Unlocking the Potential of Half-Metallic Sr2femoo6 Thin Films Through Controlled Stoichiometry and Double Perovskite Ordering

Unlocking the potential of half-metallic Sr2FeMoO6 thin films through controlled stoichiometry and double perovskite ordering

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Adam Joseph Hauser

Graduate Program in Physics

The Ohio State University

2010

Dissertation Committee:

Professor Fengyuan Yang, Advisor

Professor Leonard J. Brillson

Professor Nandini Trivedi

Professor Klaus Honscheid

Adam Joseph Hauser

2010

Abstract

Sr2FeMoO6 is the most studied half-metallic double perovskite with the potential

for room-temperature magnetoelectronic applications due to its Curie temperature above

400 K. Despite its promise, researchers have not yet succeeded in growing films of

sufficient quality to realize its potential. By identifying and controlling critical factors

that complicate attempts to grow thin films of Sr2FeMoO6, we have overcome the

obstacles of non-stoichiometry, impurity phase formation and poor double perovskite

ordering, all of which must be overcome to achieve half-metallicity. This dissertation

reports an in-depth investigation that addresses several critical issues about the deposition of Sr2FeMoO6 epitaxial films using off-axis ultrahigh vacuum sputtering.

High quality Sr2FeMoO6 films have been grown by off-axis ultrahigh vacuum DC magnetron sputtering, and characterized by a wide variety of techniques. We have discovered that sputtering gas pressure plays a dominant role in the stoichiometry and phase formation of Sr2FeMoO6 films. Film stoichiometry was found via Rutherford backscattering spectroscopy (RBS) and electron dispersive x-ray (EDX) spectroscopy to be both position dependent and pressure dependent in off-axis magnetron sputtering, changing from a Mo:Fe ratio of 1.43:1 at PTot = 70 mTorr to 1.12:1 at PTot = 6.7 mTorr.

Our Sr2FeMoO6 films exhibit a combination of desired properties expected for its

half-metallicity. X-ray-diffractometry (XRD) shows the films to be epitaxial, pure-phase,

and well ordered by Reitveld refinement (ξ = 85.4%). High angle annular dark field ii

scanning transmission microscopy (HAADF STEM) was performed to give the first

direct observation of double perovskite ordering in a film, as well as a low defect level.

Magnetic characterization was done via vibrating sample magnetometry (VSM) and

superconducting quantum interference device (SQUID) magnetometry to find a

saturation magnetization of 2.6 µB per formula unit at T = 5 K and a Curie temperature TC

of 380 K, roughly in line with expectation for the film stoichiometry and ordering level.

This dissertation also reports the first known report of distinct magnetic shape anisotropy,

suggesting a high quality film with long-range magnetic ordering. The Sr2FeMoO6 films with these attributes will provide the material base for magnetoelectronic applications that will eventually achieve its half-metallic potential.

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Dedication

This dissertation is dedicated to my parents,

Mr. Glenn W. Hauser and Mrs. Elizabeth S. Hauser.

Thank you for keeping me from being too much of an idiot. I love you both.

Acknowledgments

First and foremost, I would like to thank my advisor Professor Fengyuan Yang, who for some reason saw it fit to take in and mold a second-rate graduate student into something resembling a real physicist. Thank you for everything.

To my parents, Mr. Glenn W. Hauser and Mrs. Elizabeth S. Hauser, for keeping me in line and providing a constant source of support and warmth to carry me through tough stretches. To my little sisters Ms. Erica J. Hauser and Ms. Samantha S. Hauser, thank you for tolerating my nonsense. To the Myers Clan (in no particular order, before the “favorite aunt” argument even starts): my godmother Ms. Patricia Myers, my aunts

Mrs. Jeanne Kolakowski, Mrs. Theresa Puretz, Mrs. Rose Marie O’Hara, and my uncles

Mr. Joe Kolakowski, Mr. Jeffrey S. Puretz, and Mr. Mike O’Hara. And of course, to my cousins Jacqueline and Matthew Puretz, Sean and Scott O’Hara, and my Goddaughter

Claire Kolakowski. Thank you all.

I would like to also thank my advisory committee, Dr. Leonard J. Brillson, Dr.

Klaus Honscheid, and Dr. Nandini Trivedi, for their help and guidance over the past few years, as well as sitting through the painful ignorance displayed in both my candidacy and final oral examination.

The financial support for the work in this dissertation came from the Center for

Emergent Materials at The Ohio State University, an NSF MRSEC (Award No. DMR-

0820414). Between the access to amazing interdisciplinary faculty and facilities and the unwavering support for formerly unreachable research avenues, the impact of the CEM on my graduate education cannot be understated. A special thank you to the CEM

Program Director, Ms. Lisa Jones, who deals with much of our nonsense on a daily basis and cannot be thanked enough by us.

Through the Center and other collaborations, the number of faculty I must thank are truly numerous. With apologies to anyone I may have missed, thank you all for tolerating my insolence over the last six years: Prof. Tom R. Lemberger, Prof. Leonard J.

Brillson, Prof. Ratnasingham Sooryakumar, Prof. Patrick M. Woodward, Prof. P. Chris

Hammel, Prof. Terry L. Gustafson, Prof. Nandini Trivedi, Prof. Mohit Randeria, Prof.

Hamish L. Fraser, Prof. Ezekiel Johnston- Halperin, Prof. D.D. Sarma, Prof. Patricia A.

Morris, Prof. Wolfgang Windl, and Prof. David G. Stroud, Prof. Nitin P. Padture, and

Prof. Jonathan P. Pelz. I am truly fortunate to have been able to gain the varied experiences I have through all of you, and I find myself in each or your debts.

Of course, the rabblerousing group of miscreants I call friends must be acknowledged. Thank you all for making my life so rich and fun. In rough temporal order, though the list is sure to be incomplete: Robert Tilley, Jason Stambaugh, Umair

Suri, Jaime Lopez, John Reading, Stephen Gelb, Greg Montalbano, Scott Boyd, Jeff

Schadt, Xianwei Xiao, William Schneider, Kevin Knobbe, Nicholas Harmon, Rakesh

Tiwari, John Kerry Morrison, Rob Guidry, Mark Murphy, Sarah Parks, Jeffrey Stevens,

Gregory Vieira, Gregory Sollenberger, Steven Avery, Christopher Porter, Kevin Driver,

Grayson Williams, Taeyoung Choi, George B. Dundee, Michael Fellinger, Jeremy Lucy,

Michael Hinton, Charles Ruggiero, Lei Fang, Brian Peters, Jie Yong, Turhan Carroll,

James P. Mathis, Rebecca Ricciardo, Tricia Meyer, Matt Stolzfus, and the entire gang we

call the Columbus Red Devilz baseball team. To everyone I may have missed, know that

I truly appreciate you, but I am spilling onto the third page already and do not want to

make this any more gratuitous than it already is.

Finally, to Ms. Katherine Marie Schmidt, thank you for the love, support,

confidence, and encouragement you have given me through everything. You were there for me and I will always be there for you, because we belong together. I am so lucky to be with you every day, and I want to be with you every day until death do us part.

Will you marry me?

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Vita

2000...... Livingston High School, NJ

2004...... B.S. Physics (Honors), Rutgers University

2004...... B.S. Astrophysics, Rutgers University

2008...... M.S. Physics, The Ohio State University

Publications

M. Rutkowski, A. J. Hauser, F. Y. Yang, R. Ricciardo, T. Meyer, P. M. Woodward, A Holcombe, P. A. Morris, and L. J. Brillson. X-ray photoemission spectroscopy of Sr2FeMoO6 film stoichiometry and valence state. J. Vac. Sci. Technol. A 28, 1240 (2010)

Inhee Lee, Yuri Obukhov, Gang Xiang, Adam Hauser, Fengyuan Yang, Palash Banerjee, Denis V. Pelekhov, and P. Chris Hammel. Nanoscale scanning probe ferromagnetic resonance imaging using localized modes. Nature 466, 845-848 (2010)

T. Henighan, A. Chen, G. Vieira, A.J. Hauser, F.Y. Yang, J.J. Chalmers, R. Sooryakumar. Manipulation of Magnetically Labeled and Unlabeled Cells with Mobile Magnetic Traps. Biophysical Journal 98, 412-417 (2010)

J. Pak, W. Lin, K. Wang, A. Chinchore, M. Shi, D. C. Ingram, A. R. Smith, K. Sun, J. M. Lucy, A. J. Hauser, and F. Y. Yang. Growth of epitaxial iron nitride ultrathin film on zinc-blende gallium nitride. J. Vac. Sci. Technol. A 28, 536 (2010)

G. Vieira, T. Henighan, A. Chen, A.J. Hauser, F.Y. Yang, J.J. Chalmers, and R. Sooryakumar. Magnetic Wire Traps and Programmable Manipulation of Biological Cells. Phys. Rev. Lett. 76, 128101 (2009)

Kangkang Wang, Abhijit Chinchore, Wenzhi Lin, David C. Ingram, Arthur R. Smith, Adam J. Hauser, and Fengyuan Yang. Epitaxial growth of ferromagnetic δ-phase manganese gallium on semiconducting scandium nitride (001). Journal of Crystal Growth 311, 2265-2268 (2009)

R.A. Ricciardo, A.J. Hauser, F.Y. Yang, H. Kim, W. Lu and P.M. Woodward. Structural, magnetic, and electronic characterization of double perovskites BixLa2-xMnMO6 (M = Ni, Co; x = 0.25, 0.50). Materials Research Bulletin 44, 239-247 (2009) viii

A.J. Hauser, J, Zhang, L. Mier, R. Ricciardo, P.M. Woodward, T. L. Gustafson, L.J.Brillson, and F.Y. Yang. Characterization of electronic structure and defect states of thin epitaxial BiFeO3 films by UV-visible absorption and cathodoluminescence spectroscopies. Appl. Phys. Lett. 92, 222901 (2008)

W.C. Liu, C.L. Mak, K.H. Wong, C.Y. Lo, S.W. Or, W. Zhou, A. Hauser, F.Y. Yang and R. Sooryakumar. Magnetoelectric and dielectric relaxation properties of the high Curie temperature composite Sr1.9Ca0.1NaNb5O15–CoFe2O4. J. Phys. D: Appl. Phys. 41 125402 (2008)

Thomas R. Lemberger, Iulian Hetel, Adam J. Hauser and F.Y. Yang. Superfluid density of superconductor-ferromagnet bilayers. Journal of Applied Physics 103, 07C701 (2008)

X.W. Zhao, A.J. Hauser, T.R. Lemberger and F.Y. Yang. Growth control of GaAs nanowires using pulsed laser deposition with arsenic over-pressure. Nanotechnology 18, 485608 (2007)

Fields of Study

Major Field: Physics

Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments...... v

Vita ...... viii

Publications ...... viii

Fields of Study ...... ix

Table of Contents ...... x

List of Tables ...... xiv

List of Figures ...... xv

Chapter 1: Introduction ...... 1

1.1 Magnetism ...... 3

1.1.1 Introduction to Magnetic Theory ...... 4

1.1.2 Classifications of Magnetic Behaviors in solids...... 6

1.1.4 Magnetoresistance ...... 19

1.2 The Double Perovskite ...... 26

1.2.1 Introduction to Perovskites ...... 27

1.2.2 Double Perovskite Structure ...... 28

1.2.3 Property Control by Elemental Selection ...... 30

Chapter 2: Introduction to Sr2FeMoO6 ...... 32

2.1 Theory and Background ...... 32

2.1.1 Orbital and Electronic Band Structure...... 33

2.1.2 Effect of disorder on material properties ...... 39

2.2 Previous Work on Sr2FeMoO6 ...... 43

2.2.1 Bulk Powder ...... 43

2.2.2 Thin Films by Pulsed Laser Deposition ...... 47

2.2.3 Thin film growth by Magnetron Sputtering ...... 51

Chapter 3: Thin Film Deposition Methods ...... 55

3.1 Magnetron Sputtering ...... 55

3.2 Pulsed Laser Deposition ...... 58

3.3 Molecular Beam Epitaxy ...... 60

Chapter 4: Characterization Methods ...... 62

4.1 X-Ray Diffractometry (XRD) ...... 62

4.1.1 Introduction and Theory ...... 62

4.1.2 Focused Beam Diffractometry...... 66

4.1.3 Parallel Beam Diffractometry ...... 68

4.2 Vibrating Sample Magnetometry (VSM) ...... 70

4.2.1 Instrumentation and Theory ...... 70

4.2.2 Measurement Modes...... 72

4.3 Superconducting Quantum Interference Device (SQUID) ...... 74

4.3.1 Instrumentation and Theory ...... 74

4.3.2 Comparison to VSM ...... 79

4.3.3 Mounting Techniques in Quantum Design Cryostat ...... 79

4.4 Transmission Electron Microscopy (TEM) ...... 81

4.4.1 Theory ...... 81

4.4.2 Scanning TEM (STEM) ...... 87

4.4.3 Instrumentation – The FEI Titan...... 89

4.5 Rutherford Backscattering Spectroscopy (RBS) ...... 90

4.5.1 Theory ...... 90

4.5.2 Instrumentation: Rutgers University ...... 94

4.6 X-Ray Photoemission Spectroscopy (XPS) ...... 96

4.6.1 Theory ...... 96

4.6.2 Instrumentation: Brillson Lab ...... 98

Chapter 5: Preparation and Deposition of Sr2FeMoO6 Thin Films ...... 100

5.1 Target Preperation ...... 100

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5.2 Sputtering Geometry ...... 107

5.3 Sputter Environment ...... 112

5.4 Proof of Concept: Characterization of Sr2FeMoO6 Thin Films on SrTiO3 ...... 120

5.3.1 Sputtering conditions for high quality films ...... 121

5.3.1 X-Ray Diffractometry for structural characterization ...... 121

5.3.3 Magnetic Characaterization by SQUID/VSM ...... 126

5.3.4 Direct Observation of Structure and Ordering by HAADF STEM ...... 130

Chapter 6: Conclusions ...... 134

References ...... 136

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List of Tables

Table 1. Table of properties for strontium-based double perovskites in the Cr, Mn, and

Fe B-site families...... 30

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List of Figures

Figure 1. Simplified spin-dependent density of states (DOS) schematic relative to the Fermi energy EF for a normal ferromagnet (left) with states of both spin orientations in the conduction band, and for an ideal half metal (right) with 100% spin polarization...... 1

Figure 2. Energy level diagram depicting the Zeeman splitting of the spin states in the presence of an externally applied magnetic field Hext. The degeneracy in the Hext = 0 case is broken, resulting in a preferred spin orientation and a net magnetic response in the presence of an applied field...... 8

Figure 3. Magnetization M vs. Magnetic Field H plot of Gd3+, Fe3+, and Cr3+, illustrating paramagnetic response to an external field...... 9

Figure 4. Susceptability plots as a function of temperature for ideal materials with (a) Pauli paramagnetism and diamagnetism, (b) ideal paramagnetism, (c) ferromagnetism, (d) antiferromagnetism, and (e) ferrimagnetism. Magnetization plots are overlaid in (c- e), and dotted traces in (d) and (e) demonstrate the Weiss constant determination. [62] 13

Figure 5. Example of a ferromagnetic hysteresis loop, i.e. M vs. H plot, showing an initial track from magnetization, and then the unique loop created due to the effective field due to interaction with nearby spin moments. [68] ...... 15

Figure 6. An example of antiferromagnetic ordering in a sample with oppositely oriented nearest neighbor spin moments...... 16

Figure 7. Simplified schematic of ferrimagnetic spin ordering in magnetically polarized Sr2FeMoO6, with a saturation magnetization approaching 4 µB/f.u...... 18

Figure 8. Resistivity vs. applied magnetic field curves at room temperature for La2/3Ba1/3MnO3 films grown at 600 °C and a similarly grown sample post-annealed at 900 °C. [71] ...... 20

Figure 9. Graphs of the resistivity (top panels) and magnetization (bottom panels) as a function of field at (a) T = 4.2 K and (b) T =300 K. From Kobayashi et al.[1]...... 21

Figure 10. Schematics for the high and low resistance states of a giant magnetoresistance device, and the corresponding relative magnetization directions of each ferromagnetic layer, separated by a thin non-magnetic conducting layer...... 22

Figure 12. Graph of Tunneling Magnetoresistance (MR) as a function of the spin polarization (P) of the top and bottom ferromagnetic layers of the heterostructures, assuming ideal tunnel barrier quality. Blue dot represents MR/P position of Fe/AlOx/Fe heterostructures, currently used in TMR read reads...... 26

Figure 13. Structure of an undistorted perovskite. [60] ...... 27

Figure 17. From Ogale et al. [4], (a) Simulation of saturation magnetization for a variety of different anti-site concentrations as a function of temperature for stoichiometric Sr2FeMoO6. (b) Fitting of the saturation magnetizations at T = 5K (black squares) and Curie Temperatures (open circles) to linear fit lines as a function of anti-site defect concentration...... 40

Figure 18. (a-c) Simulations from Menegini et al. for a set long-range ordering and double perovskite ordering parameter ξ values of (a) 0.63, (b) 0.85, and (c) 0.99. (d) diagram illustrating pinning of domain walls in the vicinity of an external magnetic field...... 41

Figure 19. Resistivity and Magnetization curves (upper and lower, respectively) of bulk powder samples of Sr2FeMoO6 as a function of the applied magnetic field at temperatures of (a) 4.2K and (b) 300K. The Inset pictures are magnifications of the low-field regions of each curve. (Adapted from [1]) ...... 44

magnetoresistance of the ordered sample is clearly improved at 4.2K compared to that of Kobayashi et al. (Adapted from [13]) ...... 45

Figure 22. X-ray Diffractometry (XRD) spectra from a variety of different papers on thin film growth by Pulsed Laser Deposition...... 50

Figure 24. A general schematic for a Magnetron Sputtering system. Top: Positively charged Argon ions collide with the electrically biased target surface, ejecting material up to the substrate above. Bottom: Magnetic fields placed under the target capture secondary electrons and hold them close to the target to encourage further Argon ionization and support the deposition rate. [86]...... 56

Figure 25. A simple schematic for a Pulsed Laser Deposition System. [87] ...... 58

Figure 26. A simplified setup for a Molecular Beam Epitaxy chamber. [90] ...... 61

Figure 27. Diagram of x-ray diffraction off a simple crystal lattice. Green waves demonstrate the constructive interference that gives rise to peaks according to the Bragg equation. [91] ...... 63

Figure 28. An example of a constructed Ewald sphere. When reciprocal points intersect with the sphere boundary at a given angle θ, that angle will produce the constructive interference necessary for a diffraction peak to appear in the XRD spectra...... 64

Figure 29. Schematic drawing of Bragg-Brentano geometry used for focused beam x-ray diffractometry. [91] ...... 67

Figure 30. Picture of the focused beam XRD system at The Ohio State University’s Department of Chemistry...... 67

Figure 31. Simplified diagram of parallel beam x-ray diffractometry. [93] ...... 69

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Figure 32. D8 Discover Parallel Beam Diffractometer made by Bruker for the Department of Physics at The Ohio State University...... 69

Figure 33. LakeShore 736 Model Vibrating Sample Magnetometer in room temperature, 1.6 T mode, located in the Department of Physics, The Ohio State University...... 71

Figure 34. Schematic of a Josephson junction...... 75

Figure 35. Schematic of the DC SQUID magnetometer diagram, from the MPMS Reference Manual from Quantum Design...... 76

Figure 36. Electronic circuit diagram for the DC SQUID magnetometer, from the MPMS Reference Manual from Quantum Design...... 77

Figure 37. Simplified diagram of a DC SQUID with a bias voltage I and a screening current IS due to an externally applied flux into the page...... 78

Figure 39. Simplified schematic of parts for a simple Transmission Electron Microscope. Adapted from [96]...... 82

Figure 40. Electron beam path traced from sample to screen in a basic Transmission Electron Microscope. Adapted from [97]...... 84

Figure 41. Ray trace diagrams depicting the effects of (top) Spherical Aberration and (bottom) single-slit diffraction on the resolution of an image via transmission electron microscopy. [99] ...... 86

Figure 42. Schematic for STEM-HAADF imaging and electron energy loss spectroscopy (EELS). This diagram is drawn largely from work done on the FEI Titan with which our STEM data was collected. [99] ...... 88

Figure 43. Picutre of a FEI Titan™ 80-300. [100] ...... 89

Figure 44. Diagram depicting the classical nature of Rutherford Backscattering. Alpha particles sent into a sample will be electrically deflected at a very close distance from each atomic nucleus, and so a classical treatment of the collisions is acceptable...... 91

xviii

Figure 45. Simple diagram depicting the interactions between alpha particles and target nuclei during Rutherford Backscattering Spectroscopy...... 92

Figure 46. A picture of the 2 MeV Tandetron Accelerator Facility in the Laboratory for Surface Modification at Rutgers University...... 94

Figure 47. RBS data of a Sr2FeMoO6 film on SrTiO3 substrate, being fit to simulated data in SIMRNA to determine the stoichiometry, density, and thickness of each layer in the sample...... 95

Figure 48. Energy level diagram excitation of an electron during x-ray photoemision spectroscopy, assuming the impinging x-ray has high enough energy to eject an electron from the metal. Adapted from [95]...... 97

Figure 49. The XPS vacuum chamber, bottom left corner of picture. The MBE system to the right is set up with a vacuum transfer line for in situ measurements...... 98

Figure 50. Scanning Electron Microscopy pictures of Sr2FeMoO6 pressed magnetron sputtering targets, (a) before and (b) after sputtering has been done...... 101

Figure 51. (a) X-ray diffractometry, (b) magnetic moment vs. field at T = 5K, and (c) magnetization at an applied file of 1,000 Oe as a function of temperature for Sr2FeMoO6 powder target made and used to grow the films used in this work...... 102

Figure 52. (a) X-ray diffractometry, (b) magnetic moment vs. field at T = 5K, and (c) magnetization at an applied file of 1,000 Oe as a function of temperature for Sr2FeMoO6 powder target made by wet-grind ball mill technique, with initial heating step to prevent SrMoO4 impurities from forming...... 106

Figure 53. Photograph of off-axis sputter deposition of Sr2FeMoO6 on a SrTiO3 substrate. The substrate, visible here in mid-deposition as a dark 5 x 5 mm square, is heated from underneath by resistively heated platinum-rhodium wire in a “stove-top” like formation...... 108

Figure 54. Simplified model for positional dependence of cations in Sr2FeMoO6 due to scattering off argon atoms...... 110

Figure 55. Elaboration on Figure 54 to include effects of oxygen levels and ordering on substrate position...... 111

Figure 56. Characterization of Sr2FeMoO6 film grown by off-axis DC magnetron sputtering on (001)-oriented SrTiO3 substrates at Tsub = 800 °C and PAr = 70 mTorr. (a) Focused-beam XRD data with peak labels. (b) M-H curve by SQUID magnetometry at T

xix

= 5K. (c) M-T curve by SQUID Magnetometry at H = 3,000 Oe...... 113

Figure 57. X-ray diffractometry spectra by focused-beam Bruker D8 Advance for Sr2FeMoO6 films grown on (a) (001)-oriented and (b) (111)-oriented SrTiO3 substrates...... 115

Figure 58. SQUID Magnetometry data on Sr2FeMoO6 films grown on (111)-oriented SrTiO3 substrates. (a) Magnetic hysteresis curve at T = 5K. (b) M-T graph for an applied magnetic field of 1,000 Oe...... 116

Figure 59. RBS spectra of Sr2FeMoO6 films deposited on SrTiO3 substrates in pure Ar (a) at PAr = 70 mTorr showing Fe:Mo ratio of 1.00:1.43, and (b) at PAr = 6.7 mTorr showing Fe:Mo = 1.00:1.12. EDX spectra of Sr2FeMoO6 films on SrTiO3 give (c) Fe:Mo = 1.00:1.48 for PAr = 70 mTorr and (d) Fe:Mo = 1.00:1.13 for PAr = 6.7 mTorr...... 118

Figure 60. /2 XRD scans of (a) a Sr2FeMoO6 (001) and (b) a Sr2FeMoO6 (111) phase- pure epitaxial films deposited by sputtering in pure Ar of 6.7 mTorr. Rietveld refinements (red curve in (b)) gives a DP order parameter  = 0.854 ± 0.024...... 122

Figure 61. (a) -scans of the (110) peaks at a tilt angle  = 45° for a Sr2FeMoO6 (001) film demonstrate epitaxial relationship between the film and the SrTiO3 substrate. (b) A rocking curve of the Sr2FeMoO6 (004) peak for a Sr2FeMoO6 (001) film gives a FWHM of 0.096°. (c) Small-angle X-ray reflectometry scan of a Sr2FeMoO6 (001) film gives multiple diffraction peaks and a film thickness of 110 nm...... 124

Figure 62. Diagram explaining the effect of magnetic shape anisotropy in an ideal ferromagnetic film. (top) For an applied field in the plane of a film with good long-range ordering, easy-axis behavior results in good magnetic interaction between spin moments and hysteresis. (bottom) Due to the dimensionality of the film “out-of-plane” being much smaller than the ordering, the interaction of spins is not in the direction of the field and the film looks paramagnetic in nature up to a field equal to the disruptive field created by the anisotropy, Hani...... 126

Figure 63. In-plane (black) and out-of-plane (red) hysteresis loops at (a) T = 5 K and (b) T = 293 K of a 115-nm thick Sr2FeMoO6 (111) epitaxial film deposited in pure Ar of 6.7 mTorr. The small opening in the out-of-plane loop at T = 5 K in (a) is due to the misalignment of the sample in SQUID measurements, in which a few degrees off-perfect alignment can result in obvious change in the shape of the loop [107]. The clear anisotropy between H  film and H  film indicates strong magnetic interaction throughout the film. (c) M vs. T curve gives a TC = 380 K...... 129

Figure 64. Unfiltered aberration-corrected HAADF STEM image of (001)-oriented Sr2FeMoO6 film grown on a SrTiO3 (001) substrate with an atomically sharp interface. The schematic drawing shows the double perovskite lattice with rock-salt ordering of Fe xx

and Mo at the B/B’-site...... 130

Figure 65. A Sr2FeMoO6 (111) epitaxial film on SrTiO3 viewed along the <110> direction with bright “triplet” patterns indicative of atomic number contrast...... 132

Figure 66. An enlarged STEM image highlighting the triplets (dashed yellow box), each of which is a bright Sr-Mo-Sr chain (due to their high atomic numbers) separated by a darker Fe atomic column (lighter). It clearly shows the Mo-Fe ordering (green chain) separated by a Sr chain (red dashed line). The schematic in the figure is the projection of the double perovskite lattice along the <110> direction, which matches the pattern seen in the STEM image. The orientations here are the same as in Figure 65, indicated by the yellow axes...... 133

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Chapter 1: Introduction

Given the massive scientific and technological impact that a magnetically switchable material with high spin polarization at room temperature would have, the significant interest in ferrimagnetic Sr2FeMoO6 [1-52] since the prediction of half- metallicity, i.e. 100% spin polarization, is hardly surprising. Magnetic multilayers using giant magnetoresistance (GMR) and tunneling magnetoresistance (TMR) have dominated the data storage industry for many years using simple ferromagnetic metals such as iron and chromium [70]. As shown in Figure 1, normal ferromagnets used in current technology (most commonly iron) exhibit spin polarization closer to 40-45% due to a mixture of up and down-spin states in the conduction band.

However, for certain magnetic materials, there is only one spin state (e.g. up) available at

the Fermi energy which falls in the band gap of the other spin state (down) as shown in the right of Figure 1. These kind of magnetic materials with 100% spin polarization are called half-metallic ferromagnets (HMFs) or half-metals.

Even at room temperature where the presence of thermal fluctuations lowers the spin polarization below 100%, half-metals represent a quantum leap in electronic and computing application. Many potential half-metallic materials have been predicted and

investigated [1,72-81], although to date roadblocks have occurred in each case.

Manganite perovskites such as La2/3Sr1/3MnO3 have shown terrific quality at low

temperatures and resulted in rich science [73-74]. However, the manganites have Curie

temperatures (TC) at or below room temperature, making them undesirable for device

application. Fe3O4 is a half-metal with TC well above room temperature, but suffers from

poor conductivity [77-78]. CrO2 has both good conductivity and high TC, but is an

unstable metastable phase that makes incorporation into devices very difficult [74].

Two excellent classes yet to be fully investigated include the Heusler alloys [81]

and the double perovskites [1,79-80]. In both of these materials, the increased chemical

complexity involved in fabrication of single crystals and thin films makes controlling the

phase purity, stoichiometry, site ordering, and defect levels exceptionally difficult.

However, if achieved, these classes contain materials with the right combination of high

TC and good conductivity needed for use as a magnetically switchable half-metal.

The choice between which material to study is not a simple one. However, as

Herbert Kroemer said at his 2000 Nobel Prize Lecture, “The device is the interface.”

Although Heusler alloys generally have higher Curie temperatures than the double

perovskites, double perovskites have the distinct advantage of isostructurality between

family members with a wide variety of properties. As such, one could theoretically make

A2BB’O6 heterostructures with no sacrificial layer, i.e. no boundary region of indeterminate crystallinity due to imperfect lattice matching, and have atomically sharp interfaces where the A and O sites stay unchanged, and only the B and B’ are interchanged as necessary.

This chapter will serve as a general introduction to the physical and theoretical concepts needed in later chapters. Chapter 2 will build on this to introduce the theory and previous work on Sr2FeMoO6. A review of the deposition methods and characterization

methods will be presented in Chapters 3 and 4 respectively. Finally, our work on

Sr2FeMoO6 will be covered in the frameset of the effect of various preparation and

growth parameters.

1.1 Magnetism

The concept of magnetism can be traced back to the 6th century B.C., when the word “magnet” was formed from Greek, translating as “the stone from Magnesia,” a

Greek town centrally located on the eastern coast of the Adriatic Sea [61,62]. Aristotle attributed the discovery to the philosopher Thales regarding what were likely magnetite rocks found in Magnesia. Texts from the same age place similar knowledge in India and

China of magnetite [63-64], although proof of application did not come about until the middle ages and surviving literature regarding the invention of the compass.

Attempts to further harness and understand magnetism would wait until 1819, when Oersted discovered a relationship between electric and magnetic fields and forces.

Phenomenological work on electromagnetism continued with the work of Gauss,

Faraday, Maxwell, and many others, but a solid theory of magnetism requires use of quantum mechanics to build a freestanding theory.

1.1.1 Introduction to Magnetic Theory

Magnetic fields can be modeled by employing the quantum mechanical vector model, in which the spin and orbital moments of electrons in an atom can be found from a description of their quantum state as well as interactions with those around it.

The 4 values used to determine the state of an electron are:

1) n, the principal quantum number. n = 1, 2, 3… corresponds to the electron being

in the K, L, M… electron shell.

2) l, the orbital angular momentum quantum number. l can take values between 0

and n-1 in a given atom, and describes the orbital motion. l = 0 correlates to s

orbitals, l = 1 to p orbitals, and so on for d, f, g, etc. Additionally, one can

calculate the angular momentum of the electron as L ħ 1, where ħ is

the Dirac constant (reduced Plank constant), equal to 1.0546 x 10-34 J·s.

3) ml, the magnetic quantum number. While l describes the state of the total angular

momentum, ml defines the quantized value of the orbital momentum quantum

number in the direction of an applied field. Note that it is both quantized and a

component of l. Therefore, its possible range runs from -l to l.

4) ms, the spin quantum number. The allowed values for ms, which describe the spin

s of the electron in the direction of an applied field, can only be ± ½.

Pauli Exclusion Principle requires that no two electrons in an atom have the exact same quantum state. Therefore, no two electrons can occupy the exact same quantum state in an atom, defining the rules for orbital filling in each atom.

At this point, we see that there exist two possible sources of magnetic moment from an electron; the orbital moment and the spin moment. The orbital moment can be found by taking the electron’s orbit to be equivalent to a moving charge in a wire. We may then write the total orbital moment of an electron as

|| μ ħL μ 2 and the component in the direction of the applied field (arbitrarily chosen as the z- direction) as

μ μ

The spin moment µs, in contrast, is an intrinsic property of electrons, and related to the gyromagnetic ratio g:

μ μ

Note that g = 2.00229, which is usually approximated to 2. For example, iron, which has

5 parallel electrons in its 3d5 valance band, will have a total spin moment of 5/2, and thus a spin moment of 5 µB per Fe.

1.1.2 Classifications of Magnetic Behaviors in solids

To determine the net moment of a system in the presence of a magnetic field, we

must analyze the system for both net orbital and spin moment. We begin, however, with

a case where neither exit.

Diamagnetism

Diamagnetism is a magnetic phenomenon that occurs in every system with electrons in it. It has by far the weakest magnitude moment of each classification, and so

a material may only be classified as diamagnetic when all other types of magnetic

ordering are not present. Below is an electrodynamical treatment to show the source of

this effect. Although this classical model is not the proper way to exactly describe the

system, it succeeds in reaching the same equation for the susceptibility of a system, while

being more illustrative. For another method to classically treat this phenomenon, a clear

explanation can also be found in [65].

Every electron moving in a magnetic field while in its atomic orbit may be

thought of as if it were in a conducting wire with some length Δd. In an atom under no

external magnetic field, the electron orbits are completely randomized and as such the

orbital moment of the atom cancels out to zero. If we calculate the force on the orbiting

electron due to an external magnetic field by treating it as a Lorentz force, we have

μ = μ

where µ0 is the permissivity of free space, I is the effective current, v is the electron

velocity, and H is the magnetic field. Taking the current to be the one orbiting charge e

over time allows the description of the electron velocity v = Δd/t.

If we set the above description of the Lorentz force to be equal to mass times the

change in angular acceleration α = Δ(ω2r), we arrive at

μ 2 where m is the mass of the orbiting electron. We may then relate the change in angular

|| velocity of the orbiting electron to a change in orbital moment μ as

|| μ μ 2 4

This equation can then be used to find the classical Langevin formula for

susceptibility that agrees with the quantum mechanical result for this problem, but the

above equation shows what is necessary: The response of an orbiting electron to an

external field is an orbital moment opposite to the direction of the external magnetic

field. The orbital moment’s opposition to the field is the source of diamagnetism.

Paramagnetism

Diamagnetism is the predominant effect in materials with no unpaired electrons.

However, we now turn our attention to systems where Pauli’s Exclusion Principle leaves unpaired electrons without a partner to cancel out its spin.

In an atom under no external magnetic field, the two spin directions of an electron

are degenerate, i.e. have the same energy in either state. Therefore, any unpaired

electrons in a material will have random orientation and the composite system will have

no net moment. However, in the presence of an externally applied magnetic field H, the

energy levels will undergo Zeeman splitting proportional to the magnitude of the field,

with the difference in energy levels

ΔE = 2|µH|H = gµBH ≈ 2µBH

where g is approximated to a value of 2, and µH is the component of the spin moment in

the direction of the applied field. Figure 1 above depicts the splitting described above.

In this case, an unpaired electron will no longer randomly choose one of the two possible

values of ms, but instead favor the state corresponding to the lower of the two split states.

e P/ e e

The net magnetization per formula unit for a system with N unpaired electrons in each unit can then be written as

gμ NP P / / 2 8

The first half of the equation finds the net number of spins in the up direction

(arbitrarily made to be the majority in this example), and the second half is the moment

of a single unpaired spin. Plugging in for P/, we find

N = Ntanh

which is a constant times a hyperbolic tangent function. Figure 2 shows the experimental

agreement with the quantum mechanical theory, as the experimental graphs of M as a

function of H clearly resemble a hyperbolic tangent function.

Figure 3. Magnetization M vs. Magnetic Field H plot of Gd3+, Fe3+, and Cr3+, illustrating paramagnetic response to an external field. 9

Additionally, one should note that the paramagnetic elements in Figure 2 look linear at very low field. This is consistent with the theory: At low field, the hyperbolic tangent becomes roughly equal to its argument, and the net magnetization per fomula unit is

gμ H gμ MN kT 2

The magnetic susceptibility χ can then be calculated by a simple derivative with respect

to H, leaving us with the relation χ = C/T, where C is the Curie constant equal to the combined value of the constants in the equation. This quantum mechanical result agrees

with not only experiments but also the classical theory [66], and is known as the Curie

law.

One of two important pieces of physics we can extract here is the 1/T dependence

of the susceptibility. Experimentally, this is very useful, as it tells us that we may hunt

for paramagnetic impurities in our samples by taking measurements at low temperatures.

If there is a paramagnetic response, we see its moment begin to dominate when

approaching T = 0K.

Ferromagnetism

The second piece of physics to point out is that the Curie Law, when graphed as a

function of T, intersects the origin, as shown in Figure 3(b). When graphing the inverse

susceptibility as a function of temperature, we see that intersection of the temperature

axis is an important predictor of magnetic behavior. In the case of an ideal paramagnet,

the paramagnetic ordering holds all the way down to T = 0 K. A physical way to

10 describe this is to say that the coherence between spins is too weak for the system to remain aligned in the absence of an external field.

Let us now say that the coherence between spins is strong enough to remain aligned after removal of the external field at T = 0 K. At some finite temperature, the thermal fluctuations will exceed energy of interaction and lose the ability to self-align.

Below this temperature, the same can hold alignment and is classified as ferromagnetic with a Curie Temperature TC. At temperatures above this TC, the system behaves as a paramagnet.

In a paramagnet, there are negligible interactions between unpaired electrons and so the only magnetic field seen by each electron is that of the externally applied field H.

In a ferromagnet, however, there is a non-negligible interaction between the atoms, as the spin moments of nearby electrons will create an effective field in the direction of the magnetization. To find the susceptibility χ, then, we need to add an effective field

to the external field to properly describe the field at a given atomic site. We will adjust the Curie law phenomenologically for now to

where β is a constant. The quantum mechanical description and solution of the effective field and β is done below, but first, we can write the susceptibility as

The transition from the ferromagnetic phase to the paramagnetic occurs at the

temperature at which the magnetization drops to zero with no external magnetic field.

Therefore, to find the expression for the Curie temperature TC, one may simply solve the

above equation for T in the limit of M = 0 and H = 0. From this, we find that TC = βC

and therefore for ferromagnetic systems we can describe the susceptibility as

This modification to the Curie Law is known as the Curie-Weiss Law. Figure 3(c) shows the relation between the inverse susceptibility and the Curie temperature: when the inverse susceptibility reaches zero, the ferromagnetic ordering turns on.

To create a model for the interaction between spins in a material, the quantum mechanical Heisenberg exchange Hamiltonian is used to determine the effect on a given atomic site of its surrounding. More specifically, we are determining the effect of the internal magnetic field on a site produced by the spin moments around it. If we truncate consideration of this interaction to the N nearest-neighbor magnetic atoms, we modify the

exchange Hamiltonian from

where Jij is the exchange constant for the system, Jnn is the value for the nearest neighbor,

S is the spin of the atom being considered, and ~~is the expectation value, i.e., the~~

average value of the nearest neighbor spins. The ferromagnetic case is the case of a 12 positive exchange constant, which dictates that for the exchange Hamiltonian to minimize the energy of the system, the spins of adjacent site must be parallel.

Figure 4. Susceptability plots as a function of temperature for ideal materials with (a) Pauli paramagnetism and diamagnetism, (b) ideal paramagnetism, (c) ferromagnetism, (d) antiferromagnetism, and (e) ferrimagnetism. Magnetization plots are overlaid in (c-e), and dotted traces in (d) and (e) demonstrate the Weiss constant determination. [62] 13

~~To find a general expression for the effective field created by the neighboring spin moments, we will need to rewrite the spin as a function of the total spin~~

~~. If we do that, we can rewrite Hex as a function the moment and determine an expression for the effective field. We start by substituting into the exchange Hamiltonian~~

~~1 , and then describing as a function of µ to find~~

~~21 =~~

~~If we describe an interaction Hamiltonian between a spin moment and effective field~~

~~around it as~~

~~μμ ,~~

~~we can find an expression for the effective magnetic field on an atom as~~

~~= βM~~

~~where β, the phenomenological constant from earlier, turns out to be the Weiss constant used for describing the effective magnetic field on an atom in terms of the magnetization of the sample.~~

~~Ignoring the possibility of magnetic domains for now, the effective field in a sample now has two components: an externally applied field, and an internal field from~~

~~the interaction between spins due to previous external biasing. This creates a history~~

~~effect, or hysteresis in the sample: When the external field is turned up to fully saturate a~~

~~sample and then subsequently turned to zero, the aligning of the spins creates an effective~~

~~field that will remain when the applied field is removed. Accordingly, in order to bring~~

~~the magnetization of the sample back to zero, an oppositely oriented applied field equal~~

~~14 to the effective field is required. In an ideal ferromagnet with no domain structure, this field is known as the coercive field HC.~~

Figure 4 shows the hysteresis loop in the magnetization vs field (M vs. H) graph of a ferromagnet. Starting from no magnetic history at the origin, the initial applied field is positive and begins to approach saturation. Once the magnetization has been saturated, the field is brought down to zero, where the remnant magnetization is defined as the moment left when there is no external field and the sample is being aligned completely by . The external field continues into the negative range, flipping the magnetization to a negative value at field magnitudes exceeding the coercivity, until all spins have been flipped to the negative orientation.

Naturally, the reverse process occurs to flip the magnetization back to positive saturation. Unless the sample has its history erased with a series of ever-decreasing values of opposite direction (AC demagnetization), the sample will continue to follow the hysteresis loop like a train track as it oscillates from each saturation direction.

~~Antiferromagnetism and Ferrimagnetism~~

The arrangement of spin moments in a lattice wherein adjacent atoms with equal spin moments are anti-aligned is called antiferromagnetism. Recalling that ferromagnetic systems had an exchange Hamiltonian

~~2 wherein Jij, the exchange constant, was positive, we now look to the case where Jij < 0.~~

~~In this case, minimization of the system energy would require nearest neighbor atoms to have oppositely oriented spin orientations.~~

Figure 6. An example of antiferromagnetic ordering in a sample with oppositely oriented nearest neighbor spin moments. Oppositely oriented spin moments are also required for ferrimagnetism, in which antiferromagnetic ordering occurs but, due to differing total moments at the two anti- 16

~~aligned spins, a net moment similar in hysteresis to ferromagnetism occurs. To examine~~

~~the differences between the two classifications, we will describe the general system as a~~

two-sublattice model where we have A and B atoms that only have the other species as its nearest neighbors. If we truncate the interaction considerations to nearest neighbor pairs, as we did in the ferromagnetic case, the effective field will oppose the spin moment of the site that surrounds it. As such, we adjust the Curie Law for the ferromagnetic case,

~~Note that in addition to the change in effective field, we add notation to allow for the two~~

~~equation sublattice description~~

(

~~3 We have two Curie constants CA and CB = Nµ /3k. N is the number of atoms per unit~~

~~volume, and so for the simple case of equally spaced sublattices of equal spin moments,~~

~~we may set CA + CB = C to find~~

(

~~From this, we may describe the susceptibility of an antiferromagnet as~~

~~This equation suggests a negative curie temperature for an antiferromagnet.~~

~~Although TC in the paramagnetic and ferromagnetic cases has been indicative of the 17 magnetic ordering temperature, we cannot do the same for the antiferromagnetic case.~~

~~This is because in previous cases, TC = θp, the Curie-Weiss constant. It is clear from~~

Figure 3(d), however, that there is a transition from antiferromagnetic to paramagnetic at a positive temperature. This temperature is called the Neel Temperature TN, and represents the onset of spontaneous magnetization, i.e. paramagnetism. Determination of this temperature does not help intuition for the work in this paper, although excellent explanations can be found in the literature [62].

~~Sr2FeMoO6 is known to be a ferrimagnet, which is an intermediate magnetic state between an antiferromagnet and a ferromagnet. Ferrimagnetic materials such as~~

~~Sr2FeMoO6 have an antiferromagnetic ordering, but unequal spin moments at each site.~~

~~Figure 6 illustrates the ferromagnetic ordering, as each Fe in its sublattice has five 3d~~

~~unpaired electron spins pointing in one direction, while the single 4d unpaired spin is~~

oppositely oriented. As such there is a non-zero saturation magnetization of 4 µB/f.u. and the system is ferrimagnetic. Further discussion on the theoretical work done to determine the mechanism behind this material’s magnetic ordering is outlined in Chapter 2.

~~Figure 7. Simplified schematic of ferrimagnetic spin ordering in magnetically polarized Sr2FeMoO6, with a saturation magnetization approaching 4 µB/f.u.~~

~~1.1.4 Magnetoresistance~~

~~Magnetoresistance is defined as the change in electrical resistance due to an~~

~~applied magnetic field. This name is a catch-all term for many different effects however.~~

~~In this section, we will examine the types of magnetoresistance and their current uses,~~

~~where applicable.~~

~~Anisotropic Magnetoresistance (AMR)~~

~~It is well known that an electron moving in a magnetic field will experience a~~

~~Lorentz force. In a conducting material, it was found by Lord Kelvin in 1856 that the~~

~~resistance of the material depended on the angle between the field and the current. The~~

~~largest increase in resistance occurred when the two were parallel (or anti-parallel), and~~

~~the largest decrease came when the field and current were perpendicular to one another.~~

~~This anisotropy is used today as sensors for magnetic field direction, such as electronic~~

~~compasses. In addition, the disruption a magnetic object can have on resistance makes it~~

~~plausible to use this effect in metal detectors or traffic sensors.~~

~~Colossal Magnetoresistance~~

~~A drawback to AMR is the small (~ 5%) change that can be effected in~~

~~conventional materials. However, it was found that in more complex structures, such as~~

~~perovskites, that a much larger (in some cases an order of magnitude or more) change in~~

~~resistance exists. This effect was dubbed colossal magnetoresistance, or CMR.~~

~~Figure 8 below shows CMR results for manganese-based La2/3Ba1/3MnO3 perovskite films, in the common form of a resistance curve as a function of the applied magnetic field.~~

~~Figure 8. Resistivity vs. applied magnetic field curves at room temperature for La2/3Ba1/3MnO3 films grown at 600 °C and a similarly grown sample post-annealed at 900 °C. [71]~~

Interest in Sr2FeMoO6 was primarily generated by the discovery of temperature dependent CMR by Kobayashi et al. [1]. Figure 9 below demonstrates the change in resistance as a function of field at 4.2 K and at room temperature in the top panels, and the hysteresis at each temperature in the lower panels. The close field correlation between the magnetic domain switching in the hysteresis loops and the low-field resistivity drop suggest that the two may be related to one another. It is likely that, if the material is spin polarized to some degree, each magnetic domain in the polycrystalline sample will be randomly oriented with no magnetic field to bias them. In this case, each adjacent pair of domains will act as either a GMR or TMR device, depending on the nature of the boundary.

The low temperature saturation magnetization of 3 µB per formula unit (f.u.) drops to approximately 2.2 µB/f.u. when warmed to room temperature. Should the material be a half metal and T = 0K, Sr2FeMoO6 would still have about 60% spin polarization at room temperature, despite thermal effects. This would be a significant 20 improvement on the current metals used in MR devices, such as Fe, which is 40-45% polarized.

~~Figure 9. Graphs of the resistivity (top panels) and magnetization (bottom panels) as a function of field at (a) T = 4.2 K and (b) T =300 K. From Kobayashi et al.[1].~~

~~Giant Magnetoresistance~~

Giant Magnetoresistance refers to the heterostructure effect of two ferromagnetic layers separated by a thin non-magnetic conducting layer. Simultaneously found just over 20 years ago by Peter Gruenberg and Albert Fert, who were awarded the Nobel

Prize for the discovery in 2007, the device revolutionized the magnetic storage industry by creating micro-, and later nano-scale read heads that can be formed by nanoscale film growth. By creating a large effect out of such a nanoscale device, the memory bits were

~~21 able to be made correspondingly smaller. This proved a huge improvement over the coil- and-ferrite and metal in gap (MIG) heads used earlier, which had quickly reached a technological size limit.~~

A GMR trilayer drawing is shown below in Figure 10. The thin non-magnetic conductor separating FM1 and FM2 magnetically decouples the two ferromagnetic layers, allowing in this case the orientation of FM1 to switch independently of FM2.

~~When the two layers have antiparallel magnetic alignments as in Figure 10(a), the spin- polarized current from FM2 will (to an extent determined by the spin polarization of each~~

FM layer) not have fewer available spin state in FM1 to flow through. Those electrons will need to scatter within the non-magnetic layer until it scatters to an accessible spin state. Thus a bottleneck is created, and creating a relative high resistance state. In Figure

~~10(b), the layers are aligned, and therefore the accessible states for conduction will be~~

~~maximally compatible for the two FM layers. Accordingly, the lowest possible resistance~~

~~for the layers will be achieved in this arrangement.~~

~~If we create a layered structure such that one FM layer is unable to be switched by~~

~~a given external field (say the field from nearby magnetic storage bits), while the other~~

~~switches easily in the same field, we need only put an electric potential across a GMR~~

~~device, pass them over data storage bits oriented up and down, and read each bit’s~~

~~orientation by the current measured. This process provided the 0 and 1 signals that are~~

~~the basis of all modern computing technology, until signal improvement via TMR read~~

~~heads were created.~~

~~The technological use of the GMR device was almost exclusively a “back-and- forth” effect, but to understand the nature of the device, let us examine the hysteresis of a~~

GMR device. Figure 11 tracks both the orientation and resistance of an idealized GMR device. Starting from both ferromagnetic layers oriented to the right and following the orange path of decreasing field, the resistance remains constant until a suitably negative field flips the orientation of FM1, at which point we see an increased electric resistance.

~~Only when we reach a high enough negative field to flip FM2 to a parallel orientation to~~

~~FM1 do we see the resistance move back to the original value.~~

Figure 11. Example of ideal magnetoresistive hysteresis for a typical GMR device with different coercivities. The orange path for both the orientation switching (top diagrams) and in the R vs H plot (lower graph) runs from high positive field to high negative field. The blue path runs from the high negative field to the positive field, returning the device to its initial state. Note that the increased resistance only occurs under negative field on this half of the sweep. Once both layers are magnetically oriented to the left, we may follow the blue path of increasing/more positive field, and switch FM1 back to the right-side orientation.

This, as before, puts FM1 and FM2 antiparallel to each other and increases the resistance of the junction again. Only under higher positive field does the resistance decrease again but aligning FM2 to the right, parallel to FM1. Since the history of the GMR

~~heterostructure determines where the high resistance state occurs, this kind of data may~~

~~be called magnetoresistive hysteresis.~~

~~Tunneling Magnetoresistance~~

~~Tunneling magnetoresistance (TMR) takes the concept of GMR another step~~

~~further: By putting a very thin (~2 nm or less) insulating layer in place of the~~

~~nonmagnetic conductor in GMR heterostructures, the only method by which conduction~~

~~may occur (barring impurities, etc) is by quantum mechanical tunneling. As such, the~~

~~magnetoresistance is a simple function of the spin polarizations of the ferromagnetic~~

~~layers, according to the inset formula in Figure 12.~~

~~Originally found by Julliere et al. in 1975, the MR ratio was rather low and~~

~~ignored as an option for some time after GMR became en vogue for electronic~~

applications [82]. The discovery of higher TMR ratios (up to 70%) by use of Al2O3 tunnel barriers in the mid-1990’s [83-84] eventually led to the ubiquitous use of TMR read heads today, as the higher MR ratio allows for smaller heads as well as bit sizes.

~~Currently, bit sizes as low as 90 nm have been achieved for industrial production, with significant improvements via thermal assistance and spin transfer switching [85].~~

~~Figure 12 shows the theoretical graph of the magnetoresistance levels of an ideal~~

~~TMR device as a function of the ferromagnetic layers’ spin polarization. The blue dot on the graph shows the current state of the art, a 70% MR ratio using Al2O3 tunnel barriers.~~

As can be plainly seen, current technology barely scratches the surface of the TMR phenomenon: Any reasonable increase in the spin polarization of the TMR ferromagnetic layers would drastically change the performance, and thus size, speed, and power

~~25 efficiency, of every magnetic storage device on the planet. It is not difficult to see how research is of obvious and tremendous importance to academia, industry, and society.~~

~~The research presented herein is motivated highly by this singular feature, and it is hoped that it will move us one step closer to making next important quantum leap in computing technology.~~

The double perovskite crystal structure represents a new level of complexity in electronic and magnetic materials. The current state of the art for complex oxides is limited in most cases to the single ternary oxides such as normal perovskites with ABO3 stoichiometry. A-site doping has been shown to make some headway into property control [69], but the ability to control properties via B-site mixture of different transition 26

metals open up new opportunities for designing heteroepitaxial devices, should the challenge of making quality quaternary oxides be mastered. In this section, an introduction to the perovskite and double perovskite structures will lead into a discussion

~~of the effort to harness the vast combinations of double perovskites to make new and~~

~~unique properties, such as stable room temperature half-metallicity, a reality.~~

~~1.2.1 Introduction to Perovskites~~

~~The perovskite class of materials takes its name from CaTiO3, which was named~~

“Perovskite” for the Russian Count Lev Aleksevich von Perovski in 1839 (CaTiO3 was much later discovered to actually have a distorted perovskite structure). The ideal perovskite structure of composition ABO3 is shown in Fig. 13, with the B-site cation

~~stationed in the middle of the structure, with an A-site cation at each corner.~~

~~Figure 13. Structure of an undistorted perovskite. [60]~~

The B atoms are enclosed in each of the 6 Cartesian directions to create an O6 octahedron. Alternatively, the structure may also be described by a cubic close-packed arrangement of A-site cations and oxygen ions, with B-site ions filling the interstitial position inside each oxygen octahedron.

~~Typically, the A-site cation can be selected from the alkaline earth metals (such as~~

Calcium, Strontium, or Barium), p-orbital metals (Indium, Lead, or Bismuth are often used), or Lanthanides (Lanthanum, Cerium, Neodymium). The B-site cations are almost exclusively transition metals from the d-orbital block, due to the interesting and varied nature of those elements. Additionally, the different size and orbital structure of transition elements could help the A-B ordering when combined with the typical A-site choices.

~~1.2.2 Double Perovskite Structure~~

The double perovskite structure can be considered an elaboration of the perovskite structure. It is formed by replacing half of the cations at the B-site of the structure with another atom to create a rock-salt ordering of the B/B’ sublattice.

~~Although the physical size of the lattice may change slightly, the structure is otherwise unchanged.~~

Figure 8 below depicts a supercell of a double perovskite with ABB’O6 stoichiometry, wherein the A and B site cations still occupy the same positions relative to the oxygen octahedra. Depending on the B or B’-site cation in the middle, the planes of

~~each octahedra are correspondingly shaded purple or yellow, respectively.~~

Figure 14. A rendering of the A2BB’O6 double perovskite structure, with oxygen octahedra colored for the interior B/B’-site cation to illustrate the rock salt ordering of the B-site sublattice. A condition of mixing and matching B/B’ cations in a lattice are that the valences of the choices must be possible to wind up with a neutrally charged sample. In the case of Sr2FeMoO6, the strontium and oxygen atoms combine for a net charge of -8.

~~Therefore, the Fe and Mo must have a combined charge of +8 for the compound to be~~

~~feasible. Molybdenum can have oxidation states of +4, +5, or +6, and Fe is known to be~~

~~+2, +3, or +4, depending on its surroundings. One can see that the chemical requirement~~

~~of charge neutrality can be settled, and the lattice will choose the most energetically~~

~~favorable state.~~

~~Table 1. Table of properties for strontium-based double perovskites in the Cr, Mn, and Fe B-site families. 1.2.3 Property Control by Elemental Selection~~

~~The power of using double perovskites for application in heterostructure devices~~

~~lies in the ability to radically change the magnetic and electronic properties by chemical substitution. Within the perovskite structure, changing the elements in the A or B site~~

~~allows modification which may change several properties:~~

~~ The magnetic characterization, magnetic moment or spin polarization can be~~

~~modified via the unpaired electron number at each site.~~

~~ The electric resistivity may be modified via substitution to change the orbital band~~

~~structure.~~

~~ Isovalent substitution to the A or B sites can be used to modify lattice parameter~~

~~size to improve film-to-substrate lattice matching.~~

In the context of Sr2FeMoO6 growth, possible designs for multilayers involve keeping the strontium/oxygen sublattice to facilitate atomically sharp interface growth. An example of the vast array of ferromagnetic or antiferromagnetic materials and properties are shown in Figure 15 above. For instance, substitution of molybdenum for tungsten in

~~Sr2FeMoO6 changes the magnetic behavior from ferrimagnetic to antiferromagnetic with~~

~~TN = 40 K, and the electronic behavior from metallic to semiconducting.~~

~~The materials of interest in our collaboration include insulators for use as buffer~~

~~and tunnel layers (Sr2GaTaO6, Sr2NbCrO6), soft metallic ferrimagnets (Sr2FeMoO6), hard metallic ferrimagnets for bias layers (Sr2CrReO6, Sr2CrWO6), semiconducting~~

~~ferrimagnets for FET applications (Sr2CrOsO6), and room temperature antiferromagnets~~

~~for layer biasing (Sr2CrRuO6). By combining the properties as needed into multilayers,~~

~~nearly any type of heterostructure device may be created with atomically sharp interfaces.~~

~~Chapter 2: Introduction to Sr2FeMoO6~~

~~2.1 Theory and Background~~

Sr2FeMoO6 has enjoyed significant interest since 1998, when work by Kobayashi et al. coupled the theoretical prediction of a half-metallic ground state, i.e. 100% spin polarized, and a Curie Temperature (TC) between 410-450K [1]. Their experimental

measurements on bulk powder samples showed a TC = 415K and a negative magnetoresistance with low-field effects indicative of possible half-metallic behavior. In the years since, many papers have been published on Sr2FeMoO6 in bulk powder, single

~~crystal, and thin film form. However, the higher level of crystal and chemical complexity~~

~~needed to make a pure-phase, stoichiometric, highly-ordered quarternary oxide has made~~

~~the landscape of this work opaque, at best, due to the surprising variation in the quality of~~

~~the samples studied. As such, theoretical work has been stunted due to lack of~~

~~trustworthy data to model after.~~

~~The details of the perovskite and double perovskite structures have been laid out~~

~~in the previous chapter, as have the possibilities of isostructural substitution in the B and~~

~~B’ sites of double perovskite to create desired properties. In this section, I will give a~~

~~brief overview of the basic theory of the electronic and magnetic structures of~~

~~Sr2FeMoO6, including the theoretical basis behind the desirable properties of this~~

~~material, while touching on theoretical effects of various defects and existing disputes on~~

~~properties such as B-site valence.~~

~~2.1.1 Orbital and Electronic Band Structure~~

~~Sr2FeMoO6 has been found and characterized in the bulk powder form as a~~

nominally ferromagnetic conductor with Curie Temperature in the vicinity of 420 K since the 1960’s [51-53]. Although much of the theoretical understanding of the material at the time was nebulous at best, it was generally accepted that basic chemistry required the Fe and Mo atoms to be in the +3 and +5 oxidation states, respectively. Itoh et al. [54] found

~~a Curie Temperature of 450 K in 1996, and although that number is on the very high end of published estimates, more important was the suggestion of ferrimagnetic ordering from~~

~~superexchange interactions between Fe3+ and Mo5+ through the O2- p-orbitals, in a~~

~~similar fashion to known cousins such as Sr2MnMoO6 and Sr2FeWO6 [55]. For the next~~

~~part of the theoretical discussion, it is important to note that the above groups noticed the~~

~~metal-like conduction properties in their Sr2FeMoO6 samples, with Itoh et al. specifically~~

~~commenting on probability of unusual band structure in the Fe-containing double~~

~~perovskites.~~

~~Superexchange and Double Exchange~~

~~It is likely that the suggestion of superexchange interactions in Sr2FeMoO6~~

~~formed part of the basis for the calculations by Kobayashi et al., whose density of states~~

~~calculation results can be seen below in Figure 1 [1]. In these calculations, we see that~~

~~the up spin band is empty at the Fermi level, while the down spin band is populated by~~

the oxygen-hybridized t2g elections of both iron and molybdenum. This suggests a half- 33 metallic state with 100% spin polarization, wherein only the down spin electrons can travel through the material as conduction carriers.

Figure 15. Density of States calculation of Sr2FeMoO6 from Kobayashi et al. [1] The up spin band is shown in this work to be unpopulated in the vicinity of the Fermi Energy, leaving the populated down-spin band as the sole source of conduction. It is at this point that some divergence in opinions occurs in the literature. The problem arises, in part, due to the fact that there are difficulties in directly classifying the

~~ordering mechanism in Sr2FeMoO6 as either superexchange or, as was later offered in the~~

~~literature [6,48,49], double exchange.~~

~~For Sr2FeMoO6, the 5 electrons in the half-filled Fe 3d orbitals are localized with~~

~~1 a total moment of 5 µB and the single electron in the Mo 4d orbital has a moment of 1~~

~~µB. In superexchange model, antiferromagnetic coupling between anion-mediated, or in~~

~~this case oxygen-mediated cations, occurs when the bonds between the cations and the~~

~~oxygen form a 180 degree bond angle. In this case, we have a Fe-O-Mo-O-Fe chain in~~

~~such a bond arrangement with antiparallel alignment between the Fe 3d5 electrons and the~~

~~Mo 4d1 electron. This results in a ferromagnetically-coupled Fe sublattice with a total moment of 4 µB per formula unit (f.u.) [1].~~

Unfortunately, strict adherence to the superexchange model in the Sr2FeMoO6 system is problematic. For instance, it is pointed out in Garcia-Linda et-al. [6] that the metallic property of the compound suggests that there must be an itinerant electron, and thus likely plays a central role in the magnetic ordering of the sample. However, superexchange coupling between nearest-neighbor Fe-Fe or Mo-Mo atoms should be very weak over the large distance of the Fe-O-Mo-O-Fe chain (~ 8 Å), indicating that the magnetic interaction is not between Fe atoms or Mo atoms, but through the Fe-O-Mo interaction. This interaction between the 4d1 and 3d5 orbitals is not one of

~~superexchange, which strictly speaking has no itinerant electrons since the model~~

~~assumes equal d-shell occupancy or a difference of two. In addition, various works by~~

~~Sarma et al. [11,16,18] and Martinez et al.[49] suggest that the five-fold degeneracy of~~

~~the Mo 4d states will cause a very weak coupling to the localized Fe electrons in a~~

~~superexchange mechanism and could not be compatible with the high Curie~~

~~Temperatures seen experimentally.~~

~~Another model floated for use in describing Sr2FeMoO6 is that of a double-~~

~~exchange mechanism [6,48,49]. In double-exchange, a hopping mechanism is created for~~

~~electrons to travel between cations so as to reduce the kinetic energy of the sample.~~

~~When this mechanism is correct, itinerant electrons do not have to expend energy in~~

~~switching spin direction to satisfy Hund’s Rules. This mechanism is better for metallic~~

~~conductivity, as it allows hopping from Fe to Mo sites (and vice versa) through~~

~~hybridized oxygen 2p orbitals.~~

~~A possible problem with the double exchange mechanism is pointed out in D.D.~~

~~Sarma’s 2001 paper [18], in which he points out that the density of states calculations~~

~~include down spin Fe 3d states at the Fermi level. To satisfy Hund’s rules, the itinerant~~

~~electrons must ferromagnetically couple to the localized electrons, but the exactly half-~~

~~filled 3d Fe orbitals with 5 localized electrons have no place for more electrons.~~

~~Therefore, it is argued that double exchange is also not a suitable solution for the~~

~~mechanism of Sr2FeMoO6.~~

~~So far, one can see that the superexchange mechanism is an incorrect~~

~~interpretation for Sr2FeMoO6, and also that the double exchange mechanism in the strict interpretation (Hund’s mediated exchange) cannot exactly describe our system.~~

~~However, it was found that only small tweaks to the double exchange method may be~~

~~used to create an excellent model. To do this, we recall that we know that there is a~~

~~ferrimagnetic ordering between adjacent Fe and Mo atoms in the lattice, due to X-Ray~~

Magnetic Circular Dichroism measurements [20,25,58] that clearly show opposing magnetic moments for Fe and Mo. Therefore, we may work from the assumption that any good mechanism to describe Sr2FeMoO6 has this end result, as well as metallic conductivity.

Figure 16. Energy Level Schematic for (left column) the localized Fe 3d band states, and the delocalized Mo 4d - O 2p hyrbridized states without (center column) and including the effects of hopping interations (right column). Figure 2 below shows a series of energy level diagrams explaining a modified mechanism proposed by D.D. Sarma’s group [18,56,57]. In the left column, we see that the Fe site has two energy splitting effects occurring to the 3d level. First, the exchange splitting of both the eg and t2g levels create the large energy separation between each spin up and spin down state. This effect is known to be large for the 3d5+ configuration [11].

~~We then have the crystal field splitting of the eg and t2g states that create a separation~~

~~between the levels of the orbitals of each spin. The Fermi level in this diagram is in~~

between the two energy level pairs, closer to the lower energy side. The eg and t2g states are half-occupied, with all up-spin levels occupied by the five localized electrons on each iron site. The middle column shows the levels of the Mo 4d – O 2p hybridized states before any consideration of hopping interactions, with the lowest of the hybridized states sitting about 1.4 eV above the occupied Fe sites. One can see that there is very little exchange splitting, but a significant crystal splitting.

If we recall that the band structure calculations predict a significant Fe contribution to the down-spin density of states, it is argued in [18] that there must be a coupling between from the down spin delocalized electrons and the Fe states of the same spin due to the hopping between those sites. Thus, the high level of exchange splitting in the Fe site states would pass some of its character to the hybridized Mo-O states, splitting the spin levels and creating the column on the right. This brings the down-spin t2g state to the Fermi level, and moves the up-spin state to an even more inaccessible energy. This makes it very simple to see that the 4d1 electrons at the Mo site should have an

~~antiparallel alignment to the localized 3d5 electrons, and thus a ferrimagnetic ordering in~~

~~the system.~~

~~To do this, however, we need to loosen up our definition of double exchange to~~

~~include other mechanisms for determining itinerant spin orientations with respect to the~~

~~Fe core electron spins. If we allow this, we can cite the Pauli Exchange Principle for the~~

~~Fe 3d orbital and use this as our rule for spin determination, creating a “Pauli-Mediated~~

~~Double Exchange.” Looking at it from the other side, we would be employing the Pauli~~

~~Exclusion Principle to the half-filled Fe orbital, and determining that minimizing the~~

~~energy of the system requires that any “Mo-based” itinerant electron undergoing a hopping interaction through the Fe atom will be anti-aligned with the Fe 3d5 electrons to~~

~~avoid loss of kinetic energy due to spin disorder scattering.~~

~~2.1.2 Effect of disorder on material properties~~

~~In the ideal situation presented by Kobayashi et al. [1], the 5/2 spin number for each Fe site will be oppositely directed to each Mo 1/2 spin moment, creating a total~~

~~saturation magnetization of 4 µB per formula unit (f.u.) and a Curie Temperature of 410-~~

450 K. However, these are values that have not been reliably met, indicating some defects in the material. A flurry of experimental work to study the effects of fabrication methods on the magnetic and structural properties, many of which focus on the most likely suspect of B-site cation ordering [13-16], was published in an attempt to understand and control material properties.

~~Using the experimental results of Kobayashi et al. for comparison, Monte Carlo simulations by Ogale, Ogale, Ramesh, and Venkatesan [4] investigated the dependence of~~

~~B-site (anti-site) disorder and on the magnetic and spin properties of Sr2FeMoO6. Figure~~

~~3(a) below shows the simulation results for saturation magnetization of stoichiometric material as a function of temperature, for anti-site defect percentages of 0, 5, 10, 15, and~~

20%. We see by reorganization of the data to linear fits in Figure 17(b) that the degradation of both Curie temperature and saturation magnetization decrease linearly with defect concentration. This makes sense, as any Fe-O-Fe or Mo-O-Mo ordering will result in an antiferromagnetic ordering, locally nullifying the field. However, that does 39 not mean 20% defects correlate to a 20% lower magnetization: Any “misplaced” B-site cation will likely affect the behavior of the six nearest B-site neighbors, and likely cause the disorder to ripple out some further distance.

~~(black squares) and Curie Temperatures (open circles) to linear fit lines as a function of anti-site defect concentration.~~

It is demonstrated here that in Sr2FeMoO6 the Fe-Mo ordering that is theoretically crucial for half-metallicity has a very sensitive effect on the magnetic properties of the material. The bottom left corner of Figure 17(b) indicates that for the 13% concentration measured in Kobayashi et al. fits with the theory reasonably well, as it predicts the proper

Curie temperature and Saturation Magnetization at T = 5K. We will come back to this theoretical work in light of our experimental results later in this work to confirm the correlation of our ordering and magnetic measurements.

~~Another interesting result has very recently come out of Sarma Group, wherein~~

~~Meneghini et al. investigated correlations in the spatial nature of anti-site defects via~~

~~simulation as well as XAFS. Figure 18 shows the simulation results, challenging the~~

~~previously held assumption that such defects were homogeneously distributed throughout~~

~~the sample at any double perovskite ordering parameter ξ.~~

~~Figures 18(a)-(c) have a set coefficient for long-range ordering, and have ordering~~

~~of ξ = 0.63, 0.85, and 0.99, respectively. We see that at high disorder the defects are~~

~~indeed homogeneously distributed, but as ξ is increased, the anti-site defects segregate themselves into patches wherein the Fe and Mo are switched in site from the rest of the~~

~~material, but properly ordered with respect to the cluster. Formation of these regions~~

~~separated by anti-phase boundaries (APB) appear to be energetically favorable and would~~

~~appear at first blanch to be a very fortunate behavior, making it much easier for the vast~~

~~majority of the film to be ferromagnetically ordered and create the structure necessary for~~

~~half-metallicity.~~

~~However, it has been shown that magnetic domain walls are easily coupled to an~~

~~anti-phase boundary due to strong antiferromagnetic coupling of the atoms across APB~~

~~[59]. Illustrated in Figure 18(d), the presence of an external magnetic field does not~~

~~easily remove the pinning force at the wall. This pinning does not allow adjacent~~

~~domains to align with one another properly when the domains are plentiful. Although the~~

~~antiferromagnetic ordering of the APB itself is not likely to realign, as the ordering~~

~~improves we will have domains large enough that the pinning at the boundaries becomes~~

~~of less importance in the overall switching of the domain.~~

~~2.2 Previous Work on Sr2FeMoO6~~

~~A large amount of literature on both bulk samples and thin films of Sr2FeMoO6 has been published in the twelve years since the prediction of its half-metallicity.~~

~~Although production of bulk powder and crystal is thought to be reasonably well- understood, creation of a high-quality thin film and proof of half-metallicity are still very much open questions.~~

The following sections will attempt to summarize the progress made in synthesizing and characterizing each material form, as well as identify the obstacles that have delayed understanding and application of Sr2FeMoO6 in thin film devices.

~~2.2.1 Bulk Powder~~

~~Much of the most reliable characterization on Sr2FeMoO6 is due to work done on~~

~~bulk powder samples, as this form is the only one which has produced results found to be~~

~~repeatable by multiple groups. The majority of powder samples (including those used for~~

~~production of sputter targets in our work) roughly follow the original publication’s solid-~~

~~state synthesis procedure, including (1) calcinations of mixed strontium carbonate, iron oxide, and molybdenum oxide in air at 900°C, (2) grinding and pressing into pallets, and~~

(3) sintering in a reducing atmosphere at 1200°C [1]. Although variations on the recipe exist [6,10,40], many of the most reliable results over the years seem to come from closer adherence to this procedure[16,20,34,42].

~~Original interest from Kobayashi et al. sprung from not only the theoretical~~

~~prediction of half-metallicity but also a strong experimental implication of the significant~~

~~negative magnetoresistance (MR), as shown in Figure 2.2.1.1. The magnitude of the MR~~

~~(~40% at 4.2 K and ~10% at room temperature) implies high spin polarization close to~~

~~100% for a randomly aligned powder sample in which spin-dependant scattering occurs~~

~~at grain boundaries. More importantly, the high spin polarization largely survives at~~

~~room temperature, allowing room temperature applications of this half metal.~~

~~In addition, a Saturation Magnetization MSat= 3µB per formula unit (f.u.) was~~

~~found at T = 4.2 K, reasonably close to the theoretical ideal of ~ 4µB/f.u. , considering~~

~~that the sample was in pressed powder form as opposed to a solid crystal. A TC of 415K for the material was found.~~

~~Magnetoresistance in Bulk Samples~~

A change in MR can be a powerful diagnostic tool for probing the ordering and defects in Sr2FeMoO6. For instance, Figure 2.2.1.2 shows the effects of disorder on the magnetoresistance by comparing a disordered and an ordered sample with that of the above results. By testing against the standard from Kobayashi et al., they are able to make a case for high-level ordering [13] and thus good sample quality.

Figure 20. Magnetoresistance (MR) curves for “ordered” and “disordered” powder samples by Sarma et al., as compared with Kobayashi et. al.[1], at T = 300K (upper panel) and T = 4.2 K (lower panel). Although the difference is much less at 300 K, the magnetoresistance of the ordered sample is clearly improved at 4.2K compared to that of Kobayashi et al. (Adapted from [13]) Another example is the work of Garcia-Landa et al., who found a greatly diminished magnetoresistance with samples containing ~10% SrMoO4 impurities [6].

~~Studies on bulk single crystal [15] used MR measurements to find the effective~~

dependence of electrical transport in Sr2FeMoO6 on B/B’-site disorder. An enhanced MR during an attempt to control oxygen content in polycrystalline powder samples instead discovered the problem of uneven oxidation of grains, leading to unreacted precursor grain middles and SrMoO4 formation on the surfaces [19].

~~Magnetization Measurements in Bulk Samples~~

~~Just as ubiquitous as MR curves in the literature, magnetization measurements are~~

~~excellent indicators of B/B’-site ordering in double perovskites, as both the saturation~~

~~magnetization (Msat)and Curie Temperature (TC) require rock-salt ordering for opposite~~

~~spin moment alignment of the Fe 3d5 electrons and the Mo 4d1 electron. This creates a~~

~~ferrimagnetic behavior that is very sensitive to any anti-site (AS) disorder or non-~~

~~stoichiometry that forces incorrect atoms into non-ideal B/B’-sites.~~

An highly useful example is shown in Figure 2.2.1.3 below. Powder samples of varying Fe/Mo stoichiometry were magnetically characterized and clearly map out the degradation of both TC and Msat with increasing off-stoichiometry [42]. This roadmap is

~~particularly useful as both a tool to pre-diagnose stoichiometry problems and a basis for~~

~~understanding non-ideal magnetic response in slightly off-stoichiometric films with~~

~~otherwise ideal B/B’-site ordering. It should be noted that similar work was done in 2003~~

~~by Liu et al. [29]. Although less convincing than [42], the saturation magnetization data~~

~~follows the same linear trend and extends Sarma et al.’s data into the 25% to 50% Fe-~~

~~heavy region, while noting a variance in TC as the off-stoichiometry exceeds 30% Fe-~~

~~rich.~~

Figure 21. Magnetic Characterization of Sr2Fe1+xMo1-xO6 powder samples, showing (a) (a) Curie Temperatures and (b) Saturation Magnetizations with varying B-site stoichiometry. (Adapted from [42]) Magnetic measurements have also been used to determine the optimal sintering temperature for high magnetic ordering [14], and find the magnetic response (MSat, TC, and hysteresis shape) as a function of the level of anti-site disorder in the bulk sample

~~[14,26,31]. Work by Sanchez et al. in 2004 shed light on the effect of electron/hole doping via magnetic response by measuring samples with varying levels of La-doping~~

~~(electron doping) or Sr-deficiencies (hole doping) [36]. Finally, Fang et al. showed a good example of diminishing moment due to excess SrMoO4 from off-stoichiometry~~

~~[40], especially in conjunction with their data showing enhanced MR values with increasing SrMoO4 content, in nice agreement with [19].~~

~~2.2.2 Thin Films by Pulsed Laser Deposition~~

The vast majority of growth and characterization of thin film Sr2FeMoO6 has been done via Pulsed-Laser Deposition, or PLD. Despite the large amount of literature on thin films by this method, pure-phase films with good magnetic quality indicative of half-

~~metallicity have been scarce. In this section, I will focus on analysis of the film purity~~

~~which has proven elusive in thin film form thus far: Any analysis of reported magnetic~~

~~characterization of films becomes muddled with any introduction of impurity phases.~~

~~Also, the desirable trait of these materials, that of a half-metal, cannot be used for~~

~~applications with spin scattering impurities (particularly conducting ones, as many of~~

~~them are) present, so the primary focus should be finding the method for making a phase-~~

~~pure sample.~~

~~The most common method used in the literature to test phase-purity is x-ray~~

~~diffractometry (XRD). Although nearly every paper on the subject either shows or~~

~~alludes to XRD spectra, very few claim to have phase pure films, and of those, none~~

~~show spectra that give a compelling argument for it, due to impurity phases,~~

~~polycrystalline phases, a linear scale preventing detection of a possible non-epitaxial~~

~~phase or impurity, or some combination thereof.~~

~~Figure 22 on the following page shows a series of XRD spectra from thin films~~

~~grown by PLD over the years, each chosen for a different defect that can be seen in the~~

~~spectra. For example, Figures 22(a) and 22(b) show relatively early film growths by~~

~~Manako et al. in 1999, and were grown on (001)- and (111)-oriented SrTiO3 substrates,~~

~~respectively [2]. Although the peak at 2θ ~ 42°, seems small, the peak is most likely a~~

reasonably-sized metallic iron impurity or, depending on the exact value, a non-magnetite iron oxide, as the size is not too small compared to the main film peak, especially in light of the apparently lower signal to noise ratio of the diffractometer being used. Similar

~~features are common in PLD literature [23,24,28,33,35,44], and are either ignored or~~

~~mentioned but uninvestigated, left to conjecture on off-stoichiometry or inhomogeneity.~~

~~Figure 22(c), from Yin et al.[5], also has the same impurity peak, but it is nearly~~

impossible to see due to use of a linear intensity scale instead of a logarithmic one, as is usually the case for epitaxial thin films. Close examination also find a peak at approximately 44°, commonly identified as magnetite Fe3O4. Magnetite can grow

~~epitaxially on Strontium Titanate, and thus is a very common problem, made even more~~

~~troublesome due to its ferromagnetic properties that can obfuscate the magnetic~~

~~characterization of one’s films. Additionally, the half-metallicity of Fe3O4 may end up~~

~~causing trouble when spin-polarization measurements begin to be taken in future work,~~

~~so special care of this impurity must be taken. Examples of such found impurities are~~

~~plentiful and continue to be a problem to date [24,35,41].~~

~~More common to the literature is a combination of iron and iron oxide impurities,~~

~~as in Figure 22(d) from Besse et al. [23]. One can not only have these iron-based~~

~~impurities [5,41,44], but it is also very possible to also have Molybdenum-based phases,~~

~~most commonly SrMoO3 [37,47] or SrMoO4[24, 33, 35,45]. Interestingly, one can see~~

~~the evolution of the SrMoO4 phase as an oxidized phase in Santiso et al.’s work in Figure~~

~~22(e), wherein an increased oxygen growth pressure stimulates several orientations of the~~

~~impurity phase [24]. Figure 22(g) takes this a step further, as Sanchez et al. also found a~~

~~polycrystalline phase of Sr2FeMoO6 with increased oxygen, which was suppressed under~~

~~lower oxygen growth pressure [33].~~

~~Figure 22. X-ray Diffractometry (XRD) spectra from a variety of different papers on thin film growth by Pulsed Laser Deposition.~~

~~There remains two reports of film growth by PLD that cannot be ruled out for~~

~~being pure-phase: Shinde et al. in 2003 [27], and Kumar et al. in 2010 [45], whose~~

~~spectra are shown in Figures 22(f) and 22(h), respectively. In the former case, the data is~~

~~presented in linear scale, making it difficult to determine the impurity level. However,~~

~~the rocking curve data presented shows a Full-Width-at-Half-Maximum (FWHM) of~~

~~0.6°, which is certainly cause for concern regarding the film quality, given other reports~~

~~that place FWHM for the material below 0.3° despite impurity phases or less-than-~~

~~desired material properties [7,33].~~

~~A linear scale is also used in Kumar et al, where a low, broad feature on the film~~

~~grown on SrTiO3 seems to exist around 2θ = 43°. Additionally, c-axis lattice constant for~~

~~this sample is just above 8.02 Å, well above the bulk value and significantly larger than~~

~~what could be caused by tetragonal deformation due to the in-plane lattice strain. Despite~~

~~the relatively high moment at T = 5K reported (3.24 µB/f.u.), the hysteresis shape is poor~~

~~and indicative of a more lightly correlated system than that of Sr2FeMoO6.~~

~~2.2.3 Thin film growth by Magnetron Sputtering~~

~~Aside from the work presented later in this paper [38], literature on thin film~~

~~growth is limited to Dr. Masaaki Matsui’s group during his tenure at Nagoya University in Japan [17,21,38]. Growing in a reducing atmosphere of 5% H2 + Ar and a total~~

~~pressure of 76 mTorr, it was reported that a pure-phase film with saturation~~

~~magnetization of 3.8 µB/f.u. and Curie Temperatures around 380 K could be achieved.~~

~~Although these results will be discussed in light of our own work, an analysis of these~~

~~results as they stand alone is necessary. 51~~

~~Figure 23 below shows the XRD and magnetic hysteresis of Sr2FeMoO6 thin films grown on both bare (001)-oriented SrTiO3 substrates, and with a Barium-doped~~

~~SrTiO3 buffer layer [21]. Concerning the XRD results, it is difficult to confirm the~~

~~conclusion of phase purity by the spectra presented, as (1) it appeared that the XRD~~

~~results shown were performed on a triple-axis diffractometer, which is ideal for epitaxial~~

~~film characterization, but insensitive to impurity phases, (2) the vertical scale is cut off at~~

~~10 counts, and (2) the 2θ scale is very closely packed, both of which prevent closer~~

~~examination of features such as those in the 42-44° region (the region identified in the~~

~~previous section to be mainly attributed to metallic Fe or iron oxide phases), particularly~~

~~what may be a shoulder at ~ 44.2 degrees. In addition, a small peak at ~ 65° may be~~

~~showing itself. These possible phase impurities are found in both the buffered films of~~

~~Figure 23(a) as well as the unbuffered films in Figure 23(b). Diffraction patterns also~~

~~shown in [21] for buffered substrate alone do not appear to have any of these~~

~~irregularities and would merit further investigation to determine their cause.~~

~~Figure 23(c) displays a hysteresis loop of a film grown on buffered substrate at T~~

~~= 77 K. Vibrating Sample Magnetometry was used to magnetically characterize the~~

~~sample [17,38]. It is important to note that the claim of 3.8 µB/f.u. at room temperature is~~

~~based on the peak values of the sample at 14 kOe, the highest field shown. It is generally accepted that the saturation magnetization be taken from the linear extrapolation of the~~

~~high-field slope. As there is clearly a paramagnetic contribution to the signal, either from~~

~~the substrate, buffer layer, or impurities within the film, taking the magnetization at the~~

~~highest field clearly exaggerates the true value of the saturation magnetization. Proper~~

~~analysis is adapted into Figure 23(c), wherein a linear projection (in light green) pegs the~~

~~actual number at about 2.9 µB/f.u., a number much more in line with most literature values (including our own, as will be seen).~~

Figure 23. (a-b) X-ray Diffraction spectra of Sr2FeMoO6 thin films on (001)-oriented SrTiO3 substrates, (a) with Barium-doped SrTiO3 buffer layer, and (b) directly on substrate. (c) Magnetic hysteresis loop of film grown with buffer layer at T = 77K. Parts in green are added here for analysis of proper value of the Saturation Magnetization. (Adapted from [21]) However, this value must be taken in context with the poor hysteresis shape, which should be much squarer for an in-plane measurement of a film with the level of long-range ordering that would exist in a film of this moment. Indeed, the shape looks more rounded, close to the hysteresis from bulk samples of comparable moment [14,31], which due to grain boundaries should produce less square hysteresis than single crystal

~~53 films of the same moment. At the very least, similar shapes should be seen, but the rounding in Figure 23(c) creates questions about the film.~~

~~Chapter 3: Thin Film Deposition Methods~~

~~The ability to fabricate a high-quality double perovskite in thin film form is~~

~~critical both for study and applications. To do so, any process used would require proper~~

~~placement and stoichiometric balance of oxygen and three different cations throughout~~

the entire crystal. Impurities such as oxygen defects or anti site disorders, such as those covered in Section 2.2, could create lattice distortions or strain, non-ideal band structure or diminished magnetization or spin polarization.

Pure samples are especially critical in the thin-film regime, as impurities will be a major detriment in nanoscale devices. This is extremely crucial for half-metal devices, as the spin polarization is very sensitive to impurites. Additionally, as future applications begin to require film dimensions below that of the relaxation thickness, impurities not only become a larger proportional effect but may also cause faster strain relaxation in perovskites.

~~3.1 Magnetron Sputtering~~

~~Magnetron sputtering is a particularly flexible technique for depositing thin films~~

~~of nearly any material onto a substrate. The technique uses energetic ion bombardment~~

~~to eject atoms from a target of proper composition. Fig. 2 shows a typical arrangement~~

~~for this technique.~~

~~Magnetron sputtering first utilizes an electric field to accelerate positively charged~~

~~Argon ions towards a target. The field is generated by applying a negative voltage to the~~

~~target, and a potential of a few hundred Volts is typically necessary to give the~~

~~bombarding ions enough energy to break the binding energies at the impinged lattice site~~

~~and sputter atoms off the target’s surface. Note that the energy of the ion must be several times that of the binding energy of the material, as the energy transfer due to such a~~

~~collision may not be isolated to one atomic site.~~

~~With only an electric field, sputtering would require a prohibitively large Argon~~

~~pressure to create a meaningful deposition rate. In order to increase the ionization rate~~

~~(and thus the sputter rate), we utilize the electrons emitted from the target in a secondary~~

~~effect of the electric field. By means of a simultaneous magnetic field, the electrons are~~

~~held in a cycloidal path near the target long enough to greatly increase their chances of~~

~~colliding with and ionizing a neutral Argon atom. Each new collision creates new free~~

~~electrons, perpetuating a steady cycle of material sputtering.~~

With this second field, sputtering can occur with a useful deposition rate, and at low (several mTorr) Argon pressures as well. Sustaining a solid deposition rate at low pressures ensures that films grown via this method will adhere strongly to the substrate and favor epitaxy, especially when the substrate is heated to increase initial mobility of the film constituents. It should be noted that neither field affects the neutral atoms knocked out of the target.

Conductive films can usually be grown via a DC electric field as the electrons that perpetuate the sputtering cycle may flow freely through the target. Semiconductors and insulators have no such flow, and so for these types of films an AC (RF) power source is required to continuously neutralize the charges in the target and maintain a high ionization rate. Additionally, the nature of the magnetic fields used to trap secondary electrons cannot be uniform across the target, and as such there is a non-uniform ablation of the target, slightly decreasing the amount of material that can be used before the target is sputtered through. This effect can be minimized via magnet placement design, but will still occur to some degree. 57

~~3.2 Pulsed Laser Deposition~~

Developed in the 1960’s, pulsed laser deposition (PLD) was of little interest until the growth of high-quality YBa2Cu3O7 in 1987, which catalyzed rapid development of the technique, as well as a significant increase in systems used. The method requires a high/ultra-high vacuum chamber that can either be run in vacuum or fed certain gas environments depending on the desired growth.

Figure 25. A simple schematic for a Pulsed Laser Deposition System. [87] PLD gets its name from the laser pulses that are focused into the chamber via a window on the vacuum chamber. The pulses hit a bulk target of the material desired in the film form. The pulses are kept short (a few tens of nanoseconds) so that the target will not have time to dissipate energy through the target. As the laser hits the target, the

~~photonic energy will be converted to thermal and chemical energy, and the incident~~

~~material can reach temperatures of over 3000 ºC, decomposing the material into~~

~~particulates up to a few microns in size. These particulates spread out to create a plume of ions, neutral atoms, electrons, and molecules, which travels toward the substrate,~~

~~lands, and cools into a film. One possible arrangement is shown in Figure 25.~~

~~Pulses with energy density of a few J/cm2 typically vaporize a quantity of material equivalent to few hundred angstroms at the place of contact with the target. Only a small~~

~~fraction of that material will successfully travel across the gap between target and~~

~~substrate, and as such, the growth rate with PLD is comparatively low. By heating the~~

~~substrate to facilitate mobility within the substrate, growth of high quality thin films are~~

~~is possible via this method [88].~~

~~There are some shortcomings to PLD, such as the small angular spread of the~~

~~plume, limiting the surface area that can be deposited evenly across. Rotation of target~~

~~and substrate can be used to partially mitigate this limitation. Another difficulty exists in~~

~~the need for a uniform target, as each particulate that reaches the substrate consists of all~~

~~the material in a particular region of the target. For example, an oxygen deficient part of~~

~~a target may end up reflected in the film as oxygen vacancies, adversely straining and~~

~~thus affecting the rest of the film. Finally, care must be taken to control the position of~~

~~the plume with respect to the substrate, as getting too close to the substrate may create a~~

~~more uneven film due to higher-energy particulate splashing.~~

~~3.3 Molecular Beam Epitaxy~~

~~Molecular Beam Epitaxy (MBE) was invented in the 1960s at Bell Labs by J.R.~~

Arthur and Alfred Y. Cho as a method to study the kinetics of adsorption and desorption of Ga and As on GaAs surfaces, and simultaneously refined as a method for making high- quality films from the structures observed in those studies [89]. The method works by sending one or several atomic/molecular beams at a substrate from one or more sources via evaporation. To be sure of an even beam hitting the substrate, the growth must be done in ultra-high vacuum, preferably on the order of at least 10-10 Torr.

~~A simple MBE setup is shown in Figure 26. Effusion cells will evaporate~~

~~material at a rate from one monolayer per second to one monolayer per minute. At such~~

~~low deposition rates, one layer of atoms at a time can be deposited, and when properly~~

~~heated, the atoms can organize into atomically smooth films. In situations where~~

~~substrates need to be cooled instead of heated, Liquid Nitrogen cooled substrates afford~~

~~growth temperatures down to 77 K. Growth temperatures between 80 K and 1000 K~~

~~have been reported.~~

~~Several characterization techniques can be used in situ during the growth. A~~

~~RHEED (Reflection High Energy Electron Diffraction) detector can monitor the growth~~

~~rate by detecting the intensity of electrons reflected off the surface. The beam intensity~~

~~maximizes with a flat surface, and minimizes when a layer is approximately half formed.~~

~~As such, each intensity oscillation is an indicator of a complete monolayer forming, and a~~

~~count of these oscillations provides the film’s thickness given the width of each~~

monolayer. Additionally, Auger electron spectroscopy can give confirmation of the 60 atoms present in a sample, and modulated beam spectrometry can allow the chemical species and growth kinetics to be monitored.

Figure 26. A simplified setup for a Molecular Beam Epitaxy chamber. [90] The low deposition rate of MBE lends itself to low-impurity, nearly perfect crystal structure, relative to other methods. However, the machine requires a substantially larger financial commitment compared to other methods. Also, growth of alloys cannot be done from a single target: Multiple sources must be put into the system, and finding the proper balance of evaporation rates for complex materials such as perovskites is a very complicated problem to solve. Another problem occurs for low temperature growth, where the adsorption of impurities into the system walls require an even lower system pressure in order to maintain the same low impurity count.

~~Chapter 4: Characterization Methods~~

~~Accurate characterization of the structural, magnetic, and electronic structure of~~

~~half-metallic thin films is crucial not only to understand the underlying physics of the~~

~~material but also to guide in the search of the proper growth conditions for~~

~~stoichiometric, pure-phase films with proper ordering. In this chapter, we review the~~

~~instrumentation used in our experimental work.~~

~~4.1 X-Ray Diffractometry (XRD)~~

~~X-Ray diffractometry is a highly powerful, non-destructive technique for~~

determining the lattice spacing, phase purity, and (where applicable) the atomic ordering of powder, single crystal, or epitaxial thin films. In this section we will discuss both the simplified Bragg and electron scattering theories, and introduce the two types of diffractometers used in this work.

~~4.1.1 Introduction and Theory~~

Figure 27 shows the most basic interpretation of x-ray diffraction from an atomic lattice (in this case, a roughly cubic structure). An incident monochromatic x-ray beam with a wavelength of similar order to the atomic spacing d (~0.3 nm) will undergo constructive interference with other reflected x-rays if the difference in path lengths between reflections is an integer multiple of the wavelength of x-ray used. In this interpretation, we treat the horizontal atomic rows as planes to reflect off. Given the

angle θ as diagrammed in Figure 27, one can see that for both the incident and reflected halves of the beam’s path, the difference in path lengths is equal to d sin θ. Therefore, the total difference path lengths is twice that and we arrive at Bragg’s equation

~~sin .~~

Figure 27. Diagram of x-ray diffraction off a simple crystal lattice. Green waves demonstrate the constructive interference that gives rise to peaks according to the Bragg equation. [91] Clearly, the idea of x-rays reflecting of an imaginary plane drawn between atoms, while accurate enough for determination of d-spacing, requires refinement to extract further information from the system. Von Laue hypothesized in 1912 that there would be diffraction angles that produced constructive interference in a periodic lattice, and that for all others the integration of diffraction off every site would wash out to the background.

~~To find these points, it is easiest to use a Ewald construction to find the requisite angles, as shown in Figure 28.~~

~~For this, we map out the crystal position (origin) in real space, along with the~~

~~origin point of lattice in reciprocal space, where any of the planes in real space can here~~

be described as a point. If we describe this point as Miller indices h,k,l, we are actually describing a set of integer multiples of each point, defining a range of possible sites that would lead to diffraction, i.e. atomic sites. In the Ewald construction, a sphere of radius

1/λ is drawn around the crystal point, and if the crystal is rotated in a polar direction in the plane of the page, certain angles θ that will satisfy the Laue conditions can be identified by the intersection of reciprocal space points with the Ewald sphere.

~~By rotating through in this manner, we may find all angles θ in which constructive~~

~~interference will cause a peak to occur in the diffractometry spectra.~~

~~One should note that the angles at which constructive interference occurs does not~~

~~depend on the element from which the x-ray is diffracting [92]. However, it is very~~

~~useful to note that the intensity of said reflection may vary due to the species the~~

~~diffraction is occurring from, as some information may be gleaned as a result. Let us~~

~~model the intensity I of a certain reflection hkl as~~

~~Were F is called the structure factor of a given lattice, clp is a coefficient of absorption~~

~~due to the geometric/polarization setup of the instrument and cabs is the absorption~~

~~coefficient of the same.~~

~~Calculating the structure factor is a little bit of work. To find the structure factor~~

~~of a whole lattice, we may write the amplitude of the factor as a periodic function~~

~~for n lattice sites, to sum over. We require a description for amplitude of scattering for~~

~~each atomic site, and a description of the phase within the periodic lattice.~~

~~We will start with modeling the scattering amplitude by defining the atomic~~

~~scattering factor f. This quantity is an angle dependent ratio of the scattering amplitude~~

~~due to scattering off the atom versus the same off one electron in the atom [92]. This~~

~~changes proportionally as a function of the atomic number Z, and falls off with larger~~

~~angle θ. This has two consequences. First, different elemental orderings will change~~

~~peak intensities, allowing models of local ordering within the reach of the Ewald sphere~~

~~to be made. Secondly, peak intensities will becoming lower as one travels to higher~~

~~angles, and thus to higher order diffraction peaks.~~

~~Turning to modeling of the phase next, any hkl reflection resulting from two atoms at (0,0,0) and (x,y,z) will have a phase difference of~~

~~Combining the amplitude and phase portions, we arrive at~~

~~From this expression, models based on a unit cell may be expanded out to determine~~

~~which peaks will exist, and with what frequency. Computer programs such as TOPAS by~~

~~Bruker make the process simpler by providing simulations and fitting tools to determine~~

~~the lattice symmetry, ordering, phase, and sometimes composition of a given sample.~~

~~4.1.2 Focused Beam Diffractometry~~

~~Focused Beam Diffractometry is one of two XRD methods we have used in this~~

~~work to determine the phase purity, ordering, and lattice spacing of both bulk powder and~~

~~thin film Sr2FeMoO6 samples. This mode is created via divergence slits placed directly~~

~~after the x-ray source, as in Figure 29. The name “focused beam” does not come from~~

~~focus on the incident beam on the sample, but on the detector. The divergence slit creates~~

~~geometry wherein after reflection the beam will refocus directly on the detector, and is~~

~~referred to as Bragg-Brentano geometry. This method maximizes the intensity of~~

~~66 reflected peaks, making it ideal for high resolution of very small impurity peaks and very accurate intensity measurements for ordering.~~

~~Figure 29. Schematic drawing of Bragg-Brentano geometry used for focused beam x- ray diffractometry. [91]~~

~~Figure 30. Picture of the focused beam XRD system at The Ohio State University’s Department of Chemistry. 67~~

~~For our work, we used a Bruker D8 Advance with Bragg-Brentano geometry at~~

~~the Ohio State University Department of Chemistry. A Lynx eye detector system was~~

used to optimize the intensity for the best possible impurity and ordering analysis, and the x-rays are generated from a sealed Cu Kα source with wavelength 0.15405 nm. Figure 30 shows the system in its “flat-plate” for room-temperature measurements, which were used in our characterizations exclusively. One can easily compare to the schematic in

Figure 29 for identification of the Bragg-Brentano geometry of the system. The white/tan component on the left side of the picture is the goniometer (x-ray source), followed by the divergence slits. To the right of the sample holder, one can see the metal colored antiscattering slit, marking the front of the Lynx eye detector setup.

~~4.1.3 Parallel Beam Diffractometry~~

In contrast to Focused Beam Diffractometry, one may sacrifice high intensity detection for extremely sensitive angular resolution by replacing the diverging slits on the incident side of the diffractometer with collimating optics that project a parallel beam onto the surface. Angular filters on the detector side filter out any stray non-parallel reflections.

A diagram of the general parallel beam setup is shown in Figure 31. In this work, we have utilized a D8 Discover with a GOBOL collimating mirror and detector with both variable slit and Ge-based triple bounce mirror systems. A picture of the system in the

~~Ohio State Department of Physics is shown below in Figure 32.~~

~~Figure 31. Simplified diagram of parallel beam x-ray diffractometry. [93]~~

~~Figure 32. D8 Discover Parallel Beam Diffractometer made by Bruker for the Department of Physics at The Ohio State University.~~

~~In addition to angular resolution allowing rocking curve measurements on even~~

~~the most uniform semiconductors and oxides, parallel beam XRD allows for the detection~~

~~of Laue oscillations due to thin film interference of a near-atomically flat film. Such~~

~~oscillations would be washed out by the larger range of angles that the incident beam will~~

~~have in Bragg-Brentano geometry. This method gives a non-destructive measurement of the thickness of a thin film, in contrast to destructive methods such as chemical etching or~~

~~Transmission Electron Microscopy.~~

~~The D8 Discover also boasts a mechanized Eulerian cradle as well as x/y/z control, making it possible to take “off-axis” scans of single crystals or epitaxial thin~~

~~films, i.e. scans of any available crystallographic direction a sample may be able to provide.~~

~~4.2 Vibrating Sample Magnetometry (VSM)~~

~~4.2.1 Instrumentation and Theory~~

~~A Vibrating Sample Magnetometer, or VSM, utilizes the magnetic flux generated~~

~~due to the motion of a magnetic object in space to determine the moment of that object.~~

~~This is done by use of an apparatus generally similar to Figure 33, depicting the~~

~~LakeShore VSM model used in our experiments. A head drive generates a sinusoidal~~

~~oscillation on a quartz sample rod, upon which the sample is mounted to the tip (white~~

~~tape in picture), located centrally between both the electromagnets supplying the electric~~

~~field and the pickup coils (mounted to the ends of each core) designed to measure the~~

~~magnetic flux.~~

Figure 33. LakeShore 736 Model Vibrating Sample Magnetometer in room temperature, 1.6 T mode, located in the Department of Physics, The Ohio State University. Our VSM is a LakeShore model 736, operating at a head drive frequency of 80

Hz and a maximum magnetic field of 1.6 T, with an anti-static fan to eliminate any false moment due to static charge on the insulating quartz rod or Teflon mounting tape. When the sample is driven to a sinusoidal oscillation of this frequency in the presence of a magnetic field, the sample’s induced moment generates a sinusoidally fluctuating magnetic flux. This flux generates an induced electromotive force and thus a current in

~~the nearby pickup coils as per Faraday’s law. The sinusoidal current is then measured by~~

~~a pick-up amplifier and converted by calibration constants to a net moment number.~~

~~4.2.2 Measurement Modes~~

~~Room Temperature (Normal) Mode~~

~~The most basic mode of our VSM is room-temperature mode, where the system~~

~~works as seen in Figure 33. In a series of 7 different range settings, the pickup coils can~~

~~measure from 40 emu to ~1 µemu with careful measurements and proper time averaging.~~

It is important to be sure that the water cooling system is active and flowing, as one can easily overheat the electromagnets without it. Samples are typically mounted onto the quartz rod via a Teflon tape wrap that has been determined to have no ferromagnetic moment, using as little tape as possible so as to more easily align thin film samples as

~~close to in-plane and out-of-plane to the external field as possible.~~

~~Low Temperature (Cryostat) Mode~~

~~For low temperature measurements, a crystat add-on to the VSM system is~~

~~available for both Liquid Helium and Liquid Nitrogen temperatures. The quartz rod sits~~

~~into a cryogen bath, which is surrounded by a vacuum jacket which is typically pumped~~

~~down to the order of 1 mTorr for Liquid Nitrogen-temperature applications. Next to the~~

~~tip position is a resistive heater, which is used by a computer controlled system to balance~~

~~with the cryogen flow to put the sample at the desired temperature. From here on out, we~~

~~discuss the cryostat use for Liquid Nitrogen, as use of Helium with this system is~~

~~wasteful and rarely done. The reliable temperature range of this mode with Liquid~~

~~Nitrogen is 80-400 K. Although it is possible to push the heater to as high as 450 K, it is 72~~

~~not something to do unless given no other choice. For temperatures over 400 K, see the~~

~~next section on the high-temperature oven mode.~~

~~The cryogen flow rate from the dear must be necessarily low so as to not overtax the heater. Typically, half a turn opening of the transfer rod valve is enough to have the~~

~~specification-mandated 20-25% heater power when in equilibrium at 80 K. At this heater~~

~~output (the lowest temperature that is reliable for Liquid Nitrogen), the heater is still in a~~

~~safe output range at 400 K and is in no danger of breaking quickly.~~

Caution must be taken when using either the cryostat or the high-temperature oven to avoid the vibrating sample from touching any of the walls, as the insertion cylinder is 5-6 mm wide. Touching the walls will change the vibration rate and affect the current reading that the lock-in amplifier, which is set to 80 Hz, reads. Also, care must be taken to close the vacuum jacket valve prior to turning off the pump, or opening the valve before the line is well-pumped, as oil that gets sucked into the jacket in this manner will degrade insulation of the cryostat.

~~High-temperature (oven) mode~~

~~The general method of the high temperature mode is very similar to that of the~~

~~low-temperature cryostat. The system is added onto the regular mode VSM in the same~~

~~manner and the vacuum jacket must be well pumped for a full temperature range to be~~

achievable. The internal heater, however, is not balanced by any cryogenic liquid, but rather by room temperature Argon gas. Within the thermal insulation, this allows for an available temperature range of 300-1273 K.

~~4.3 Superconducting Quantum Interference Device (SQUID)~~

~~4.3.1 Instrumentation and Theory~~

~~Magnetometry using a SQUID-integrated system works on two principles: flux~~

~~quantization in a superconducting ring and the properties of a Josephson junction. We~~

~~will examine the physics behind each one briefly before integrating them into a detection~~

~~system.~~

~~It is well documented that the one of the quantum mechanical results of Cooper~~

~~pairs within a superconducting ring must be an integer value of the flux quantum~~

~~when an inducing field B creates an induced magnetic flux through the loop [94]. 2e is~~

~~the value of a Cooper pair in the ring. The flux quantum is calculated to be 2 x 10-15 weber, an extremely small value that is utilized to give Magnetometry by SQUID its excellent sensitivity.~~

The wave function of the Cooper pairs within the ring must be the same at each point in the ring, regardless of what number of times a particular pair have circled. This means that the phase at a point must only be factors of 2π from each other. The total magnetic flux through the loop may then be written not only as a combination of the external and supercurrent-induced fluxes, but also as an integer multiple of the flux quantum Φ0:

~~to satisfy the conditions placed upon the ring.~~

Note that the external flux through the ring has no requirement of quantized flux, so the screening current must adjust to meet this requirement. This is a very important point to understanding SQUID Magnetometry. If we induce a phase disturbance within the system, the supercurrent must create a countercurrent to restore quantization of the flux, via an induced flux.

Figure 34. Schematic of a Josephson junction. We engineer a change in phase via the second concept necessary for a SQUID, that of a Josephson junction, an example of which is shown in Figure 34. By placing a insulating gap on the order of 1 nm thickness between superconductors. Below a critical current (not the critical current of the particular superconductor to resume normal resistivity, but a smaller value specific to the junction), Cooper pairs from either superconductor will simply tunnel through the barrier with no resistance. Josephson showed that in the ring from before, a phase shift in the junction current must occur that from the quantization restriction must be some factor of 2π.

~~There are two types of SQUID setups for Magnetometry: the DC SQUID, which is more sensitive for low moment detection due to lower signal amplification noise, and the RF~~

SQUID, which is less sensitive but generally cheaper. The system for our measurements is a Quantum Design XL Magnetic Property Management System (MPMS) with a longitudinal DC SQUID SYSTEM. The larger system is shown in Figure 35.

Figure 35. Schematic of the DC SQUID magnetometer diagram, from the MPMS Reference Manual from Quantum Design. Note that the superconducting wire wraps in a solenoid to make a vertical applied magnetic field, and the sensor coils are similarly directed for moment detection in the 76 field direction. Figure 36 shows the electronic setup for the instrument. As the magnetic sample is lifted in steps through the detector array, the current induced into the superconducting wire reaches a peak at the step in between the middle loop pair.

Figure 36. Electronic circuit diagram for the DC SQUID magnetometer, from the MPMS Reference Manual from Quantum Design. The current passes through an isolation transformer before reproducing the original flux from the sample at the SQUID. There is little to no loss of signal, since the electronics up to the Josephson junction in the SQUID are made entirely of superconducting wire.

A DC SQUID is effectively two parallel superconducting wires in some loop geometry, each with a Josephson’s junction within each path. Figure 36 shows a generalized setup, where the Josephson junctions are the two blue boxes attaches to the superconducting wires, drawn in black. As stated earlier, a Josephson’s junction will have some critical current IC above which the tunneling of the junction will cease and the

~~junction will become an Ohmic resistor. To take advantage of this, we place the device~~

~~under a constant bias current equal to twice the critical current of either junction, thus~~

~~putting each junction directly at the superconductor-normal transition. This creates a~~

~~device where any induced current will create a voltage difference across the SQUID leads~~

~~due to normal current flow.~~

Figure 37. Simplified diagram of a DC SQUID with a bias voltage I and a screening current IS due to an externally applied flux into the page. In Figure 37, we see an induced screening current in the counter-clockwise

direction adding a current IS to the current in the left path, and equally subtracting from the current in the right path. Since the screening flux must be quantized, the screening current will begin to flow when the net flux exceeds half a quantum. As that point, the current energetically favors flowing via the right path, until the current resets to its initial state half a quantum later. This periodic oscillation can be detected by the voltage generated in a nearby pick-up coil via an amplifier. Each oscillation is indicative of the 78

~~detection of one magnetic flux quantum, and so a computer program is employed to~~

~~simply count the total number of oscillations to determine the moment through the detection coils.~~

~~4.3.2 Comparison to VSM~~

~~SQUID magnetometry’s quantum counting and low electronic noise levels make it far and away more sensitive than other common macroscopic techniques such as VSM.~~

~~However, the time required to change fields, slowly step the sample through the detection coils, and count the oscillations at each step make SQUID Magnetometry generally a~~

~~much slower process than VSM. VSM can switch fields quickly and its 80 Hz vibration~~

~~allows a lock-in amplifier to immediately measure a voltage signal that, if need be, can be~~

~~time averaged for precision approaching a few µemu (10-6 emu). Due to the noise levels~~

~~inherent in the non-superconductive electronics needs for VSM, however, it cannot~~

~~approach the 1 x 10-7 emu precision that can easily be achieved via SQUID detection.~~

~~New approaches utilizing both the speed and time averaging of the vibrating sample setup with the low noise and high quantized precision of SQUID detection are~~

~~now available commercially, with VSM-like speed and precision as low as 1 x 10-8 emu.~~

~~4.3.3 Mounting Techniques in Quantum Design Cryostat~~

~~Accurate measurement of the magnetic behavior of thin films offers challenges for sample mounting to ensure proper orientation of the sample with respect to the film.~~

~~Misorientation or large vertical displacement of a sample will result in incorrect results or inability to move the sample fully through the coil for accurate moment detection. The~~

~~79 proper sample positions are shown in Figure 38, viewed from the side as they would be lowered into the SQUID magnetometer, which is also displayed in the figure.~~

Figure 38. (left) Example of thin film sample mounting in “perpendicular” orientation, i.e. magnetic field out-of-plane to the film surface. (center) MPMS-5 system with SQUID magnetometry cylinder installed. (right) Example of film sample with film surface parallel to the magnetic field. The sample material is mounted inside a nonmagnetic plastic straw, taped to a long sample rod with and capped below to prevent sample loss with Kapton tape. The straw is just smaller than the insertion tube width, making the maximum sample width for any orientation approximately 5.5 millimeters.

~~To mount a film in the direction of the magnetic field, a string is tied around it and taped to either end of the straw. The proper mounting, viewed from the side, is 80~~

~~shown in the right panel of Figure 38. The perpendicular arrangement as shown in the~~

~~right panel is achieved by flattening two pieces of cotton and pressing the sample flat~~

~~between the two of them. Note that for this orientation, no diagonal dimension of the sample may be larger than the diameter of the straw to properly fit.~~

~~4.4 Transmission Electron Microscopy (TEM)~~

~~Double Perovskite growth is a particular challenge due to the high level of crystal~~

~~complexity in the lattice. Any amount of non-stoichiometry, disorder, energetic damage~~

from growth, or anti-phase boundary will cause degradation in the spin polarization of a material. Therefore, it is important to directly observe the crystal structure and atomic ordering of any thin film grown to assess and correct nanoscale defects. This is only truly possible through direct observation by Transmission Electron Microscopy.

~~4.4.1 Theory~~

First, let us take a look at the Transmission Electron Microscope system as a whole. Figure 39 below shows a general, simplified schematic. The electron source at the top is typically made from tungsten filaments or LaB6 and focused through a dual

~~condenser array with apertures to block electrons that are not aligned vertically [92].~~

~~After the electrons pass through or are deflected by the atoms within the sample, Figure~~

40 shows the magnification of the image for projection onto the screen or camera. Once one has a highly directed beam of electrons pass through a given cross-section of a sample, an image is made that is effectively a map of where the electrons are scattered by

~~atoms within the sample. Noise is then removed prior to magnification via apertures after~~

~~the objective lens.~~

Figure 39. Simplified schematic of parts for a simple Transmission Electron Microscope. Adapted from [96]. The primary innovation of electron microscopy over optical microscopy lies in the ability to increase the resolution of an image by switching the probe from visible light to focused electrons. Since the resolution is limited by the wavelength of the probing particle or wave, the de Broglie wavelength of an electron accelerated from a voltage B will be

~~1.23 2 √~~

~~Compared to the many hundreds of nanometer wavelength of visible light, transmission~~

~~electron microscopy clearly has the potential to image samples to the sub-nanometer or even sub-angstrom range, given a high enough voltage.~~

The limiting factors to TEM imaging at the moment, however, do not include the accelerating voltage of the electrons, but rather lie in the magnification and projection optics after the electrons have exited the sample. The spherical aberration CS of an optic describes the extra bending of a beam incident on a converging lens close to the lens edges. This causes the rays from the outer edges to converge on the beam axis at increasingly closer positions than the rays near the optic center, and is depicted in the top diagram of Figure 41. The minimum resolution, dmin, then becomes a function of the spherical aberration and the aperture angle α:

~~1 2~~

~~Reasonable system values of 1mm for the spherical aberration and 10 mrad for the~~

~~aperture angle limit the resolution to a ideal case of 0.5 nm [99].~~

~~Figure 40. Electron beam path traced from sample to screen in a basic Transmission Electron Microscope. Adapted from [97].~~

~~Clearly, one could simply narrow the aperture of the lens to minimize the effects~~

~~of spherical aberration, which has a cubic dependence on the aperture angle. This would bring the rays to all converge directly at the position of the intended image plane. Doing~~

~~this must be balanced against the single-slit diffraction that will occur with small aperture~~

~~size, however. The diffraction will cause a blurring of width roughly equal to the width~~

~~of the central maximum of the pattern and is shown schematically in the lower panel of~~

~~Figure 41. The width of the central maximum is defined above as d0, defined as~~

~~0.61~~

~~The inverse dependence of the aperture angle on the resolution is in opposition to~~

the cubic dependence of dab with α. This would indicate that there will be a non-zero, non-infinite aperture for a given optic with aberration CS that will make the resolution as good as possible. If we estimate the total resolution from the combination of diffraction and aberration as

~~0.61 1 2~~

~~Minimization of dmin as a function of the aperture then gives~~

~~0.66~~

A slightly more complete model gives a coefficient of 0.61 instead of 0.66. Plugging in for electrons accelerated through a 200 kV potential, the absolute best resolution one may achieve is calculated to be 1.53 Ǻ at optimal aperture.

~~To achieve sub-Angstrom resolution for clear pictures of individual atoms, spherical aberration correction is necessary to make lower resolutions at larger aperture~~

~~85 sizes possible. We will discuss the FEI Titan’s sub-angstrom resolution after a review of the dark field technique.~~

~~Figure 41. Ray trace diagrams depicting the effects of (top) Spherical Aberration and (bottom) single-slit diffraction on the resolution of an image via transmission electron microscopy. [99]~~

~~4.4.2 Scanning TEM (STEM)~~

We have discussed how standard transmission electron microscopy operates by passing a parallel beam through a cross-sectional area of a sample. We then obtain a map of shadows made by the blockage of the atomic positions. In this section, we will discuss the focusing of this incident beam into a small spot on the sample and scanning through positions in a technique call scanning transmission electron microscopy, or STEM. This technique opens up the ability to analyze the elemental and chemical attributes of a sample to the sub-angstrom spatial resolution afforded by aberration-corrected transmission electron microscopy. Figure 42 below shows a schematic for Scanning

TEM with a high-angle annular dark field (HAADF) detection system. The incident electrons are focused to a sub-angstrom spot size at the sample, and either is used in bright field mode for standard TEM or electron energy loss spectroscopy (EELS), or in

~~HAADF mode.~~

Dark field mode ignores the majority of electrons that pass through to the bright mode detector, and instead focuses on the electrons deflected some angle from their original paths [92]. HAADF focuses only on a ring deflected within a necessarily high angle range for separation, and puts an annular detector in that range to measure the intensity of deflection from that sample point. The reflection probability scales as Z3/2, and by cutting a thin film of order 50 nm thickness with proper choice of crystal orientation, one may create an elementally differentiated map by scanning for the intensity across a sample region.

~~Figure 42. Schematic for STEM-HAADF imaging and electron energy loss spectroscopy (EELS). This diagram is drawn largely from work done on the FEI Titan with which our STEM data was collected. [99]~~

~~4.4.3 Instrumentation – The FEI Titan~~

~~Transmission electron microscopy for this work was done on the FEI Titan™ 80-~~

~~300 by the group of Professor Hamish Fraser in the Department of Materials Science~~

~~Engineering at The Ohio State University. The Titan, shown in Figure 43, is currently~~

~~known as the state-of-the-art for aberration-corrected HAADF STEM, boasting STEM~~

~~resolution resolution of approximately 80 picometers via active vibration isolation,~~

~~aberration correction, and 300 kV electron acceleration.~~

~~Figure 43. Picutre of a FEI Titan™ 80-300. [100] For the purposes of the work described herein, the Titan was used in HAADF mode on~~

~~50 nanometer cuts of Sr2FeMoO6 so as to look down the (00n), (nn0), and (nnn) lattice directions.~~

~~4.5 Rutherford Backscattering Spectroscopy (RBS)~~

~~Rutherford Backscattering is a excellent non-destructive method for determining~~

~~the depth-dependent stoichiometry of a material. The accuracy of the method exceeds~~

~~electron dispersive x-ray (EDX) spectroscopy due to the chemical dependence of the~~

~~latter method. In addition, RBS can be treated in a purely classical treatment, making the~~

~~theory and thus the spectra analysis relatively simple.~~

~~4.5.1 Theory~~

~~Rutherford backscattering spectroscopy (RBS) uses incident positively charged~~

~~particles scattering from atomic nuclei in elastic, hard-sphere collisions. Alpha particles~~

~~are used in the RBS work done in this paper, so we will assume this to be the impinging~~

~~particle from here on. The DeBroglie wavelength for an alpha particle λ = h/mv is of~~

~~order 10-4 Ǻ. This is much smaller than the space between atomic nuclei (~ 1 Ǻ), and~~

~~therefore any collisions that occur must be direct or nearly direct. Thus, a classical~~

~~treatment of the experiment is appropriate.~~

~~The closest an alpha particle can get to nucleus is determined by setting the initial~~

~~kinetic energy of the shot particle equal to the electrostatic potential at the minimum~~

~~distance rmin, giving~~

~~where q1 and q2 are the charges of the ion and target atom, respectively, and ε0 is the~~

~~permittivity of free space. For a target atom with a Z value of order 10, the electron can reach of order 10-4 Ǻ. This is important to justify modeling the system as an unscreened~~

~~cross section for the target atom: If the alpha particle could not penetrate the radius of the~~

~~orbiting electrons, there would be no repulsive force between particle and nucleus, and~~

~~the model would not correctly describe the collisions.~~

~~Figure 45 below. A helium atom with mass m1 is accelerated to an energy E0 and~~

~~collides with the stationary target nuclei with mass m2. From the initial path of the alpha~~

~~particle, we define the magnitude of the deflection angle for M2 as ϕ and the magnitude~~

of the deflection angle for M1 as θ. The target atom is not actually ejected, being held in the lattice by interatomic bonding forces, but since the collision occurs quickly compared significant onset of the restoring force, the recoil can be treated from freely floating masses with M2 > M1, and accurately model the interaction.

~~In this collision, both energy and momentum are conserved. Therefore, we may~~

~~write the conservation of energy of the system as~~

~~1 1 1 2 2 2 91~~

~~where v is the initial velocity of the alpha particle as it approaches the target, v1 is the~~

~~velocity of the recoiling alpha particle after the collision with the target nucleus, and v2 is the recoil velocity of target nuclei instantaneously after impact.~~

Figure 45. Simple diagram depicting the interactions between alpha particles and target nuclei during Rutherford Backscattering Spectroscopy. We can then employ the conservation of momentum in the direction of the initial alpha particle velocity v as

~~cos cos~~

~~and the same for the direction perpendicular to v as~~

~~0 sin sin .~~

~~We can control the initial energy E0 of the alpha particle and set the position of the nuclear particle detector θ that gives us the reflected energy E1 of the alpha particle of~~

~~known mass M1. Therefore, given an equation where one can write M2 as a function of~~

~~these other variables, we may determine the Z number of the target nuclei based on the~~

~~energy of the scattered alpha particle. This is the basis of Rutherford Backscattering~~

~~Spectroscopy. When we combine the equation describing conservation of energy with the two equations describing conservation of momentum, we arrive at~~

~~One may also use RBS for depth profiling. As an alpha particle passes deeper~~

~~into the crystal lattice of a sample, non-scattering interactions cause the particle to lose~~

~~energy. The typical rate for energy loss for a particle of MeW-order initial energy is 30-~~

~~60 eV per angstrom penetrated prior to backscattering [95,102]. As a result, the plot of~~

~~intensity vs. energy from the particle detector will show something resembling a plateau~~

~~for a given element, where the highest received energy value indicates scattered alpha~~

~~particles from the surface of the sample, and continuing to lower and lower energies until~~

~~the sample portion with that element no longer exists at that penetration depth, or until~~

~~one has scattered all the particles, somewhere in the range of many microns. Note that,~~

~~for the film work presented in Chapter 5, we run out of film prior to this limit, as the~~

~~films were of order 100 nm in thickness. The intensity measured relative to the other~~

~~elements present gives us a ratio of the elements in the sample, and the energy separation~~

~~of different thicknesses allows us to pick any given depth and analyze the stoichiometry~~

~~on that plane. This makes measurements of heterostructures, intermixing at interfaces,~~

~~and uniformity tests of thin film work extremely useful.~~

~~4.5.2 Instrumentation: Rutgers University~~

~~Rutherford Backscattering Spectra were taken at the 2 MeV Tandetron~~

~~Accelerator facility in the Laboratory for Surface Modification at Rutgers University.~~

~~Electrons are accelerated to 2 MeV and shot into the sample. The exit and scattering~~

~~angles are set to 17 and 163 degrees, respectively.~~

Figure 46. A picture of the 2 MeV Tandetron Accelerator Facility in the Laboratory for Surface Modification at Rutgers University. Figure 46 above is a picture of the facility, with the particle accelerator in the background and the alpha particles moving towards the camera towards the central chamber in the forefront, which deflects the beam to the chamber seen to the left. The 94 chamber is pumped down to high (10-6 Torr) vacuum, and it contains the sample holder, a camera for aligning the 2 x 2 mm beam spot, and an ORTEC surface barrier detector with energy resolution 15 keV. The results are analyzed with an analysis program called

~~SIMNRA, shown below in Figure 47. The red circles are the experimental data to which one runs simulations to match with the data to determine the sample properties.~~

Figure 47. RBS data of a Sr2FeMoO6 film on SrTiO3 substrate, being fit to simulated data in SIMRNA to determine the stoichiometry, density, and thickness of each layer in the sample. In the figure above, the blue line is the combined simulation line, i.e. the sum of each individual element’s simulated spectra, which are also shown below the blue line. Note that the green-yellow line corresponding to the strontium extends across the entire energy spectrum. This sample is a Sr2FeMoO6 film on SrTiO3 substrate, and so the Sr scattering

~~occurs at every depth. In general, one must line up the highest energy part of each~~

~~elemental plateau first, which corresponds to the part closest to the surface with that~~

~~element, and adjust the thickness of the sample layer or layer, and/or the stoichiometry to~~

~~match the simulation to the experimental data.~~

~~4.6 X-Ray Photoemission Spectroscopy (XPS)~~

~~4.6.1 Theory~~

~~X-ray photoemission spectroscopy (XPS) is one of a broad range of photoelectron spectroscopy techniques that take advantage of Einstein’s photoelectric effect, in which a~~

~~photon sent into a material surface with high enough frequency, and thus energy, will~~

~~eject electrons from the sample surface [103]. In XPS, x-rays are used to add enough~~

~~energy to eject electrons from both the valance levels and core levels, the latter of which~~

having increasingly higher binding energies to overcome as one probes deeper into the electron shells of a given atom. A full table of energies for deciphering spectra, as well as an excellent treatment of XPS [95], can be found in the literature.

Figure 48 below shows the process in terms of an energy level diagram. The solid black vertical line represents the boundary between the metal (left side) and the vacuum outside of the metal (right side). When an electron absorbs a photon with energy hν, escape from the material requires enough energy to first excite the electron out of the atom and then enough to escape the surface boundary of the sample. Escape from the atom requires the electron to have energy equal to the Fermi Energy, and the energy

~~required to excite a given stable electron to this level is called the electron binding energy~~

~~Ei, and is shown in the figure below in red. This brings the electron to the conduction~~

~~level and it can move to the surface.~~

Figure 48. Energy level diagram excitation of an electron during x-ray photoemission spectroscopy, assuming the impinging x-ray has high enough energy to eject an electron from the metal. Adapted from [95]. For the electron to jump the surface of the material, it must have energy equal to

~~what is called the vacuum energy level outside the sample. This level is depicted in~~

~~Figure 48 as the solid black line on the vacuum side of the diagram. The difference~~

~~between this level and the Fermi level is known as the work function qΦW and shown in~~

~~blue in the above figure. If the imparted energy hν onto the electron exceeds the sum of~~

~~the work function and the binding energy Ei, the electron will leave the surface with kinetic energy equal to the leftover energy. We may write this in equation form as~~

~~97 where Ekin is the kinetic energy of the escaped electrons, and is the measurable quantity in our XPS measurements.~~

~~Figure 49. The XPS vacuum chamber, bottom left corner of picture. The MBE system to the right is set up with a vacuum transfer line for in situ measurements. 4.6.2 Instrumentation: Brillson Lab~~

XPS spectra for this work were acquired in Professor Leonard J. Brillson’s lab in the Department of Physics at The Ohio State University. The system is shown in the bottom left hand corner of Figure 49 above, with the molecular beam epitaxy system in the background of the picture. The systems are designed with a transfer module so samples grown by MBE can be measured in situ, without breaking vacuum.

Measurements are taken at a base pressure of 1.2 x 10−7 Pa and at room temperature using a monochromatic AlK source. The energy of the source is 1486.6 eV, a pass energy of 23.5 eV and an energy step of 0.05 eV. The measured binding energies

~~98 were calibrated against the C 1s binding energy of 284.8 eV, and standards are used to produce sensitivity ratios for quantitative analysis.~~

For analysis of thin films, two techniques are used. First, one may alter the beam angle to change the penetration depth of the x-rays, in a technique known as angle- resolved XPS, or ARXPS. By taking very glancing angles, one may isolate the top few nanometers of a film for measurement, or increase the angle to provide information on interior layers. This is very useful to investigate inhomogeneity in a film, or to identify defect states at the film surface.

~~Secondly, the chamber is equipped with an ion mill, which accelerates charged~~

Ar+ ions into the surface of the sample. By adjusting the energy and intensity of the ions, this can have several uses. One may wish to clean residue from a sample prepared ex situ via gentle, slow milling, to avoid large signals from oxidized states or organic residue.

One may also use it to ablate away layers of a film, alternating between ablation and measurements to gain information on each successive layer. However, one must be careful to avoid crystal damage in complex oxides such as Sr2FeMoO6 by milling with

~~Argon ions with too high energy [46].~~

~~Chapter 5: Preparation and Deposition of Sr2FeMoO6 Thin Films~~

~~High-quality films of complex oxides are very difficult to achieve due to their~~

~~high chemical complexity. Even small disorders or local off-stoichiometry can easily~~

~~destroy the electronic order of the sample and diminish desired properties. In this~~

~~chapter, we will go over the requirements and obstacles in growing high-quality~~

~~Sr2FeMoO6 thin films, and our findings on how to overcome these problems.~~

~~5.1 Target Preperation~~

~~In magnetron sputtering, a bulk target is ablated away by energetic ions, typically~~

~~Ar. If there are impurity phases in the Sr2FeMoO6 target or the target composition is~~

~~inhomogeneous (which can easily happen in Sr2FeMoO6 unless great care is taken in bulk~~

~~synthesis of Sr2FeMoO6), the distribution of the atoms at the film surface will not be~~

~~homogeneous. When this happens, well-ordered, pure-phase films are nearly impossible~~

~~to obtain, especially if the level of disorder and stoichiometry at the target surface is~~

~~constantly changing due to the selective sputtering of various phases and compositions in~~

~~the Sr2FeMoO6 target. Thus, the first step to growing half-metallic thin films of~~

~~Sr2FeMoO6 is creating a well-ordered, pure-phase target.~~

~~For the purposes of the films grown in this paper, targets were prepared by standard solid state synthesis. A combination of SrCO3, MoO3, and Fe2O3 powders were~~

~~mixed and ground via mortar and pestle and heated at 1050 °C for 10 hours in a tube~~

100 furnace under a flow of forming gas (5% H2 / 95% N2). The resulting powder was then reground and heated at 1100 °C for 10 hours in a tube furnace in forming gas. Then the powder was reground and pressed into a target, and sintered at 1200 °C for 3 hours in the same environment to create a solid target for sputtering. Figure 50(a) below shows scanning electron microscopy (SEM) images taken of the sputtering target used. The grain size is of order a few to 20 µm, with significant variability.

Figure 50. Scanning Electron Microscopy pictures of Sr2FeMoO6 pressed magnetron sputtering targets, (a) before and (b) after sputtering has been done. Magnetron sputtering is an energetic process and depends significantly on the surface morphology of the target. Figure 50 (b) shows the results of the same target after sputtering. The target surface appears to be smoother due to that the “stand-out” grains were preferentially sputtered away, leaving a smoother surface behind. We find that for a target with inhomogeneity or impurity phases found via x-ray diffractometry, the quality of the Sr2FeMoO6 films keeps changing even all the growth conditions remain the same.

~~This may be because the surface morphology and composition keep changing with~~

101 sputtering. In other words, a grain may have varying compositions from outside to inside. Also, porous targets with uneven distribution of grain sizes as shown in Fig. 50 also contribute to the inhomogeneous growth of the Sr2FeMoO6 films.

~~102~~

Under the growth conditions listed above, including use of hand grinding of powders by mortar and pestle, the best results were achieved by long careful mixing and grinding (~ 3 hours). The X-ray diffractometry spectrum of this target, shown in Figure

51(a), shows only the double perovskite Sr2FeMoO6 peaks, with no visible impurity peaks. Although powder diffraction spectra are normally shown with a linear vertical axis, this graph is shown in log scale to more convincingly show the phase purity.

~~SQUID Magnetometry done on a pressed pellet of the target material determined the saturation magnetization at 5K, which is shown in Figure 51(b) with a net moment of~~

2.7 µB/f.u. Additionally, the magnetization of the powder under an applied field of 1 kOe was measured as a function of temperature by VSM, as shown in Figure 51(c), in which the Curie temperature can be estimated at approximately 410 K. Although the Curie

Temperature is close to the predicted ideal value, the net moment is less than 70% of the theoretical ideal of 4.0 µB/f.u.. With no apparent impurity phases, we might attribute the lowered moment to B-site disorder. As discussed in Chapter 2, such disorder also causes a lowering in TC, which we do not clearly see here. It is feasible that a small impurity with higher TC may be maintaining the effective field in the powder and enhancing the proper TC of the sample, although this remains an open question.

Several significant problems tend to occur in target synthesis using the above recipe. For instance, it is very easy to develop a SrMoO4 phase if the sintering conditions are not reducing enough, or if the powder is not ground finely enough. This is the problem we most commonly found, and particularly problematic: Once this impurity occurs, removal does not happen easily and it is easier to simply create a new powder

~~103~~

batch. A target containing SrMoO4 for sputtering will result in thin films that contain some level of SrMoO4 impurity, regardless of sputtering conditions. In addition, the formation of SrMoO4 will cause an accompanying iron and/or iron oxide impurity from the leftover ingredients. These impurities are often found to translate into any films grown and make any such targets unsuitable for our work.

It is also important to note that we have not achieved films with magnetic moment higher than that of the bulk target. For instance, we will see that the best films grown via the target in Figure 51 have saturation magnetizations of 2.6 µB/f.u. at a temperature of

~~5K. Targets of high B-site disorder and large impurity levels with low-temperature~~

~~saturation magnetizations of 1-2 µB/f.u. begot films capped at those values. It is not~~

~~unreasonable to assume that there is a connection between the quality of the powder and~~

~~that of the film.~~

However, the sputtering deposition creates mixing during the ejection process far more than the small distance between B-sites. Therefore, the local ordering of the B-sites should not matter very much. Also, use of ideal temperature and environment during

~~synthesis is not guaranteed to give high ordering and moment using hand grinding. As~~

~~such, it is likely that the correlation between the ordering of the powder and the~~

~~properties of the films grown from that powder are not correlated through the local~~

~~amounts of the B/B’ site ordering. It is conceivable that the powder ordering and purity~~

~~are merely indicative of the uniformity of the target. If this is true, the ability to facilitate~~

~~high film quality hinges on the synthesis of homogeneous targets.~~

~~104~~

~~To test this, we combined the initial heating in Argon discussed above with use of~~

~~a ball mill before each step of the process. By utilizing a “wet-grind” technique, wherein~~

the powder and agate balls are suspended in an ultra-pure methanol solution, an overnight run is enough to reduce the average grain size to sub-micron. The characterization results from such a method are shown in figure 52 below.

The XRD spectrum in figure 52(a) shows a pure-phase Sr2FeMoO6 powder with strong peak intensity. A measure of the ordering within a sample can be determined by comparing the intensity of the (111) peak at a 2θ angle of approximately 19.5° to the

~~(222) peak intensity at around 39.5°. This orientation creates B/B’-site superlattice horizontal “sheets” of alternating Fe and Mo layers in the probe direction. When these~~

~~horizontal layers are properly staggered, each B site cation has a B’ below and above it,~~

~~and following structure factor calculations for this material, we see a higher intensity for~~

~~the (111) peak. Conversely, poor ordering can easily move the (111) ordering peak to~~

~~very low counts, even making it impossible to see in poor quality targets.~~

~~Comparing the ball mill XRD spectrum with that of the hand-ground sample’s~~

~~XRD spectrum show in figure 51(a), we see that the (111) peak is much more prominent~~

~~in the ball milled sample. Although XRD analysis is not conclusive evidence in such a~~

~~complex oxide, the results support the conclusion that we have improved B-site ordering in the powder. For further proof, we must look at the magnetic characterization, shown~~

~~in M-H and M-T form in figures 52(b) and 52(c), respectively.~~

~~105~~

~~106~~

From this data, both taken via SQUID Magnetometry, we can see an obvious improvement in powder quality. Figure 52(b) shows the M-H curve at T = 5K, and shows a significantly improved MSat of 3.67 µB/f.u., close to the ideal ferrimagnetic

~~moment of 4.0 µB/f.u. The coercivity is found to be 100 Oe, making Sr2FeMoO6 a soft ferromagnet ideal for switching layers in magnetic tunnel junctions.~~

~~The M-T curve for the same powder sample is shown in Figure 52(c). A TC of~~

~~approximately 385 K is found. This value is lower than that of the hand-ground powder,~~

~~despite obvious increases in both B-site ordering and magnetic moment, which is~~

~~enhanced by nearly 40%. A possible clue lies in the shape of the M-T curve, which is~~

~~significantly improved via the new techniques. This lends credence to the possibility~~

~~suggested earlier that there is a small magnetic impurity phase in the handmade samples~~

~~altering the Curie temperature of those powders. Further optimization of the synthesis~~

~~conditions will leading to improvement of TC.~~

~~5.2 Sputtering Geometry~~

~~UHV magnetron sputtering can be done in a variety of ways. In this section, we~~

~~will discuss the geometry and spacing of the substrate relative to the sputtering target and~~

~~their effects on Sr2FeMoO6 thin film deposition.~~

~~5.2.1 On-axis and off-axis sputtering methods~~

It has been known for some time that off-axis sputtering is advantageous for sputter deposition of epitaxial films of complex oxide films [104]. Conventional on-axis sputtering, in which a substrate is placed directly above the sputter gun, can eject high energy atoms which cause significant damage in epitaxial films [105]. However, in off- 107

axis sputtering, the substrate is oriented perpendicularly to the surface of the target and moved to the side, avoiding the bombardment the high energy particles, and only landing lower energy, scattered atoms to create a gentler growth. An example of the off-axis growth is shown in Figure 53. The purple glow is emanating from the surface of the vertical Sr2FeMoO6 sputter target. One can see the cone-like emanation from the

~~relaxation of exited-state electrons in the plasma. This demonstrates that the area directly~~

~~in front of the target surface has the highest ejection energies, as it takes much longer to~~

~~relax and create a photon in this area. As such, we place the 5 x 5 mm square substrate~~

~~heated substrate in off-axis geometry as shown.~~

~~5.2.2 Effect of off-axis positioning on thin film growth~~

~~The advantage of off-axis growth is well-known as its ability to ward off energetic bombardment damage. However, it is less well-known that a side effect to~~

~~improved energetics from off-axis positioning is that the stoichiometry of films will~~

~~change as one positions the substrate differently in the space to the side of the gun. This~~

~~is due to the different sizes and masses of each element coming out of a given target.~~

~~Each element will necessarily scatter differently in a medium of argon atoms, and thus~~

~~each element will have an invisible “plume” with its own density distribution. Chao et al.~~

~~demonstrated that this effect is element specific and significant in TbFeCo films [106].~~

~~In the case of DC magnetron sputtering of Sr2FeMoO6, strontium and~~

~~molybdenum will scatter very similarly in this model, as they have similar atomic~~

~~masses. However, iron will scatter significantly differently due to its lighter mass.~~

~~Oxygen also scatters differently, although the content of oxygen in a film can be~~

~~compensated by either adding oxygen to the growth atmosphere or removing oxygen via~~

~~pump rates in the sputter chamber.~~

~~The dynamics for off-axis sputtering growth, then, requires a balancing act of~~

~~each element for stoichiometric films. It is fortunate that each sputtering target has a 2”~~

~~diameter, as it creates an array of points from which the distributions emanate from, and~~

~~the blending of these points gives a wider area of stoichiometry. This makes growth of a~~

~~stoichiometric film of reasonable size possible even for complex oxides such as double~~

~~perovskites.~~

~~109~~

~~A basic diagram showing the positional dependence of the cations in Sr2FeMoO6 is shown in Figure 54, with the atomic numbers and masses for each cation for reference.~~

The heavier elements, strontium and molybdenum, are heavier and thus will scatter less with each collision. The lighter iron atoms, by contrast, scatter more widely, creating a scarcity of Fe at shallow angles and an iron-rich region at steeper angles that strontium and molybdenum atoms have a lower probability of reaching. In this model, there will likely be a midpoint region between the Sr/Mo-rich region and the Fe-rich area where films will be stoichiometric. In Figure 54, this is simplified to a line. Note that the stoichiometric region is not linear as one moves the substrate further from the target.

~~This makes sense, as the atoms will continue to scatter as they move away from the sputter target.~~

~~Figure 54. Simplified model for positional dependence of cations in Sr2FeMoO6 due to scattering off argon atoms.~~

~~110~~

~~We find that this model works well for predicting the cation stoichiometry of~~

~~growths at a given sputter pressure and applied DC voltage. However, this is not the entirety of the model: We need to also consider the effect of position on both the oxygen~~

~~content and growth rate. Figure 55 is an elaboration of figure 54 and represents the~~

~~qualitative model used by our group for finding the position that yields stoichiometric~~

~~films. Although we speculate that the strontium and molybdenum distributions have~~

~~different shapes and may not follow our simple model well further from the target, the~~

~~model reasonably predicts film stoichiometry in the region of the best position.~~

~~Figure 55. Elaboration on Figure 54 to include effects of oxygen levels and ordering on substrate position. While moving further away from the target should slow down growth and~~

~~ostensibly improve B-site ordering and film quality by giving each atom more time to~~

~~organize itself, it also appears to allow the oxygen to cation ratio to increase in the film,~~

~~111~~

~~resulting in poor conduction and lower magnetic moment. Moving closer will result in~~

~~conducting films with less oxygen and high magnetic moment, but at a certain point the~~

~~cation to oxygen level becomes too great. Additionally, films very close to the target~~

~~have higher growth rates, allowing less time for a film to order and lowering film quality,~~

~~ordering, and at a point even the phase purity of the film. By combining the cation and~~

~~oxygen/growth rate effects in our model, we may find a region in which stoichiometric~~

~~films may be grown.~~

The position of the stoichiometry can change with the total pressure of the growth requirement, as well. For instance, we could not obtain stoichiometric films at total gas pressures above 20 mTorr, since higher pressure magnifies the scattering such that no position will provide a stoichiometric position. This will be discussed in the next section.

For reference, the best films we have were grown with a pure argon environment with a total pressure of 6.7 mTorr. At this pressure, we found roughly stoichiometric films grow approximately 2” from the target surface, and 3.5” below the center line of the gun.

~~5.3 Sputter Environment~~

~~Choosing the right environment during sputtering is critical for high quality films~~

~~of Sr2FeMoO6 due to the off-axis scattering mechanism outlined above. In this section,~~

~~we will outline the results of our experiments to determine the ideal conditions for sputter~~

~~deposition of pure-phase, epitaxial thin films. We will focus on the cross-section of~~

~~growths attempted at the best temperature found for high quality double perovskites, which is approximately 800°C.~~

~~112~~

~~Following previous reports [9,17,21] on thin film deposition, we started our growth attempts at a total pressure of 70 mTorr. Figure 56 shows the results of such a~~

~~growth in a pure argon environment. Focused-beam XRD measurements in Figure 56a~~

~~show epitaxial Sr2FeMoO6 (00n) phases just to the left of each SrTiO3 peak, with an out-~~

~~of-plane lattice constant of 7.902 Ǻ, comparable to the bulk value of 7.894 Ǻ. The films~~

~~show significant SrMoO4 and Fe3O4 impurity phases and a polycrystalline Sr2FeMoO6 phase at approximately 32 degrees as well.~~

~~SQUID Magnetometry data is shown in Figures 56 (b) and (c). The former shows the hysteresis curve at T = 5K, revealing a very low saturation magnetization of 0.7~~

µB/f.u. In addition, the paramagnetic phase in the film must be significant, as the substrate is diamagnetic and no other object is in the area of measurement within the magnetometer. Figure 56 (c) shows the magnetization as a function of temperature upon heating with an applied field of 3,000 Oe. Although the Curie temperature of the film appears to be high at first glance, the linear behavior of the curve above room temperature is indicative of non-ideal film quality and is likely artificially increased by the ferrimagnetic Fe3O4 impurity found in the sample by XRD.

In an attempt to purge the impurities and improve sample quality, we attempted to repeat the growth methods of Asano et al., who used Ar with 0.5-5% H2 in their work to achieve pure phase [17,21]. Although no study of film stoichiometry was published, it was assumed that impurities were a result of the oxidation levels during film growth, and that addition of hydrogen created a single, pure-phase sample of proper stoichiometry. In our work we determined that the oxygen content has little or no effect on the cation stoichiometry, but as shown in Figure 57, films grown on both (001)- and (111)-oriented

~~SrTiO3 substrates are pure phase, with only epitaxial peaks showing even under careful focused-beam x-ray diffractometry. This sample was made with 0.5% hydrogen content.~~

~~Further addition of hydrogen was found to make no magnetic improvement and only served to decrease the film’s XRD peak heights, suggesting an overly reduced state.~~

~~One can use structure factor calculations to simulate XRD spectra via Reitveld refinement. Useful information such as strain, stoichiometry, and structure identification~~

~~114~~

~~may be extracted by these simulations. In section 5.1, we discussed how the Fe/Mo~~

~~ordering in Sr2FeMoO6 thin films may be analyzed by simulating the amount of order in~~

~~a (111)-oriented film and matching the ratio of the (111) peak area to that of the (222)~~

~~peak. We will be using this process quantitatively later in this section, but for the~~

~~purposes of Figure 57(b) we will only qualitatively point out the prominence of the (111)~~

~~peak. Prior to introduction of hydrogen, we had not yet seen the Sr2FeMoO6 (111) peak in any of our films at PAr = 70 mTorr.~~

~~Figure 57. X-ray diffractometry spectra by focused-beam Bruker D8 Advance for Sr2FeMoO6 films grown on (a) (001)-oriented and (b) (111)-oriented SrTiO3 substrates.~~

~~115~~

~~might expect magnetic properties improved over the MSat = 0.7 µB/f.u. value at T = 5K, as~~

~~well as a more ideally shaped M-T curve with high TC. However, as Figure 58 shows,~~

~~SQUID Magnetometry showed little improvement over films grown in pure argon, and a~~

~~large degradation of TC to below room temperature. In addition, the coercivity of the~~

~~film has increased over tenfold to order 1,000 Oe, far exceeding any reasonable value for use as a switching layer in computing applications.~~

~~116~~

~~To determine the source of the low magnetization, the cation stoichiometry was~~

~~checked first by energy dispersive x-ray (EDX) spectroscopy in the Department of~~

~~Materials Science Engineering, and then confirmed by Rutherford backscattering~~

~~spectroscopy (RBS) at Rutgers University at the facility described in section 4.5.2. EDX~~

~~Spectroscopy was carried out on a FEI Sirion Scanning Electron Microscope (SEM), with~~

~~an electron energy of 15 keV. Higher beam energies had little effect on the stoichiometry~~

~~results given, as all relevant x-ray energies emitted exist below 10 keV.. Backscattering~~

~~was taken to rule out the possibility of inaccurate EDX measurements due to chemical~~

~~dependency.~~

~~Figure 59 shows the RBS and EDX spectra for Sr2FeMoO6 films grown in pure~~

~~argon at total pressures of PAr of 70 mTorr and 6.7 mTorr. At PAr = 70 mTorr, both RBS~~

~~(Figure 59(a)) and EDX (Figure 59(c)) give a 43% - 48% excess Mo over Fe. For Sr, it is~~

~~difficult to get an accurate measure of stoichiometry for both RBS and EDX due to the Sr~~

~~signal from the SrTiO3 substrate. However, both RBS and EDX suggest that the amount~~

~~of Sr is roughly comparable to the sum of Fe and Mo for most of our Sr2FeMoO6 films.~~

~~The idea of a single-phase double perovskite with non-equal amounts of B-site cation species is possible, as the class of materials is not a point compound, i.e. not~~

~~limited to any set B/B’ site ratio if the B and B’ sites are of similar size. In the case of~~

~~Sr2FeMoO6, excess Mo can replace and occupy the Fe sites up to 100% (which becomes~~

~~3+ 5+ SrMoO3) given favorable reducing environment. This is because: (1) Fe and Mo have almost identical ionic radii; (2) Fe cannot have any valence state higher than 3+; and (3)~~

~~Mo can take 4+, 5+, or 6+ valence depending on the oxygen content in the environment~~

~~117~~

[42]. As a result, a wide range of Mo-heavy off-stoichiometry is allowed in Sr2FeMoO6 films without obvious change, although due to the wider scattering Fe-heavy Sr2FeMoO6 films are extremely difficult to obtain. However, incorrect B-site stoichiometry will adversely affect the band structure and thus the half-metallicity of Sr2FeMoO6 and thus

~~must be improved before any useful application may be had.~~

~~pressure off-axis sputtering of Sr2FeMoO6, that of B-site off-stoichiometry. At 70 mTorr, no sample location in the off-axis position will yield films with less than 40% more~~

~~118~~

~~molybdenum than Fe. Thicker films were used to gain higher spectral intensity in a~~

shorter amount of time, but upon analysis of thinner films, we found that the thickness of the films did not change the results appreciably. In addition, we found that the stoichiometry across a sample of 5 mm by 5 mm size was constant within the uncertainty of each measurement, found to be a few percent by repeated measurements during different SEM sessions.

A systematic study of stoichiometry in bulk Sr2FeMoO6 by Topwal et al. indicates that the magnitude of this off-stoichiometry (~45% Mo rich) drastically lowers the magnetization and Tc in Sr2FeMoO6 [42]. By decreasing the Ar pressure to 6.7

~~mTorr, the stoichiometry is significantly improved to Fe:Mo = 1.00:1.12 by RBS (Figure~~

~~59(b)) and Fe:Mo = 1.00:1.13 by EDX (Figure 59(d)). At this level of off-stoichiometry,~~

~~both MS and Tc only decrease slightly compared with stoichiometric Sr2FeMoO6 [42].~~

~~We varied the Ar pressure from 6.7 mTorr up to 300 mTorr and found that the~~

~~Sr2FeMoO6 films monotonically become more off-stoichiometric with increasing pressure.~~

The physics behind element-specific scattering in off-axis magnetron sputtering has been explained in section 5.2.2, and can be simply extended to explain the pressure dependence of film stoichiometry. At high pressures, the sputtered species experience more scattering, which magnifies the imbalance in scattering effects between Fe and Mo, leading to considerable off-stoichiometry in the Sr2FeMoO6 films. At low pressures, the atoms experience less scattering and the substrate can be positioned for proper stoichiometry.

~~119~~

~~5.4 Proof of Concept: Characterization of Sr2FeMoO6 Thin Films on SrTiO3~~

The long term goal of our work on double perovskite thin films is the fabrication of electronic devices such as magnetic tunnel junctions with performance far exceeding current technology. In order to achieve this goal, materials that are ideal or nearly ideal half-metals with ordering temperatures well above room temperature to avoid too much loss of spin polarization due to thermal fluctuations are desired. Therefore, a necessary first step to device fabrication is confirmation of high-quality “building block” materials via characterization. A strong candidate for device introduction should have:

~~ Half-metallic behavior at low temperature.~~

~~ Single crystal, phase-pure, epitaxial growth with low interfacial defects due to~~

~~careful choice of interfacial lattice matching.~~

~~ A close-to-ideal saturation magnetization with magnetic ordering well above~~

~~room temperature.~~

~~ Proper B/B’-site cation ordering to create the theorized half-metallic behavior.~~

Confirmation of half metallicity in our films has not yet been attempted as of yet. A point contact Andreev reflection (PCAR) system is currently being assembled and tested to determine the spin polarization of our films directly. In the meantime, we have characterized our samples in terms of the other desired properties to find the best deposition parameters. In this section, we will review the progress of our work by characterization of films grown via our best determined parameters.

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~~5.3.1 Sputtering conditions for high quality films~~

~~Films were grown by DC magnetron sputtering on both (001)- and (111)-oriented~~

~~SrTiO3 substrates heated to a temperature of T = 800 °C. The off-axis position at 6.5 cm~~

~~from and 9 cm below the target is the optimal position in our system for deposition of~~

~~Sr2FeMoO6 films with the best structural and magnetic properties. The DC current found~~

to give the best film quality was IDC = 5 mA, equivalent to a bias voltage for our target of approximately 200 V. As outlined in the last section, a pure argon environment with total pressure 6.7 mTorr was used, and provided films with Mo:Fe ratio of about 1.12:1.00.

~~With these conditions, a growth rate of 4.05 nm/hr was determined by direct STEM~~

~~observation of the final thickness of 115 nm films.~~

~~5.3.1 X-Ray Diffractometry for structural characterization~~

~~Figure 60(a) shows the /2 XRD scan of a Sr2FeMoO6 (001) film grown at PAr =~~

6.7 mTorr. The scan was performed on the focused-beam Bruker D8 Advance specifically to look for any defects that may exist in the film. Only the (00l) film peaks with a c-axis pseudocubic lattice constant apc = 7.909 Å are detected, indicating that the

~~film is epitaxial and phase-pure. As stated previously, the broad feature in the vicinity of~~

~~2θ = 30° is from the plastic sample holder used during our diffractometry measurements.~~

~~The pseudocubic lattice constant is slightly larger than the bulk value of 7.894 Å [1], suggesting that the film may have a small degree of in-plane strain due to the 1% lattice mismatch with SrTiO3.~~

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~~122~~

Figure 60. /2 XRD scans of (a) a Sr2FeMoO6 (001) and (b) a Sr2FeMoO6 (111) phase-pure epitaxial films deposited by sputtering in pure Ar of 6.7 mTorr. Rietveld refinements (red curve in (b)) gives a DP order parameter  = 0.854 ± 0.024. 122

~~X-ray diffraction on a (111)-oriented Sr2FeMoO6 film grown in parallel to the~~

~~(001)-oriented film is shown above in Figure 60(b) reveals only the (hhh) peaks with apc~~

~~= 7.982 Å. As with the (001)-oriented film, this indicates phase purity for both~~

~~orientations investigated in this work. In addition, the Sr2FeMoO6 (111) film exhibits a~~

~~strong (111) peak which reflects the DP ordering of Fe and Mo. Using Rietveld~~

~~refinements, we fit the /2 scan of the Sr2FeMoO6 (111) film and extracted the doubl perovskite (DP) ordering parameter  = 0.854 ± 0.024, where  = 2(gFe – 0.5), and gFe is~~

~~the refined occupancy of Fe on the Fe-site in the DP structure [108]. At  = 0.854, 92.7%~~

~~of the Fe atoms are correctly ordered in a DP lattice. Given the estimated stoichiometry~~

~~of Sr2Fe0.94Mo1.06O6 which allows a maximum gFe = 0.94 and  = 0.88, the Fe and Mo~~

~~ions are within experimental error as fully ordered as can be realized for this~~

~~stoichiometry.~~

~~The uniformity, epitaxy, and smoothness of a film are critical components for any~~

~~part of a heterostructure grown for device applications. Figure 61 shows XRD work done~~

~~via the triple-axis Bruker D8 Discover x-ray diffractometer for parallel-beam analysis.~~

~~The sample was positioned off the normal “out-of-plane” orientation in order to observe~~

~~the (110) lattice reflections. The sample was then slowly spun in plane, also known as~~

~~scanning through the Φ angle or Φ-scan, in order to observe the epitaxy of the film. The spectra for (110) Φ-scan of the film and substrate for the (001)-oriented film are shown in~~

~~Figure 61(a). The matching peak positions for the (110) reflection indicates a high level of epitaxy between substrate and film. We will directly observe this in HAADF STEM work later in the section.~~

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~~124~~

~~Figure 61(b) shows the rocking curve of the Sr2FeMoO6 (004) peak for a~~

~~Sr2FeMoO6 (001) film. Rocking curves are a strong indicator of both the crystal quality~~

~~and the uniformity of a film, and are very sensitive to dislocations, shifted orientations, or~~

~~twinning due to substrate defects. The full-width-at-half-maximum (FWHM) of 0.096°~~

~~found for the sample investigated is typical for sample made under the conditions stated~~

~~in this section. Generally, a FWHM under 0.3° has been considered acceptable for high~~

~~quality perovskite films; our samples have generally ranged from 0.04° to 0.2°,~~

~~depending on a series of factors, such as the substrate quality, base oxygen levels, and~~

~~target quality. Our data demonstrates the high uniformity and crystallinity that our off- axis sputtering method yields under proper conditions.~~

Determination of the surface of a film grown is critical to characterization efforts, as an atomically smooth interface will give the most ideal interfacial properties for device application and thus is of high interest. The small-angle X-ray reflectometry (XRR) scan

~~(shown in Figure 61(c)) of a Sr2FeMoO6 film shows more than 15 diffraction peaks,~~

~~indicating smooth film surface and a sharp Sr2FeMoO6/SrTiO3 interface. By using the~~

~~Bruker D8 Advance at extremely glancing angles, one may more easily extract information via basic thin film interference in the form of oscillatory peaks. These peaks~~

~~will only show themselves in extremely smooth films that allow a precise thin film~~

~~constructive interference to occur. For any but a nearly-atomically flat surface, the~~

~~varying thicknesses will cause interferences that vary at different points on the surface~~

~~and cancel each other to a level below the system noise when averaged over the entire~~

~~125 beam spot. From the spacing between peaks, the thickness of the film is calculated to be~~

~~110 nm.~~

~~5.3.3 Magnetic Characaterization by SQUID/VSM~~

Figure 62. Diagram explaining the effect of magnetic shape anisotropy in an ideal ferromagnetic film. (top) For an applied field in the plane of a film with good long- range ordering, easy-axis behavior results in good magnetic interaction between spin moments and hysteresis. (bottom) Due to the dimensionality of the film “out-of- plane” being much smaller than the ordering, the interaction of spins is not in the direction of the field and the film looks paramagnetic in nature up to a field equal to the disruptive field created by the anisotropy, Hani.

An important feature of Sr2FeMoO6 is its magnetic properties, due to its ferrimagnetic ordering and propensity toward arranging disorder to anti-phase boundaries, as in Figure 18. Any sample with half-metallic band structure brought on by the ferrimagnetic ordering of alternating Fe and Mo atoms is likely to have near the theoretical ideal of 4.0 µB/f.u. at low temperature. In addition, a film with low amounts

~~126~~

~~of disorder will have few anti-phase boundaries to disrupt the long-range ordering in the film. In the case where a ferromagnet has few disruptions, the length scale of the long-~~

~~range ordering may exceed the size in one dimension of the sample. In these cases we~~

~~begin to see shape anisotropy, wherein the lack of material in one direction creates a hard~~

~~axis in that direction due to a smaller number of spins to interact with.~~

Figure 62 above shows the effect shape anisotropy has on the hysteresis loop of an ideal ferromagnet. When the field is applied in the plane of the film, as it is in the top half of the figure, the spin moments are in their preferred plane and ideal hysteresis will occur. However, when field is applied perpendicular to the plane of the film, the interaction between spins is lessened, resulting in the loss of hysteresis and a pseudoparamagnetic behavior. The anisotropic field Hani indicates the level of

~~anisotropy, and by extension information regarding a film’s long range ordering. An~~

~~ideal ferromagnet will have the pseudoparamagnetic behavior of the film persist to a~~

~~value 4, where MSat is the saturated magnetic moment per unit volume.~~

~~Figures 63(a) and (b) shows the in-plane (H  film) and out-of-plane (H  film)~~

~~magnetic hysteresis loops of a phase-pure Sr2FeMoO6 (111) epitaxial film at T = 5 K and~~

~~293 K, respectively. The hysteresis loops at both T = 5 K and room temperature show a~~

~~distinct shape anisotropy between H  film and H  film. The hysteresis loops with H ~~

~~film (easy axis) have sharp reversal with square-like loops while those with H  film~~

~~(hard axis) have slanted loops. The magnetic shape anisotropy originates from the~~

~~minimization of magnetostatic energy and exists in most ferromagnetic films. To our~~

~~best knowledge, there has been no report of the expected magnetic shape anisotropy in~~

~~127~~

~~Sr2FeMoO6 films. The lack of magnetic shape anisotropy of the films is likely due to the~~

~~fact that the films are comprised of isolated magnetic domains with lateral sizes~~

~~comparable to or smaller than the film thickness. As a result, the magnetic behavior of~~

~~the films is similar to an ensemble of decoupled magnetic nanoparticles. The decoupling~~

between the magnetic domains could be attributed to impurity phases (e.g. SrMoO4), non-magnetic defects (e.g., Fe/Mo antisite disorders), or off-stoichiometry. The clear magnetic shape anisotropy in Figure 63 indicates strong magnetic coupling over a range much larger than the film thickness.

~~As discussed earlier, in order to accurately measure the film thickness, which is critical in determining MS, we used a combination of profilometry, XRR (Figure 61(c)),~~

~~STEM (Figure 64, below), and RBS. From this analysis, we can determine from the data~~

~~in Figure 63(a) that the saturation magnetization MS is 2.6 B/f.u. at T = 5K. This value~~

~~is in good agreement with bulk results for samples with similar stoichiometry. For the~~

~~fact that it is still well below the expected 4 B/f.u., we attribute mainly to the remaining~~

~~off-stoichiometry (12% excess Mo) and epitaxial-strain-induced defects. The M-T curve~~

~~in Figure 63(c) shows a clean single ferromagnetic phase transition with a Tc = 380 K.~~

~~Although there are a few reports of Sr2FeMoO6 films with MS values near 4 B/f.u., the~~

~~predicted full magnetization for Sr2FeMoO6, none of them demonstrated the combination~~

~~of stoichiometry investigation, phase purity, and distinct magnetic shape anisotropy as~~

~~presented in Figure 62 [9, 21, 33, 35].~~

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Figure 63. In-plane (black) and out-of-plane (red) hysteresis loops at (a) T = 5 K and (b) T = 293 K of a 115-nm thick Sr2FeMoO6 (111) epitaxial film deposited in pure Ar of 6.7 mTorr. The small opening in the out-of-plane loop at T = 5 K in (a) is due to the misalignment of the sample in SQUID measurements, in which a few degrees off- perfect alignment can result in obvious change in the shape of the loop [107]. The clear anisotropy between H  film and H  film indicates strong magnetic interaction throughout the film. (c) M vs. T curve gives a TC = 380 K.

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~~5.3.4 Direct Observation of Structure and Ordering by HAADF STEM~~

The ability to directly observe complex oxide samples with atomic resolution has become increasingly more important as perovskites are targeted for defect-sensitive uses in device application. This is due in large part to the very slight defects that off- stoichiometry and disorder can play in films with more than one cation but that will not show up in XRD characterization. This problem is compounded in the double perovskite, where the alternating B-site cation ordering, a feature absolutely critical in the engineering of a half-metallic band structure, can only be indirectly implied by any means but direct observation and should be considered a must for any proof of high quality thin films.

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~~The HAADF STEM image in Figure 64 shows the sharp interface between a~~

Sr2FeMoO6 (001) film and the SrTiO3 substrate viewed along the <100> direction. A schematic drawing of the double perovskite (DP) lattice is shown next to the STEM image. Note that since we are looking down columns with both Fe and Mo atoms, no

~~contrast between B-sites is seen. We must carefully select a direction, then, where Fe and~~

~~Mo sites sit exclusively in the same column. This is most easily achieved by cutting a film to look down the <110> direction.~~

Figure 65 presents direct observation of Fe/Mo ordering in a Sr2FeMoO6 (111) film by HAADF STEM along the <110> direction. When viewed along the <110> direction of the DP lattice, each lattice site becomes a column of pure Sr, Fe, or Mo atoms, in the ideal case. Since each element gives its unique brightness in STEM images due to their differences in scattering probability of electrons related to their atomic numbers, each site can be identified as Sr, Fe, or Mo. Due to the small atomic number, oxygen is essentially invisible by STEM. The most evident feature in Figure 65 is the bright Sr-Mo-Sr triplets separated by a darker Fe atom. These triplets are excellent evidence of high ordering levels, as substitution of Fe and Mo with each other would not have allowed such a beautiful contrast in unfiltered pictures. It is possible that one fault with the films can be seen in this figure, as the overall brightness appears to be uneven for a portion of the sample. We have ruled out the possibility of microscope error here, so two possibilities exist: (1) A non-uniform stoichiometry in the film, or (2) a non- uniformity in the thickness of the film cut via ion beam, creating a darker are due to a

~~131 thinner film. Given the non-ideal target used and the expertise of Fraser group in cutting these films, we are more inclined to speculate for the former.~~

~~Figure 65. A Sr2FeMoO6 (111) epitaxial film on SrTiO3 viewed along the <110> direction with bright “triplet” patterns indicative of atomic number contrast.~~

Figure 66 shows a high magnification STEM image of the Sr2FeMoO6 (111) film that represented a zoomed in version of Figure 65. The Sr, Fe, and Mo atoms are labeled to clearly show the DP ordering. A schematic drawing of the projection of DP lattice 132 along the <110> direction is shown in the bottom right corner of Figure 66, which matches perfectly with the STEM image. To our best knowledge, this result is the first direct observation of clear DP ordering in Sr2FeMoO6 by STEM [41]. The XRD results and the STEM images clearly demonstrate the high DP ordering in our Sr2FeMoO6 films.

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~~Chapter 6: Conclusions~~

~~In this paper, we have reviewed previous work and given an overview on the theoretical model for half-metallic Sr2FeMoO6, with an eye toward work on achieving~~

~~near-ideal spin polarization in thin films. We have identified the obstacles and~~

~~roadblocks towards this goal and reviewed our progress towards this goal: improving~~

~~sputter target quality, utilizing off-axis sputtering for low energy deposition, proper~~

~~substrate positioning and chamber pressure for improved stoichiometry. Despite direct~~

~~observation of excellent film quality, more work remains to done. Despite superb~~

~~ordering, it is likely that local off-stoichiometries and anti-phase boundaries occur. We~~

~~see possible direct evidence by HAADF STEM, as well as indirect evidence such as~~

~~saturation magnetization (2.6 µB/f.u.) and Curie temperature (380 K) values that are significantly below the ideal theoretical values (4.0 µB/f.u. and 410 K, respectively).~~

~~In future work, we intend to use the knowledge of the best growth conditions~~

found in conjunction with the newfound bulk powder synthesis outlined in section 5.1 to improve sample quality with a higher quality target. In addition, point contact Andreev reflection will be performed to directly measure the spin polarization of Sr2FeMoO6 thin films, a measurement that has not yet been done but necessary for determination of half- metallicity and suitability for spintronic applications.

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Work has been done in parallel with Sr2FeMoO6, a strong candidate for switching layers due to its low coercivity, to create other double perovskite films for device fabrication. Examples include Sr2CrReO6, an excellent candidate for magnetic tunnel junction pairing with Sr2FeMoO6 due to its much larger coercivity (~1000 Oe) at room temperature and its prediction as a half metal. Sr2CrOsO6 has also been investigated in the same vein, although it should be noted that osmium is both expensive and potentially hazardous when oxidized, complicating production of a pure bulk target. However, this material is notably theorized to also be a semiconductor, possibly paving the way to improved-performance field effect transistors, which would be of enormous interest.

Nonmagnetic layers also play an important role in any future double perovskite device fabrication as buffer or tunneling layers. Chosen for their insulative properties, materials such as Sr2GaTaO6, Sr2NiWO6, and Sr2CrNbO6 can avoid sacrificial layers due to their isostructurality with the other strontium-based double perovskites listed. One may avoid size limits by creating atomically sharp interfaces with unbroken strontium- oxygen latticework, with only the B-site cations switching over a unit cell’s distance. It is our hope that we will soon be able to move forward with device fabrication of magnetic tunnel junctions for application investigations.

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