides of the indium are rolled over the wire

to help hold it in place. With the wire pressed, we place a small piece of indium on top and

press it forming a sandwich securing the wire to the pad. These steps are repeated for all

the pads keeping in mind that pressing indium on pads after dipping does not adhere as well

as pressing them before dipping. Once all the connections are made to the quick dipper,

we secure the sample using some thread by wrapping it around the dipper’s brass base and

the sample. Resistance measurements are made through triax connections on the top side

of the quick dipper to ensure proper wiring. The final step in the setup process is to place

the mu-metal sheath over the sample area and secure it set screws. The mu-metal sheath

in used to prevent external magnetic noise to alter our measurement process. The dipper is

slowly lowered into the dewar to avoid excessive boiling off of the helium. The lowering time

depends on the specific dipper that is being used.

3.4.2 Single junctions

There are two types of transport measurement systems in the lab. For samples with large

critical currents, more than a few microAmps, we use a room temperature electronics system

that can measure up to five samples every cool down. For samples with small critical currents,

in the microAmp range, we use a measurement system that has low-temperature Phase

48

Sensitive Measurements-Superconducting Quantum Interference Device (SQUID) electronics

and can measure one sample at a time. The first measurement taken is for optimizing

parameters as the sample is in the virgin state. The virgin state measurement is taken

without applying an external magnetic field and is taken at zero field. For samples that

contain nickel as one of the ferromagnetic layers, before the measurement, we must initialize

at high field in order to push out all domain walls.

If the initialization field is higher

than 1200 Oe (Ni is initialized at 3000 Oe), we must remove magnetic flux trapped in the

superconducting leads after the large field is applied. To remove trapped flux, we must lift

the dipper out of the liquid helium in order to have the niobium leads no longer superconduct.

We take a resistance measurement through the sample using an Ohmmeter as we raise the

dipper out of the liquid helium. The sample resistance will show a non-zero value when the

sample goes normal. When the sample has gone normal, we disconnect the Ohmmeter and

wait for 10 seconds before lowering the dipper into the liquid helium again. To start taking

measurements we make the field sweep start from the same direction as the initialization

field. For these measurements, the data is processed with a fitting program that fits the

I-V curves to a square root function that gives the critical current for each magnetic field

measurement.

3.4.3 Phase Sensitive Measurements-Superconducting Quantum Interference Device

The further characterization of our junctions is done by phase sensitive measurements.

We fabricate a SQUID loop with two of our Josephson junctions along with an on-chip flux

line. The flux line generates a local magnetic field that couples flux through the SQUID

loop. A schematic diagram is shown in chapter 6. The connection and mounting procedure

is the same as the one used for the single junctions. For these measurements, the external

49

magnetic field is used to set the direction of the magnetization of the ferromagnetic layers

in the junctions before the measurement. The external field is off during the experiment

as we step through the flux line recording a SQUID oscillation. Depending on the relative

orientations of the layers we can see shifts in the SQUID oscillation plots.

3.5 Improvements to measurement and fabrication systems

During my time in the Birge group, as a part of the thesis work, I made several contri-

butions to the development of shared infrastructure in the lab. This work involved improve-

ments and added functionality to measurement equipment, measurement software and a new

high-vacuum sputtering chamber named the “Rezanator”.

3.5.1 Room temperature electronics:

· Built System Wiring and testing of new electronics

· Created measurement software Using previous versions of software a new version was cre-

ated

· Measurement improvements Added faster data acquisition by adjusting measurement pa-

rameters

· Programmed Arduino micro-controller Persistence switch controller was made using an

Arduino micro-controller

3.5.2 Low temperature electronics:

· Measurement speed improvement Adjustable measurement parameters to improve speed

of data acquisition

50

· Added measurement features Added time delay, major/minor loops, SQUID data format-

ting for easy plotting and repeatable loops for toggle switching

3.5.3 Rezanator and sputtering chamber:

· Helped develop co-sputtering capability

· Ion mill characterization Helped characterize and profile new ion mill for rotating sample

· Made indexing arm attachment Designed and machined indexing attachment for linear

arm

· Helped design hand-off system Helped with the design and fabrication of the hand off

system (motor holder, motor spindle, sample holder and Arduino motor controller

with LabVIEW controller software

· Pratt sputtering chamber Added ion mill and gun 7 to the sputtering software

51

Chapter 4

Shuffled and Triplet Josephson junctions

In this chapter we compare two types of Josephson junctions that contain the same

ferromagnetic layers but in different orders; we will call them “triplet” and “shuffled”. Both

types of junctions contain three distinct magnetic layers. The triplet junctions are made

up of two Ni layers that are either 1.2 or 1.6 nanometers thick. Between the two Ni layers

is a Pd/Co multilayer that can vary in number of repeats. The shuffled junctions contain

the same magnetic layers, but the two Ni layers are now adjacent to each other followed by

the Pd/Co multilayer. The junctions can either propagate spin triplet supercurrent or spin

singlet supercurrent. In Section 2.4.3 of Chapter 2 I discussed how short-range spin-singlet

pairs can be converted to long-range spin-triplet pairs in Josephson junctions containing three

ferromagnetic layers, where adjacent layers have non-collinear magnetizations. The Pd/Co

multilayer used in this chapter has perpendicular magnetic anisotropy (PMA), whereas the

two Ni layers have in-plane magnetic anisotropy, so sandwiching the Pd/Co between the two

Ni layers enables the generation of spin-triplet supercurrent. Shuffled junctions, because of

the order of the magnetic layers, can only generate spin-singlet supercurrent.

Joseph Glick, former Birge group graduate student, first studied spin-triplet junctions

that contained Pd/Co multilayers with PMA, but his PMA layers were arranged as synthetic

antiferromagnets (SAFs), i.e., two PMA multilayers sandwiching a thin Ru spacer layer so

that their magnetizations are coupled antiparallel to each other. Joseph found that triplet

junctions containing a PMA-SAF had a somewhat shallower decay of their IcRn product as a

52

Figure 4.1: Singlet and Triplet: Side view of general singlet (a) and triplet (b) Josephson
junctions, where the middle layer has the form of a PMA-SAF with out-of-plane magnetiza-
tion. The Ni or Py layers in the triplet have in-plane magnetization. All the magnetic layers
are separated by Cu spacers (not shown) to prevent magnetic coupling between adjacent
layers.

function of Pd/Co repeats when compared to his singlet junctions. That was expected since

spin-triplet pair correlations should be long range in the Pd/Co multilayer, whereas spin-

singlet correlations are short range. Joseph also found that for the thinnest PMA-SAF triplet

junctions, junctions with the least number of repeated Pd/Co layers, the critical current

was smaller than in similar PMA-SAF singlet junctions. That was puzzling, but a direct

comparison between those types of junctions was not meaningful because the spin-triplet

junctions contained two additional magnetic layers compared to the spin-singlet junctions.

The motivation for the work described in this chapter is directly related to Joseph results.

Our goal is to determine how much spin-singlet supercurrent propagates through the spin-

triplet Josephson junctions. We do that by comparing the magnitude of the supercurrent

in spin-triplet and shuffled junctions that contain the same number and kind of magnetic

layers, but in different sequences.

53

Figure 4.2: PMA-SAF and Shuffled junctions: Side view of the triplet (a) and shuffled (b)
PMA-SAF Josephson junctions.

Figure 4.1 shows magnetic layers in both singlet(a) and triplet(b) Josephson junction

configurations. The singlet junction on the left contains a PMA-SAF while the triplet on

the right has two Ni layers with the same PMA-SAF layer sandwiched in between them. An

important property of the PMA-SAF is that it minimizes stray fields that might interfere

with the behavior of our Ni layers. The directions of magnetization in the figures are labeled
only for reference – they may be flipped by 180◦.

Figure 4.2 shows a side view schematic of both the triplet junction (a) on the left and

shuffled junction (b) on the right. For S1, we use a Nb/Al multilayer because it provides

a much smoother surface than a pure Nb layer of the same thickness. The magnetic layers

are separated by Cu spacers to prevent magnetic coupling of adjacent layers. The first F’

layer, Ni in this case, is sputtered before any other ferromagnetic layers and directly on the

Cu spacer. For the triplet junctions the next layer deposited is the PMA-SAF layer and for

54

the shuffled junctions it is another Ni layer. Finally, we have the remaining layer, Ni for the

triplet and the PMA-SAF for the shuffled junctions. The final step is to deposit a thick Nb

top lead.

For the triplet junctions the first Ni layer allows the conversion of singlet (s = 0) pair

correlations to short-range triplet (s = 1, ms = 0). The PMA-SAF converts the short-range
triplet to long-range triplet (s = 1, ms = ±1) pair correlations. The final Ni layer converts

back to singlet pair correlations which can enter back into the other superconducting elec-

trode, thereby allowing the propagation of the supercurrent through the junction. Looking

at the shuffled junction geometry we can clearly see that although we do convert to long-

range triplet pair correlations, we never convert them back into singlet pair correlations.

This means that only spin singlet supercurrent can propagate through this type of junctions.

4.1 Magnetic characterization of Pd/Co multilayers

The first step of the process was to understand the magnetic behavior of the ferromagnets

that we would like to use as the central ferromagnet in the junction stack. The selection

of Pd/Co multilayers as the central layer was done in order to take advantage of their out

of plane magnetization. The Pd/Co multilayer system can have either an in-plane or out-

of-plane (OOP) magnetization, depending on the thicknesses of the individual Pd and Co

layers. We have fabricated and measured Pd/Co multilayers of varying thickness to produce

a stack that will have an out of plane magnetization relative to the substrate surface. We first

need to find the correct thickness and verify that the multilayers are indeed magnetized out

of plane. We also would like to know the strength of the magnetization of these multilayers.

We begin by sputtering thin films of both PMA and the PMA-SAF magnetic layers on

55

Figure 4.3: Magnetic force microscopy of Pd/Co multilayers: Top down view of Pd/Co
multilayers imaged through a magnetic force microscope. Left image: virgin state, right
image: after application of and removal of a magnetic field applied out of plane.

substrates that were prepared for sputtering using the cleaning process described in the

experimental techniques chapter. Samples that are sputtered for magnetic measurement are

placed directly into substrate holders without a mask or lithography step. The shutter on the

substrate holder provides almost complete exposure, when opened, to the sputtering guns.

Samples were first grown looking specifically at the Pd/Co multilayers. We grew samples

with varying number of Pd/Co repeats. A thin layer of Nb is deposited on the substrate

which gives the following layers better adhesion to the substrate. Samples are grown at -20

Celsius just as the junctions.

Once the samples are sputtered, we unload them in a class 100 clean room and load

them into vials for measurement. Some of the samples were measured in a magnetic force

microscope. The MFM scans the sample and images the domains in the multilayer that

are aligned OOP. Figure 4.3 shows two MFM images of the Pd/Co multilayers measured

after sputtering. The image on the left was measured as grown directly from the sputtering

chamber. The image shows the domains can vary greatly in size and shape leading to a very

disordered structure. The image on the right is the same film after we applied a field out of

56

plane to align all the domains in the multilayer. This image on the right shows that after

magnetizing the domains OOP they stay in that configuration.

The remaining films were measured using the MPMS3 SQUID magnetometer. The sub-

strates that we dice measure 0.5 x 0.5 in2. To measure the samples with the SQUID mag-

netometer they first need to be mounted in plastic straws. The straws provide a simple and

reproducible holder with a consistent background signal that can be removed after the mea-

surement is taken. The substrates are scribed into four pieces and broken along the scribe

marks. Because of the strength of the magnetic material, we only need to place two of the

quarter pieces into the straw. They are placed back-to-back and pressed into the correct

position in the straw. The centering of the samples is done at 10K. The sequence file we use

for the measurement steps through a series of magnetic fields while the magnetic moment of

the samples is measured. For the PMA samples we measured magnetization (M) vs. field

(H) with the field oriented both in plane and out of plane. This measurement also tells us

the initialization field needed to align the magnetization out of plane.

Figure 4.4 shows a hysteresis curve where the applied field is oriented out-of-plane with

respect to the substrate. The figure shows that at large applied field the multilayer is fully

saturated, and as the applied field is ramped down to zero the magnetization stays saturated.

The magnetization stays saturated even as the field switches into the opposite direction, until

the magnetization begins to switch at -1500 Oe. Figure 4.4 shows that the field needed to

initialize the PMA layer is small enough so that it can be done at room temperature with a

permanent magnet. The figure also shows us that the PMA system is very rigid and switches

cleanly when initialized in the opposite direction. The plot shows a clean switch of the PMA

layer near 1500 Oe.

In Figure 4.5 we have a hysteresis curve of a Pd/Co multilayer with the magnetic field

57

Figure 4.4: Pd/Co multilayer thin film out-of-plane: Hysteresis curve of Pd/Co multilayers
measured out-of-plane. Clean switching is observed at a field of about 1500 Oe. Saturation
occurs above 4 kOe.

applied in the plane of the substrate. We see a slow, almost linear, reversal of the magneti-

zation with field. The magnetization saturates at -50 kOe. Figure 4.5 show that after a large

IP field is applied and removed there is very little remnant magnetization. These hysteresis

curves give us a clear indication that the Pd/Co multilayers exhibit PMA. Figure 4.5 also

reveals that we can apply large in-plane fields to manipulate the Ni layers without worry of

ruining the out-of-plane magnetization of the Pd/Co multilayer. The Pd/Co multilayer is

very rigid in this system of 2 repeated layers.

Another important property that we take advantage of in these junctions is that we can

grow a thin layer of ruthenium between the Pd/Co multilayers at certain thicknesses which

causes the magnetic layers to couple antiferromagnetically and create a SAF. The reasoning

behind the use of PMA-SAF’s as one of the magnetic layers is to minimize stray fields that

58

Figure 4.5: Pd/Co multilayer thin film in-plane: Hysteresis curve of Pd/Co multilayers
measured in-plane. Gradual switching is observed. Saturation occurs at about 50 kOe.

can interfere with the behavior of our Ni layers. Figures 4.4 and 4.5 all are measurements of

PMA films. For similar magnetic measurements of PMA-SAFs please refer to Figure 8.2 in

Joseph Glick’s dissertation [95].

4.2 Fabrication of junctions containing Pd/Co

The next step in the experiment was to fabricate junctions that were identical except

for the central ferromagnetic layer where we have the following differences, S/Cu/Ni/Cu/

[Pd/Co]n/Ru/[Co/Pd]n/Cu/Ni/Cu/S (triplet) and S/Cu/Ni/Cu/Ni/Cu/[Pd/Co]n/Ru/[Co/

Pd]n/Cu/S (shuffled). Note that the first S at the bottom of the stack is a [Nb/Al] multi-

layer, whereas the top S is pure niobium. These Josephson junctions contain some of the

most complicated stacks that our group fabricates. Fabrication of these stacks requires devi-

ations from our standard junction fabrication process. The reason behind the complexity is

59

the limitations of the sputtering chamber. The junctions contain five metals that we sputter

from large targets: Nb, Al, Ni, Pd and Co, and three metals we sputter from small targets:

Ru, Cu and Au. The chamber is designed to hold seven sputtering targets (four large and

three small) at once along with an ion mill. Since the process calls for 5 large targets, this

means we need to exchange one of the targets during the sputtering process. This exchange

of targets involves breaking vacuum and replacing one of the targets while the chamber is

kept warm and with an argon environment. The exchange needs to be done as quickly as

possible to avoid sample contamination. The sample must also have a layer of Au sputtered

on it before breaking vacuum that must be milled off before continuing with the sputtering

process. For all our junctions we start first with the photolithography of the bottom lead.

The bottom lead lithography is the most important step of the fabrication process. The

layers deposited need to be as smooth as possible. Most of the process is carried out inside

of a class 100 cleanroom to avoid debris adhering to the bare substrate. Any contaminants

would propagate through all the layers. The smoothness of the layers gives more consistent

switching characteristics of the Ni layers. The photomask we use has room for the connection

of six junctions. The bi-layer photoresist recipe mentioned in chapter 3 is required for this

process. This ensures well defined features after lift-off.

Figure 4.6 shows the bottom lead mask where we have two pads that are used as common

connections for all 6 junctions. The four outer features along with the feature near the

center of the mask, indicated with green circles, are the alignment marks that will be used

for aligning the top lead to the bottom lead later in the process. There are smaller features

near pairs of junctions that are used to align for EBL. The diamond pattern of the top pad

is used for reference orientation when the samples are being handled without microscopes.

The photolithography process is the one discussed in chapter 3. The alignment process

60

Figure 4.6: Photolithography bottom Lead : Top down perspective of the bottom lead pho-
tolithography mask. Two pads are the common connections for measurement. Alignment
marks are indicated by green circles.

is not as important for the bottom lead as it is for the top lead. The important step is

the contact pressure. The better the contact pressure the more accurately the features

on the mask are reproduced on the chips. Setting up the sputtering chamber for bottom

lead sputtering includes having the process ready for breaking vacuum during the run and

replacing some of the targets for sputtering the second step in the bottom leads.

After the bottom leads are deposited, the chips are taken back into the cleanroom for lift-

off. The rest of the junction fabrication process is described in Chapter 3 and summarized in

Figure 3.1. The junctions we fabricate are elliptical to take advantage of the shape anisotropy

61

Figure 4.7: Sample mounted on QDI : Electrical connections using Indium for sample
mounted on QDI.

for controlling the in-plane magnetic layers. The junctions have lateral dimensions of 1.25 x

0.5 µm2. The Ni layers point along the longer axis of the ellipse which is called the easy axis.

If we apply a large magnetic field in the opposite direction the Ni magnetization direction

changes but still tends to point along the easy axis. Because we are using two Ni layers

in addition to the PMA layer, we should observe the switching of both layers at similar

fields when sweeping the external magnet. This experiment will give the parallel state of the

junctions when measured.

4.3 Measurement

Before we start handling any samples, we must use a static wrist guard to prevent dam-

aging them during the wiring process. Depending on the expected sample critical current

value we can either use room temperature electronics or low temperature electronics. Once

the sample is placed on the dipper, we use sewing thread and wrap it around the sample and

brass base to mount the sample.

Figure 4.7 is an image of sample mounted on Quick Dipper 1 (QDI). The base is isolated

62

Figure 4.8: Bottom Lead : Cartoon representation of the bottom and top lead with the
junctions sandwiched between.

from the sample by waxed paper. The connections to the pads are made using Indium.

The voltage wires connected to the SQUID are superconducting while the current lines are

copper. The external superconducting magnet is wound on the brass barrel that slides over

the sample once the connections are tested.

Once the samples have been connected, we test for proper connections using a multi-meter

set to high resistance range, 2 kOhms, to avoid damaging the samples. The measurement

data is taken using a LabVIEW program created and updated in the Birge group. The

measurement program controls current sources that drive the superconducting magnet and

the sample as well as voltmeters that measure the voltage drop across a precision resistor to

calculate the current through the magnet and the voltage across the sample. Figure 4.8 shows

a cartoon representation of the top and bottom leads with the junctions between them. We

use the bottom lead as common voltage and current connections and the top lead is used to

select which junction we want to measure. Since these junctions contain Ni, initialization is

done at a field of 2000 Oe to ensure the Ni domains are all pointed along the same direction.

Sometimes we must initialize the Ni several times to “train” the layers. This training effect

can be observed when the same sample is measured after similar initialization steps in a

63

I of a Josephson junction: Plot of voltage vs. current for a typical
Figure 4.9: V vs.
Josephson junction. The red line is a fit to the data of the square-root function discussed in
the text.

single dip. The Fraunhofer pattern looks smoother and more defined after you repeat the

initialization process several times. It is important to point out that the sample must be

taken into the normal state before each measurement if the initialization field is greater than

1500 Oe. Since the samples and measurement system contain Nb superconductors for the

leads and wires, the initializing of the sample causes flux trapping that persists after the

field is turned off. When the field exceeds 1500 Oe we remove the trapped flux by raising

the sample out of the liquid helium bath and let it warm up enough so that it is no longer

superconducting. We check this by connecting a multimeter to the sample as we raise the

dipper to notice an increase in the resistance of the sample. Figure 4.9 shows a typical I

vs. V curve taken from our measurement system. The blue points are actual data from
the measurement while the red line is the square root (SQR) |V | = R

I2 − I2

(cid:113)

c0 function

we use to fit the data. The sharp point on either side of the origin is the critical current

64

value taken from the fit. Since these junctions have a smaller than typical critical current,

we observe rounding near the fitted critical data value. The data can be fit using another

model, Ivanchenko-Zilberman (IZ) model, which considers the thermal rounding for smaller

critical current junctions. The IZ model takes much more time to fit and sometimes has

problems fitting nearly-linear I-V curves when the Ic value is very small. The difference in

the fits gives a slightly higher critical current for the IZ model so using the SQR model gives

us a lower bound to the data.

4.4 Results

Once we have collected all the IV curves we can now move on to extraction of the critical

currents of the data. For each step of the magnetic field, we will plot a critical current.

Figure 4.10 is a plot of critical current vs. field, which is known as a Fraunhofer pattern

of one of the triplet PMA junctions. We can see that Ic goes to zero between each lobe

signifying that our sample has no shorts. In this case the sample was initialized with the

field in the negative direction and the measurement was taken with the field stepping in the

positive direction. The measurement procedure was stopped when the field reached 20 mT

to avoid causing the Ni magnetization to switch in the other direction. For this sample, the

maximum Ic was about 0.4 mA. These measurements were done for both types of junctions

with similar initialization procedures. For the Ic of each junction we used the maximum value

taken at the peak of the Fraunhofer pattern.

In figure 4.11 we show data for both triplet and

shuffled PMA-SAF junctions with Ni thicknesses of 1.2 and 1.6 nanometers. We notice that

the triplet junctions in either thickness have similar IcRn products of about 1µV. The plot

also shows that the shuffled junctions have a much smaller critical current when compared to

65

Figure 4.10: Ic vs. H : Plot of critical current vs. external magnetic field of a PMA Josephson
junction. For this measurement, the pillar was initialized with the magnetic field in the
negative direction. The field was then swept in the positive direction passing zero field and
stopped just before the Ni magnetization switches to the opposite direction.

the triplet junctions. We can also see what we expect to see when observing singlet critical

current, namely that the thicker Ni junctions have a smaller IcRn product when compared to

the thinner Ni junctions. This decay of critical current as thickness increases is a signature

of supercurrent in singlet Josephson junctions.

4.5 Conclusions

The chapter shows the fabrication, measurement and data collecting procedure as well

as the interpretation of triplet and singlet Josephson junctions. Since singlet supercurrent

doesn’t depend on the order of the various magnetic layers, the shuffled junctions allowed us

66

-80-60-40-200200.00.10.20.30.4Sweep directionIc (mA)0Hext (mT)Initialization directionFigure 4.11: IcRn vs. Ni Thickness: Plot of IcRn vs Ni thickness. This plot shows the
IcRn product of PMA-SAF triplet junctions (triangles) and PMA-SAF shuffled junctions
(squares) of with two different Ni thickness plotted with corresponding . Triplet junctions
shows similar IcRn product for either thickness. Shuffled junctions show a smaller value of
IcRn for the larger Ni thickness.

to obtain a direct comparison of the triplet and singlet supercurrent in Josephson junctions.

The supercurrent in triplet Josephson junctions is shown to be dominated by spin triplet pair

carriers by the observation of the larger IcRn products of triplet junctions when compared

to shuffled junctions.

We can now understand what Joseph Glick’s work showed when he compared his triplet

and singlet junctions. In junctions with the thinnest Co/Pd multilayers (with one Co/Pd

bilayer on each side of the SAF), the larger supercurrent he observed in his singlet junctions

67

0.010.1110Triplet Ni(1.2)Triplet Ni (1.6)Shuffled Ni(1.2)Shuffled Ni(1.6)IcRN (V)Ni (1.2)      Ni (1.6)was simply because those junctions contained fewer magnetic layers, and fewer interfaces,

than his triplet junctions. Once the total number of Co/Pd bilayers increased to n = 4

or greater (two bilayers on each side of the SAF), then triplet junctions had larger Ic, as

expected.

The decay of the supercurrent with Ni thickness is a more subtle issue. We know from

Chapter 2 that singlet pair correlations and associated supercurrent oscillate and decay with

F-layer thickness. For Josephson junctions containing a single layer of pure Ni, Baek et

al. have shown that the oscillations in Ic have minima at Ni thicknesses of about 0.9 nm

and 3.5 nm. In our shuffled junctions, putting two 1.6-nm Ni layers back-to-back may act

similarly to a single Ni layer of thickness 3.2 nm, which is close to the minimum at 3.5 nm.

So, the smaller value of IcRn in the 1.6-nm shuffled junctions may be a signature of the

oscillation, rather than the overall decay with thickness. Nevertheless, the lack of decay of

the supercurrent with Ni thickness in triplet junctions suggests that these junctions carry

mostly spin triplet pair correlations.

68

Chapter 5

PMA-SAF and PMA Josephson junctions

In this chapter we will look at two types of spin triplet Josephson junctions that contain

three ferromagnetic layers. The motivation for this work stems from the previous work done

by, former graduate student, Joseph Glick on spin triplet Josephson junctions. Joseph was

able to control the ground-state phase difference across these junctions between 0 and π

by switching one of the three ferromagnetic layers by 180 degrees without disturbing the

other two layers. Such a phase-controllable junction could be used as a memory element in a

superconducting computer. Joseph’s junctions had critical current values up to 5µA, which

is too small for use in a memory element. Because of this, the next goal is to increase the

critical current in these spin-triplet Josephson junctions while maintaining phase control.

As in the previous chapter, the junctions studied here are composed of three ferromagnetic

layers, where one of the layers has an out of plane magnetization and the other two layers

have in plane magnetization. These junctions can convert spin singlet supercurrent into spin

triplet supercurrent in their central ferromagnetic layer. The ability to convert to spin triplet

is due to the layers having non-collinear magnetization between adjacent layers. The spin

triplet supercurrent, as we have seen in chapter 4, can propagate further in a ferromagnetic

layer when compared to spin singlet supercurrent. The work in this chapter is focused on

the central Pd/Co multilayer that has out-of-plane (OOP) magnetization. The complete

junction stacks are composed of two in plane ferromagnetic layers surrounding an out of

plane ferromagnetic layer. The OOP layer in these junctions can be either in the form

69

as a single Co/Pd multilayer, which we will refer to as PMA for perpendicular magnetic

anisotropy, or as two multilayers coupled antiferromagnetically, which we refer to as PMA-

SAF. We have seen that spin triplet supercurrent is the dominant supercurrent in these

junctions and now we will be focusing on increasing the amount of spin triplet propagation

in Josephson junctions.

5.1 Magnetic Properties

All Josephson junction fabrication starts with first understanding the magnetic proper-

ties of the individual layers. Similar to the work done from chapter 4 we begin by looking at

the Pd/Co multilayers. In figure 5.1a we see the PMA stack which is composed of repeated

layers of Pd(0.9nm) and Co(0.3nm) sputtered directly on top of each other. The PMA-SAF

stack has the same layers as the PMA, but with the Pd layer in the very middle replace by

a Ru(0.95nm) layer. The Ru layer causes the adjacent Co layers to couple antiferromagneti-

cally. The total number of Co layers in the PMA-SAF is even, with the same number above

and below the Ru, which gives a net zero magnetization to the PMA-SAF. The Figure shows

uniform magnetization pointing out of the plane for both the PMA and PMA-SAF stacks,

but the up and down directions might be reversed in the latter. Measurements needed to

show which layer is pointing in a specific direction are not available in our lab. The specific

direction of the magnetization is not as important as the overall net magnetization for either

stack: magnetization is out of plane for our junction design to be compatible with the spin

triplet design.

For magnetic measurements we refer to chapter 4. From figure 4.3 we know that the

Pd/Co multilayers, in their virgin state, have large domains that are non-uniform in size

70

Figure 5.1: PMA-SAF and PMA: Side view of the PMA (a) and PMA-SAF (b) ferromagnetic
stacks with palladium/cobalt multi-layers. PMA-SAF on the left has a ruthenium spacer
between the multilayers to couple them antiferromagnetically

and shape. Figures 4.4 and 4.5 have shown that the Pd/Co multilayers exhibit strong out

of plane magnetization with very little in plane as well as a very high switching field when

trying to change the magnetization to the opposite direction.

5.2 Fabrication of spin triplet PMA and PMA-SAF junctions

Figure 5.2 show the stacks for the PMA-SAF (a) and PMA (b) Josephson junctions.

When we fabricate the PMA and PMA-SAF triplet Josephson junctions we do both in the

same sputtering run to avoid any run-to-run variations in the samples. We also face the

same issue that we did before where the number of guns in the sputtering chamber limited

the number of materials that can be sputtered in one run. The fabrication of these samples

requires five materials that are sputtered from large targets: Nb, Al, Ni, Pd and Co, and up

to three materials sputtered from small targets: Ru, Cu and Au for the PMA-SAF. Since the

chamber is designed to hold seven sputtering targets (four large and 3 small targets) at once

along with an ion mill, we must sputter the superconducting layer first then break vacuum,

71

Figure 5.2: PMA-SAF and PMA schematic diagram: PMA-SAF and PMA Josephson junc-
tion schematic diagrams.

replace the targets, and seal the chamber to sputter the ferromagnets.

The photomask used is the same as the previous chapter which has room for 6 junctions.

The bi-layer photoresist recipe mentioned in chapter 3 is required for this process. This

ensures well defined features after lift-off. The single junctions pattern used is the same as

in chapter 4 figure 4.6. The four outer features along with the feature near the center of the

mask, indicated with green circles, are the alignment marks that will be used for aligning

the top lead to the bottom lead later in the process. We then use electron-beam lithography

with the negative e-beam resist ma-N2401 and Ar ion milling to define the junctions. The

junctions are elliptically shaped with lateral dimensions of 1.25 x 0.5 µm2. Ion milling is

72

immediately followed by thermal evaporation of SiOx without breaking vacuum, to isolate

the bottom and top superconducting electrodes. After the e-beam resist is removed, top leads

of Nb(150)/Au(15) are sputtered through another photolithographic stencil after gentle in-

situ ion milling of the protective Au layer. The diamond pattern in figure 4.6 is used for

reference when the samples are being handled for measurement. The alignment process is

not as important for the bottom lead as it is for the top lead since the bottom lead is going

on a blank substrate. The important step to be cautious with is the amount of contact

pressure. The better the contact pressure the more resolved the feature of the mask will be

on the substrate.

5.3 Measurement

We use I-V curves to characterize these junctions as a function of field applied along the

direction of the long axis of the ellipse. These I-V curves follow the standard shape of an

RSJ model for an overdamped junction. There is some rounding that occurs for current

values near Ic that are visible in junctions with Ic less than about 10 µA. Figure 5.3 shows a

typical Fraunhofer pattern for one of the spin-triplet junctions containing a PMA stack. The

main central lobe and two side-lobes are clearly visible in the negative sweep. We typically

stop the field sweep when the field passes through zero and reaches 20 mT in the direction

opposite to the initialization direction. Continuing the field sweep past that point results in

a distorted pattern due to the gradual switching of the two Ni layer magnetizations.

73

Figure 5.3: PMA Triplet Fraunhofer pattern: Fraunhofer pattern for a PMA triplet Joseph-
son junction containing Ni outer layers and a Pd/Co PMA central layer. The red data
points were acquired during a field sweep from negative to positive after initialization at a
large negative field. The green data points had a positive initialization. We chose not to go
past a field of 200 Oe after passing through zero field because the slow reversal of the Ni
magnetization causes distortions in the Fraunhofer pattern.

5.4 Results

The primary goal of this work is to understand the difference in supercurrent transmission

between spin-triplet junctions containing a PMA-SAF and those containing a single PMA

layer of the same total thickness. The data for IcRN as a function of the total number

N of [Co/Pd] bilayers in the PMA junctions are shown as green diamonds in figure 5.4,

while the data for the PMA-SAF junctions are shown as red triangles. The data exhibit a

striking difference between the PMA and PMA-SAF junctions. The decay of Ic with N is

much shallower in the PMA junctions than in the PMA-SAF junctions. Least-squares fits
of an exponential decay of the form IcRN (N ) = A0exp(−αN ) to the data in figure 5.4 give
CoP d = 0.191 ± 0.017 for the PMA junctions, and αP M A−SAF
= 0.751 ± 0.047 for the
αP M A

CoP d

74

Figure 5.4: PMA-SAF Ic vs. Thickness: IcRn product vs Pd/Co repeats. PMA triplet:
green diamonds. PMA-SAF triplet: red triangles. Singlet junctions: blue circles.

PMA-SAF junctions. The ratio of those slopes is 3.9 ± 0.4. In addition, the value of Ic is

larger in the PMA junctions than in the PMA-SAF junctions for all values of N , including

the smallest value, N = 2. This result is very promising for practical memory devices, if we

are able to fabricate controllable-phase PMA junctions by replacing one of the two Ni layers

with NiFe, as we did with PMA-SAF junctions

There are two theoretical works [96, 97] that deal with the kind of system studied here.

The “P-state” and “AP-state” in those works correspond to our PMA and PMA-SAF junc-

tions, respectively. (The fact that their F layer is in plane as opposed to ours being out of

plane is not relevant; only the relative orientations of the different magnetizations matter.)

Both theoretical works predict that the critical current in the AP state will be slightly larger

than in the P state, which clearly disagrees with the data shown in Fig. 5.4 That is not

75

24680.010.1110IcRN (mV)Pd/Co Repeats, Nsurprising. Both theoretical works utilize the quasi-classical theory, which does not account

for differences in transport properties between majority and minority spin bands in the bulk

of the F materials and at F/N interfaces. The disagreement with experiment highlights the

fact that the differences we observe between our PMA and PMA-SAF junctions are due to

those band structure effects.

To understand what is causing this shallower decay we must first have a brief understand-

ing of how a three layer spin-triplet junction converts spin-singlet supercurrent to spin-triplet

supercurrent. When spin-singlet pairs enter the first ferromagnet F’ from the bottom super-

conducting electrode they oscillate between singlet and ms=0 triplet states as they propagate

through the magnet. When the pairs enter the F layer, and assuming the ms=0 triplet am-
plitude is not zero, they are converted to ms=±1 states in the new rotated basis. These

triplet pair propagate freely in the F layer until they reach the F” layer where they are now

converted back into the ms=0 triplet pairs. As they propagate from F” the pairs again

oscillate between the ms=0 triplet and singlet states. The singlet component is allowed to

enter the top superconducting electrode to be measured as a supercurrent.

Looking at normal-state spintronics can give some insight of what happens to current

passing through ferromagnets. When charge current passes through a ferromagnetic material

F it becomes partially spin-polarized due to the differences in density of states, Fermi velocity,

and mean free path between majority and minority spin electrons. Since F acts as a spin
filter for normal electrons, we expect that it also acts as a spin filter* for ms = ±1 spin-triplet

electron pairs. [98–100]. Let us assume that the majority band triplet component has higher

transmission through a [Co/Pd]n multilayer than the minority band component. The spin-

*The term ”spin filter” often refers to tunneling through magnetic insulators – either of single electrons or of
electron pairs in Josephson junctions. But spin filtering is also an intrinsic property of metallic ferromagnets
and their interfaces

76

triplet supercurrent passing through the multilayer then becomes partially spin-polarized, so
that the ms = +1 triplet component has larger amplitude than the ms = −1 component.

In the PMA-SAF junctions, however, the majority-spin pairs in the first PMA multilayer

become minority-spin pairs in the second PMA multilayer, and vice versa. As a result, both

triplet components suffer from the lower transmission amplitude of the minority component

somewhere in the system. In the PMA junctions, in contrast, the majority pairs propagate

through the whole F layer with high transmission. If that were the whole story, then we

would expect the Ic data from the PMA-SAF samples to be shifted downward in figure

5.2 with respect to the Ic data from the PMA samples. But that is not what we observe.

Rather, the slope of the data vs N is steeper in the former, meaning that the downward shift

increases with the number of bilayers N . That implies that the spin-filter efficiency of the

PMA system increases with N , at least for N as large as 8, which is the largest value probed

in this work.

A possible explanation for the increase in spin-filter efficiency with N is that each indi-

vidual Co/Pd interface acts as a partial spin filter, due to a spin-scattering asymmetry at

the Co/Pd interface favoring transmission of majority-spin pairs over minority-spin pairs.

Unfortunately, the spin-scattering asymmetry at the Co/Pd interface has not been mea-

sured. Fortunately, however, the interfacial spin-scattering asymmetry has been determined

for several other material interfaces by analyzing Giant Magnetoresistance data obtained

from metallic multilayers and spin valves [101]. The analysis is based on the “two-current

series resistor (2CSR) model”, [102–104] which has been very successful in describing a large

collection of experimental results. [101, 105] The 2CSR model ascribes different effective re-

sistivities to majority and minority-band electrons inside F materials, and different effective

interface resistances at F/N or F1/F2 interfaces. A good example is the Co/Ni interface,

77

where the spin-scattering asymmetry was found to be quite large [106]: the area-resistance

↑
Co/N i = 0.03± 0.02f Ωm2 while the
product for majority-band electrons was found to be AR
↓
Co/N i = 1.00 ± 0.07f Ωm2. Hence the

minority band interface resistance is much higher: AR

Co/Ni interface acts very strongly to spin-polarize a normal current, and we suspect it does

the same for supercurrent. In addition, the probability for an electron to flip its spin at the
interface has also been measured. It is expressed as P=1-exp(−δ), with δCo/N i = 0.35±0.05.

We now present a model that can be helpful to understand the slopes in Figure 5.4. [24]

We start with the assumption that the total supercurrent through the junctions is equal to

the sum of the ms=+1 and ms=-1 triplet components of the supercurrent in the central F

layer of the junction, which we write in shorthand as

Ic ∝ Tms=+1 + Tms=−1

(5.1)

where Tms=+1 and Tms=−1 represents the transmission amplitudes of the ms=+1 and

ms=-1 triplet components through the central F layer of the junction. We will assume that

each of those amplitudes can be expressed as a product of transmission amplitudes as the

interfaces inside the F layer.

(We neglect bulk effects for simplicity.) Let t↑ and t↓ be

the transmission amplitudes through a single Co/Pd interface for the majority-band and

minority-band electron pairs, respectively. A PMA junction with N Co/Pd bilayers contains

2N Co/Pd interfaces, hence we have

ms=+1 = t2N↑ , T P M A
T P M A

ms=−1 = t2N↓

(5.2)

A PMA-SAF junction contains, in each half of the SAF, N -1 Co/Pd interfaces and one

Co/Ru interface. To keep the formulas as simple as possible, we will assume that the Co/Ru

78

interface has the same properties as the Co/Pd interface, so we can say that each half of the

SAF has N Co/Pd interfaces. (Deviations from that assumption will affect the intercept but

not the slope of the line depicting log(Ic) vs N .) Since majority-band pairs in one half of

the SAF become minority-band pairs in the other half, we have:

T P M A−SAF

ms=+1

= T P M A−SAF

ms=−1

= tN↑ tN↓

Putting all this together gives:

IP M A
c

∝ t2N↑ + t2N↓

IP M A−SAF

c

∝ 2tN↑ tN↓

If we define the ratio r = tN↑ /tN↓ , then we can write

IP M A−SAF

c

IP M A
c

=

2rN

1 + r2N

If r2N (cid:28) 1, then we get the simple result:

(5.3)

(5.4)

(5.5)

(5.6)

ln(IP M A−SAF

c

) − ln(IP M A

c

) = ln(2) + N ln(r)

(5.7)

If each Ic depends exponentially on N , as the data in Figure 5.4 show, then equation

5.7 implies that the difference between the exponential slopes of the PMA and PMA-

SAF junction data should be ln(r). From the values for the Co/Pd interfaces, we found
-αP M A−SAF

CoP d = -0.751+0.191 = -0.56, which gives rCoP d = 0.57. It would be ben-

CoP d

+αP M A

79

Figure 5.5: PMA-SAF Decay: PMA-SAF Decay. Visual interpretation of the decay mech-
anism in PMA-SAF Josephson junctions containing a Pd/Co multilayer sandwiched by two
Ni layers. Moving from left to right, the smaller circles indicate suppression of the indicated
component of the pair correlation function.

Figure 5.6: PMA Decay: PMA Decay. Visual interpretation of the decay mechanism in
PMA Josephson junctions containing a Pd/Co multilayer sandwiched by two Ni layers.

eficial to compare that value to an independent measurement of r using GMR techniques,

but that has not been done. This model does not incorporate spin-flip and spin-orbit scat-

tering, which suppress spin-triplet supercurrent, although we would expect them to cause

equal suppression of Ic in the PMA and PMA-SAF junctions.

We also present a simple figure to help motivate the previous discussion. Figure 5.5 is

a cartoon interpretation of the decay in spin-triplet PMA-SAF Josephson junctions. We

notice in the F’ layer that we have both singlet and ms=0 triplet pairs. In the first stack
of Pd/Co multilayers the ms=0 triplet pairs are converted to ms=±1 triplet pairs. Some

of the pairs are suppressed which we will call the minority band while the majority band is

80

not suppressed. The triplet pairs pass through the Ru layer and enter the second Pd/Co

multilayer where the magnetization is in the opposite direction of the first multilayer. The

second multilayer suppresses the majority band and lets the minority band pass through

untouched. The triplet pairs are then converted back into ms=0 triplet which enters the

superconductor to be measured.

Figure 5.6 is a cartoon representation of the decay in a spin-triplet PMA Josephson

junction. Picking up in figure 5.5 where the pairs enter the first Pd/Co multilayer we can

see the suppression of the minority band pairs in the F layer. We now enter directly into

the F” layer where we convert to ms=0 triplet which is converted to singlet and enters the

superconducting electrode. We can see from the cartoon in 5.6 that we have only one of the

bands is suppressed. The higher number of repeats in the Pd/Co multilayers the higher the

suppression of that particular band. This gives a graphical interpretation of what we see in

Figure 5.4. The higher the number of repeats the more suppression of the IcRn products in

both the PMA and PMA triplet junctions. The PMA-SAF has this suppression occur for

both majority and minority spin band cause a larger suppression as we increase N.

5.5 Conclusions

In conclusion, we have measured the supercurrent in both spin triplet PMA and spin

triplet PMA-SAF Josephson junctions that contain Pd/Co multilayers as the central out-

of-plane ferromagnet and Ni as the in-plane ferromagnetic layers. The critical currents in

the PMA-SAF junctions decay far more rapidly with increased number of multilayer repeats

N , compared to the critical currents in the PMA junctions. We attribute that difference to

the strong increase of spin polarization of the supercurrent with increasing repeats N , due

81

to the cumulative spin-filtering effect of the interfaces in the PMA multilayers. The triplet

PMA junctions have larger critical current at the lowest number of Pd/Co repeats, and the

critical current decays much more slowly as a function of Pd/Co repeats. An important

point to mention is that although in our experiments we like to avoid the suppression of

critical current that occurs with increasing the number of Pd/Co repeats, this result may be

important for other fields of electronics. The ability to produce a spin triplet supercurrent in

a Josephson junction that is highly polarized may have some applications in the spintronics

field.

82

Chapter 6

Phase Controllable SQUIDS

In the previous chapters we were working towards the goal of increasing the propagation

of supercurrent through spin triplet Josephson junctions. The goal of this chapter is to build

on that previous work and show controllable switching of the triplet Josephson junctions

through phase sensitive measurements. To accomplish this goal, we must be able to make a

junction that can switch between its zero and π ground states. The tool needed for making

phase measurements is a Super Conducting QUantum Interference Device (SQUID). To

fabricate this tool, we need two Josephson junctions in parallel around a SQUID loop. As

discussed in section 2.6 a SQUID can detect differences in the phase between current flowing

through the two junctions in the loop. The fabrication of these SQUIDS is similar to the

previous work, but care needs to be taken in some key points that will be mentioned in the

fabrication section.

In this chapter we plan to show phase control of Josephson junctions of the same type

as presented in chapter 5. We want to demonstrate switching of the soft magnetic layer by
changing its magnetization direction by 180◦, without disturbing the other magnetic layers,

causing switching between zero and π states. We have fabricated samples with varying

repeats of Pd/Co layers. The measurements of the SQUIDs in this chapter confirm the

result from the previous chapter that the spin triplet PMA junctions have larger critical

current when compared to the spin triplet PMA-SAF junctions. Figure 6.1 show a cartoon

diagram of the junctions we use in these SQUIDS. The junctions contain a similar stack as

83

Figure 6.1: Triplet PMA Josephson Junction: Side view of the triplet PMA stack with Ni
and Py. Py, as the soft layer, is at the bottom of the stack and is deposited as soon as
possible to be as smooth as possible.

in the previous chapter, but we have replaced the bottom Ni layer with Permalloy (Py), a

NiFe alloy with low coercivity. The Py is deposited on the bottom of the stack to keep this

layer as smooth as possible. The Py layer will act as the switching layer since it has a smaller

switching field compared to Ni. The Py layer is referred to as the soft layer. We will also

show how training of the sample changes the switching behavior of the same sample in a

single cool down.

6.1 Magnetic characterization

As is done for all magnetic samples before going through the complete fabrication process

we first need to look at the magnetic behavior of the layers. These measurements will

help us understand the switching fields for these junctions with the PMA as the central

ferromagnet. We start with sputtering films similar to what the junctions will contain except

84

Figure 6.2: Easy axis magnetometer of elliptical and hex arrays: major loops: M vs. H plots
of arrays containing Ni(1.2) and Py(1.2) for both elliptical and hex arrays. This large field
sweep switches both ferromagnetic layers. The Permalloy layer switches abruptly close to
zero field, while the Ni layer switches slowly over the field range 0-1000 Oe.

for the bottom Nb layer being thinner that what we use for junctions. The film contains

Nb(10)/Cu(2)/Py(1.2)/Cu(4)/PMA/Cu(4)/Ni(1.2)/Cu(2)/Au(2) where the PMA layer is

[Pd(0.9)/Co(0.3)]N /Pd(0.9) and N is the number of repeated Pd/Co bilayers. The films

are sputtered together for consistency since we will fabricate both elliptical and hexagonal

arrays for direct comparison. The ellipses have an aspect ratio of 2.0 while the hexagons

have an aspect ratio of 3.0, with both maintaining 0.5µm2 in cross-sectional area. There

needs to be a significant difference in the switching field of the elliptical junctions compared

to the hexagonal junctions since we need the soft layer (Py) of the ellipse to switch before

the hexagon does for the SQUIDs to work properly. Figure 6.2 shows M vs. H curves of

large arrays of elliptical and hexagonal nanomagnets. These arrays have 45x45 patterns that

each contain 39x99 individual nanomagnets (or “pillars”). The arrays must contain many

pillars to have a signal that is strong enough to measure in a SQUID magnetometer. These

figures show the switching of both magnetic layers in the junctions. The Py layers appear

to switch abruptly at very low field in these plots, while the Ni layers switch gradually over

85

Figure 6.3: Easy axis magnetometer of elliptical and hex arrays: minor loops: Minor loop M
vs. H plots of arrays containing Ni(1.2) and Py(1.2) for both elliptical and hex arrays. The
vertical shift is due to the magnetization of the Ni layer, while the horizontal shift is due to
trapped flux in the magnet. The minor loops let us measure the switching field for only the
Py layer without disturbing the Ni layer. The coercive fields for the ellipse and hex arrays
are 25 Oe and 35 Oe, respectively.

a very broad field range. Figure 6.3 shows M vs. H curves but taken at small field to switch

only one of the magnetic layers. These data represent minor loops where we can see an offset

in the vertical and horizontal direction. The horizontal and vertical shifts are due to the

trapped flux in the magnet and the magnetization of the Ni layers, respectively, but those

are not important for this measurement. These data show the actual coercive field for the

elliptical and hexagonal arrays. For the elliptical arrays we get about 25 Oe and for the hex

arrays we get about 35 Oe. In the ideal case, each nanomagnet in the array would switch

abruptly and all elements would switch at the same field, hence the switching of the arrays

would be perfectly vertical on the M vs. H diagram. The finite slope observed is due either

to a spread of switching fields in the array, or to slow switching of individual array elements

by domain wall motion.

86

Figure 6.4: Photolithography SQUID mask design: Left to right, full chip, top and bottom
lead overlap, ultra low inductance SQUID blow up. These masks are on quartz glass and
measure five inches by five inches in size.

6.2 SQUID fabrication

The fabrication of the SQUIDS containing spin triplet Josephson junctions is similar to

the previous experiments. There are two types of SQUID masks that are available to use for

these SQUIDS. One is the Symmetric SQUID, and the other is the Ultra Low Inductance

SQUID (ULI). For these samples we chose to use the ULI design since we have made previous

SQUIDs that gave good results for this design. Figure 6.4 shows the photolithography mask

set for this SQUID design. The mask is designed using AutoCAD. From left to right we see

the first design shows the full mask. In this image we can see the top leads on the left side

and the bottom leads on the right. The bottom lead pattern has five large alignment markers

that are used to align with the similar markers on the top lead pattern. There are ten pads

on the bottom lead while the top lead has eight. The two extra pads the bottom lead has

are for the on-chip flux line. Moving to the middle image we see the top and bottom lead

overlap. This is what we expect to see on the substrates once we are finished with fabrication

of the samples. In this image you can see the tapering of the leads as they get closer to the

center of the design. The tapering of the lines helps prevent unwanted lift off the leads during

87

Figure 6.5: Top and orthographic view of ULI SQUID design: Top-down view of the ULI
SQUID design(a) and Orthographic view of the ULI SQUID design(b).

processing. The previous mask design showed more lift off issues because it had much smaller

leads further from the center of the chip. The image on the right shows a close-up of the

ultra low inductance SQUID design. This is the design we used for this experiment. The ULI

SQUID design has four SQUIDs per sample. This image shows the eight L-shaped electron

beam lithography alignment marks. The bottom lead is four microns in width nearing the

SQUID while the top lead of the SQUID is 3 microns wide at the center. Figure 6.5 shows

the top down view and orthographic view of the ULI SQUID design. Figure 6.5a shows the

two different shapes we used in the SQUIDS. The upper junction in the figure is shaped as

an ellipse with an aspect ratio of 2.0 while the lower junction is shaped as a hexagon with an

aspect ratio of 3.0. These shapes were selected to take advantage of their shape anisotropy.

Figure 6.5b shows the SQUID loop where we couple magnetic flux via current If lux through

an on-chip flux line. Hset is the field that is used to switch the soft layer in these junctions.

Hset is produced by an external superconducting magnet.

88

Figure 6.6: Wiring diagram for SQUID using QDI : Wiring diagram for SQUID 1 mounted
on QDI for measurement. Not all the contact pads on the chip are shown.

6.3 Measurement

The measurement procedure has several differences from the procedure discussed in the

previous two chapters. The single pillar measurements were taken in field to generate a

Fraunhofer pattern for each junction to extract the maximum critical current. The SQUID

measurements on the other hand are taken in zero field since we are trying to look at the

phase of the current through the junctions. To begin the measurement process, we first need

to make connections to the SQUID. The connections are different than that of the single

junctions since we measure one SQUID at a time as opposed to six junctions per dip. Figure

6.6 show a wiring diagram for use when measuring a SQUID on QD-I. This wiring scheme is

for measuring SQUID 1 of the ULI SQUID mask. The red lines are the sample current lines.

The green and orange lines are the sample voltage lines. The black lines are the flux lines.

To measure the rest of the SQUIDs on the sample all the connections must be moved except

for the flux line leads. Since most of the wires are copper, they must be replaced frequently

except for the superconducting voltage leads. To replace the copper wires, we must first

remove the insulation from the new copper wires. The superconducting wire has insulation

while the flux and current wires are bare. The superconducting wires are connected to a

89

Figure 6.7: Measurement Flow Diagram: Flow diagram going clockwise from the top left.

Quantum Design SQUID mounted inside the Quick Dipper. Since these wires are connected

to a SQUID special care needs to be taken when connecting and handling them. The wires

must lay flat and avoid having loops as well as being smooth avoiding any bends. Figure

6.7 shows a flow diagram of our measurement procedure for the SQUIDs. For samples that

contain a PMA multilayer as one of the ferromagnets we first initialize the samples with a

field pointing out of plane. A strong permanent magnet is used to initialize the samples at

room temperature by lowering the sample mounted on the dipper over the magnet. The

dipper is then lowered slowly into the dewar filled with liquid helium. Just as before the Ni

must be initialized in-plane using the external magnetic field Hset. We tried initialization

values between 1200 and 3000 Oe, but it was not clear which value produced the optimal

magnetic behavior of the samples. Then the probe is lifted slowly until the sample is slightly

above the liquid helium level, at which point the sample goes normal and trapped magnetic

flux is removed. After the sample is lowered back into the liquid helium, we measure Ic vs

If lux to observe SQUID oscillations. We then start stepping the in-plane field Hset in the

90

Figure 6.8: Initial measurements: A. Initial flux line sweep after initializing sample. B. First
magnetic field sweep to measure first junction switch. C. Second flux sweep to check for
phase switch. D. Second field sweep to switch back to initial state. E. Final flux sweep to
compare to initial state. In this run, the phase of the final state differs slightly from the
phase of the initial state.

direction opposite to the initialization direction, while measuring Ic vs If lux at each step.

If all goes well, the SQUID oscillations suddenly shift by π, indicating that one of the two

junctions has switched from the 0-state to the π-state or vice versa. Finally, Hset is stepped

in the opposite direction to bring the SQUID back to its initial state. Figure 6.8 shows a

series of measurements. In panel a, we first sweep the flux line from negative to positive

91

to get a baseline for the SQUID oscillation. In panel b, we step the in-plane field in the

opposite direction of the initialization to try to switch the soft magnetic layer of one of the

junctions without switching the other junction. To save time in these initial measurements

we do not measure the SQUID oscillation at each field step. Instead, we take a series of IV

curves at each step while keeping the flux line fixed at a maximum or minimum value of the

SQUID oscillation. While stepping Hset we wait for the first switch of the junction, and we

measure a change in Ic. Once the switch happens, panel c shows a flux sweep measurement

to see if the sample underwent a π phase shift. In panel d, we step the field back in the

other direction to recover the initial state. When that occurs, we can take a final flux sweep,

part e, to verify we are back to the original state. These initial measurements will give the

parameters for the much more time-consuming waterfall plots. The waterfall plots can take

several hours so careful monitoring of the measurements may be needed in order to assure

proper switching. Note that panels a and e in Figure 6.8 do not match perfectly. The second

phase change from c to e is much closer to π than the first phase change from a to c. This

happens often, but the behavior of the samples often improves with repeated cycling through

the field-stepping procedure.

6.4 Results

To better understand these samples, we have chosen to present the data as 3d plots

where the x and y axis are flux current and magnetic field Hset and the z axis is the critical

current. Waterfall plots will give a clear indication of switches and phase information when

reported this way. The waterfall plots will show when we have clear SQUID oscillations by

showing a progression of peaks and valleys following along the same flux line current value.

92

When a π phase switch occurs, the peaks should go to where valleys were and vice versa for

the valleys. Figure 6.9 shows an example of a waterfall plot with promising results. This

sample was initialized at 3000 Oe. The measurement was then made by stepping Hset in

the negative direction. First, we notice the sample undergoes a π phase switch at about -25

Oe. Following the first switch we see another switch occurring above 60 Oe. This switch

may be due to the Py in the hexagonal pillar switching. The measurement is then taken in

the positive direction, and we notice another π switch near 25 Oe. This SQUID showed a

maximum critical current near 35 µA, which is significantly higher than the 10 µA critical

currents observed in the previous triplet PMA-SAF SQUIDs measured by Joseph Glick.

After initialization, both junctions in the SQUID should be in the parallel state, meaning

the magnetizations of the Py free layer and Ni fixed layer are parallel. After the first switch,

the elliptical junction should be in the antiparallel state. Theory suggests that the parallel

state is expected to have the same critical current as the anti-parallel state, but due to a

small field shift of the Fraunhofer pattern we might expect the parallel-state critical current

to be smaller than the antiparallel-state critical current. In our experiments we have seen

many samples where one state has higher current than the other state. Although there is

an increase in the critical current through the triplet PMA SQUIDs when compared to the

triplet PMA-SAF SQUIDs we do see a detriment in the magnetic behavior of these samples.

Measurement of the samples show clear phase shifts but with some slight phase slipping in

both directions. Depending on how the triplet PMA samples are initialized greatly effects the

overall characteristics of the samples. We do see some of the expected results where we can

measure higher critical current in the anti-parallel state after the first switch occurs in the

Py layer of the elliptical junction. In Figure 6.9, the critical current for the anti-parallel state

is more than 35µA. The parallel state initially gave about 27µA and the final parallel state

93

Figure 6.9: Sample 1a SQUID 3 before training: Sample 1a contains Py(1.2), Pd/Co repeats
of N=2 and Ni(1.2) for the ferromagnetic layers. The sample was measured with an initial-
ization field of 3000Oe. Left panels: Hset is swept in the negative direction to switch one of
the junctions in the SQUID from the π-state to the 0-state. Right panels: Hset is swept in
the positive direction to switch back to the initial state. Magnetic switching is observed at
fields near 25 Oe in both sweep directions. We observe critical current values of up to 35µA.

gave about 15µA. Although the critical current is not the same in the initial and final state

the phase looks to have been recovered after the switching of the Py layer. The samples that

Joseph Glick fabricated which contained triplet PMA-SAF junctions gave critical currents

near 10µA [95].

After seeing that the initialization as well as the measurement can affect the behavior

of the samples, we decided to initialize the sample as before but then we switched the Py

94

Figure 6.10: Sample 1a SQUID 3 after training: Sample 1a is the same sample as in the
previous figure. The sample training was done in the same cooldown and followed the
previous sample measurement. We can see improvements to the magnetics, no phase slipping,
in this sample after training but we also notice a decrease in the critical current to about
20µA.

free layer back and forth several times using Hset. In most measurements the switch was

done up to 20 times, but we see more consistent switching with just 10. We describe some

of the measurements below as the samples were measured before and after training of the

junctions.

Figure 6.10 shows data from the same SQUID sample in a separate cool-down. The

SQUID gave different results after it was trained by making the Py layer perform several

switches. We see that the critical current has dropped to about 20µA when compared to the

95

Figure 6.11: Sample 1a SQUID 1 : Sample 1a SQUID 1 run6 shows the initial negative
sweep to behave poorly in terms of magnetics. The positive sweep starts to behave better
magnetically after switching back from the negative sweep. We observe critical currents near
45µA.

previous anti-parallel state. The switching behavior appears to be much cleaner but now we

also see that the phase shift is not as close to π.

Figure 6.11 shows data from one of the first samples measured. In this figure we see that

on the negative sweep there are initially very small SQUID oscillations, then a large jump in

critical current after the first switch. On the positive sweep we can see improvements in the

magnetics and cleaner SQUID oscillations. There are several places where we have phase

slipping but never really have a π phase change.

Figure 6.12 now shows what some training can do to improve the magnetics of a sample.

96

Figure 6.12: Sample 1a SQUID 1 : This measurement was taken after the previous figure
measurement. These initial improvements seen in these measurements were motivation used
to start training the following samples. We see a significant increase in critical current
compared to the previous measurement. Critical current values are as high as 60µA.

97

Figure 6.13: Sample 4a SQUID 2 : This sample was measured after the training process. We
see phase slipping in the negative sweep direction but very clean SQUID oscillations in the
positive sweep direction. The switching field for this SQUID is rather high – about 80 Oe in
both sweep directions.

This measurement was taken after some training where we swept Hset up and down causing

the soft layer to toggle several times while trying to keep the hard layer fixed. Improvements

in critical current and magnetics were seen. The switching behavior was not quite π but

in showed improvement over the initial measurements. One surprise in this sample is that

we observe two distinct π phase changes in both sweep directions. We attribute the second

switch to the Py layer in the hexagonal junction switching.

In figure 6.13 we see close to 0-π switching in both the positive and negative sweeps. There

98

Figure 6.14: Sample 4a SQUID 3 : This sample is measured after the training process.
The critical current has a large offset (i.e., it never approaches zero) in the higher critical
current state indicating that the critical currents of the two junctions in the SQUID are quite
different. There are clear switches in both the positive and negative sweep directions which
are nearly 0-π switching.

is some phase slipping in the negative directions hinting at possible issues with the magne-

tization of the Ni layer. The positive sweep looks very promising showing great switching

with limited phase slipping.

In figure 6.14 we see nearly 0-π switching in both the positive and negative sweeps. These

sweeps show a large difference in the critical currents in the parallel and anti-parallel states.

There is some limited phase slipping. We also notice a large critical current in this sample

as high as 70µA.

In figure 6.15 we see some great switching, essentially π, in both directions. The sample

also has almost no phase slipping. The following three tables summarize the properties of

99

Figure 6.15: Sample 6a SQUID 1 : This sample shows a similar offset to the previous sample.
The higher critical current state is offset by about 10µA. We do notice that there is some
0-π switching in this sample. This sample also shows very little phase slipping.

100

Sample Py (nm) Pd/Co repeats (N) Ni (nm)

1a

3a

4a

6a

1.2

1.2

1.2

1.2

2

2

4

4

1.2

2

1.2

2

Table 6.1: Sample parameters for each ferromagnetic layer : The Py for all samples is 1.2
nm in thickness. The PMA layers consist of Pd/Co repeats that are 0.9 nm and 0.3 nm,
respectively. The Ni layer is either 1.2 nm or 2.0 nm in thickness.

all the SQUID samples measured in this work. Unfortunately, the critical current is smaller

than expected even with reasonable resistance values as seen in Table 6.3.

Maximum critical current (µA)

Sample SQUID 1 SQUID 2 SQUID 3 SQUID 4

1a

3a

4a

6a

64

79*

53

26

NA

100*

51

NA

35

NA

78

16*

BAD

NA

NA

NA

Table 6.2: Maximum measured critical current for each sample: These are the maximum
critical currents for each sample. The asterisks indicate samples that were measured for
initial flux sweeps but not waterfall 3d plots. NA samples were not measured.

101

Resistance (mΩ)

Sample SQUID 1 SQUID 2 SQUID 3 SQUID 4

1a

3a

4a

6a

7.2

0.97*

10

9.6

7.6*

11

13

7.4

8.7*

Table 6.3: Sample resistance: Sample resistance in mΩ for each sample from fit using lowest
critical current value. Asterisk samples had initial flux sweeps measured but not waterfall
3d plots. The Py for all samples is 1.2 nm in thickness. The PMA layers consist of Pd/Co
repeats that are 0.9 nm and 0.3 nm, respectively. The Ni layer is either 1.2 nm or 2.0 nm in
thickness.

6.5 Conclusions

This chapter shows the initial steps taken to verify proper control of the magnetic layers

in the triplet PMA Josephson junctions. We presented the design of the SQUIDs used in

the experiment and show where the flux line is and how it couples magnetic flux into the

SQUID loop. We presented the exploratory measurements used to test whether a sample

is working properly as well as to find parameters to be used in the setup process for the

3d waterfall plots. Finally, we show the 3d waterfall plots of a sample where the data was

taken in a single dip. As expected from the single-junction results discussed in the previous

chapter, the SQUIDs made from triplet PMA junctions show higher critical current when

compared to the triplet PMA-SAF SQUIDs measured previously by Joseph Glick. However,

the higher critical current comes with a detriment to the magnetics in the sample. Often,

the samples did not show clean 0-π switching and high critical current in the same run.

We suspect that the problem is that the central PMA multilayer causes stray magnetic

102

fields that can interfere with magnetic behavior of the F’ and F” layers. In the PMA-SAF

system we have, in the best conditions, a complete cancellation of any out-of-plane fields

caused by the middle layer. This means that in terms of magnetics the PMA-SAF system

is superior for reproducible phase control. The PMA system on the other had has better

triplet supercurrent propagation but with inconsistent magnetics. We hoped that the PMA

multilayers would generate stray fields only along the edges of the junction since the MFM

images showed single domain behavior. If that were the case the stray field effect would have

not played such a strong role in the magnetic behavior of the junctions.

103

Chapter 7

Conclusions and outlook

In this chapter we will summarize the work discussed in the previous chapters and elab-

orate on some previously talked about points. We also mention what the goals of this work

were when we first began along with what we accomplished along the way. Finally, we look

at where we are with this work and possible future plans for spin triplet Josephson junctions.

We start in chapter 1 where we introduced important concepts and some of the motivation

and overall goals of this work. The idea of being able to reduce the strain of energy cost for

computer storage was one of the main driving forces and long-term goals we are looking to

attain.

Chapter 2 goes into details about the interplay of superconductivity and ferromagnetism

that govern our Josephson junctions. There are many theoretical concepts that are presented

which play important roles in our experiments. We also introduced some nomenclature that

was used throughout the rest of the chapters. We also briefly explained how our phase

measurements using SQUIDs can be understood.

Chapter 3 explained in detail the fabrication and measurement processes of our samples.

We discussed the initial investigative procedures of characterizing materials that are used

for the experiment, which must be done before any samples are fabricated. The charac-

terizing of materials for Josephson junctions may include patterning of arrays for magnetic

measurement, which was also briefly mentioned in this chapter. We went through step-by-

step instructions for the fabrication process of the junctions including small details that are

104

specific to the fabrication of spin triplet Josephson junctions. This chapter also mentions

details about the measurement sequences and sputtering chambers that are used in our lab.

One sputtering chamber is used for most of the sample fabrication. The smaller sputtering

chamber (nicknamed the “Rezanator”) is used more for exploratory physics.

Chapter 4 goes into details comparing the Shuffled and spin triplet Josephson junctions

using a PMA-SAF as the central ferromagnet. Comparing the decay and amplitude differ-

ences of the supercurrent in the triplet and shuffled junctions gives us strong confirmation of

the presence of the spin triplet supercurrent generation in spin-triplet Josephson junctions.

Once this was established, we could move on to the next step which was to optimize the

propagation of triplet supercurrent. For completeness we mention the reason behind fabri-

cating samples that had two thickness of Ni. This was done to avoid the possibility that

the shuffled junctions may have had the two adjacent Ni layers combine to fall on a 0-π

minimum. If this were the case for the shuffled junctions, we could have measured a critical

current near zero. For that case we could not have compared the supercurrents of these two

junctions correctly.

In chapter 5 we showed data on samples that were fabricated with either a PMA-SAF or

a PMA stack as the central ferromagnetic layer. In the previous chapter, chapter 4, we had

shown that spin triplet pairs were the dominant contribution to the supercurrent in these

junctions, but since the critical current was smaller than we needed we planned to find a way

to fabricate junctions that could propagate more triplet supercurrent. We introduced the

PMA multilayer in place of the PMA-SAF and fabricated both kinds of junctions at the same

time for direct comparison. We observed larger supercurrent in the PMA junctions, and we

discussed what could be causing the suppression of triplet supercurrent in the PMA-SAF

junctions. Once we obtained junctions with higher critical current, we were able to move on

105

to the next step of the project.

In chapter 6 we presented measurements of several SQUID samples that had different

ferromagnetic layer thicknesses, using different initialization procedures. In this chapter we

were trying to show phase control in the spin triplet junctions along with increasing critical

current propagation. The results of this chapter did show phase control in some cases after

some extensive initialization procedures. The critical current in some cases were significantly

higher when compared to Joseph Glick’s SQUIDs containing PMA-SAF junctions [29]. The

possibility of having both high critical current and phase control proved to be more elusive

than with the PMA-SAF samples. The samples with large critical current had no phase

control until they were taken through an extensive initialization procedure. Some samples

then showed great phase control but had smaller critical current than expected although still

larger than similar samples with PMA-SAFs.

Going back to the initial motivation for this work, one can ask if these spin-triplet Joseph-

son junctions could be used in Northrop Grumman’s JMRAM memory? The answer for now,

unfortunately, is no, for two reasons. First, the phase-controllable junction in a JMRAM

memory cell should have a critical current in the range of 100-200 µA. Making our junctions

larger to increase the critical current is not a good strategy, because then the NiFe free layer

is likely to break up into multiple domains. For clean switching, it is better to have the free

layer be single-domain. Second, the magnetic behavior of the junctions studied in Chapter

6 is not consistent and reproducible enough for applications, at least at this point.

Although we were unable to measure samples that had good phase control along with

high critical current the possibility still exists that finding better initialization procedures

for aligning both the PMA layers as well as the nickel layers may be able to produce better

behaving samples. We believe that the current samples may have had stray fields from the

106

Figure 7.1: φ0 junction: Cartoon diagram of a φ0 junction. The outer two layers have in-
plane magnetization while the central layer has out-of-plane magnetization. This geometry
can produce spin triplet supercurrent that will propagate through the central ferromagnetic
layer, but with the current-phase relation offset by any arbitrary phase.

PMA layer that caused detrimental behavior when coupled with the nickel layers, giving

lower critical current or bad magnetic behavior.

An exciting prospect for further expanding this work is to create a so-called φ0 junction,

where the ground-state phase difference across the junction can have an arbitrary value, not

just zero or π [107–114]. Theory predicts that one can achieve a φ0 junction using a spin-

triplet junction of the kind discussed in this thesis, but with an arbitrary angle between the

magnetizations of the top Ni fixed layer and the bottom NiFe free layer. To achieve such a

state, we would fabricate a new type of junction that has no shape anisotropy. The pattern

of the junction would no longer be shaped as an ellipse but would be a circle. The junction

would contain a similar stack as the ones we have in the SQUID measurements from chapter

6.

107

The patterning for that measurement would be to have one junction on the SQUID be

hexagonal to not have any movement of any of the ferromagnetic layers in that stack, while

the other would be the circular junction where we could set the orientation of the NiFe

free layer in any direction. The signature of the φ0 junction would be SQUID oscillations

with varying phase shift, depending on the magnetization angle set by the external field.

To achieve this goal, the magnetics of such a junction would have to be very stable and

reproducible. Not only would the physics of a φ0 junction be interesting to explore but the

practical application of a superconducting phase battery could be valuable in some future

work [115–118].

Figure 7.1 shows a cartoon diagram of a possible φ0 junction. In this diagram the outer

two ferromagnetic layers have their magnetization pointing in-plane while the central layer

has an out-of-plane magnetization. As mentioned previously the junction shape would be

circular rather than an ellipse. The measurement of such a junction would also be slightly

different compared to the previous work. For this measurement we would need an additional

magnet that could produce a field that is in-plane but perpendicular to the field Hset used

to magnetize the Ni fixed layer. The measurement would start by aligning the Ni as we

did in the previous experiment, but now we would not switch the free layer from parallel to

anti-parallel. Instead, we would rotate the free layer to some arbitrary angle and measure

the SQUID oscillation.

Figure 7.2 shows the three F layers on the left. Assuming we initialized the outer layers

to the right as shown by the F’ layer, the rotation of the magnetization of the F” layer by

an angle φ would correspond to the SQUID oscillation shifting by as we see in the plot of

critical current vs magnetic flux through the SQUID loop. The application of this type of

junction as a phase battery or rectifier could prove useful in some type of future work.

108

Figure 7.2: φ0 phase: The left figures show the magnetization directions of the three fer-
romagnetic layers in the φ0 junction. The figure on the right represents a plot of Ic/Ic0
vs. magnetic flux Φ normalized by the flux quantum, Φ0, and multiplied by 2π to make
the correspondence between flux and phase angle. The blue curve represents the standard
current-flux relation of a SQUID with two identical Josephson junctions. The purple curve
represents the situation where one of the two junctions has its current-phase relation shifted
by the angle φ0 by rotation of the magnetization of the soft layer by an angle φ0, as shown
in the figure on the top left.

109

At the beginning of this thesis, we discussed the major application for superconducting

computing to be large-scale energy-efficient computing or data storage facilities. But there

is another application that may be more practical in the short run. Many groups around

the world are working on building quantum computers. One of the leading technologies for

quantum computers is based on superconducting qubits running at milliKelvin temperatures

in a dilution refrigerator. Currently such quantum computers are being controlled by mi-

crowave pulses generated at room temperature, and carried into the cryostat via a very large

number of coaxial cables. It would be much more efficient to have a classical superconducting

computer operating in the cryostat, at a temperature near 4 K, located only a few inches

away from the ultra-cold quantum computer. The classical computer would then control

and read out the quantum computer [119–121]. Replacing the room temperature electronics

with cryogenic digital components would allow for error correction close to the quantum

computer, producing a vast improvement in the efficiency of the process overall.

110

APPENDIX

111

Appendix

Array run file and LabVIEW measurement software

In this appendix we provide more details regarding the run files for the Nanometer Pattern

Generation System (NPGS) software that was used to pattern the arrays used for magnetic

characterization. We will also show the front panel of the Labview software used to control

the low temperature electronics in the shielded room. My worked in adding functionality to

the software is highlighted and discussed in detail below.

Figure 1: NPGS array run file: Text file image of the NPGS run file for a typical array.
The array is copied 45 times in X and Y. The MoveOnly -2500,-2500 command is used to
move to the center of the chip after aligning to a mark near the corner of the chip to avoid
exposing the writing area to the beam. The 100, 100 is the center to center spacing between
the writing of each 39x99 array.

112

Figure 2: Labview front panel: Top: The front panel of the Labview software used with Quick-
dippers I and II. 1: Used to configure the voltmeter to allow changes in the resolution,by
changing the averaging over line cycles, and range, 10 volts in this image. 2: Allows for
hysteresis mode, taking measurements on the up and down ramp of the current with the
option to save the the ramp measurement. You also have the option to select the size of the
step on the ramp down using the ramp down factor. 3a: Repeats the entire measurement
where 3b can repeat major and minor with the parameters set in 3c. All these options
can measure minor and major loops several times. 4 The option allows a wait time for the
persistence switch to be on for each loop. 5: Allows setting the time between the voltage
measurements in the IV plot.

113

Figure 3: LabVIEW front panel: Bottom: The front panel of the Labview software used with
Quick-dippers I and II. 6a and 6b: These options allow for the flux line to be on or off and
to step it which was vital for the SQUID measurements taken in chapter 6. 7: This option
sets a wait time after the persistence switch is closed to allow the magnet to settle.

114

REFERENCES

115

REFERENCES

[1] D. S. Holmes, A. L. Ripple, and M. A. Manheimer. Energy-efficient superconduct-
IEEE Trans. Appl. Supercond.,

ing computing—power budgets and requirements.
23(3):1701610, 2013.

[2] A. S. G. Andrae and T Edler. On Global Electricity Usage of Communication Tech-

nology: Trends to 2030. Challenges, 6:117–157, 2015.

[3] I. Cutress.

Intel’s manufacturing roadmap from 2019 to 2029: Back porting,
7nm, 5nm, 3nm, 2nm, and 1.4 nm. https://www.anandtech.com/show/15217/intels-
manufacturing-roadmap-from-2019-to-2029, Dec 2019.

[4] E. Strohmaier, H. Simon, J. Dongarra, and M. Meuer. Top500 expands exaflops capac-
ity amidst low turnover. https://www.top500.org/lists/top500/2020/11/press-release/,
Nov 2020.

[5] M. Halper.

Supercomputing’s

to do about
https://cacm.acm.org/news/192296-supercomputings-super-energy-needs-and-

super energy needs, and what

them.
what-to-do-about-them/fulltext, 2015.

[6] B. D. Josephson. Possible new effects in superconductive tunnelling. Physics Letters,

1(7):251–253, 1962.

[7] B. D. Josephson. Supercurrents through barriers. Advances in Physics, 14(56):419–451,

1965.

[8] K. K. Likharev, O. A. Mukhanov, and V. K. Semenov. Resistive single flux quantum
logic for the Josephson-junction digital technology. In SQUID’85, pages 1103–1108.
Walter de Gruyter, Berlin, 1985.

[9] T. Ortlepp, O. Wetzstein, S. Engert, J. Kunert, and H. Toepfer. Reduced Power
Consumption in Superconducting Electronics. IEEE Transactions on Applied Super-
conductivity, 21(3):770–775, 2011.

[10] M. Tanaka, A. Kitayama, T. Koketsu, M. Ito, and A. Fujimaki. Low-Energy Con-
IEEE Transactions on Applied

sumption RSFQ Circuits Driven by Low Voltages.
Superconductivity, 23(3):1701104–1701104, 2013.

[11] 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. Super-
conductor Science and Technology, 26(1):015002, nov 2012.

116

[12] Q. P. Herr, A. Y. Herr, O. T. Oberg, and A. G. Ioannidis. Ultra-low-power supercon-

ductor logic. J. App. Phys., 109(10):103903, 2011.

[13] N. Takeuchi, Y. Yamanashi, and N. Yoshikawa. Energy efficiency of adiabatic super-

conductor logic. Superconductor Science and Technology, 28(1):015003, nov 2014.

[14] C. Bell, G. Burnell, C. W. Leung, E. J. Tarte, D.-J. Kang, and M. G. Blamire. Con-
trollable Josephson current through a pseudospin-valve structure. Appl. Phys. Lett.,
84(7):1153–1155, 2004.

[15] V. V. Ryazanov, V. V. Bol’ginov, D. S. Sobanin, I. V. Vernik, S. K. Tolpygo, A. M.
Kadin, and O. A. Mukhanov. Magnetic Josephson junction technology for digital and
memory applications. Physics Procedia, 36:35–41, 2012.

[16] T. I. Larkin, V. V. Bol’ginov, V. S. Stolyarov, V. V. Ryazanov, I. V. Vernik, S. K.
Tolpygo, and O. A. Mukhanov. Ferromagnetic Josephson switching device with high
characteristic voltage. Appl. Phys. Lett., 100(22):222601, 2012.

[17] I. V. Vernik, V. V. Bol’ginov, S. V. Bakurskiy, A. A. Golubov, M. Y. Kupriyanov, V. V.
Ryazanov, and O. A. Mukhanov. Magnetic Josephson Junctions With Superconducting
Interlayer for Cryogenic Memory. IEEE Trans. Appl. Supercond., 23(3):1701208, 2013.

[18] M. Abd El Qader, R. K. Singh, S. 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):022602, 2014.

[19] B. Baek, W. H. Rippard, S. P. Benz, S. E. Russek, and P. D. Dresselhaus. Hybrid
superconducting-magnetic memory device using competing order parameters. Nat.
Commun., 5:3888, 2014.

[20] E. C. Gingrich, B. M. Niedzielski, J. A. Glick, Y. Wang, D. L. Miller, R. Loloee,
W. P. Pratt Jr., and N. O. Birge. Controllable 0 − π Josephson junctions containing a
ferromagnetic spin valve. Nat. Phys., 12(6):564–567, 2016.

[21] J. A. Glick, M. A. Khasawneh, B. M. Niedzielski, R. Loloee, W. P. Pratt, N. O.
Birge, E. C. Gingrich, P. G. Kotula, and N. Missert. Critical current oscillations
of elliptical josephson junctions with single-domain ferromagnetic layers. Journal of
Applied Physics, 122(13):133906, 2017.

[22] J. A. Glick, R. Loloee, W. P. Pratt, and N. O. Birge. Critical current oscillations
of Josephson junctions containing PdFe nanomagnets. IEEE Trans. App. Supercond.,
27(4):1–5, 2017.

[23] J. A. Glick, S. Edwards, D. Korucu, V. Aguilar, B. M. Niedzielski, R. Loloee, W. P.
Pratt, N. O. Birge, P. G. Kotula, and N. Missert. Spin-triplet supercurrent in joseph-

117

son junctions containing a synthetic antiferromagnet with perpendicular magnetic
anisotropy. Phys. Rev. B, 96:224515, Dec 2017.

[24] V. Aguilar, D. Korucu, J. A. Glick, R. Loloee, W. P. Pratt, and N. O. Birge. Spin-
polarized triplet supercurrent in Josephson junctions with perpendicular ferromagnetic
layers. Phys. Rev. B, 102:024518, Jul 2020.

[25] I. M. Dayton, T. Sage, E. C. Gingrich, M. G. Loving, T. F. Ambrose, N. P. Siwak,
S. Keebaugh, C. Kirby, D. L. Miller, A. Y. Herr, Q. P. Herr, and O. Naaman. Ex-
perimental demonstration of a josephson magnetic memory cell with a programmable
π-junction. IEEE Magnetics Letters, 9:1–5, 2018.

[26] A. E. Madden, J. C. Willard, R. Loloee, and N. O. Birge. Phase controllable Josephson
junctions for cryogenic memory. Superconductor Science and Technology, 32(1):015001,
2018.

[27] B. M. Niedzielski, T. J. Bertus, J. A. Glick, R. Loloee, W. P. Pratt, and N. O. Birge.
Spin-valve josephson junctions for cryogenic memory. Phys. Rev. B, 97:024517, Jan
2018.

[28] B. M. Niedzielski, E. C. Gingrich, R. Loloee, W. P. Pratt Jr., and N. O. Birge. S/F/S
Josephson junctions with single-domain ferromagnets for memory applications. Super-
cond. Sci. Technol., 28(8):085012, 2015.

[29] J. A. Glick, V. Aguilar, A. B. Gougam, B. M. Niedzielski, E. C. Gingrich, R. Loloee,
W. P. Pratt, and N. O. Birge. Phase control in a spin-triplet SQUID. Science Advances,
4(7), 2018.

[30] T. S. Khaire, M. A. Khasawneh, W. P. Pratt Jr., and N. O. Birge. Observation of
Spin-Triplet Superconductivity in Co-Based Josephson Junctions. Phys. Rev. Lett.,
104:137002, 2010.

[31] C. Klose, T. S. Khaire, Y. Wang, W. P. Pratt, N. 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.

[32] E. C. Gingrich, P. Quarterman, Y. Wang, R. Loloee, W. P. Pratt Jr., and N. O. Birge.
Spin-triplet supercurrent in Co/Ni multilayer Josephson junctions with perpendicular
anisotropy. Phys. Rev. B, 86:224506, 2012.

[33] W. M. Martinez, W. P. Pratt Jr., and N. O. Birge. Amplitude Control of the Spin-
Triplet Supercurrent in S/F/S Josephson Junctions. Phys. Rev. Lett., 116:077001,
2016.

118

[34] H. K. Onnes and K. Hof. Commun. Phys. Lab. Univ. Leiden., 120b, 122b, 124c, 1911.

[35] W. Meissner and R. Ochsenfeld. Ein neuer effekt bei eintritt der supraleitf¨ahigkeit.

Naturwissenschaften, 21(44):787–788, 1933.

[36] J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Microscopic theory of superconductivity.

Phys. Rev., 106(1):162, 1957.

[37] J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Theory of superconductivity. Phys.

Rev., 108(5):1175, 1957.

[38] J. Balasubramanyam, M. Lohith K S, and S. Thomas. Lecture Notes on Engineering

Physics. 01 2014.

[39] Ashima Arora. Optical and electric field control of magnetism. PhD thesis, University

of Potsdam, 01 2018.

[40] A. F. Andreev. The thermal conductivity of the intermediate state in superconductors.

Sov. Phys. JETP., 46(5):1823–1828, 1964.

[41] L¨uth H. Collective Phenomena at Interfaces: Superconductivity and Ferromagnetism.

Springer, 2015.

[42] P. G. De Gennes. Boundary Effects in Superconductors. Rev. Mod. Phys., 36:225–237,

Jan 1964.

[43] G. Deutscher and P. G. De Gennes. Superconductivity, volume 2. Marcel Dekker, New

York, 1969.

[44] A. I. Buzdin, L. N. Bulaevskii, 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. Pis’ma Zh. Eksp. Teor. Fiz., 35(4):147–148, 1982. [J. Exp. Theor.
Phys. Lett., 35, 4, 20 (1982)].

[45] A. I. Buzdin and M. Yu. Kupriyanov. Josephson junction with a ferromagnetic layer.
Pis’ma Zh. Eksp. Teor. Fiz., 53(6):308–312, 1991. [J. Exp. Theor. Phys. Lett., 53, 6,
321 (1991)].

[46] 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.

[47] Z. Radovi´c, M. Ledvij, L. Dobrosavljevi´c-Gruji´c, A. I. Buzdin, and J. R. Clem. Transi-
tion temperatures of superconductor-ferromagnet superlattices. Phys. Rev. B, 44:759–
764, Jul 1991.

119

[48] E. A. Demler, G. B. Arnold, and M. R. Beasley. Superconducting proximity effects in

magnetic metals. Phys. Rev. B, 55:15174–15182, 1997.

[49] L. S. Abdallah, T. M. Tawalbeh, I. V. Vasiliev, S. Zollner, C. Lavoie, A. Ozcan, and
M. Raymond. Optical conductivity of Ni1−xPtx alloys (0<x<0.25) from 0.76 to 6.6
eV. AIP Advances, 4(1):017102, 2014.

[50] A. I. Buzdin. Proximity effects in superconductor-ferromagnet heterostructures. Rev.

Mod. Phys., 77:935–976, 2005.

[51] D. E. Eastman, F. J. Himpsel, and J. A. Knapp. Experimental Band Structure and
Temperature-Dependent Magnetic Exchange Splitting of Nickel Using Angle-Resolved
Photoemission. Phys. Rev. Lett., 40:1514–1517, Jun 1978.

[52] D. E. Eastman, F. J. Himpsel, and J. A. Knapp. Experimental Exchange-Split Energy-

Band Dispersions for Fe, Co, and Ni. Phys. Rev. Lett., 44:95–98, Jan 1980.

[53] L. N. Bulaevskii, V. V. Kuzii, and A. A. Sobyanin. Superconducting system with weak

coupling to the current in the ground state. Sov. JETP Lett., 25(7):290–294, 1977.

[54] V. V. Ryazanov, V. A. Oboznov, A. Yu. Rusanov, A. V. Veretennikov, A. A. Golubov,
and J. Aarts. Coupling of two superconductors through a ferromagnet: Evidence for
a π junction. Phys. Rev. Lett., 86:2427–2430, Mar 2001.

[55] Y. Blum, A. Tsukernik, M. Karpovski, and A. Palevski. Oscillations of the supercon-
ducting critical current in Nb-Cu-Ni-Cu-Nb junctions. Phys. Rev. Lett., 89:187004,
2002.

[56] T. Kontos, M. Aprili, J. Lesueur, F. Genˆet, B. Stephanidis, and R. Boursier. Josephson
Junction through a Thin Ferromagnetic Layer: Negative Coupling. Phys. Rev. Lett.,
89:137007, 2002.

[57] H. Sellier, C. Baraduc, F. Lefloch, and R. Calemczuk. Temperature-induced crossover

between 0 and π states in S/F/S junctions. Phys. Rev. B, 68:054531, 2003.

[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-
Ferromagnet-Superconductor Junctions. Phys. Rev. Lett., 96:197003, 2006.

[59] 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.

[60] V. Shelukhin, A. Tsukernik, M. Karpovski, Y. Blum, K. B. Efetov, A. F. Volkov,
T. Champel, M. Eschrig, T. L¨ofwander, G. Sch¨on, and A. Palevski. Observation

120

of periodic π-phase shifts in ferromagnet-superconductor multilayers. Phys. Rev. B,
73:174506, 2006.

[61] 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.

[62] 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, 2007.

[63] A. A. Bannykh, J. Pfeiffer, V. S. Stolyarov, I. E. Batov, V. V. Ryazanov, and M. Wei-
des. Josephson tunnel junctions with a strong ferromagnetic interlayer. Phys. Rev. B,
79:054501, 2009.

[64] F. S. Bergeret, A. F. Volkov, and K. B. Efetov. Josephson current in superconductor-
Phys. Rev. B,

ferromagnet structures with a nonhomogeneous magnetization.
64:134506, 2001.

[65] A. Kadigrobov, R. I. Shekhter, and M. Jonson. Quantum spin fluctuations as a source
of long-range proximity effects in diffusive ferromagnet-super conductor structures.
EPL (Europhysics Letters), 54(3):394, 2001.

[66] M. Eschrig, J. Kopu, J. C. Cuevas, and G. Sch¨on. Theory of half-metal/superconductor

heterostructures. Phys. Rev. Lett., 90:137003, 2003.

[67] A. F. Volkov, F. S. Bergeret, and K. B. Efetov. Odd triplet superconductivity in
superconductor-ferromagnet multilayered structures. Phys. Rev. Lett., 90:117006, 2003.

[68] F. S. Bergeret, A. F. Volkov, and K. B. Efetov. Odd triplet superconductivity and re-
lated phenomena in superconductor-ferromagnet structures. Rev. Mod. Phys., 77:1321–
1373, 2005.

[69] R. S. Keizer, S. T. B. Goennenwein, T. M. Klapwijk, G. Miao, G. Xiao, and A. Gupta.
A spin triplet supercurrent through the half-metallic ferromagnet CrO2. Nature,
439(7078):825–827, 2006.

[70] I. Sosnin, H. Cho, V. T. Petrashov, and A. F. Volkov. Superconducting phase coherent
electron transport in proximity conical ferromagnets. Phys. Rev. Lett., 96:157002, 2006.

[71] J. W. A. Robinson, J. D. S. Witt, and M. G. Blamire. Controlled Injection of Spin-

Triplet Supercurrents into a Strong Ferromagnet. Science, 329(5987):59–61, 2010.

121

[72] D. Sprungmann, K. Westerholt, H. Zabel, M. Weides, and H. Kohlstedt. Evidence
for triplet superconductivity in Josephson junctions with barriers of the ferromagnetic
Heusler alloy Cu2MnAl. Phys. Rev. B, 82:060505, 2010.

[73] M. S. Anwar, F. Czeschka, M. Hesselberth, M. Porcu, and J. Aarts. Long-range
supercurrents through half-metallic ferromagnetic CrO2. Phys. Rev. B, 82:100501,
2010.

[74] J. Wang, M. Singh, M. Tian, N. Kumar, B. Liu, C. Shi, J. K. Jain, N. Samarth, T. E.
Interplay between superconductivity and ferromag-

Mallouk, and M. H. W. Chan.
netism in crystalline nanowires. Nat. Phys., 6(5):389–394, 2010.

[75] P. V. Leksin, N. N. Garif’yanov, I. A. Garifullin, Ya. V. Fominov, J. Schumann,
Y. Krupskaya, V. Kataev, O. G. Schmidt, and B. B¨uchner. Evidence for triplet super-
conductivity in a superconductor-ferromagnet spin valve. Phys. Rev. Lett., 109:057005,
2012.

[76] V. I. Zdravkov, J. Kehrle, G. Obermeier, D. Lenk, H.-A. Krug von Nidda, C. M¨uller,
M. Yu. Kupriyanov, A. S. Sidorenko, S. Horn, R. Tidecks, and L. R. Tagirov. Ex-
perimental observation of the triplet spin-valve effect in a superconductor-ferromagnet
heterostructure. Phys. Rev. B, 87:144507, 2013.

[77] N. Banerjee, C. B. Smiet, R. G. J. Smits, A. Ozaeta, F. S. Bergeret, M. G. Blamire,
and J. W. A. Robinson. Evidence for spin selectivity of triplet pairs in superconducting
spin valves. Nat. Commun., 5:3048, 2014.

[78] N. Banerjee, J. W. A. Robinson, and M. G. Blamire. Reversible control of spin-
polarized supercurrents in ferromagnetic Josephson junctions. Nat. Commun., 5:4771
EP, 2014.

[79] A. Iovan, T. Golod, and V. M. Krasnov. Controllable generation of a spin-triplet

supercurrent in a Josephson spin valve. Phys. Rev. B, 90:134514, 2014.

[80] X. L. Wang, A. Di Bernardo, N. Banerjee, A. Wells, F. S. Bergeret, M. G. Blamire,
and J. W. A. Robinson. Giant triplet proximity effect in superconducting pseudo spin
valves with engineered anisotropy. Phys. Rev. B, 89:140508, 2014.

[81] A. A. Jara, C. Safranski, I. N. Krivorotov, C. Wu, A. N. Malmi-Kakkada, O. T. Valls,
and K. Halterman. Angular dependence of superconductivity in superconductor/spin-
valve heterostructures. Phys. Rev. B, 89:184502, 2014.

[82] M. G. Flokstra, T. C. Cunningham, J. Kim, N. Satchell, G. Burnell, P. J. Curran, S. J.
Bending, C. J. Kinane, J. F. K. Cooper, S. Langridge, A. Isidori, N. Pugach, M. Es-
chrig, and S. L. Lee. Controlled suppression of superconductivity by the generation of
polarized Cooper pairs in spin-valve structures. Phys. Rev. B, 91:060501, 2015.

122

[83] A. Singh, S. Voltan, K. Lahabi, and J. Aarts. Colossal Proximity Effect in a Super-
conducting Triplet Spin Valve Based on the Half-Metallic Ferromagnet CrO2. Phys.
Rev. X, 5:021019, 2015.

[84] J. Linder and J. W. A. Robinson. Superconducting spintronics. Nat. Phys., 11(4):307–

315, 2015.

[85] M. Eschrig. Spin-polarized supercurrents for spintronics: a review of current progress.

Rep. Prog. Phys., 78(10):104501, 2015.

[86] A. Di Bernardo, S. Diesch, Y. Gu, J. Linder, G. Divitini, C. Ducati, E. Scheer, M. G.
Blamire, and J. W. A. Robinson. Signature of magnetic-dependent gapless odd fre-
quency states at superconductor/ferromagnet interfaces. Nat. Commun., 6:8053, 2015.

[87] Z. Feng, J. W. A. Robinson, and M. G. Blamire. Out of plane superconducting

Nb/Cu/Ni/Cu/Co triplet spin-valves. Appl. Phys. Lett., 111(4):042602, 2017.

[88] C. Cirillo, S. Voltan, E. A. Ilyina, J. M. Hernandez, A. Garcia-Santiago, J. Aarts, and
C. Attanasio. Long-range proximity effect in Nb-based heterostructures induced by a
magnetically inhomogeneous permalloy layer. New J. Phys., 19(2):023037, 2017.

[89] M. Houzet and A. I. Buzdin. Long range triplet Josephson effect through a ferromag-

netic trilayer. Phys. Rev. B, 76:060504, 2007.

[90] M. Eschrig. Spin-polarized supercurrents for spintronics. Phys. Today, 64:43, 2011.

[91] 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.

[92] A. Barone and G. Patern`o. Physics and applications of the Josephson effect. Wiley,

1982.

[93] B. Chesca, R. Kleiner, and D. Koelle. The SQUID Handbook, Volume 1. Wiley-VCH

Verlag GmbH & Co. KGaA, 2005.

[94] 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.

[95] J. A. Glick. Ferromagnetic Josephson Junctions Carrying Spin-Triplet Supercurrent

For Cryogenic Memory. PhD thesis, Michigan State University, 2017.

[96] A. F. Volkov and K. B. Efetov. Odd spin-triplet superconductivity in a multilayered

superconductor-ferromagnet Josephson junction. Phys. Rev. B, 81:144522, 2010.

[97] L. Trifunovic and Z. Radovi´c. Long-range spin-triplet proximity effect in Josephson

junctions with multilayered ferromagnets. Phys. Rev. B, 82:020505, 2010.

123

[98] J. S. Moodera, T. S. Santos, and T. Nagahama. The phenomena of spin-filter tun-

nelling. Journal of Physics: Condensed Matter, 19(16):165202, apr 2007.

[99] Z. H. Barber K. Senapati, M. G. Blamire. Spin-filter Josephson junctions. Nature

Materials, 10(849), 2011.

[100] A. F. Volkov F. S. Bergeret, A. Verso. Spin-polarized Josephson and quasiparticle
currents in superconducting spin-filter tunnel junctions. Physical Review B, 86(060506),
2012.

[101] J. Bass in Spin Transport, Magnetism edited by E. Tsymbal, and I. Zutic. Spin

Transport and Magnetism. CRC Press, 2011.

[102] P. M. Levy S. F. Zhang. Conductivity perpendicular to the plane of multilayered

structures. Journal of Applied Physics, 69(4786), 1991.

[103] S. F. Lee, W. P. Pratt, Q. Yang, P. Holody, R. Loloee, P. A. Schroeder, and J. Bass.
Giant magnetoresistance in magnetic nanostructures. Journal of Magnetism and Mag-
netic Materials, 136:335–359, 1994.

[104] A. Fert T. Valet. Theory of the perpendicular magnetoresistance in magnetic multi-

layers. Physical Review B, 48(7099), 1993.

[105] J. Bass. CPP magnetoresistance of magnetic multilayers: A critical review. J. Magn.

Magn. Mater., 408:244 – 320, 2016.

[106] H. Y. T. Nguyen, R. Acharyya, E. Huey, B. Richard, R. Loloee, W. P. Pratt Jr.,
J. Bass, S. Wang, and K. Xia. Conduction electron scattering and spin flipping at
sputtered Co/Ni interfaces. Phys. Rev. B, 82:220401, 2010.

[107] A. Buzdin. Direct Coupling Between Magnetism and Superconducting Current in the

Josephson ϕ0 Junction. Phys. Rev. Lett., 101:107005, Sep 2008.

[108] J. Liu and K. S. Chan. Anomalous Josephson current through a ferromagnetic trilayer

junction. Phys. Rev. B, 82:184533, Nov 2010.

[109] I. Margaris, V. Paltoglou, and N. Flytzanis. Zero phase difference supercurrent in ferro-
magnetic Josephson junctions. Journal of Physics: Condensed Matter, 22(44):445701,
oct 2010.

[110] S. V. Bakurskiy, N. V. Klenov, T. Y. Karminskaya, M. Y. Kupriyanov, and A. A.
Golubov. Josephson φ-junctions based on structures with complex normal/ferromagnet
bilayer. Superconductor Science and Technology, 26(1):015005, nov 2012.

[111] I. Kulagina and J. Linder. Spin supercurrent, magnetization dynamics, and ϕ-state in

spin-textured Josephson junctions. Phys. Rev. B, 90:054504, Aug 2014.

124

[112] M. A. Silaev, I. V. Tokatly, and F. S. Bergeret. Anomalous current in diffusive ferro-

magnetic Josephson junctions. Phys. Rev. B, 95:184508, May 2017.

[113] S. V. Bakurskiy, V. I. Filippov, V. I. Ruzhickiy, N. V. Klenov, I. I. Soloviev, M. Yu.
Kupriyanov, and A. A. Golubov. Current-phase relations in SIsFS junctions in the
vicinity of 0 − π transition. Phys. Rev. B, 95:094522, 2017.

[114] S. Pal and C. Benjamin. Quantized Josephson phase battery. EPL (Europhysics

Letters), 126(5):57002, jul 2019.

[115] D. B. Szombati, S. Nadj-Perge, D. Car, S. R. Plissard, E. P. A. M. Bakkers, and L. P.
Kouwenhoven. Josephson φ0-junction in nanowire quantum dots. Nature Physics,
12(6):568–572, Jun 2016.

[116] H. Ren, F. Pientka, S. Hart, A. T. Pierce, M. Kosowsky, L. Lunczer, R. Schlereth,
B. Scharf, E. M. Hankiewicz, L. W. Molenkamp, B. I. Halperin, and A. Yacoby.
Topological superconductivity in a phase-controlled Josephson junction. Nature,
569(7754):93–98, May 2019.

[117] A. Assouline, C. Feuillet-Palma, N. Bergeal, T. Zhang, A. Mottaghizadeh, A. Zimmers,
E. Lhuillier, M. Eddrie, P. Atkinson, M. Aprili, and H. Aubin. Spin-Orbit induced
phase-shift in Bi2Se3 Josephson junctions. Nature Communications, 10(1):126, Jan
2019.

[118] W. Mayer, M. C. Dartiailh, J. Yuan, K. S. Wickramasinghe, E. Rossi, and J. Sha-
bani. Gate controlled anomalous phase shift in Al/InAs Josephson junctions. Nature
Communications, 11(1):212, Jan 2020.

[119] Caleb Howington, Alex Opremcak, Robert McDermott, Alex Kirichenko, Oleg A.
Mukhanov, and Britton L. T. Plourde. Interfacing superconducting qubits with cryo-
genic logic: Readout.
IEEE Transactions on Applied Superconductivity, 29(5):1–5,
2019.

[120] R. McDermott, M. G. Vavilov, B. L. T. Plourde, F. K. Wilhelm, P. J. Liebermann,
O. A. Mukhanov, and T. A. Ohki. Quantum–classical interface based on single flux
quantum digital logic. Quantum Science and Technology, 3(2):024004, Jan 2018.

[121] E. Leonard, M. A. Beck, J. Nelson, B.G. Christensen, T. Thorbeck, C. Howington,
A. Opremcak, I.V. Pechenezhskiy, K. Dodge, N.P. Dupuis, M.D. Hutchings, J. Ku,
F. Schlenker, J. Suttle, C. Wilen, S. Zhu, M.G. Vavilov, B.L.T. Plourde, and R. Mc-
Dermott. Digital coherent control of a superconducting qubit. Phys. Rev. Applied,
11:014009, Jan 2019.

125