Determining Spin Polarization of Ferromagnets Using Superconducting Spectroscopy Jazcek Guy Braden

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2006 Determining Spin Polarization of Ferromagnets Using Superconducting Spectroscopy Jazcek Guy Braden

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COLLEGE OF ARTS AND SCIENCES

DETERMINING SPIN POLARIZATION OF FERROMAGNETS USING SUPERCONDUCTING SPECTROSCOPY

JAZCEK GUY BRADEN

A dissertation submitted to the Department of Physics in partial fulﬁllment of the requirements for the degree of Doctorate of Philosophy

Degree Awarded: Spring Semester, 2006 The members of the Committee approve the dissertation of Jazcek Guy Braden defended on January 27, 2006.

Peng Xiong Professor Directing dissertation

P. Byrant Chase Outside Committee Member

Stephan von Moln´ar Committee Member

Pedro Schlottmann Committee Member

Ingo Wiedenhover Committee Member

The Oﬃce of Graduate Studies has veriﬁed and approved the above named committee members.

ii To my loving mother without whom none of this would have been possible

iii ACKNOWLEDGEMENTS

I would like to say first and foremost what an honor it has been to receive the guidance of Prof. Peng Xiong. His extensive knowledge of materials fabrication and experimental results has been an indispensable resource in my studies. I would also like to thank Prof. Stephan von Molnár for sharing his experience and resources with me, Prof. Pedro Schlottmann for his countless contributions and for developing the theory involved in this work, and our postdocs Dr. Daniel Read and Dr. Jens Mueller who provided considerable instruction and helping hands in the course of my work, and Dr. Cong Ren for his considerable help in my own research and for the work done on the barrier dependence. I would like to thank Ray Kallaher for his help in photolithography and Jeff Parker for all his assistance, specifically the measurements on (Ga,Mn)As. I would also like to thank Prof. Nitin Samarth and co workers at Penn State who provided the (Ga,Mn)As samples for this work. I offer my gratitude to the entire staff of MARTECH for providing the high level of support that made the lab function at it’s high level of excellence. Ian Winger and the rest of the MARTECH machine shop proved to be remarkably skilled and creative engineers, designing and building many components used in the work here. I would like to thank Jim Valentine for his maintenance, design and support of the electronics for our labs. I would also like to thank Kurt Koetz for maintaining a constant supply of Helium and for his support of our cryogenics. Lastly I would like to thank Eric Lochner for the instruction and maintenance provided with the various MARTECH facilities. All of the research presented here was funded by DARPA through the Office of Naval Research.

iv TABLE OF CONTENTS

List of Tables ...... vii

List of Figures ...... viii

Abstract ...... xiii

1. Introduction ...... 1

2. Spintronics ...... 3 2.1 Spin Polarization ...... 3 2.2 Spintronic device concepts ...... 5 2.3 Spintronic Compatible Materials ...... 10

3. Superconducting Spectroscopy ...... 13 3.1 Review of Superconductivity ...... 13 3.2 Zeeman Resolved Tunnel Junctions ...... 16 3.3 Andreev Reﬂection Spectroscopy ...... 20 3.4 Zeeman Resolved Andreev Contacts ...... 27

4. Spin Polarization of (Ga,Mn)As ...... 34 4.1 Background ...... 34 4.2 Sample Fabrication ...... 35 4.3 Experiment ...... 36 4.4 Analysis ...... 38 4.5 Interface Sensitivity ...... 42 4.6 Conclusions ...... 42

5. Spin Polarization of EuS ...... 44 5.1 Introduction ...... 44 5.2 Sample Fabrication ...... 46 5.3 Experiment and Analysis ...... 47 5.4 Conclusions ...... 52

6. Spin Polarization Dependence on Barrier Thickness ...... 53 6.1 Introduction ...... 53 6.2 Fabrication ...... 53

v 6.3 Experiment and Analysis ...... 54

7. CONCLUSIONS ...... 59

APPENDICES ...... 61

A. Fabrication Techniques ...... 61 A.1 Growth Techniques ...... 61 A.2 Patterning ...... 63

B. Measurement Techniques ...... 68

C. List of Terminology ...... 71

REFERENCES ...... 72

BIOGRAPHICAL SKETCH ...... 78

vi LIST OF TABLES

3.1 Normalized spin-orbit scattering rate b from tunneling measurements. .... 15

3.2 Table of P values determined via Zeeman Resolved Tunnel Junctions and ARS 19

3.3 Probabilities for transmission and reﬂection at the interface of an S/NM for both above and below gap regions from the original BTK model [42] 2 2 2 2 2 2 2 2 1 E2−∆2 (γ = [u0 + Z (u0 v0)] and u0 =1 v0 = (1 + 2 )) ...... 21 − − 2 q E

vii LIST OF FIGURES

2.1 Schematic diagram of the spin resolved DOS available to electrons in (a) a normal metal, (b) a ferromagnetic metal, and (c) a half metal...... 4

2.2 Longitudinal magnetoresistance of three diﬀerent Fe/Cr superlattices at 4.2K. Taken from Ref [6] ...... 6

2.3 Schematic representation of spin-polarized transport in GMR structures where for anti-parallel moments certain conduction channels are forbidden, resulting in a increased resistance in a) CPP conﬁguration and b) CIP conﬁguration. c) Diagram of a GMR spin valve based read head in a hard drive. The resistance of the spin valve (shown in green) is measured through iin and iout as it passes over magnetic bits (shown in red) which rotate the soft layer up or down. Figures taken from [8] ...... 6

2.4 Representation of the MR switching behavior in a MTJ. The arrows indicate the orientations of the magnetic moments...... 7

2.5 Schematical outline of MRAM designs taken from [8] (a) GMR spin valve based structure in which the bit and word lines are electrically isolated from the sense line (b) MTJ based structure where they are not electrically isolated, allowing for a four terminal resistance measurement...... 9 2.6 Spin FET structure described in Ref [15]. Spin is injected and detected by the FM electrodes and is transported through the 2DEG where it can be made to rotate by an electric ﬁeld created by the Au electrode...... 10

2.7 Parallel resistor model of spin oriented conduction in a spin FET structure in the case of (a) parallel aligned magnitizations and (b) anti-parallel aligned magnetizations taken from Ref [16] ...... 12 2.8 Injected polarization versus injector polarization for diﬀerent ratios of semiconductor (σsc) to ferromagnetic (σfm) conductivities...... 12

3.1 (a)Normalized parallel HC versus reduced temperature (t = T/Tc) for various thicknesses of Pt. (b) Spin orbit scattering rate versus Pt thickness. Both taken from [24] ...... 15

viii 3.2 Theoretical density of states for spin-down (solid lines) and spin-up (dashed lines) electrons in a magnetic ﬁeld H = 0.2 ∆/µ with b values of (a) 0.02, (b) 0.1, (c) 0.3, and (d) 0.6 ...... 16

3.3 (a) The band structure depiction of an S/I/N junction with an applied bias voltage. (b) A plot of normalized conductance versus eV/∆ of a S/I/N structure at T = 0, directly reflecting the BCS DOS (Eq. 3.1) of the superconductor. (c) The effects of a finite temperature on the conductance of a tunnel junction, plotted same as previous with T/Tc = 0.25...... 19 3.4 (a) The up (down) spin density of states at zero temperature plotted in blue dotted (red dashed) lines Zeeman split by a field H. (b) The conductance spectra for the up (down) spin plotted in red dashed (blue dotted), along with the normalized sum of the components plotted in black. σx corresponds to the G(V) values chosen in the Meservey-Tedrow approximation of P . .. 19 | | 3.5 Dependence of P of LSMO on the chosen V taken from [33], the arrow denotes the value that would have been chosen in the Meservey-Tedrow approximation. 20

3.6 Energy vs momentum diagram taken from Ref [42]. Open circles denote holes, solid circles denote electrons, and the arrows indicate group velocity. Starting with an incident electron with momentum q+ (0), the possible transmitted (2,4) and reﬂected particles (5,6) are diagrammed...... 21

3.7 (a) AR process at a normal metal/superconductor interface where an incident electron with E < ∆ pairs with an electron of opposite spin to form a Cooper pair, reflecting| | a hole and doubling the conductance. (b) AR in a ferromagnet/superconductor (P = 75%) where the same incident electron finds no opposite spin to pair with, is normally reflected and decreases the conductance enhancement...... 23

3.8 Spin-polarized BTK model applied in planar conﬁguration on (a) Al/Al2O3/NiFe and (b) Al/Al2O3/EuS structures with intermediate to high Z values. .... 25

3.9 (Top) ARS applied to CrO2 in the (a) high Z and (b) low Z limits from both consistent with the predicted half-metal P. (Bottom) High Z CrO2 junction ﬁtted to BTK (left) and an inelastic scattering model (right). Adapted from [40] ...... 26

3.10 (a) Conductance spectra for a CrO2/Al junction at several fields, adopted from [40]. The effect of the field merely shifts the spectra in energy implying P = 100%. (b) Zeeman split Andreev conductance model applied to the B = 2.5 T curve from (a), confirming the expected high P...... 28

ix 3.11 (a) An AC, four terminal R vs T (see Appendix B) of a typical low resistance ◦ junction showing a large spontaneous 180 phase shift at Tc, the inset shows a close-up view of the area covered by the dotted circle. (b) Conductance spectra of the junction showed in (a) at T = 360mK, demonstrating the switching of direction of both the AC signal and DC signal simultaneously...... 29

3.12 (a) Diagram of a ideal four terminal measurement with the black lines indicating the current ﬂow and the dotted lines representing the equipotential lines. (b) An over simplized cartoon of the current ﬂow in a psuedo four terminal measurement from a cross stripe geometry in which the potential leads no longer lie on equipotential lines ...... 30

3.13 Rotated picture of cross stripe depicting the equipotential lines expected in the small junction area limit. Figure taken from [59]...... 31

4.1 Zinc-Blende structure of Ga1−xMnxAs with lattice constants a, b, and c. .. 35

4.2 M versus T of a Ga0.95Mn0.05As ﬁlm used in this study showing a TC of 65K. 37

4.3 Schematical diagram of the Ga0.95Mn0.05As structure and contact setup. ... 37

4.4 Normalized conductance spectra of two Ga0.95Mn0.05As samples from the same growth...... 38

4.5 Resistance versus temperature of the P = 85% sample, clearly showing an enchancement in Tc ...... 39

4.6 Conductance spectra of the Ga0.95Mn0.05As samples (red) along with the ﬁts provided using a weighted BTK model (blue)...... 40

4.7 Conductance spectrum taken from [55] shown for a BTK model modified to separate physical scattering effects and effects from Fermi velocity mismatch. Zσ represents the amount of potential scattering, F represents spin-flip scattering, and X is a measure of the spin splitting energy which gives good indication of P...... 41

4.8 Theoretical prediction of GaMnAs spin polarization vs band splitting for diﬀerent hole concentrations, taken from [73]...... 42

4.9 After mild annealing, the conductance spectrum of the P = 85% samples signiﬁcantly changes, indicating a smaller P value. (Pre-anneal in black, post- anneal in red) ...... 43

5.1 Rock salt crystal structure of EuS. The Eu-S distance is 2.98 A˚ and the Eu-Eu distance is 4.21 A.˚ ...... 44

x 5.2 (a) Magnetization versus temperature for several EuS ﬁlms grown at diﬀerent growth temperatures in which the higher growth temperatures lead to the stoichiometric limit. (b) Resistivity versus Temperature in which the resistance peak is shifted to higher temperatures with decreasing growth temperature . 45

5.3 Hall data on EuS taken at 10K revealing an increase in carrier concentration with lower growth temperatures adopted from [85]...... 46

5.4 EuS/Al junction structure shown from (a) the side view (b) top down view with contacts labeled as golden circles ...... 47

5.5 Normalized conductance versus bias voltage curves spetra of Al/EuS junctions at a temperature of 0.38 K and zero magnetic field. The growth temperatures for EuS films are: (a) room temperature (34◦C); (b) -2◦C; (c) 34◦C and (d) 120 ◦C. The solid lines are the best fits to a modified BTK theory. The fitting parameters are indicated in the figures...... 48

5.6 The ﬁtted P as a function of Z for various Al/EuS junctions with diﬀerent EuS growth temperatures...... 49

5.7 Graph of EuS/In junction demonstrating Schottkey barrier tunneling. .... 50

5.8 (a) The conductance curves of the junction of Fig 5.5(a) at applied fields of 0.60 T and 0.75 T. The solid lines are the fits to the modified BTK theory with Maki’s density of states of Al. An orbital depairing ζ = 0.10 and spin- orbit interaction b = 0.14 are employed to fit to the data; (b) The enhanced exchange field B* as a function of applied field Ha...... 51

6.1 The resistance of a Al/AlOx/Py/Au junction as a function of temperature. The barrier was formed by natural oxidization in O2 for 20 minutes at atmospheric pressure...... 55

6.2 Tunneling conductance dI/dV versus bias voltage V for junctions with different RA at base temperature T=0.34 K in zero field (filled symbols) and magnetic fields (open symbols). The solid curves are the fits to the data measured in the precense of a magnetic field using the Maki-Fulde theory outlined in section 3.2...... 56

6.3 The extracted P versus the barrier thickness. The error bars for P are from the range in P which allowed for acceptable ﬁts to the curves the curves in Fig 6.2, and for t from the averaged barrier thickness of using 2.0 and 3.0 eV for barrier height [Eq. 6.1]. The solid line is the ﬁt to the data using Eq. 6.4. 57

A.1 Illustrations of the diﬀerent conﬁgurations of evaporators with (a) The BOC Edwards Auto 306 and (b) evaporator of in house construction...... 64

A.2 Schematical diagram of the e-beam chamber used to grow EuS...... 64

xi A.3 Illustration of Microscience IBEX 2000...... 66

A.4 Illustration of the AJA 1800 F sputtering system...... 66

A.5 Illustration of steps involved in a window deﬁning process using (left) photoresist and liftoﬀ, (right) polyimide...... 67

B.1 dVdI ...... 69

B.2 dIdV ...... 70

B.3 Circuit diagram for analog linear voltage sweep ...... 70

xii ABSTRACT

The tremendous interest in using the spin degree of freedom in electronic devices has led to an extensive endeavor to investigate the intrinsic spin polarization of various magnetic materials. The work done here expands upon existing methods to develop a more general technique of precise electrical determination of spin polarization using superconducting spectroscopy with or without the presence of a magnetic field. As part of this effort, the use of Andreev reflection in planar junction configuration was explored on several ferromagnetic materials including the dilute magnetic semiconductor (DMS) Ga1−xMnxAs and the concentrated magnetic semiconductor EuS. This work also led to the exploration of the effects of barrier strength on the measured spin polarization.

Traditionally, using superconducting spectroscopy to measure spin polarization (P) was limited to the case of a tunnel junction in a magnetic field or Andreev reflection measurements in point contact structures in zero-field. This project aimed to develop a method that bridged these two regimes to allow for determination of spin polarization in more practical device structures, such as planar junctions, with arbitrary barrier strength.

This work led to the ﬁrst direct electrical determination of P on the representative

DMS Ga1−xMnxAs by measuring GaMnAs/Ga structures using Andreev reﬂection in planar conﬁguration. The analysis of the conductance spectra on highly transparent junctions consistently yielded P values of at least 85%. These experiments also revealed an extreme sensitivity of P to the interfacial properties.

Another major part of this work was the measurement of the P of doped EuS using zero- ﬁeld and Zeeman-split Andreev reﬂection spectroscopy (ARS) on EuS/Al planar junctions

xiii are reported. The zero-field ARS spectra can be fit straightforwardly to a spin-polarized BTK model, which consistently yield P on the order of 80% regardless of the barrier strength. Moreover, we performed ARS in the presence of a Zeeman-splitting of the quasiparticle density of states in Al. The Zeeman-split ARS spectra are well described theoretically by combining the solution to the Maki-Fulde equations with the spin-polarized BTK analysis. The results have provided an independent verification of the validity of the zero-field ARS, and helped demonstrate the utility of field-split superconducting spectroscopy on Andreev junctions of arbitrary barrier strengths.

Additionally the eﬀect of barrier thickness on the measured spin polarization was explored in Al/Al2O3/Ni79Fe21 tunnel junctions. Planar tunnel junction structures were formed by natural oxidation of Al; by varying the oxidation time the barrier thickness could be controlled. The measured spin polarization increased with increasing barrier thickness which is attributed to the interplay of both the sp and d electronic states of the NiFe.

xiv CHAPTER 1

Introduction

The continued advancements in modern micro-electronics have established it as one of the most lucrative markets in the world and become an indispensable element of our economy and everyday life. It is the continuous miniaturization of the basic building blocks of these devices that have made this possible. However this miniaturization that has been the driving force of the semiconductor industry seems destined to reach an impasse soon, calling for new research directions to be explored. Today’s microprocessors are a perfect demonstration of this miniaturization. Micro- processors are made from an array of transistors, resistors, and capacitors arranged into integrated circuits that perform logic operations. The miniaturization of the transistors allows for more transistors to be arranged in a given area, increasing the computing power of the processor. Intel’s 8080 processor introduced in 1975 contained only 6,000 transistors which cost about 1 cent each to produce, while the Pentium 4 introduced in 2002 contains over 42 million transistors which cost 1/10,000 of a cent to produce [1]. Early in the semiconducting electronics era, Gordon Moore made a bold prediction which has become known as Moore’s Law [2], which states that the computing power of a microprocessor would double every 18 months as the size of the electronic devices decrease. The technological development has followed this prediction surprisingly well, but now the miniaturization has proceeded to the point that it is hindered by physical limitations. Traditionally, 1’s and 0’s in logic operations of our digital devices are represented by “on” and “oﬀ” of electrical (charge) current, but by utilizing the spin of the electron, alone or along with the charge, the power of these devices can be well extended into the future. This is why it is of great interest to explore spin-dependent transport and the spin polarization of materials, which are essential elements of spintronics.

1 This thesis is formatted as follows: Chapter 2 provides a background into the spintronics initiative and outlines the concept for several important representative spintronic devices. Chapter 3 reviews existing methods of superconducting spectroscopy, including a brief review of the relevant properties of superconductors. Chapter 3 also introduces a new model of determining spin polarization and some of the work done to verify this model. Chapter 4 describes the work that was done on the spin polarization measurement on Ga1−xMnxAs. Chapter 5 demonstrates the use of superconducting spectroscopy techniques, including the new model introduced in Chapter 3, in the determination of P of EuS. Chapter 6 presents the work on the exploration of the eﬀects of barrier thickness on spin polarization.

2 CHAPTER 2

Spintronics

2.1 Spin Polarization

In order to proceed with an overview of spin electronic (spintronic) device concepts, it is ﬁrst necessary to deﬁne spin polarization. In ferromagnets there exists an imbalance between the number of charge carriers having a particular spin orientation at the Fermi level, EF , leading to a net spin polarization of the conduction electrons. This imbalance is illustrated in Fig 2.1, highlighting the extreme cases of a normal metal, where there are equal number of each spin oriented carriers, and the so called half metal [3], when only one spin species is present at

EF . The spin polarization P of a material is deﬁned by

n↑ n↓ P = − (2.1) n↑ + n↓ where n↑ represents the number of carriers at EF having their spin aligned parallel to the magnetization and n↓ number of carriers having their spin aligned anti-parallel to the magnetization. The parallel and anti-parallel aligned carriers are also referred to as carriers with majority and minority spin, respectively [4]. Eq. (2.1) is purely a density of states (DOS) definition of P, which becomes inadequate in that transport phenomena usually are not defined by DOS alone. Generally electrical determination of P is done by measuring current densities, P = (J↑ -J↓)/(J↑ + J↓), which can result in slightly different definitions depending on the measurement [5]. In the case of a metallic contact such as the work on GaMnAs in Chapter 4, J↑(↓) is found by integrating the density of states times the velocity of the electron at a given energy over the Fermi Surface of each band, and multiplying by a spin relaxation time (i.e. J↑ ↓ < n↑ ↓ v > τ, where ( ) ∝ ( ) τ is the spin relaxation time). Assuming τ is equal for each spin orientation, this gives the

3 Figure 2.1: Schematic diagram of the spin resolved DOS available to electrons in (a) a normal metal, (b) a ferromagnetic metal, and (c) a half metal.

measured spin polarization as

< n↑v > < n↓v > P = − (2.2) < n↑v > + < n↓v > In the case of intermediate barrier junctions such as those used in Chapter 5, this changes to 2 2 < n↑v > < n↓v > P = 2 − 2 (2.3) < n↑v > + < n↓v > Finally in the case of tunnel junctions such as those used in Chapter 6, P is found by

2 2 n↑ M↑ n↓ M↓ P = | |2 − | |2 (2.4) n↑ M↑ + n↓ M↓ | | | | where M↑ ↓ are the spin dependent tunneling matrix elements, which when assumed to | ( )| be equal reduces to Eq. 2.1. From Eq.’s 2.2 and 2.3 it is evident that the measured spin polarization can result from not only an imbalance in the relative DOS but the mismatch in Fermi velocities. Spintronic devices are designed around the use of the spin to represent data and perform logic operations. In this regard it becomes essential to be able to control, as well as detect, the spin of a carrier. In electrical devices, ferromagnets are ideal sources for spin polarized carriers because of their inherent spin polarization. This is one major motivation into the probing of the spin polarization done in this work.

4 2.2 Spintronic device concepts

The topic of spintronics has become a vast area of research in the field of condensed matter physics for the past 15 years. The discovery of giant magneto-resistance (GMR) by Baibich et al. in 1988 [6], was generally considered to be the beginning of the spintronics initiative, igniting a slew of research into other spin dependent phenomenon. The remarkably rapid adoption of GMR based magnetic read heads in computer hard drives allowed for the storage densities in hard drives to rapidly increase. The adoption of GMR into a commercial device fueled the industrial efforts into developing other spintronic technologies. The spintronic initiative gives promise of devices that consume less power, are non-volatile, and even perform quantum computations. Metal based devices such as the GMR spin valve and magnetic tunnel junctions (MTJ) have already proven successful, while semiconductor based technologies such as the spin field effect transistor (spin-FET) are still being heavily pursued.

2.2.1 GMR spin valve

GMR occurs in heterostructures of alternating ferromagnetic and nonmagnetic metallic layers, whose resistance changes according to the relative orientations of the ferromagnetic layers. The original work of Baibich et al. [6] was done on Fe/Cr superlattices grown by molecular beam epitaxy (MBE). The magneto resistance (MR) is deﬁned by

∆R R(H ) R(0) MR = = s − (2.5) R R(Hs) where R is resistance and Hs is the magnetic field at which the resistance saturates. Fig 2.2 is a graph taken from [6] showing the MR of several Fe/Cr superlattices with varying thicknesses of Cr. The MR values in these structures were 100% at 4.2K and had Hs values of 10 - 20 kOe. which is far too high for practical use. This effect was also seen in simple multilayer systems grown by magnetron sputtering [7], which allowed for faster growth and better real world device integration than MBE (see Appendix A for explanation of different growth techniques). Since then these devices have been grown with only a few layers achieving ∼ 8% MR at room temperaure with Hs of 10-20 Oe, making them pratical for detecting the small magnetic fields used in magnetic information storage. Fig 2.3, adopted from [8], diagrams GMR in current perpendicular to plane (CPP) and current in plane (CIP) configurations. The high resistance state in these structures occurs

5 Figure 2.2: Longitudinal magnetoresistance of three diﬀerent Fe/Cr superlattices at 4.2K. Taken from Ref [6]

Figure 2.3: Schematic representation of spin-polarized transport in GMR structures where for anti-parallel moments certain conduction channels are forbidden, resulting in a increased resistance in a) CPP conﬁguration and b) CIP conﬁguration. c) Diagram of a GMR spin valve based read head in a hard drive. The resistance of the spin valve (shown in green) is measured through iin and iout as it passes over magnetic bits (shown in red) which rotate the soft layer up or down. Figures taken from [8]

6 when the magnetization of the neighboring ferromagnetic layers are anti-parallel, resulting from scattering at the ferromagnetic (FM)/normal metal (NM) interface due to lack of available states. Conversely in the parallel magnetization state the resistance is low, resulting from a reduction in scattering at the FM/NM interface. Generally an anti-ferromagnetic layer is grown near one of the ferromagnetic layers,“pinning” its magnetization so that it requires a larger ﬁeld to reverse the magnetization direction. Fig 2.3(c) diagrams a spin valve structure for magnetic read heads. The read head is scanned over the surface of the medium and as the spin valve moves over a magnetic bit its resistance changes. IBM ﬁrst introduced the GMR spin valve based magnetic read head in their hard drives in 1998, which prompted large increases in hard drive capacity and performance. Since then, GMR has become the dominant technology for read heads, establishing a multi-billion dollar industry.

2.2.2 MTJ

The MTJ is a device which involves two ferromagnetic layers with diﬀerent switching ﬁelds,

Hsw1(2), separated by a thin tunneling barrier. Here the resistance is also controlled by the relative magnetization of the ferromagnetic layers and the tunneling resistance is determined by comparing the density of states of the ferromagnets on each side of the barrier. Shown in Fig 2.4 is the resistance versus relative magnetization relations of an MTJ. At high ﬁeld the magnetization of both ferromagnets are aligned parallel providing a ﬁnite tunneling current that depends on the matching of density of states of each spin orientation relative

Figure 2.4: Representation of the MR switching behavior in a MTJ. The arrows indicate the orientations of the magnetic moments.

7 to each side of the barrier. As the ﬁeld is lowered through zero, reversed and increases past

Hsw1 the magnetization of one layer switches and the ferromagnetic layers are aligned in the anti-parallel configuration. This causes a mismatch in the number of states of a particular spin orientation relative to the other side of the barrier, which results in a lower tunneling current and a high resistance state. As the field increases past Hsw2, the other ferromagnetic layer switches, providing again a parallel magnetization state and a return to the normal resistance. This process occurs identically as the field is swept in the opposite direction. This effect was first observed my Julliére [9] on Co/Ge/Fe junctions, in which he observed an MR of 14% at 4.2 K which disappeared at room temperature. He explained this effect using a model that proposed the tunneling magneto-resistance (TMR) was based on the spin polarization of the two layers by the relation ∆R R R 2P P T MR = = ap − p = 1 2 (2.6) R R 1 P P p − 1 2 where Rap, Rp are the anti-parallel and parallel resistances respectively, and P1, P2 are the spin polarization values determined by the Zeeman resolved technique (see Chapter 3). In this model it is evident that the P of the materials greatly the affects the TMR of the structure. Further work on various ferromagnets have resulted in TMR values of 30-40% with aluminum oxide barriers [10, 11, 12], and more recently 220% with MgO barriers [13]. As was shown, the TMR observed in MTJ structures results from a decrease of tunneling current due to fewer available states on opposite sides of a barrier. In constrast GMR results from increased scattering in metallic systems for carriers of a particular spin at an interface with a layer with opposite alignment of magnetization. As such MTJ’s have much larger resistances and hence much larger signal to noise ratio, making them more suitable for small signal detection. Also the CIP GMR devices which are currently used only allow for two terminal measurements, while the MTJ’s have the possiblilty to be measured in a four terminal configuration. This is why numerous applications of the MTJ have been developed such as MTJ based scanning magnetic microscopes [14], and many more are being pursued such as MTJ based magnetic read heads.

2.2.3 MRAM

The large, sharp change of resistance of GMR spin valve devices and MTJ makes them highly sensitive magnetic ﬁeld sensors. Another major industrial application that is set to

8 Figure 2.5: Schematical outline of MRAM designs taken from [8] (a) GMR spin valve based structure in which the bit and word lines are electrically isolated from the sense line (b) MTJ based structure where they are not electrically isolated, allowing for a four terminal resistance measurement.

revolutionize the market is magnetic random access memory (MRAM). In MRAM 1’s and 0’s are stored as high and low resistances of either GMR or MTJ structures, whose resistance state is controlled by an external magnetic field, which is illustrated in Fig 2.5 In a GMR structure the resistance of a CIP spin valve is controlled by the magnetic fields produced by current passing through the word and bit lines. The word and bit lines are electrically isolated from the sense line, allowing a two terminal resistance measurement of the sense line that is independent of the current in the other lines. In the MTJ structures the resistance is also controlled by the magnetic fields from two neighboring wires. However now they are not electrically isolated, which allows for a four terminal measurement of the resistance. Since the resistance of these devices changes only when a magnetic field is applied, the stored information is non-volatile and requires power only when the information is read or changed. In contrast, the semiconductor DRAM used as main memory in computers, which uses a transistor and capacitor to form a memory cell, retains information only if the memory elements are refreshed periodically, which is why it is referred to as volatile memory, and requires high power consumption. MRAM also has advantages over other non-volatile memory technologies, such as flash ram, in that it performs at speeds comparable to modern DRAM memories.

9 Figure 2.6: Spin FET structure described in Ref [15]. Spin is injected and detected by the FM electrodes and is transported through the 2DEG where it can be made to rotate by an electric ﬁeld created by the Au electrode.

2.2.4 Spin FET

The development of two-terminal metal base spintronic devices such as the spin valve and the MTJ has proved to be a great success in fundamental science and marketplace. There is a considerable amount of effort to extend these successes into three-terminal, semiconductor based devices for performing logic operations. The spin FET is the prototypical semiconductor spintronic device first proposed by Datta and Das [15]. The basic idea of the device is illustrated in Fig 2.6. Ferromagnetic contacts are used to inject spin polarized carriers into a two dimensional electron gas (2DEG) that can be formed in semiconductor heterostructures, specifically with InAlAs and InGaAs. The Au gate contact can then be used to apply a gate voltage Vg. Through spin-orbit coupling the electric field produced by Vg creates an effective magnetic field which causes the spin to undergo Larmor precession. The ferromagnetic detector then is able to detect the rotation of the spin. It is the ability to perform arbitrary rotations with Vg on the carrier which may make quantum computation operations possible in this type of device. While the concept of this device is well understood, there are many obstacles in the realization of the devices. A major problem is injecting and detecting spin polarized carriers in semiconductor based devices, discussed in the next section. 2.3 Spintronic Compatible Materials

The problem of injecting and detecting spin polarized carriers into a semiconductor arises from the fact that most traditional ferromagnets are metals. Schmidt et al. [16] showed that the conductivity mismatch between metals and semiconductors causes a greatly diminished injection eﬃciency of spin polarized carriers. This can be illustrated by the use of a parallel

10 resistance model of the spin FET structure listed previously, as diagrammed in Fig 2.7, in which each spin current is conducted along a separate channel. The relative sizes of the resistors in this ﬁgure indicate the relative resistance values of each channel component.

Conduction in the 2DEG is taken to be spin independent making Rsc↑ = Rsc↓. Since the voltage across each channel must be equal, when the ferromagnets are aligned parallel and R ↑ + R ↑ = R ↓ + R ↓, the voltage drop across R ↑ and R ↓ are unequal, fm1 fm2 6 fm1 fm2 sc sc giving a spin polarized current in the semiconductor. However in the case of anti-parallel alignment, Rfm1↑ + Rfm2↑ = Rfm1↓ + Rfm2↓ resulting in identical voltage drops across Rsc↑ and Rsc↓, and the total polarization in the semiconductor is zero. The spin polarization in the semiconductor is then given by: σ 2 α = β sc (2.7) σsc 2 σfm 2 + (1 β ) σfm − where β is the polarizationg of the ferromagnet with σsc and σfm being the conductivities −4 of the semiconductor and ferromagnet, respectively. With typical materials σsc = 10 σfm, leading to a greatly diminished injected spin polarization, which strongly depends on the spin polarization of the injecting ferromagnet. Plotted in Fig. 2.8 is the injected spin polarization versus injector spin polarization for σsc/σfm = 1, 0.1, and 0.01. The solutions to this conductivity mismatch problem that workers are pursuing include using materials with near 100% spin polarization to eliminate one of the spin conduction channels, using tunneling contacts to inject the spin from a ferromagnetic metal, or to use a spin polarized material with low conductivity, such as a ferromagnetic semiconductor. This desire for highly spin polarized materials highlights the need to investigate the spin polarization of various materials, such CrO2 and EuS, as well as inspire the strong research interest in the ferromagnetic semiconductor (Ga,Mn)As.

11 Figure 2.7: Parallel resistor model of spin oriented conduction in a spin FET structure in the case of (a) parallel aligned magnitizations and (b) anti-parallel aligned magnetizations taken from Ref [16]

Figure 2.8: Injected polarization versus injector polarization for diﬀerent ratios of semiconductor (σsc) to ferromagnetic (σfm) conductivities.

12 CHAPTER 3

Superconducting Spectroscopy

3.1 Review of Superconductivity

To provide a description of superconducting spectroscopy it is worthwhile to begin with a brief review of the relevant properties of superconductivity. The discussions hereafter are limited to that of conventional BCS type superconductors, which are better understood, and in which the following spin eﬀects have been observed, as opposed to other types of superconductors such as the high Tc materials.

3.1.1 History

Superconductivity was first reported by Kamerlingh Onnes in 1911, three years after he first liquefied helium, by observing that when cooled below 4.2K Hg suddenly lost all electrical resistivity. Later in 1933 Meissner and Ochsenfeld observed that a superconductor behaved as a perfect diamagnet and that all magnetic fields are expelled from the interior of the superconductor. These effects were observed in a wide range of materials indicating it was a universal phenomenon. Many models were developed in the following years to explain the phenomenological observations, but in 1957 Bardeen, Cooper and Schreiffer (BCS) [17] advanced a quantum mechanical theory of superconductivity that provided a microscopic picture. The BCS theory was thought to provide a complete picture of superconductivity until the 1980’s when the high temperature superconductors were discovered. The BCS theory introduced the idea that electrons in a material interact through the phonons in the crystal lattice. The interaction is selective in that it only involves electrons with energies near the Fermi level and that only electrons of opposite spin and momentum (k~↑,

-k~↓) interact, forming what is known as a Cooper pair. The minimum distance between paired electrons is called the coherence length, ξ. The pairing also leads to an energy gap around

13 the Fermi level where single particles are no longer stable against Cooper pair formation. The superconducting energy gap, ∆, becomes evident in the single particle density of states (DOS), which is given by E N(E)= N(0)Re( ) (3.1) √E2 ∆2 − where N(0) is the DOS of the normal state at EF .

3.1.2 Eﬀects of a magnetic ﬁeld

When a magnetic field is applied to a superconductor, a surface current is formed to generate a magnetic field to cancel the applied field within the body of the superconductor. The surface current is formed only within a certain distance known as the penetration depth, λ. At some critical applied field Hc, the free energy associated with the surface current overcomes the superconducting condensation energy and the superconductor reverts to its normal state. The magnetic field also breaks the time-reversal symmetry of the superconducting state and tends to break up the superconducting pairs. This pair-breaking effect was described by Maki [18], which can be accounted for by a dimensionless orbital depairing parameter, ζ. It is also important to note that in a superconducting thin film, with d < λ, when the magnetic field is applied parallel to the plane of the film, the screening currents are reduced and the magnetic field penetrates the superconductor uniformly. This allows for the Hc in thin films to be greatly increased.

3.1.3 Eﬀects of Spin-Orbit Interaction

Spin-orbit interaction in superconductors was originally proposed in order to account for the non-vanishing Knight shift in superconductors observed by Reif [19] and by Andereos and Knight [20]. The Knight shift should be directly proportional to the spin susceptibility, which is predicted by BCS theory to vanish in the superconducting state. The work by Ferrell [21] and Anderson [22] introduced the spin-orbit interaction as a spin flip scattering process that does not break the Cooper pairs, which acts to greatly reduce the Knight shift. Abrikosov −4 and Gorkov [23] calculated that the spin-orbit scattering time τso was proportional to Z where Z is the atomic number. The normalized spin-orbit scattering rates b = ~/3∆τso have been measured for a variety of materials some of which are shown in Table 3.1. The effects of b also act to increase the HC of a given film with a known gap value which is taken to be

14 Table 3.1: Normalized spin-orbit scattering rate b from tunneling measurements.

Superconductor b = ~/3τso∆ Al 0.05 [24] Be 0 [25] Ga 0.16∼ [26, 27, 28] V 0.07 [29]

Figure 3.1: (a)Normalized parallel HC versus reduced temperature (t = T/Tc) for various thicknesses of Pt. (b) Spin orbit scattering rate versus Pt thickness. Both taken from [24]

constant. This was demonstrated in the work by Tedrow and Meservey [24] in which thin films of Pt were deposited at varying thickness below an Al layer in order to increase and measure b, as plotted in Fig 3.1(b). The effect of the enhanced critical field with added b is illustrated in Fig 3.1(a).

3.1.4 The Maki-Fulde Equations

The eﬀects of ζ and b listed previously have been accounted for by incorporating them into the DOS via the Maki-Fulde equations [30]. Since the spin up and spin down DOS are now coupled, the traditional BCS DOS now becomes

N(0) u± N↑↓(E)= sgn(E)Re( ) (3.2) 2 √u± 1) −

2.0 (a) (b) 2.0

1.5 1.5

1.0 1.0

0.5 0.5 ) Δ

Ε 0.0 0.0 (

2.0 (d) 2.0 (c)

1.5 1.5

1.0 1.0

0.5 0.5

0.0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 E/Δ E/Δ

Figure 3.2: Theoretical density of states for spin-down (solid lines) and spin-up (dashed lines) electrons in a magnetic ﬁeld H = 0.2 ∆/µ with b values of (a) 0.02, (b) 0.1, (c) 0.3, and (d) 0.6

where u+ and u− are implicitly deﬁned by

E µH u± u∓ u± u± = ∓ + ζ + b − (3.3) ∆ 1 u2 1 u2 − ± − ± p p Notice here that the b acts to couple the spin up and spin down equations due to the spin flip process. Fig 3.2 shows the spin-up and spin-down density of states for a range of b. With increasing b there is an increase in spin flip scattering which decreases the separation of the spin-up and spin-down peaks. When b > 1 (making the spin-orbit scattering length lSO <ξ) the separation vanishes and the effects of spin oriented carriers are no longer seen. Table 3.1 list the b values for several materials. 3.2 Zeeman Resolved Tunnel Junctions

Early work in spin-polarized superconducting spectroscopy was pioneered by Meservey and Tedrow which utilized the eﬀects of conductance measurements of a superconducting tunnel junction (STJ) in the presence of a magnetic ﬁeld. A tunnel junction is a structure consisting of two electrodes, separated by a thin insulating barrier, providing that elastic tunneling is

16 the only conduction process. The work of Giaever [31] on superconductor/insulator/normal metal (S/I/N) junctions, showed that when one electrode was in a superconducting state, the conductance spectra directly reﬂected the BCS DOS (Eq. 3.1). In equilibrium, the Fermi level of the normal side of the barrier aligns midway of the gap of the superconducting side, giving a null tunneling current due to the lack of single particle states in the superconductor to tunnel to and from. As illustrated in Fig 3.3, an applied bias acts to rigidly slide the DOS of the electrode and counter-electrode past one another, leading to a tunneling current which is directly proportional to the product of the number of occupied states on one side of the barrier to the number of unoccupied states on the other side of the barrier, i. e. :

I ρ(E)N(E) f(E) f(E eV ) dE (3.4) ∝ Z { − − } where ρ is the BCS DOS, N is the normal metal DOS, and V is the applied voltage. dI(V ) The normalized conductance is found simply by G(V ) = dV , applying to Eq. 3.4 and normalizing by GN gives: G(V ) = ρ(E)N(E)β(E + eV )dE (3.5) GN Z where β is the derivative of the Fermi-Dirac distribution, speciﬁcally

E e kB T β(E)= E (3.6) k T 2 kBT (1 + e B ) At finite temperature the only conduction when V < ∆ occurs from thermal excitation. | | e Meservery and Tedrow [32] developed a technique of measuring P in STJ structures that utilized the effects of a magnetic field on the superconducting DOS. Neglecting spin-orbit interaction a magnetic field (H) would split the majority and minority carriers by 2µBH in energy. This results in separate currents for different spin oriented carriers at a given applied bias, which becomes evident in the conductance spectrum as in Fig 3.4. The positive bias direction is always defined relative to the current flowing from the Al to the FM layer. They based their analysis on the Maki-Fulde equations (Eq 3.2). STJ structures were measured in the prescence of a magnetic field and the Zeeman splitting of the DOS was observed. Al was originally chosen since it has a low atomic number and hence a low b. Al also has the advantages that it can be deposited as thin as 4nm with relative ease, allowing for a greatly enhanced H , and that it forms a self liming surface oxide ( 2nm) which is the ideal c ∼ thickness for a tunnel barrier.

17 Tedrow and Meservey did not take the step to solve the Maki equations in order to ﬁt the entire conductance spectrum. They instead used the following approximation which is based upon the conductance taken at several speciﬁc values of bias (see Fig 3.4). (σ σ ) (σ σ ) P = 2 − 4 − 1 − 3 =2a 1 (3.7) (σ σ )+(σ σ ) − 2 − 4 1 − 3 where

σ = G( V µH) σ = G( V + µH) 1 − − 2 − σ = G(V µH) σ = G(V + µH) 3 − 4 V was usually chosen to be ∆/e which was believed to result in the most accurate determination of P. It was later found that this scheme could in fact lead to highly inaccurate values for P without a complete solution for the conductance spectrum for all voltages. The fundamental reason for this inaccuracy is the approximation assumes a simple Zeeman splitting of the DOS, i. e. no spin-orbit interaction (b = 0). Fig 3.5 shows the dependence of P on chosen V in the Meservey-Tedrow approximation from an experiment on the ferromagnet LSMO [33]. Concurrent work by Parkin and Monsma [34] and by Worledge and Geballe [33] provided numerical solutions to the Maki equations and spin-up and spin-down DOS in a magnetic ﬁeld. The conductance at an arbitrary bias could then be calculated by G(V ) 1 P 1+ P = − N↓(E)β(E + eV )dE + N↑β(E + eV )dE (3.8) GN Z 2 Z 2 Table 3.2 lists several P values provided by this method. The complex structure of the Zeeman-split conductance spectrum makes the determination of P highly accurate and reliable. A typical STJ is grown by depositing a thin layer of Al ( 4-5nm thick) by either thermal ∼ evaporation or by sputtering (see Appendix A for description). Then a barrier (1-2nm thick) is formed by oxidizing the Al, which can be done by exposure to near atmospheric of O2 (as done in this work), but is more generally done by exposing the Al layer to an oxygen plasma which has been found to provide a more uniform and reproducible barrier, and provides rapid oxidation times [41]. Finally a ferromagnetic layer is deposited, often as a cross stripe and a standard four terminal AC measurement technique (see Appendix B) is used to measure the conductance spectrum.

18 Figure 3.3: (a) The band structure depiction of an S/I/N junction with an applied bias voltage. (b) A plot of normalized conductance versus eV/∆ of a S/I/N structure at T = 0, directly reflecting the BCS DOS (Eq. 3.1) of the superconductor. (c) The effects of a finite temperature on the conductance of a tunnel junction, plotted same as previous with T/Tc = 0.25.

Figure 3.4: (a) The up (down) spin density of states at zero temperature plotted in blue dotted (red dashed) lines Zeeman split by a ﬁeld H. (b) The conductance spectra for the up (down) spin plotted in red dashed (blue dotted), along with the normalized sum of the components plotted in black. σx corresponds to the G(V) values chosen in the Meservey- Tedrow approximation of P . | |

Table 3.2: Table of P values determined via Zeeman Resolved Tunnel Junctions and ARS

Spin Polarization(%) ARS Zeeman Resolved Tunneling Co 39-45 [35, 36] 32-38 [37] Fe 42-43 [35, 36] 38-42 [37] Ni 37-40 [35, 36] 20-26 [37] NiFe 35 [35] 26-30 [37] LSMO 77-83 [35, 38] 72 [33] CrO2 90-97 [35, 39] 100 [40]

19 Figure 3.5: Dependence of P of LSMO on the chosen V taken from [33], the arrow denotes the value that would have been chosen in the Meservey-Tedrow approximation.

Zeeman resolved spectroscopy provides an unambiguous determination of both the sign and magnitude of P. One major drawback to this technique is that it requires a high quality tunnel junction with a well formed tunneling barrier on an ultra-thin Al electrode which is often diﬃcult to achieve on many materials.

3.3 Andreev Reﬂection Spectroscopy

3.3.1 Developement

Andreev reflection spectroscopy (ARS) uses a unique conduction process at a superconductor/ferromagnetic interface to determine the magnitude of P. Andreev reflection (AR) is the process in which an electron in a normal metal at a S/N interface pairs with an electron of opposite spin and momentum in order to form a Cooper pair and enter the superconducting condensate at the other side of the interface, doubling the subgap electrical conduction of the system. A hole is then retro reflected into the normal metal in order to conserve charge, spin and momentum. Blonder, Tinkham and Klapwijk (BTK) [42] developed a theory that incorporates the effects of all transport processes (AR, normal reflection, and single particle tunneling) and an interfacial barrier of arbitrary strength. The interfacial barrier is modeled by a δ-function scattering potential at the normal metal/superconductor interface. In the metallic limit the barrier height is zero, no scattering occurs and all incoming particles with energies below

20 Figure 3.6: Energy vs momentum diagram taken from Ref [42]. Open circles denote holes, solid circles denote electrons, and the arrows indicate group velocity. Starting with an incident electron with momentum q+ (0), the possible transmitted (2,4) and reﬂected particles (5,6) are diagrammed.

Table 3.3: Probabilities for transmission and reﬂection at the interface of an S/NM for both above and below gap regions from the original BTK model [42] (γ2 = [u2 + Z2(u2 v2)]2 0 0 − 0 2 2 1 E2−∆2 and u0 =1 v0 = (1 + 2 )) − 2 q E

A B C D

∆ E < ∆ 2 2 2 2 2 1 - A 0 0 | | E −(∆ −E )(1+2Z )

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 u0v0 (u0−v0 ) Z (1+Z ) u0(u0−v0 ) (1+Z ) u0(u0−v0 ) Z E > ∆ 2 2 2 2 | | γ γ γ γ

∆ are transmitted as Cooper pairs through AR, while in the tunneling limit the barrier height becomes infinitely large so that AR becomes forbidden, and tunneling through the barrier becomes the only possible mechanism for a quasi-particle to be transmitted across the barrier. BTK theory introduces a dimensionless parameter Z to characterize the interfacial scattering strength, defined by Z = H ~/vF which includes the band structure effects (Fermi velocity and effective mass mismatches, etc) as well as that of a physical barrier of height H. The extremes of this barrier are the metallic limit, Z = 0, and the tunneling limit, Z = . ∞ The BTK model identifies four processes, illustrated in Fig 3.6 that can occur at a S/NM

21 interface: Andreev reﬂection (A), normal reﬂection (B), transmission with branch crossing (C), and transmission without branch crossing (D). The probabilities of these processes are determined from the Bogoluibov transport equations [43] which are shown in Table 3.3 for both above and below gap regions. The current is then computed from these probabilities weighted by the Fermi-Dirac function, f(E), at a given temperature T:

I =2eANvF f(E eV )[1 A(E) B(E)] + f(E)[C(E)+ D(E)] dE (3.9) Z { − − − } where A is a geometrical factor and N refers to the single particle DOS. The conservation of probability (A + B + C + D = 1), allows us to rewrite this as

I =2eANvF (f(E V ) f(E))(1 + A(E) B(E)) dE (3.10) Z − − − This model has since been modiﬁed to include the eﬀects of an S/FM junction [35, 44].

This is done through a two current model, one spin polarized (Ip) and one unpolarized (Iu), where the total current is given by

I = (1 P )I + P I . (3.11) t −| | u | | p

Iu behaves exactly as described in the BTK model. However, with Ip the imbalance of carriers of a particular spin of the FM results in some electrons not being able to pair with electrons of opposite spin, suppressing Andreev reflection (forcing Ap = 0). These effects are illustrated in Fig 3.7. In the limit of Z = 0, P can be simply determined from the zero | | bias conductance by the suppression of Andreev reflection by: G(0) = 2(1 P ) (3.12) GN −| | However at finite Z the entire conductance spectrum must be fit to extract P . | | 3.3.2 PCAR

As the BTK model was developed in the limit of a point contact, ARS was first implemented [35, 44, 36, 45] as point contact Andreev reflection (PCAR). In the method a superconducting (ferromagnetic) tip is brought into contact with a ferromagnetic (superconducting) film. The point contacts are made by either nano-patterning techniques, or more commonly by mechannical means, which provides for a method to vary Z within a single sample.

22 Figure 3.7: (a) AR process at a normal metal/superconductor interface where an incident electron with E < ∆ pairs with an electron of opposite spin to form a Cooper pair, reflecting a hole and doubling| | the conductance. (b) AR in a ferromagnet/superconductor (P = 75%) where the same incident electron finds no opposite spin to pair with, is normally reflected and decreases the conductance enhancement.

However there remains several limitations and unresolved issues with PCAR. First, a point contact typically does not represent an interface in a realistic device structure, while the magnitude and even the sign of P is known to depend on the nature of the interface [46]. Furthermore, the fitting of the PCAR measurement often requires an artificially large spectral broadening [47] (or equivalently, the use of a temperature in the Fermi function much greater than the actual measurement temperature), and sometimes superconducting gaps much different from the expected values [36, 45, 47]. Finally there are ubiquitous observations of a precipitous decline of measured P with increasing Z in a variety of systems [36, 45, 48, 49], which remain unexplained.

3.3.3 Parameterization of Z

The Z parameter as used in the BTK model originally was developed in a point contact geometry in which the contact size was smaller than any other scattering length in the system to ensure ballistic transport. From the point contact limit the normal state resistance is just

23 the spreading resistance, or the Sharvin [50] resistance of the contact given by

1+ Z2 RN = 2 (3.13) 2N(0)e vF A where here A is the effective area of the junction (which is not necessarily the cross sectional area of the junction). The characterization of the barrier by Z has since been extended to other configurations such as planar junctions [51]. It should be noted in extending the application of ARS beyond the original point geometry, the Z parameter is treated as a phenomenological parameter which has no direct physical interpretation. This phenomenological treatment is consistent with theoretical work which interprets Z in different transport regimes and non ideal barrier situations [48]. However, as the original BTK model was worked out for a point contact, many workers [52] have come to believe that this model is only applicable in the point contact configuration and only when transport is in the ballistic regime. Despite these objections, during the course of this work, ARS was successfully applied to many planar junction systems, including but not limited to: GaMnAs/Ga structures discussed in Chapter 4, Al/AlOx/EuS structures discussed in Chapter 5 and Al/AlOx/Py as well as Al/AlOx/EuS structures as plotted in Fig 3.8. In fact, in most of these applications, the conductance spectra can be fit to the modified BTK model straight-forwardly, with no spectral broadening and always using the expected gap values. As another confirmation of the success of the application of ARS in the planar configuration is that in point contact measurements there is a widely reported systematic decrease of measured P with increases Z values, which has not been observed in planar junction measurements. As mentioned earlier the Z parameter also includes band structure effects. A mismatch between the Fermi velocities of the two materials, even in the case of the absence of a physical barrier, can result in a finite Z value. Blonder and Tinkham [53] proposed that the effect of a Fermi velocity mismatch is to introduce an effective Z (Zeff ) which differs from the Z resulting from a physical barrier (Zphy) by

(1 r)2 Z = Z2 + − (3.14) eff r phy 4r where r is the ratio of the two Fermi velocities (note that an identical Zeff is obtained regardless if r = v1F /v2F or r = v2F /v1F is used). In contrast to this work by Zutic

1.8 Al/Al O /NiFe 2 3 Al/Al O /EuS 1.6 Fit ∆ = 220 µV, 2 3 Z = 1.4, P = 28% Fit ∆ = 220 µV, Z = 0.98, P = 74% 1.4

1.2

1.0 N

0.8 G(V)/G 0.6

0.4

0.2

0.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 V (mV) V (mV)

Figure 3.8: Spin-polarized BTK model applied in planar conﬁguration on (a) Al/Al2O3/NiFe and (b) Al/Al2O3/EuS structures with intermediate to high Z values.

and Valls [54] on Fm/S systems as well as by Zutic and Das Sarma [55] on ferromagnetic semiconductor/S systems have shown that the spin polarization as well as the nature of the materials plays a large role in the transmission probabilities of quasi-particles, indicating that the effects of the Fermi velocity mismatch can not be completely accounted for by Eq 3.14. While ARS is valid over the whole gamut Z, the analysis becomes more diffuicult in the high Z limit. In the low Z limit, Z 0, the effects of P and Z are easily distinguishable ∼ as each has a considerable effect on the shape of the conductance spectrum. However as Z increases, the spin independent tunneling process become dominant, which easily masks the effects of P. Also any inelastic scattering processes in the barrier will act to broaden and reduce the height of the peaks in the conductance spectra at ∆, which in the high Z ± limit may become comparable to the effects of P. Dynes et al. [56] introduced an inelastic scattering parameter in which the quasi-particle energy E in the BCS DOS (Eq 3.1) adopts a phase factor associated with inelastic scattering, specifically E E + iΓ. Fig 3.9 shows the → BTK fit and Dynes model fit for a high-Z value junction of CrO2 [40]. Clearly, the modified BTK theory based on AR produces a better fit to the data. Nevertheless, the closeness of the two types of fits in Fig 3.9 implies that the interpretation of data from high-Z junctions requires extra caution and the extraction of P from the zero-field conductance becomes increasingly unreliable as Z increases. In order to extract P reliably for high-Z junctions

25 Figure 3.9: (Top) ARS applied to CrO2 in the (a) high Z and (b) low Z limits from both consistent with the predicted half-metal P. (Bottom) High Z CrO2 junction ﬁtted to BTK (left) and an inelastic scattering model (right). Adapted from [40]

beyond ambiguity, it becomes necessary to Zeeman-split the superconducting DOS. ARS is a convenient and rather flexible tool to determine spin polarization. However it is limited in that ARS is insensitive to the sign of P and can only measure the magnitude of P. Also as pointed out previously, in the high Z limit, while ARS is still a valid model the effects of P become less noticeable, making the analysis more difficult. The desire to provide a model with the wide range of flexibility of ARS and the umabiguity of the Zeeman resolved tunnel junctions directly led to the development of the Zeeman resolved Andreev spectroscopy described below.

26 3.4 Zeeman Resolved Andreev Contacts

3.4.1 Introduction

With an understanding of the advantages and limitations of both ARS and Zeeman resolved tunneling, the need for a new method that combines their strengths and removes the limitations can be imagined. The Zeeman resolved tunnel junctions provide an unambiguous determination of the spin polarization and is sensitive to the sign of P, but it has the drawback that it requires the use of a high quality tunnel junction which is often difficult to achieve. ARS has the advantage that it works with an arbitrary barrier between the S/FM interface but can only measure the magnitude of P and becomes less useful in the high Z limit. Thus it would be useful to have a method which has the unambiguousness of the Zeeman resolved structures and is suitable for an arbitrary barrier strength that spans the entire gamut from metallic to tunneling contacts. Recently a model [57] has been developed that provides these advantages. Similar to the BTK model, the probabilities of A, B, C, D are obtained in the presence of a magnetic field by using the Maki-Fulde equations (Eq 3.2) to solve for the spin dependent DOS and applying the Bogoliubov transformations. It is important to note that, while this model may seem to depend on many parameters (b, ζ, Z, H, T , and P), P is in actuality the only free parameter. H and T are experimentally set and not varied (as in contrast to some models in which T is varied as an effective temperature in order to make accurate fits [36]). The parameters b and ζ are severely constrained by the material used (Al) and the magnitude of the applied field. Z is determined from the zero field conductance spectrum and is left constant in the non-zero field fits. This leaves P as the only freely adjustable parameter in the fits. The complexity of Zeeman-split conductance curves further ensures the unique determination of the parameters.

3.4.2 Work to date

Several years of this work was dedicated to the experimental realization of the Zeeman resolved Andreev contacts in order to facilitate a direct comparison with the theory, the results of which have been mixed. However it is worthwhile to discuss the entirity of the work done to realize Zeeman resolved Andreev contacts, speciﬁcally the experimental complications and what we have learned from them.

27 Figure 3.10: (a) Conductance spectra for a CrO2/Al junction at several fields, adopted from [40]. The effect of the field merely shifts the spectra in energy implying P = 100%. (b) Zeeman split Andreev conductance model applied to the B = 2.5 T curve from (a), confirming the expected high P.

Low Z Junctions

The first direction taken to demonstrate Zeeman resolved Andreev contacts was in the case of Z 0, which has previously never been field-split and only measured with zero-field ARS. ∼ Both sputtering and evaporation techniques were used to grow a thin layer, 100-200 A,˚ of Al. The layer was briefly (< 2 minutes) exposed to air as it was transfered to a sputtering system to deposit the FM (Co or Ni79Fe21) electrode. The barrier achieved in this method was inconsistent between growths, sometimes demonstrating an undesired barrier and sometimes a metallic contact. Since the FM layer was thought to oxidize much less rapidly than Al, samples were also grown with the FM at the bottom, which consistently yielded low resistance metallic contacts. In all cases when the junction resistance was low (less than 1Ω) many strange effects occurred. The effects were similar if not identical in numerous samples grown in different ways, which suggested this to be some sort of universal phenomena that is occurring in these systems due to the low junction resistances. Normally, at the temperature that corresponds to the Tc of the superconducting film, the junction resistance is either expected to increase rapidly with decreasing T if the transport is dominated by tunneling processes due to the lack of subgap states in the superconductor, or to decrease if dominated by Andreev reflection. However in these low resistance samples at Tc there appears to be a spontaneous reversal of current direction, which clearly is an artificial phenomenon. In an AC measurement the magnitude of the signal quickly reduces to zero where the phase spontaneously shifts by 180◦, and signal quickly increases again. Fig 3.11(a) shows this effect

25 25 (a) 0

-25 20 0 ) Ω -50 10 ׉

Ω 0

R (m R -75 R (m R -10 -25 -100 -20 G(V)/G(1.0 mV) G(V)/G(1.0

-125 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Temperature (K) (b) -150 -50 0 100 200 300 -1.0 -0.5 0.0 0.5 1.0 Temperature (K) V (mV)

Figure 3.11: (a) An AC, four terminal R vs T (see Appendix B) of a typical low resistance ◦ junction showing a large spontaneous 180 phase shift at Tc, the inset shows a close-up view of the area covered by the dotted circle. (b) Conductance spectra of the junction showed in (a) at T = 360mK, demonstrating the switching of direction of both the AC signal and DC signal simultaneously.

at Tc for a typical sample. Also in a DC measurement the voltage spontaneously switches direction relative to the current resulting in an apparent negative resistance. Fig 3.11(b) is a plot of the AC conductance versus a DC applied bias, which simultaneoulsy demonstrates the observed reversal of voltage in both the AC and DC measurements. These eﬀects were eventually attributed to current crowding eﬀects.

Current Crowding

Current crowding is a spurious potential drop that results from inhomogeneous current distributions in the junction. The idealized picture can be thought of in the following way; in a true four terminal measurement, the potential leads themselves carry no current and lie on equipotential lines, which result in no potential drop from the leads themselves. However, in the pseudo four terminal measurements that are traditionally made on these structures the changing direction of the current results in a bending of the equipotential lines, which results

29 V-

a) V+ V- b)

I + V+ I + I -

I -

Figure 3.12: (a) Diagram of a ideal four terminal measurement with the black lines indicating the current ﬂow and the dotted lines representing the equipotential lines. (b) An over simplized cartoon of the current ﬂow in a psuedo four terminal measurement from a cross stripe geometry in which the potential leads no longer lie on equipotential lines

in the potential leads themselves not being equipotentials themselves anymore and having artificial potential drops across them. These situations are illustrated in Fig 3.12. This effect was treated in great detail in MTJ systems where it was first observed as a lower than expected TMR and occasionally a negative resistance value. This originally was thought to occur from contact resistance resulting from the sheet resistance of the electrodes. However a complete description of current crowding effects generally require finite element analysis, which is highly geometry dependent, but the general result shows that the resistance x area (RA) product should be much greater than the sheet resistance (R/ where represents a single square of material) of the electrodes. For specific geometries 1D and 2D analytical solutions have been developed. Of particular interest is the work by Chen et al. [58] which presents a 2D analytical model under the assumptions that the electrodes lengths and widths are at least a factor of 10 larger than the junctions, as in the case of the photolithography defined junctions describe later. Shown in Fig 3.13, in this limit the equipotential lines are cyldrically symmetric despite the junction being square, allowing the cross stripe to be rotated to a parallel configuration without loss of generality. The most important observation −1 is in the small junction limit, the junction resistance is proportional to Ajuncion while the 1 − 2 resistance associated with the current crowding is proportional to ln(Ajunction), regardless of the sheet resistance of the electrodes. In theory, with small enough junction areas the

30 Figure 3.13: Rotated picture of cross stripe depicting the equipotential lines expected in the small junction area limit. Figure taken from [59].

eﬀects of current crowding can be neglected, driving the motivation behind optically deﬁned contacts.

Optically Deﬁned Andreev contacts

As pointed out in the previous section, reducing the area of the junction relative to the contact provides a method to reduce current crowding effects. The smallest structures that can be made with shadow mask techniques are on the order of 100µm x 100µm, however photolithography lends the ability to make structures down to 1µm2 scale (see Appendix A for description). A photo-definable polyimide (PI) material is used to make junctions on the order of 10 µm x 10 µm, due to the fact that the PI is itself an excellent insulator and that after development there are only smooth features left behind which will not lead to discontinuities in deposited thin films. However an incompatibility in the development process makes these devices difficult to pattern in that the developing solution for the PI also quickly etches Al. This results in a small window of time between underdeveloped, and overdeveloped. The solution here may be to intentionally underdevelop the samples and then use an oxygen plasma to etch away the excess PI material. This process would also inadvertently introduce an oxide barrier in the Al formed by the energized oxygen plasma. The other option is for the FM layer to be grown at the bottom which will not be affected by the developer and then either deposit a thin Al electrode, or deposit a thin Al layer to be oxidized as a barrier and then have a thin Al electrode placed on top.

31 High Z Junctions

As mentioned in the previous section the problem of current crowding can be circumvented by having a high junction resistance (as compared to lead resistance). One way to increase the junction resistance is to increase the barrier thickness. This led to the fabrication of junctions with high Z, which are not necessarily in the tunneling limit. Again, bottom electrodes of Al were deposited by both thermal evaporation and sputtering techniques. From studies on MTJ barrier formation [41] the oxidation rate and barrier quality depend strongly on the exact growth conditions and smoothness of the Al films. In the case of thermally evaporated Al thin films, a smoother film can be achieved by evaporating at slow rates of by lowering the substrate temperature during growth. In the case of sputtered Al thin films, smoother films are generally achieved in literature by ion etching techniques or by introducing a small amount of metallic dopant, the latter being the method used during this study. It has been well established in the semiconductor industry that a small amount of Cu or Si (in our case 2% by weight) in the Al target can produce smoother Al films. In Zeeman resolved tunnel junction studies, Al(Si) or Al(Cu) were generally used as buffer layers onto which a layer of pure Al was grown and oxidized. It has also been shown that electrodes made entirely of Al(Si) also make good tunnel junctions after oxidation. In order to demonstrate that Al(Si) was a suitable candidate for use in this study, S/I/S´ junctions made of Al(Si)/AlOx/Pb were grown. First a 30 nm layer of Al(Si) was sputtered onto an Si(001) substrate, exposed to air for approximately 10 mintues and then a 500 nm layer of Pb evaporated as the top electrode. The conductance curves were measured in a modulated current 4 terminal AC configuration (see Appendix B), which showed excellent tunneling properties when the temperature was between the Tc(Al) and

Tc(Pb) and also exhibited signatures of S/I/S´ junctions when below Tc(Al).

Next the AlOx barrier was formed, which was generally done by natural oxidation due to lack of other available methods. The best results were found when the film was removed from the deposition chamber and placed in a separate chamber which was then evacuated and back filled with several 100 Torr of pure O2. It was found that with lower O2 pressures it was difficult to produce useful junctions. Other techniques explored during this work was using an oxygen plasma formed in a reactive ion etcher, but it was found difficult to control since the high energy oxygen atoms etched away the Al layer at the same time as oxidizing

32 it. Finally the FM layer (Py or Co in this case) was sputtered as the top electrode. Evaporated materials such as Ag and Au were found to trivially form tunnel junctions while sputtered FM often shorted through the barrier. This is believed to be because of the relatively high energies of the sputter deposited materials ( 10eV for sputtered materials ∼ and 1eV for evaporated materials). To solve this problem, the FM was sputtered at lower ∼ powers ( 20W) and higher pressures (7-10 mTorr) which reduces the initial sputtered energy ∼ and increases the scattering rate which acts to lower the incident energy. While this helps prevent the FM material from puncturing the barrier, the sputter rate for these ﬁlms was very slow and often diﬃcult to get a low resistance electrode. This is why the FM was generally deposited about 20 nm thick and then an Au top layer was evaporated in order to provide a lower resistance electrode.

3.4.3 Future Directions

The Zeeman resolved ARS model has to date only been applied in the high Z limit, where it has been able to provided excellent fits to the data. The lower Z values have yet to be successfully explored due to the problematic current crowding effect. This is why the exploration of the optically defined junction areas is of great importance in the immediate future. Another tool that would provide a great advantage in the goals of achieving intermediate Z values is the use of an in situ non local plasma source for forming oxide barriers that would create oxygen ions of low enough energy as not to etch the surface.

33 CHAPTER 4

Spin Polarization of (Ga,Mn)As

4.1 Background

4.1.1 Introduction

Ga1−xMnxAs is a “canonical” ferromagnetic semiconductor that remains the most thoroughly studied of all such materials [59]. Recent experiments demonstrate that the Curie temperature (TC ) of this material can be as high as 150 K or more [60, 61], showing promise for possible room temperature technological relevance. Ga1−xMnxAs is believed to be able to provide a high P while having a conductivity comparable to a conventional semiconductor, meeting the criteria outlined in Sect 2.3.

4.1.2 Structure

Ga1−xMnxAs has a zinc-blende crystal structure as shown in Fig 4.1. The extracted lattice parameters indicated a linear dependence on Mn doping (a = 5.66(1 - x) + 5.98x)A[˚ 62, 63]. The Mn can ideally enter the lattice as a substitutional dopant, where the Mn2+ directly replaces a Ga3+ atom and acts as an acceptor. It can also enter as an interstitial, where it acts as a double donor, compensating the holes provided by the acceptor sites. The TC of these ﬁlms has been shown to increase with the reduction of interstitial Mn sites, which can be minimized by growth conditions or annealing [64].

4.1.3 Magnetic/Electrical Properties

The appearance of ferromagnetism in Ga1−xMnxAs is related to the magnetic exchange interaction mediated by carriers. This relation is evident in the fact that the TC depends directly of the free hole concentration [60] (roughly T p1/3). It is widely believed the C ∼

34 Figure 4.1: Zinc-Blende structure of Ga1−xMnxAs with lattice constants a, b, and c.

carrier mediated ordering of the local Mn spins arises form a Ruderman-Kittel-Kasuya- Yosida (RKKY) interaction [65] or indirect exchange mechanisms such as double and super exchange [66]. The work by Dietl et al. [67] based on a double exchange mechanism was able to describe the magnetic and electrical behavior of Ga1−xMnxAs and predicted the behavior in other II-VI systems.

4.1.4 Implied Polarization

The large tunneling magneto-resistance observed in magnetic tunnel junctions derived from this material implies that P may be large even for small Mn concentrations [68, 69]; this is consistent with band structure calculations that predicted P = 100% for x 0.125 [70] and ≥ indicate P is still near 100% for x = 6.3%.[71] However, there have been no direct electrical measurements of P for this important material. The central result of this project is such a measurement using ARS in Ga0.95Mn0.05As/Ga junctions. 4.2 Sample Fabrication

An extensive range of samples were fabricated for the purposes of this study. These include:

(a) superconductor/ ferromagnetic semiconductor (S/FS) junctions made entirely in situ under ultrahigh vacuum (UHV) conditions by depositing the superconductor electrode

(Ga, Al, or Zn) immediately after the Ga1−xMnxAs growth

35 (b) S/FS junctions made by transferring As-passivated Ga1−xMnxAs epilayers to an ex situ vacuum system for the deposition of the superconductor after desorption of the As cap layer

deposition of a thin layer of Al which was oxidized via exposure to O2, before the deposition of an Al or Pb layer

(d) S/I/FS junctions similar to (c), but where the Ga1−xMnxAs epilayer was exposed to an oxygen plasma before the deposition of the Al or Pb layer

(e) in situ grown Ga1−xMnxAs/AlAs/Al tunnel junctions wherein AlAs serves as a tunnel barrier

(f) ex situ grown Ga1−xMnxAs/AlAs/Pb, with the superconductor as in (b)

As discussed later, we ﬁnd that spin polarization measurements for these systems are extremely sensitive to the details of the interfaces. Hence, we focus on the in situ fabricated

Ga1−xMnxAs/Ga junctions since these high transparency junctions exhibit the clearest conductance spectra, that indicates high P for Ga0.95Mn0.05As.

The Ga1−xMnxAs/Ga junctions demonstrated in Fig 4.3 were fabricated as follows: ﬁrst, a 20 nm thick, p-doped GaAs:Mn buﬀer layer was grown on a heavily p-doped (001) GaAs:Zn substrate using molecular beam epitaxy (MBE) under standard conditions for high quality

GaAs growth. A Ga − Mn As epilayer (typically around 100 nm thick and with x 0.05) was 1 x x ∼ then grown by low-temperature MBE (T 250◦C) using growth conditions described substrate ∼ elsewhere. The as-gown GaMnAs ﬁlm has a T 65 K, as shown in Fig 4.2. Immediately C ∼ ◦ after the Ga0.95Mn0.05As growth, the substrate temperature was lowered to 10 C and a thick layer (> 500nm) of Ga was deposited under UHV conditions in the same MBE chamber.

4.3 Experiment

The conductance spectra of the samples were measured with a contact conﬁguration as depicted schematically in Fig 4.3, using phase-sensitive detection in a 3He cryostat (see Appendix for a detailed description). Two of the contacts were made on the conducting substrate, while the other two contacts were made on top of the Ga electrode. This setup,

36 Figure 4.2: M versus T of a Ga0.95Mn0.05As ﬁlm used in this study showing a TC of 65K.

Figure 4.3: Schematical diagram of the Ga0.95Mn0.05As structure and contact setup.

instead of the cross-stripe geometry, was used to circumvent the current crowding problem due to the relatively high sheet resistance of the Ga1−xMnxAs compared to the low junction resistance. Fig 4.4 shows the normalized conductance as a function of bias voltage taken at 370 mK for two Ga0.95Mn0.05As/Ga junctions from the same growth. At ﬁrst glance, this conductance spectrum is typical of that for a high transparency metallic contact between a superconductor and a ferromagnet with high P; the conductance peaks at ∆ corresponding ± to quasiparticle tunneling are completely absent. On the other hand, the subgap conductance is suppressed, instead of enhanced, from GN due to the large imbalance of spin populations in the ferromagnet. Using Eq. 3.12 the data in Fig 4.4 yields a spin polarization of 90% for this Ga1−xMnxAs sample. However, several aspects of the data warrant further analysis.

1.2

1.0

0.8 N 0.6 /G

) V (

G 0.4

G(0) = 0.3 G(0) = 0.2 0.2

0.0 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 V (mV) V (mV)

Figure 4.4: Normalized conductance spectra of two Ga0.95Mn0.05As samples from the same growth.

4.4 Analysis

Although the conductance spectrum resembles that from a metallic S/Fm contact, the entire spectrum cannot be ﬁt straightforwardly to the modiﬁed BTK theory. Moreover, the approximate energy gap for Ga inferred from the shoulders of the spectrum is 1.4 ∼ meV, which corresponds to a Tc much higher than the Tc for bulk crystalline Ga (1.1 K).

These discrepancies can be explained with a distribution of the energy gap and Tc in the

Ga film. It is known that several phases of Ga have Tc substantially higher than 1.1 K, and amorphous thin films of Ga have been found to have Tc as high as 8.4 K.[72] The Ga film in our device was grown at a low temperature of 10◦C and has a granular morphology. It is probable that differences in grain size and crystallinity may result in local variations of

Tc and energy gap in the film. Fits of the conductance spectra to the modified BTK theory were made by including a distribution of energy gaps in the superconductor. Fig 4.6 shows the results of such a fit for two junctions from the same growth. Clearly, excellent fits are obtained for both samples. More importantly, an identical distribution is used in both fits.

Further validating the distribution in Tc, the resistance versus temperature of the samples showed signiﬁcant decrease of resistance well above the expected Tc of 1.1K. Shown in Fig 4.5

1.0 0.8 N 0.6

G(0)/G 0.4 0.2 0.0 0 2 4 6 8 10 Temperature(K)

Figure 4.5: Resistance versus temperature of the P = 85% sample, clearly showing an enchancement in Tc

is the resistance versus temperature for the P = 85% sample; it is important to note that the measurement perform was not able to give an accurate measurement of temperature between 1.5 and 10K, and unfortuneately the sample was altered during annealing before a more accurate measurement could be performed. The distribution was created as an ad hoc weighting and reflects that significant portions of the Ga film have Tc around 1.1K and

8.4K, and less with intermediate TC values. The ﬁts resulted in Z values close to zero and P of 85% and 90% respectively, consistent with values calculated from G(0). Another complication in analyzing the conductance spectra of a S/FS junction lies in the large mismatch in the Fermi velocity always present between a semiconductor and a metal. In the BTK model, the eﬀect of the Fermi velocity mismatch can be included in the parameter Z which measures the overall interfacial scattering strength. It is therefore quite a surprise that we were able to obtain an apparent Z of 0. Under the conditions used in the

MBE growth of our samples, Ga1−xMnxAs samples with x = 0.05 typically have a carrier 20 −3 (hole) density of 3 10 cm ; assuming that the (heavy) holes in Ga − Mn As have the ∼ × 1 x x same effective mass as in GaAs, we estimate a Fermi velocity of 4.6 105 m/s compared to × 2.0 106 m/s for Ga. Such a large mismatch should result in a substantial Z even in the × absence of any physical barrier at the interface. Zutićand˘ Das Sarma [73] generalized the BTK analysis, specifically applying to superconductor/semiconductor junctions, by

1.0

0.8 N 0.6

0.4 G(V)/G P=85% 0.2 P=90% Z=0.15 Z=0.05 0.0 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 V(mV) V(mV)

Figure 4.6: Conductance spectra of the Ga0.95Mn0.05As samples (red) along with the ﬁts provided using a weighted BTK model (blue).

separating the effects of the physical barrier (potential scattering) and the mismatches in effective mass and Fermi velocity between the superconductor and the semiconductor. This findings are illustrated in Fig 4.7. Indeed, they found that these mismatches lead to much decreased junction transparency for a superconductor/conventional semiconductor contact, signified by a substantial decrease of G(0) from 2G and pronounced peaks at ∆ N ± in the conductance spectrum even when the interfacial potential scattering is completely absent (Zσ = 0). However, in a ferromagnetic semiconductor, the spin polarization actually enhances junction transparency. Specifically, the conductance peaks at ∆ from the Fermi ± velocity mismatch can be completely suppressed by a moderate spin polarization in the FS. In contrast, the conductance peaks at ∆ due to potential scattering are not affected by ± the spin polarization. Therefore, the complete absence of any peaks at ∆ in our data is ± consistent with high transparency of the Ga1−xMnxAs/Ga interface (Zσ = 0) and high spin polarization for the Ga1−xMnxAs. According to Ref[55], the increase of P in the FS also results in a consistent decrease in G(0). Hence G(0) is still a good measure of the spin polarization in high transparency S/Sm junctions. In fact, our calculation from Eq. 3.12 may represent a conservative estimate of the spin polarization for Ga1−xMnxAs.

40 Figure 4.7: Conductance spectrum taken from [55] shown for a BTK model modified to separate physical scattering effects and effects from Fermi velocity mismatch. Zσ represents the amount of potential scattering, F represents spin-flip scattering, and X is a measure of the spin splitting energy which gives good indication of P.

It is also somewhat surprising that we were able to obtain Ga1−xMnxAs/Ga junctions with essentially no interfacial barrier considering the large diﬀerences in carrier density. On the other hand, the experience in our laboratory has shown that ohmic contacts can be readily made on Ga1−xMnxAs with several diﬀerent types of metallization. I-V measurements of the junctions at temperatures above Tc of Ga showed strictly linear behavior.

Finally, it is known that the holes in Ga1−xMnxAs responsible for the ferromagnetic interaction between the local Mn moments suffer strong spin-orbit scattering. This might lead one to conclude that high spin polarization for the conducting holes would not be possible in this material, which is apparently in contradiction to the experimental results reported here and elsewhere [68]. The key to understanding this lies in the large spontaneous spin splitting of the valence band in Ga1−xMnxAs. Using a mean field model, Dietl et al. [74] showed that the destructive effect of the spin-orbit coupling is quickly diminished with increasing band splitting (see Fig 4.8), which was measured to be at least 44 meV at low temperatures by resonant tunneling spectroscopy for x = 0.035 [75], which is in agreement with our observations on Ga0.95Mn0.05As.

41 Figure 4.8: Theoretical prediction of GaMnAs spin polarization vs band splitting for diﬀerent hole concentrations, taken from [73].

4.5 Interface Sensitivity

While the intrinsic spin polarization for Ga0.95Mn0.05As inferred from our experiments is close to 100%, we found that it is extremely difficult to maintain this high spin polarization at many types of GaMnAs/metal interfaces. In fact, in many cases we failed to see any signatures in the conductance spectra related to superconductivity in the counter electrode, a phenomenon also observed by others in similar setups.[76] Moreover, we have examined the effect of annealing on the Ga1−xMnxAs/Ga junctions that did yield high P; even a very mild vacuum annealing at 100◦C resulted in a significant deterioration of the conductance spectrum and spin polarization, as shown in Fig 4.9. The spin polarization of Ga1−xMnxAs at its surface appears to be extremely sensitive to the nature and quality of the interface.

4.6 Conclusions

To summarize this work, we have carried out a series of experiments to directly measure the spin polarization of the ferromagnetic semiconductor Ga1−xMnxAs. Andreev reﬂection spectroscopy from high transparency Ga0.95Mn0.05As/Ga junctions consistently yielded a spin polarization greater than 85% for Ga0.95Mn0.05As. We believe that this may represent a lower limit of the intrinsic spin polarization for this material because of the diﬃculties in

42 Figure 4.9: After mild annealing, the conductance spectrum of the P = 85% samples signiﬁcantly changes, indicating a smaller P value. (Pre-anneal in black, post-anneal in red)

maintaining the high spin polarization at the interface with the superconducting metals in a planar junction device structure. The apparently high interfacial sensitivity may pose a challenge in constructing spintronics devices using Ga1−xMnxAs.

43 CHAPTER 5

Spin Polarization of EuS

5.1 Introduction

Another class of magnetic semiconductor materials which have been actively pursued to overcome the conductivity mismatch problem described in Section 2 are the Eu chalcogenides such as EuO and EuS. A considerable amount of work has been devoted to these systems since the 1960’s, primarily in bulk single crystal form, with their high magnetization and wide range of conductivity tunability being particularly appealing. These materials have been demonstrated as eﬀective spin ﬁlters [77, 78, 79] in the insulating state and as spin injectors when doped [80, 81], however the low TC (10-30K) makes these materials impractical for room temperature, real world devices, but make an ideal system for proof-of-concept semiconductor spintronic studies.

Figure 5.1: Rock salt crystal structure of EuS. The Eu-S distance is 2.98 A˚ and the Eu-Eu distance is 4.21 A.˚

44 Figure 5.2: (a) Magnetization versus temperature for several EuS ﬁlms grown at diﬀerent growth temperatures in which the higher growth temperatures lead to the stoichiometric limit. (b) Resistivity versus Temperature in which the resistance peak is shifted to higher temperatures with decreasing growth temperature

EuS is a prototypical concentrated ferromagnetic semiconductor and has a rock salt structure. The composition as well as magnetic, optical and transport properties of EuS films have been found to vary with choice of substrate [82], growth temperature [82, 83, 84, 85], and annealing [86]. In pure stoichiometric EuS the magnetic properties are due to the well- localized spins on the Eu2+ ions, while an indirect exchange occurs between the Eu2+ ions when charge carriers are present. Fig 5.2(a) plots the magnetization versus temperature of thin films of EuS grown at different temperatures, revealing that the higher growth temperatures provide more stoichiometric EuS films. With decreasing growth temperature, the TC increases and the ferromagnetic transition broadens, which are indicative of increasing carrier concentrations in the films. Similar trend in resistance versus temperature is shown in Fig 5.2(b) for several films with different growth temperatures, in which the resistance peak is shifted to higher temperatures with lower growth temperatures. Fig 5.3 plots the Hall data taken at 10K, which directly demonstrates an increase in carrier concentration with decreasing growth temperature. This variation in film conductivity and carrier density is likely due to increasing sulfur deficiency in the EuS films at decreasing growth temperature. The control of the growth temperature provides a way to tune the conductivity and magnetic properties of a film without extrinsic doping.

0 )

Ω -1 T = 10K -2 -3 -4 T : -5 Substrate o -6 (200 C) o -7 (100 C) -8 (34 o C)

Hall Resistance ( -9 012345678 B (T)

Figure 5.3: Hall data on EuS taken at 10K revealing an increase in carrier concentration with lower growth temperatures adopted from [85].

5.2 Sample Fabrication

The junctions used in this work were deposited on either Si (001) or glass coverslip (Corning) substrates, which had been prepared by rinsing with acetone, methonal, and finally isoproponal. A 0.4 mm wide stripe of Al was thermally deposited through shadow masking techniques to a thickness of 30-50 nm to serve as a low resistance lead to the EuS electrode. Next a 100 nm thick layer of EuS was deposited in a UHV electron beam evaporator at growth temperatures ranging from -2◦C to 120◦C to control the doping level of the film. Finally a 0.4 mm wide cross-stripe top electrode of Al was thermally deposited through a shadow mask. This structure is identical to the ones used in EuS/In Schottkey barrier studies [87] and the results can be directly compared. A sideview and top down illustration of these junctions is provided in Fig 5.4, with the contacts to the EuS labeled as golden circles. The effective area of these junctions, which is solely defined from the low resistance Al contacts, is 0.4 0.4 mm2 and the junction resistance varied from 3 to 15 kΩ. ×

46 Figure 5.4: EuS/Al junction structure shown from (a) the side view (b) top down view with contacts labeled as golden circles

5.3 Experiment and Analysis

Conductance spectra of the junctions were measured in a 3He system using standard phase- sensitive lock-in detection techniques (see Appendix B). Of particular importance to note is that in all of these measurements the bottom Al/EuS junction serves as a low resistance Ohmic contact and does not contribute appreciably to the measured junction resistance. This is verified by the fact that in the application of a magnetic field on the order of 1 kG, which is large enough to drive the bottom Al electrode normal but far below the critical field of the top Al electrode, there is little effect on the conductance spectrum. Also the I-V characteristics of the EuS/Al junctions at temperatures above the Tc of the top Al electrode show a linear behavior, which is in contrast to the EuS/In junctions, which show a highly nonlinear I-V typical of a Schottky barrier [87]. Shown in Fig 5.5 are the conductance, dI/dV, as a function of bias voltage V for four EuS/Al junctions of different barrier strengths in zero magnetic field. Each conductance spectrum is normalized by the corresponding one at a magnetic field above the critical field for the Al. Qualitatively these spectra are consistent, within the spin polarized BTK theory, with junctions of intermediate Z and large P for the Fm, as judged from the much diminished quasiparticle peaks near ∆, and the low subgap conductance. These features ± are in contrast to the case of pure tunneling in EuS/In junctions, shown in Fig 5.7 where a Schottky barrier is present [87]. Quantitatively, these spectra can be analyzed within the

1.2 (a) (b)

1.0

0.8 N

0.6

G(V)/G 0.4 Δ = 235 μeV Δ = 220 μeV Z = 0.65 Z = 0.56 0.2 P = 90% P = 83%

0.0 (c) 1.2 (d)

1.0

0.8 N

0.6

G(V)/G 0.4 Δ = 235 μeV Δ = 215 μeV Z = 0.85 Z = 0.98 0.2 P = 79% P = 76%

0.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 V (mV) V (mV)

Figure 5.5: Normalized conductance versus bias voltage curves spetra of Al/EuS junctions at a temperature of 0.38 K and zero magnetic field. The growth temperatures for EuS films are: (a) room temperature (34◦C); (b) -2◦C; (c) 34◦C and (d) 120 ◦C. The solid lines are the best fits to a modified BTK theory. The fitting parameters are indicated in the figures.

spin-polarized BTK model. Excellent fits with physically sound parameters are obtained, as shown in Fig 5.5. We emphasize that the fitting is always done in a straightforward manner and the only real adjustable fitting parameters are Z and P) T in all of the fits are the actual measurement temperature, no extra thermal broadening is necessary. This is strong evidence that Joule heating, magnetic pairing breaking and other inelastic effects are immeasurably small in these junctions; 2) The Al gaps used are between 0.215 meV and 0.245 meV, values expected of thin Al films. The small variation is most likely due to differences in the Al thickness; 3) The measured P show no decline with increasing Z within experimental uncertainty, as shown in Fig 5.6 in which we plot P from five such junctions as a function of Z. This is in comparison to the results from point contact ARS in many systems where substantial decline of P with Z was observed in a similar Z range [48]. The

100

P (%) 60

0 0.4 0.6 0.8 1.0 1.2 Z

Figure 5.6: The ﬁtted P as a function of Z for various Al/EuS junctions with diﬀerent EuS growth temperatures.

result indicates that there is no intrinsic increase of spin ﬂip scattering with Z in these planar S/Fm junctions. A more detailed analysis of the measured conductance spectrum and the resultant Z, P values for these Al/EuS junctions are presented below. In this work, EuS typically has a carrier (electron) density of 1020 cm−3 under the conditions used in the e-beam growth ∼ of these samples [79]. We estimate that vEuS/vAl = 0.1 (electron density of Al is 18 1022 F F ∼ × −3 cm ). From Eq 3.14 an Zeff ∼= 1.4 in the absence of any physical barrier at the interface is obtained. However, an oxide layer should be present on the EuS ﬁlm surface forming after the EuS growth, which would lead to a higher Z value for our Al/EuS junctions. In contrast, Z values of our Al/EuS junctions are in the range from 0.5-1.0, beyond the reach of the prediction of BTK model. The argument here is the same as in Section 4.4 in that the high spin polarization of EuS actually enhances the junction transparency, with all the observations in the conductance spectrum applying identically to the EuS case as in the

Ga0.95Mn0.05As case. The use of planar junction structure and thin Al electrodes allowed for the opportunity to Zeeman-split the SDOS and apply the Zeeman resolved ARS technique described in Section 3.4. Fig. 5.8(a) shows the conductance curves of the EuS/Al junction of Fig. 5.5(a) at in-

1.5

1.0 N

G(V)/G 0.5

T=380 mK BCS fitting

0.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Voltage (mV)

Figure 5.7: Graph of EuS/In junction demonstrating Schottkey barrier tunneling.

plane magnetic fields of 0.6 and 0.75 T. The Al electrode had to be made relatively thick (7-8 nm) since in this case it was grown on top of the EuS, which resulted in a critical field that was relatively low (<2 T) for these types of measurements. However, even these relatively low magnetic fields induce a sizable shift of the conductance curve to the left. With the exception of noticeable asymmetry near the peaks, there are no observable additional features due to the minority spins. Qualitatively, these observations indicate a large positive P for the doped EuS. The solid lines in Fig. 5.8(a) are the best fits to the data using the theoretical framework developed for Zeeman resolved ARS (Section 3.4). The fits yield P of 78% and 73% for applied fields of 0.6 T and 0.75 T, respectively. In the fits the following parameters are used: ζ = 0.10, b = 0.14 and effective magnetic field B∗ of 0.65 T and 0.63 T respectively. The parameter Z (0.65 in this case) is determined independently from the zero-field data [Fig 5.5(a)]. Although there are a number of parameters in the fitting, the complexity of the Zeeman-split conductance spectra makes the determination of the parameters highly unique and reliable. The necessity to use an effective magnetic field B∗ different from the applied field is readily apparent from the large shift of the conductance minimum from the zero bias. In ∗ Fig. 5.8(b) we plot B as a function of Ha (which are all greater than the saturation field of the EuS). These observations are consistent with the enhanced Zeeman splitting in junctions where the Al films were in direct contact with an insulating EuS barrier [78, 77]. This

1.25 (a)

1.00

N 0.75

0.50 G(V)/G

H =0.60 T, B*=1.25 T 0.25 a H =0.75 T, B*=1.38 T a 0.00 -0.8 -0.4 0.0 0.4 0.8 V -V (mV) Al EuS 2.0 (b) 1.5

1.0

B* (T) 0.5

0.0 0.0 0.2 0.4 0.6 0.8 1.0 H (T) a

Figure 5.8: (a) The conductance curves of the junction of Fig 5.5(a) at applied fields of 0.60 T and 0.75 T. The solid lines are the fits to the modified BTK theory with Maki’s density of states of Al. An orbital depairing ζ = 0.10 and spin-orbit interaction b = 0.14 are employed to fit to the data; (b) The enhanced exchange field B* as a function of applied field Ha.

enhanced Zeeman splitting originates from the exchange interaction of EuS on Al due to the intimate contact between them in these junctions. This is to be contrasted with the case of tunnel junctions where the Al is separated from the ferromagnet by a nonmagnetic insulator [33, 34]. This intimate contact also results in the large ζ and b compared to that in pure Al, similar to the much enhanced spin-orbit interaction in thin Al with heavy impurities such as rare earths [88, 89] and noble metal [37] on the surface. The P determined from the fittings is close to the value from zero-field ARS on the same junction, but there appears to be a small but systematic decrease of the measured P with increasing magnetic field. This decrease in P is beyond the experimental uncertainty and presently we do not have an explanation for

51 this observation. 5.4 Conclusions

In summary, we have performed a set of experiments to determine the spin polarization of the magnetic semiconductor EuS using Andreev reflection spectroscopy. Zero-field ARS on a series EuS/Al junctions of different barrier strengths consistently yielded conductance spectra that fit straightforwardly to the spin-polarized BTK model and P on the order of 80% for the naturally doped EuS, regardless of the barrier strength. Perhaps more importantly, we have for the first time realized ARS in a large Zeeman-splitting magnetic field in an S/Fm Andreev junction. The complex Zeeman-split spectra are well described via the Zeeman resolved Andreev contact technique. The zero-field results provided strong evidence for the applicability of the spin-polarized BTK model to ARS in planar S/Fm junctions and the validity of its application for the determination of the spin polarization of magnetic semiconductors. The Zeeman resolved ARS technique offered additional independent support for the conclusion. The high P in the doped EuS films makes them an attractive source of spin-polarized electrons in proof-of-concept spintronics studies.

52 CHAPTER 6

Spin Polarization Dependence on Barrier Thickness

6.1 Introduction

The Zeeman resolved ARS work described in section 3.4 led directly to a study of the effects on measured spin polarization with changing barrier thickness. Magnetic tunnel junctions (MTJ’s) have already shown usefulness as magnetic sensors and commercial applications like MRAM as discussed in section 2.2.3. It has been widely observed that the tunneling magneto resistance (TMR) in these structures shows a strong dependence on barrier thickness, attaining a peak value at some optimal thickness [90, 91], which was often attributed to the over- or under-oxidation of the oxide barrier. However in order to compete with modern electronics these structures need to have highly tunable resistances in order to impedance match existing electronic device components such as CMOS preamps. The MTJ’s resistance can be controlled by either scaling the junction area or the barrier thickness. Since device density controls the size of the junctions, the junction thickness is often the only variable. This makes finding an optimal trade off between TMR signal and acceptable resistance a major part of MTJ engineering. In this study we directly measured the effect of the barrier thickness on the spin polarization of a ferromagnet with superconducting spectroscopy.

6.2 Fabrication

The junctions investigated in this work were fabricated as follows: an Al ﬁlm of 40-45A˚ thick was ﬁrst thermally evaporated through a shadow mask on glass substrates, which was then transferred to a separate chamber to be naturally oxidized in pure O2. The oxidation was performed by controlling the oxidation time and O2 pressure. After oxidation, the sample was placed into a magnetron sputtering chamber with a base pressure in the 10−7 Torr range. A

53 Py cross stripe was then sputtered at low power (20 W) to a thickness of 600-800A.˚ Finally a 200-300A˚ layer of Au was thermally evaporated on the Py stripe to circumvent the relatively high sheet resistance of the thin Py ﬁlm (ρP y = 50 µΩ cm). In the fabrication of all the junctions studied the only parameter that was varied was the barrier thickness t, which was controlled by varying the oxidation. The junctions had areas of 0.1 x 0.1 mm2, which were well deﬁned by shadow masking. 6.3 Experiment and Analysis

Junction resistance R versus temperature T was monitored for all of the junctions investigated while cooling from room temperature. Shown in Fig 6.1 is the R(T) curve of a low resistance junction. Evidently, even this low resistance junction shows a weakly insulating behavior with a resistance ratio of R(T=4.5 K)/R(T=300K) 2.5, indicating a tunnel ∼ barrier without any metallic pinholes [92, 93]. To obtain the barrier thickness, we measured the current-voltage (I-V) characteristics at T=4.5 K. The zero-bias junction resistance is obtained by measuring the I-V curve in a small bias range, in which the I-V curves show Ohmic behavior. We assume that the barriers are simple rectangular potential barriers with a mean barrier height, then RC can be obtained by using the Simmons or Brinkman-Dynes- Rowell formula, in the limit of small bias voltage: [94]

t 1/2 R = RA =3.17 10−6( )e1.025tΦ , (6.1) C × Φ where RA is expressed in units of kΩµm2, Φ is in eV and t in A.˚ Values of Φ obtained from MTJs with similar barriers are in the range of 2-3 eV at room temperature [95, 96]. To compare directly with the MTJs, we used a barrier height of 2.5 eV for our AlOx barriers at

T=4.5 K. Using a value of 2.5 eV for Φ, RC is calculated and displayed in Fig 6.2 for each junction. Figure 6.2 shows the main results of this experiment. Tunneling conductance dI/dV versus bias voltage V for junctions with different barrier thicknesses were measured with standard ac-modulation technique listed in Appendix B at T=0.34 K in zero and finite magnetic fields. For all junctions, the conductance curves at zero field clearly reveal the superconducting energy gap of the Al, and the subgap conductance is near zero. All these are evidence of the high quality of the tunneling barrier in these junctions and that the transport across the barrier is dominated by elastic tunneling. Also shown in Fig 6.2 are

4 ) Ω

R ( 3

2 50 100 150 200 250 300 T (K)

Figure 6.1: The resistance of a Al/AlOx/Py/Au junction as a function of temperature. The barrier was formed by natural oxidization in O2 for 20 minutes at atmospheric pressure.

the conductance spectra in the presence of a magnetic ﬁeld. These Zeeman resolved tunnel junctions are analyzed using the Maki-Fulde theory outlined in section 3.2, using appropriate values for b and ξ. The exact values for P are extracted from the excellent ﬁts obtained.

For high resistance junctions, the extracted P is around 28%. With decreasing RC , P drops systematically, reaching a value of 13.5% with RC=56 kΩmum2 (t 8.5A).˚ The polarization ∼ is plotted as a function of the barrier thickness in Fig 6.3. The error bars for P are determined from the range of P that produce acceptable ﬁts to the curves the curves in Fig 6.2. It is obvious that the polarization begins to decrease drastically below 10.5A˚ of AlOx barrier thickness. To understand the reason for the decrease in spin polarization with the thinner tunneling barrier, a two current model is used which assumes that the tunneling current iT emitted from the ferromagnetic metal originates from two parallel channels of the localized 3d-like states (id) and the delocalized 4sp-like states (isp)[97, 98], i. e.,

iT = id + isp (6.2)

The tunneling current depends exponentially on the product of the tunneling barrier width and the square root of the mean barrier height, i exp[ (2t/~)(2m Φ)1/2] with d(sp) ∝ − d(sp) 55

2.0

1.5

1.0

0.5 RA=60 M Ω um 2 H=2.75 T P=0.275

0.02.0

1.5

1.0

0.5 RA=25.6 M Ω um 2 P=0.265 H=2.75 T

0.02.0

1.5

1.0

0.5 RA=900 k Ω um 2 P=0.23 H=2.75 T

2.00.0

1.5

1.0

0.5 2 RA=120 k Ω um P=0.15 H=2.5 T

2.00.0

1.5

1.0

RA=56 k Ω um 2 0.5 H=2.3 T P=0.135

0.0 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 Bias (mV)

Figure 6.2: Tunneling conductance dI/dV versus bias voltage V for junctions with different RA at base temperature T=0.34 K in zero field (filled symbols) and magnetic fields (open symbols). The solid curves are the fits to the data measured in the precense of a magnetic field using the Maki-Fulde theory outlined in section 3.2.

56 Figure 6.3: The extracted P versus the barrier thickness. The error bars for P are from the range in P which allowed for acceptable ﬁts to the curves the curves in Fig 6.2, and for t from the averaged barrier thickness of using 2.0 and 3.0 eV for barrier height [Eq. 6.1]. The solid line is the ﬁt to the data using Eq. 6.4.

−1 md(sp) being the effective mass of d-like (sp-like) electrons. The decay length κj for j=d(sp) is related to barrier height κ (2/~)(2m Φ)1/2 . Generally, 3d-like electrons are highly j ∝ d localized and have a large effective mass with a low Fermi velocity. In contrast, 4sp-like electrons are light and highly mobile with high Fermi velocity. Thus, it is expected, that the sp-like states, given their highly delocalized nature, contribute substantially to the tunneling current. On the other hand, the 3d-like levels are expected to exhibit a short decay length at the surface as compared to sp-like levels. This implies that the mean barrier height as seen by 3d-like tunneling electron is different from that by 4sp-like electron, i.e., Φd > Φsp. The measured spin polarization is the 3d-like and 4sp-like polarizations weighted by the tunneling current:

iT P = idPd + ispPsp (6.3) where Pd and Psp are the polarization of the 3d and 4sp-like states, respectively. According to the theoretical models [99, 100], 3d-like state electrons provide most of the magnetization of transition metals while 4sp-like state electrons are polarized by exchange interaction with the localized d-state electrons consequently having a smaller polarization with opposite sign. From Eqs. 6.2 and 6.3, and assuming P P , Munzenberg and Moodera deduced the | sp|≪| d| dependence of spin polarization on the barrier thickness [97]:

−βt P = Psp + αe (6.4)

57 where α P and is related to the ratio of 3d- to 4sp-like levels at the interface. β is the ∝ d diﬀerence in the inverse decay length, β = κ κ . Since P is negative ( -100%) [97, 98], sp − d d ∼ maximum positive spin polarization is expected when the tunneling barrier is very thick, with the 3d-like current decaying much faster in the barrier, and only the 4sp-like levels contributing to the tunneling current. As tunneling barrier thickness decreases, the 3d-like levels, besides 4sp-like levels, will contribute increasingly to the tunneling current injected across the barrier. This should compensate the 4sp-like current, leading to a reduction of spin polarization. It is noted that the extracted spin polarization of Py for our junctions with thick barrier thicknesses is low compared with the well-established value of 43% [96, 37]. This is believed to arise from a smaller magnetization of the Py prepared in this experiment compared to that of typical Py used in others experiments. However, neglecting this eﬀect and using Psp = 43% for Py in the thick barrier limit in Eq. 6.4, the polarization would be about 28% with a barrier thickness of 8.5 A.˚ This value is in good agreement with that recently obtained in

Py/Al2O3/Py MTJs with Al2O3 barrier of 8 A[˚ 101].

58 CHAPTER 7

CONCLUSIONS

The intrinsic spin polarization of several ferromagnetic materials has been determined by using a variety of superconducting spectroscopy techniques. These techniques have allowed for the determination of the spin polarization of Ga0.95Mn0.05As, an important ferromagnetic semiconducting material with possible real world semiconductor spintronics applications. This work also experimentally investigated the validity of a new model of analysis of superconducting spectroscopy which is inclusive of junctions of arbitrary barrier strength with and without a Zeeman-splitting field, as well as explored the barrier dependence of spin polarization in Al/Al2O3/Ni79Fe21. We have demonstrated that superconducting spectroscopy is a robust method of determining spin polarization. Zero-field Andreev reflection spectroscopy was shown to provided a quick and widely applicable method to determine the spin polarization of a material from junctions with an arbitrary barrier between the superconductor and ferromagnet, but suffers from the fact that it is insensitive to the sign of the polarization and that it provides less meaningful analysis in the high Z limit. Zeeman resolved tunneling was shown to provide an excellent and unambiguous determination of spin polarization, but has the drawback that it requires well defined tunnel junctions to be applicable. The method of Zeeman resolved ARS, which was developed over the course of this work, was shown to have the unambiguity of the tunnel junctions, but provided the large range of applicability found in the Andreev reflection techniques.

Andreev reﬂection spectroscopy was used to explore the polarization of Ga0.95Mn0.05As, which was found to have a minimum spin polarization of 85%. This work also reveal the high sensitivity of the spin polarization on the exact nature and quality of the interface. Zeeman resolved tunnel junctions were used to invistigate the eﬀects of barrier thickness on

59 measure spin polarization with Al/Al2O3/Ni79Fe21 structures, where the barrier thickness was controlled by natural oxidation time. The decreasing spin polarization with increasing barrier thickness is believed to be from the interplay of the sp- and d- like electronic states.

60 APPENDIX A

Fabrication Techniques

A.1 Growth Techniques

The films used in the course of this work were grown using a variety of techniques including thermal evaporation, magnetron sputtering, and electron beam evaporation. These films were then processed or patterned into multilayer structures. This appendix is written to give a brief description of these techniques and the advantages of each. All deposition processes are done under high vacuum conditions in order to minimize interactions with residual air molecules. In thermal evaporation a large current (10-100 Amps) is passed through a metallic boat and/or source material, evaporating the source through resistive heating and the evaporated material is then deposited onto the substrate, whose deposition rate and thickness are monitored by a quartz thickness monitor mounted nearby. In electron beam evaporation the process is similar to thermal evaporation except that the source material is now heated via a focused electron beam. This allows for materials with evaporation points too high for thermal evaporation to be deposited. With sputtering a several hundred volt potential difference (DC or RF) is placed across two electrodes separated by a small distance ( 2mm) in the presence of a process gas (generally Ar since it is inert), ∼ forming a plasma of ionized gas. The Ar+ ions are then accelerated to the surface of one electrode where it transfers kinetic energy, knocking some surface material free. In magnetron sputtering a series of magnets located near one electrode causes free electrons to travel in a helical path, ionizing many more gas particles and allows for lower operating pressures (several mTorr). Since the source material acts as one of the electrodes, DC operation can only be used when the source is a metal. When the source is an insulator, RF techniques must be used. There were two diffusion pumped, bell jar evaporation systems used in the course of this

61 work. The first was a BOC Edwards Auto 306, which had up to four possible sources that were selectable by a rotatable mounting plate. This system was also equipped with a carbon resistor heater block that allowed for growth temperatures from room temperatures to up to 200◦. The second evaporator is a manually operated system of in house construction with two possible source that were selectable via a relay connected to the power supply. This evaporator was equipped with cooling lines that allowed the sample to be cooled to liquid nitrogen temperatures during growth. There were also two sputtering chambers used in this study. The first chamber (Fig a) was a Microscience IBEX 2000 18” chamber. There were four magnetron sputter guns which could be mounted with 2” diameter sources and used in both DC and RF modes. Two of these guns were optimized for use with magnetic sources. The guns were mounted at an angle pointing the to the sample which is mounted approximately in the center, to allow for co-deposition. The system was driven by 2 DC power supplies and 2 RF power supplies with corresponding phase matching networks. This allowed for the co-deposition of up to 2 insulating sources and 2 metallic sources at one time. The chamber was pumped by a diffusion pump with base pressures in the mid 10−7 Torr range, and the chamber was sealed via a hinged front-loaded viton sealed door. The major advantage to this system is that it allowed for the rapid extraction and mounting of different sputtering targets, while the major disadvantage was that because of the angled gun design, there was a 10%-20% over 1 mm thickness non-uniformity issue in sputtered films. The second chamber used (Fig b) was an AJA International 1800 F 18” chamber, which also had four 2” RF/DC magnetron sputtering guns, two of which were optimized for magnetic targets. Here the guns were mounted such that they could be continously angled to point to the sample location to allow for co-deposition. The sample was mounted on a quartz lamp heated, rotating substrate platen assembly, which allowed for vertical translation (Z-axis) of several inches. The sputter gun angle could be varied in situ in order to optimize the desired Z-axis position. The platten assembly provided rotation in order to achieve a uniformity of up to 1% over 25 mm. The quartz lamps allowed the substrate to be heated up to 800◦C while the sample was rotated. In this setup there were 3 DC power supplies and 1 RF power supply with corresponding auto phase matching network. The chamber was pumped by a cryopump, was sealed by a top mounted viton seal and samples were introduced thourgh an attached turbo pumped load lock, which achieved a base pressure of 10−9 in the main chamber and 10−8 in the load

62 lock. During the course of this work several observations about the dependence of film properties on the growth techniques were made. First, it was found that tunnel junction structures were more easily formed with evaporated Al bottom electrodes as opposed to sputtered Al. This is believed to be because evaporated Al films are in general considerably smoother that sputtered films. This observation is independent of substrate used as Si(001),

GaAs(001), and amorphous SiO2 all provided identical results when an Al ﬁlm or tunnel junctions structure was grown on them. Also evaporated top electrodes generally made higher quality junctions than sputtered top electrodes. This is believed to be because of the relatively higher energies of the incoming sputtered materials, which may puncture the tunnel barrier. This is why in general top electrodes often have to be sputtered at lower powers and higher pressures than in normal processes.

A.2 Patterning

The structures used in this studies were formed by a variety of techniques, specifically mentioned here are that of shadow masking and lithography patterning. Unless otherwise stated, the samples grown in this work were done through the use of shadow masks. Shadow masks have the limitations that the smallest feature size possible is on the order of 100 µm and that there is a non-uniformity in thickness near the edges, which is more severe in sputtering than evaporation. Photolithograpy provides a way to make patterns with sharp edges with feature sizes down to 1µm. In photolithography a layer of an organic material ∼ that changes properties when exposed to light (photoresist) is pattern by illuminating light of a specific frequency through a patterned mask. The exposed portions of photoresist change in such a way that it is dissolved much more rapidly by certain developing chemicals as compared to an unexposed portion. The sample is then placed in the developer solution, dissolving away all exposed areas and leaving photoresist pattern behind in the unexposed areas. There are two main procedures used in lithography, etching and liftoff. In etching the photoreist is applied on top of the film to be patterned, exposed, developed, and finally etched with the photoresist acting as a protective layer. In lift off, the photoresist is first applied, exposed, and developed to make the pattern. Then the film to be patterned is deposited on top of the patterned photoresist, which is then dissolved in acetone, which also

63 Glass Bell Jar

(a) (b)

Quartz Thickness Monitor Heater Block Copper Block

Shutter Quartz Metal Enclosure Thickness Monitor

Metal Enclosure Shutter

Source Source

Rotatable Source Power Supply Selection Plate Liquid Power Suppl;y N2 Line

Figure A.1: Illustrations of the diﬀerent conﬁgurations of evaporators with (a) The BOC Edwards Auto 306 and (b) evaporator of in house construction.

Figure A.2: Schematical diagram of the e-beam chamber used to grow EuS.

64 removes any film deposited directly above the remaining photoresist. In the case of the photo defined Andreev contacts, a photo definable polyimide (PI) material was used. This material forms considerably thicker layers and is used in industry as a dielectric layer because of its excellent insulating properties. In order to use the traditional photoresist these structures would have to be grown in the following order: a) Deposit bottom contact, b) apply, expose, and develop photoresist, b) deposit thick layer of SiO2, c) lift off in acetone, d) deposit top electrode. With PI, steps d and c can be skipped since the PI material itself is the insulator. Also the PI material does not form very sharp features which becomes important when growing thin films as the top layer since sharp features could lead to discontinuities. It should be noted that one major drawback to the use of PI materials is that they require a relatively high (300-400◦C) cure temperature, which may be incompatible with some materials.

65 Figure A.3: Illustration of Microscience IBEX 2000.

Figure A.4: Illustration of the AJA 1800 F sputtering system.

66 Figure A.5: Illustration of steps involved in a window deﬁning process using (left) photoresist and liftoﬀ, (right) polyimide.

67 APPENDIX B

Measurement Techniques

The majority of the measurements made in this work were of diﬀerential resistance. The setup diagrammed in Fig B.1 was done as follows. A low frequency AC signal (generally

VRMS = 1V at 11.3 Hz) was passed through a load resistor whose resistance was much greater than that of the sample in order to provide a constant amplitude AC current to sample. The differential voltage was then measured with a lock-in amplifier, which directly gives the differential resistance when divided by the AC current. In the case of the conductance versus applied bias a DC current was generated by another load resistor on a separate DC power supply, which was connected in parallel with the AC current. A DC voltmeter connected in parallel with the lock-in measured the applied DC voltage. The DC power supply was then set to change with a constant rate, in turn giving a constant change in current. The AC load resistor was generally at lest 100 times greater than the DC load resistor, this provided the input signal as a DC current with a small AC component, namely

I = Idc + Iac (B.1)

A Taylor expansion of V(I) gives dV V (I + I )= V (I )+ I cos(ωt)+ O(I2 ) (B.2) dc ac dc dI ac ac Idc

This allows the AC and DC components to be seperated as the voltmeter measures V (Idc) and dV the lock-in measures the ﬁrst-harmonic Iac, and the conductance is then caluclated dI Idc as dI I G(V )= = ac (B.3) dV V − Idc lock in The important thing to note here is that this method is inaccurate when dealing with the S/I/S’ structures listed in section. In this case the voltage is no longer a well deﬁned function

68 R R R V LAC LDC S Lock In

V ~ AC V DC

Figure B.1: dVdI

being multivalued at certain points. In this case the appropriate solution is to measure the diﬀerential conductance directly by applying DC voltage with a small AC component directly to the sample and measure the diﬀerential current in the sample with the lock-in.

The expansion of I(Vdc + Vac) goes identically as V(I) except now the lock-in measures dI dV Vac This method suﬀers from the disadvantage that it is a two terminal measurement dV whereas dI can be measured in four terminal conﬁguration. The lock-in used in these studies included analog models PAR 124 and EG&G 5301, as well as, a digital model EG&G 7265. The voltmeters used were either HP 34401 or HP 3458B. The DC power supply was occasionally provided by the a Ketihely 2400 source-meter, however was more traditionally by a analog linear voltage sweep circuit whose diagram is given in Fig B.3.

69 V ~ AC V DC R S Lock In

Figure B.2: dIdV

Figure B.3: Circuit diagram for analog linear voltage sweep

70 APPENDIX C

List of Terminology

The following is to provide a quick reference for symbols and abbreviations used in the main text.

P Spin polarization Z A dimensionless parameter that characterizes the barrier strength at a metal/superconductor interface TC The Curie temperature of a ferromagnet Tc The superconducting transition temperature Hs The switching field of a ferromagnet ∆ Superconducting energy gap b Normalized spin-orbit scattering rate ζ Dimensionless orbital-depairing parameter ARS Andreev Reflection Spectroscopy DOS Density of States GMR Giant Magneto-Resistance MTJ Magnetic Tunnel Junctions MBE Molecular Beam Epitaxy BCS Theory of superconductivity developed by Bardeen, Cooper, and Schreiffer BTK Model that describes the conduction in a metal/superconductor interface developed by Blonder, Tinkham and Klapwijk

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77 BIOGRAPHICAL SKETCH

Jazcek Guy Braden

Education

2006 Ph.D. in Physics Dept. Physics, Florida State University, Tallahassee, FL

2000 B.S. in Physics Dept. Physics and Astronomy, Michigan State University, East Lansing, MI

Experience

2002-present Graduate Research Assistant Spintronics Research Thin Film Growth and Characterization Superconducting Spectroscopy

2000-2002 Teaching Assistant Introductory Physics Labs

Publications

“Direct Measurement of the Spin Polarization of Ga1−xMnxAs” J.G. Braden, J.S. Parker, P. Xiong, S. Chun, and N. Samarth Phys. Rev. Lett. 91(5), 56602 (2003)

“Measurement of the spin polarization of the magnetic semiconductor EuS with zero-ﬁeld and Zeeman-split Andreev reﬂection spectroscop” C. Ren, J. Trbovic, R. L. Kallaher, J. G. Braden, J.S. Parker, P. Schlottmann, S. von Molnr, and P. Xiong (submitted to Phys. Rev. Lett.)

“Barrier thickness dependence of the interfacial spin polarization of Ni79Fe21 in Al/Al2O3/Ni79Fe21 junctions” C. Ren, J. G. Braden, P. Schlottmann, S. von Molnr, and P. Xiong, (in prepartion)