X-RAY ABSORPTION SPECTROSCOPY AND MICROSCOPY …short notice, and Kyusik Sin and Ken Yamada fabricated exchange-biased samples for me. Guarav Khanna introduced me to Latex, and Vidya

X-RAY ABSORPTION SPECTROSCOPY AND

MICROSCOPY STUDY OF FERRO- AND

ANTIFERROMAGNETIC THIN FILMS, WITH

APPLICATIONS TO EXCHANGE ANISOTROPY

a dissertation

submitted to the department of applied physics

and the committee on graduate studies

of stanford university

in partial fulfillment of the requirements

for the degree of

doctor of philosophy

Thomas J. Regan, III

March 2001

c© Copyright by Thomas J. Regan, III 2001

All Rights Reserved

ii

I certify that I have read this dissertation and that in

my opinion it is fully adequate, in scope and quality, as

a dissertation for the degree of Doctor of Philosophy.

Robert L. WhiteDepartment of Materials Science and Engineering

(Principal Advisor)




Joachim StohrStanford Synchrotron Radiation Laboratory




Malcolm R. BeasleyDepartment of Applied Physics

Approved for the University Committee on Graduate

Studies:

iii

Abstract

Understanding exchange anisotropy—the unidirectional coupling of a ferromagnet to

an adjacent antiferromagnet—may be the canonical problem of current magnetics

research. Its solution requires spatially-resolved magnetic, elemental, and chemical

information about a buried interface. X-ray absorption spectroscopy (XAS) and

XAS-based microscopy techniques are uniquely able to provide this information.

The element-specificity of XAS makes it suitable for investigating magnetic het-

erostructures. Buried interfaces may be characterized with submonolayer sensitivity.

Sensitivity to both ferromagnetic and antiferromagnetic ordering, and to chemical en-

vironment, enables XAS to determine much of the information relevant to a complex

system in a single experiment. Finally, the implementation of XAS as a microscopy

technique allows the acquisition of the above information with spatial resolution,

which is crucial to understanding exchange anisotropy and other interfacial phenom-

ena.

We show conclusively that oxidation/reduction reactions occur at a metal/oxide

interface. A typical sample was 10 A Fe, Co, or Ni adjacent to 10 A NiO or CoO,

grown at room temperature and not (except as noted below) annealed. The XAS

spectrum of the nominally-metal layer revealed the presence of 0.5–3 A oxidized-

metal at the metal/oxide interface. Similarly, the spectrum of the nominally-oxide

layer revealed a reduced-oxide region at the interface. Samples with different el-

emental constituents were shown to have differing degrees of reactivity, in accord

with thermodynamic considerations, and annealing to typical device temperatures

was shown to increase the amount of reaction. The reduced-oxide interfacial region

may be the source of the interfacial spins responsible for the exchange anisotropy

iv

interaction at an antiferromagnetic oxide/ferromagnetic metal interface.

Other results demonstrate the applicability of XAS-based microscopy to magnetic

systems. The first unambiguous images of the antiferromagnetic structure of a sur-

face are described. Temperature-dependent x-ray magnetic linear dichroism (XMLD)

measurements show that linelike structures on the surface of epitaxial (001) NiO have

an antiferromagnetic ordering temperature lower than that of the remainder of the

sample. The spin axis orientation of a cracked polycrystalline NiO film was imaged

and found to change near the cracks. An explanation of the change in spin axis

orientation as a consequence of an inhomogeneous film strain is presented.

v

Acknowledgments

This work began at Stanford in close collaboration with industry. I obtained an

excellent introduction to magnetics research by assisting Chih-Huang Lai in investi-

gations of NiO and exchange anisotropy. Tom Anthony (Hewlett-Packard) deposited

biased metal layers on our oxide layers and was always available for consultation. Ed

Murdock (Seagate Technology) underwrote this early work. Professor R. S. Feigel-

son (Stanford Materials Science and Engineering Department) generously provided us

with time on his MOCVD chamber, and Sang-Yun Lee provided significant assistance

after Chih-Huang’s graduation.

After some time I decided that a new approach to the study of exchange anisotropy

was needed. The solution was just up the road (and across the Bay) in Jo Stohr’s

XAS group at the Stanford Synchrotron Radiation Laboratory (SSRL) and the Ad-

vanced Light Source (ALS) at Lawrence Berkeley National Laboratory. The Stohr

group members taught me just about everything I know about spectroscopy and spent

many hours on the beamline on my behalf. Jan Luning, Frithjof Nolting, Hendrik

Ohldag, and Christian Stamm assisted me in experiments at SSRL. At the ALS, An-

dreas Scholl developed methods for PEEM microscopy and spectromicroscopy, and

obtained the PEEM images of Chapters 7 and 8. The PEEM microscope was de-

signed by Simone Anders. Early in the project, Thomas Stammler and I attempted

to image the domain structure of nickel oxide thin films. The failure of these early

attempts, coupled with the success of recent studies of cleaved NiO surfaces, consti-

tutes an interesting scientific question, perhaps involving the different strain states of

the systems.

At SSRL, where the spectroscopy experiments were performed, I benefited from

vi

the skills of the technical and research staff. Curtis Troxel, Jeff Moore, and Jan

Luning kept the beamline running. Nels Runsvick improved the design of the sample

transfer system and machined it in short order. This system was crucial to in situ

growth of metal/oxide sandwich samples at the beamline and was immediately used

for many experiments besides mine. Stephen Sun performed a hydrofluoric acid dip to

remove oxides from our silicon substrates on several occasions; I very much appreciate

this assistance.

Thanks to Jo I was able to collaborate with the scientists at IBM-Almaden. Robin

Farrow shared his expertise on many occasions over the years. Mike Toney verified

my x-ray reflectivity calculations, providing much-needed confirmation of the layer

thicknesses of my samples. Matt Carey made samples for me on several occasions,

including the thick polycrystalline nickel oxide films described in Chapter 8, which

were annealed by Tim Reiley. Mahesh Samant graciously rearranged his beam time

more than once to accomodate my experiments.

Fabrication of samples for the synchrotron experiments required a deposition sys-

tem able to deposit and characterize in situ very thin several-layer samples. This

well describes the molecular beam synthesis (MBS) chamber of Prof. M. R. Beasley’s

group in Stanford’s Applied Physics Department. The debt owed to the MBS group is

obvious—two-thirds of the experiments described in this thesis were studies of samples

from their machine. MBS architect Bob Hammond, Charles Campbell, and especially

Nik Ingle and Jim Reiner, who performed most of the chamber maintenance, deserve

much thanks, as these experiments would not have been possible without their con-

stant assistance.

Debts within Stanford’s magnetics community—the Clemens, Wang, and White

groups—are many. Fred Mancoff deposited metal capping layers on my samples on

short notice, and Kyusik Sin and Ken Yamada fabricated exchange-biased samples for

me. Guarav Khanna introduced me to Latex, and Vidya Ramaswamy and Hope Ishii

were helpful Latex references. I’d also like to thank Brennan Peterson for keeping the

printer running. This has been very important to me of late. Professor W. D. Nix

(Materials Science and Engineering Department) devoted a significant amount of time

to getting me started on the strain calculations of Chapter 8.

vii

Samples used in these experiments were extensively characterized. Most of the

characterization employed the facilities of the Center for Materials Research at Stan-

ford. Gaurav Khanna and Erica Lilleoden have kept the AFM in excellent condition;

the improvement in capability of the machine since they took over is significant. Sev-

eral people have worked to keep the x-ray diffraction machines going; I’d like to thank

Glenn Waychunas, Helen Kirby, and Igor Smolsky for their efforts. Turgut Gur has

worked hard to keep CMR afloat through difficult financial times. At the Ginzton

Crystal Shop, Chris Remen ensured that I wouldn’t have to worry about the quality

of my MgO substrates by experimenting to find the correct polishing conditions.

Through my advisors’ network of contacts, I was able to enlist the advice and

collaboration of experts around the world. Julie Borchers at NIST-Gaithersburg

taught me about the capabilities of neutron diffraction. Gerrit van der Laan at SRS-

Daresbury calculated the XAS spectrum of cobalt oxide the day after I asked; our

group seems to consult this spectrum every other week. Frank deGroot of Utrecht

University provided helpful answers to my questions about XAS.

I’d like to thank Prof. G. E. Brown (School of Earth Sciences and SSRL) for

agreeing to chair my dissertation committee, Prof. K. A. Moler (Applied Physics

Department) for serving on the committee, and Prof. Beasley (Applied Physics De-

partment) for serving on the committee and reading my thesis.

Considering all the resources that were available to me in my graduate career, I

must conclude that I was lucky to have Prof. R. L. White and Jo Stohr as advisors.

Professor White got me started on a great research project and then allowed me the

freedom to take the project in the direction I preferred. Through his comprehensive

knowledge of magnetics and extensive network of associates I was able to obtain just

about any assistance I required. Jo Stohr was a similar source of synchrotron expertise

and a link to the worldwide synchrotron community. As a member of his group, I

spent my graduate career at the forefront of magnetics research.

The early stages of this project were supported by Seagate Technology and by the

Center for Materials Research at Stanford. Timely support from International Disk

Drive Equipment and Materials Assocation, via the 1998-1999 IDEMA Fellowship,

smoothed the transition to the synchrotron studies. The final stages of the work were

viii

funded by the National Science Foundation, grant ECS-9810185. The synchrotron

work was supported by the Director, Office of Basic Energy Sciences, of the U.S.

Department of Energy under Contract No. DE-AC03-76SF00098. The MBS chamber

is supported by AFOSR grant F49620-98-1-0017.

Finally I would like to thank Jacqueline Regan, nee Kuo, for supporting me

throughout my graduate career, and my parents, for helping me with my spelling

words when I was young.

ix

Contents

Abstract iv

Acknowledgments vi

1 Introduction 1

2 Review of Exchange Anisotropy 3

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Definition and Manifestations . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Preparation, Systems, and Applications . . . . . . . . . . . . . . . . . 5

2.4 Simple and More Complicated Models . . . . . . . . . . . . . . . . . 6

2.5 Investigation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.6 XAS Spectroscopy and Microscopy Techniques . . . . . . . . . . . . . 12

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Structure of Nickel Oxide 15

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 NiO Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Crystallographic Structure and Magnetic Ordering . . . . . . 15

3.2.2 Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Magnetic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.1 180◦ Superexchange and the Multi-Axis Structure . . . . . . . 20

3.3.2 Confinement to a Single Spin Axis . . . . . . . . . . . . . . . 22

3.3.3 Orientation of the Spin Axis Within The Plane . . . . . . . . 23

x

3.3.4 Note on Terminology . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Antiferromagnetic Domains . . . . . . . . . . . . . . . . . . . . . . . 24

3.4.1 NiO Domain Structure . . . . . . . . . . . . . . . . . . . . . . 24

3.4.2 Origin of Multidomain Configurations in Antiferromagnets . . 24

4 Mean-Field Calculations 26

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 Temperature Dependence of 〈M〉 . . . . . . . . . . . . . . . . . . . . 27

4.3 Temperature Dependence of 〈M2〉 . . . . . . . . . . . . . . . . . . . . 28

4.4 〈M〉 and 〈M2〉 at T = 0 and T = TN . . . . . . . . . . . . . . . . . . 29

4.5 Equivalence of the Two Expressions for 〈M2〉 . . . . . . . . . . . . . 30

5 XAS, Linear Dichroism, and SpectroMicroscopy 34

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2 X-Ray Absorption Spectroscopy . . . . . . . . . . . . . . . . . . . . . 34

5.2.1 Photon-In, Electron-Out . . . . . . . . . . . . . . . . . . . . . 35

5.2.2 Comparison of XAS to XPS . . . . . . . . . . . . . . . . . . . 36

5.2.3 XAS Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2.4 Lineshape of X-Ray Absorption Spectra . . . . . . . . . . . . 41

5.2.5 Multiplet Description . . . . . . . . . . . . . . . . . . . . . . . 45

5.3 Linear Dichroism Theory and Experiment . . . . . . . . . . . . . . . 48

5.3.1 Linear Dichroism Theory . . . . . . . . . . . . . . . . . . . . . 48

5.3.2 Importance of Multiplet Splitting . . . . . . . . . . . . . . . . 51

5.3.3 A Linear Dichroism Experiment on NiO . . . . . . . . . . . . 52

5.3.4 Comparison of NiO L2 Peak Ratio and 〈M2〉 . . . . . . . . . . 54

5.4 XAS SpectroMicroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.4.1 PhotoEmission Electron Microscopy (PEEM) . . . . . . . . . 55

5.4.2 Linear Dichroism Imaging via PEEM . . . . . . . . . . . . . . 57

6 Interfacial Chemical Effects 60

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

xi

6.2.1 Sample Design . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.2.2 Samples Prepared Ex Situ . . . . . . . . . . . . . . . . . . . . 62

6.2.3 Samples Prepared In Situ and on NiO Single Crystal . . . . . 63

6.2.4 Standard Samples . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.2.5 XAS Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.3 XAS Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.3.1 Sample Structure Assumed for Analysis . . . . . . . . . . . . . 66

6.3.2 XAS Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.3.3 Quantitative Analysis of Electron-Yield Spectra . . . . . . . . 70

6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.4.1 Qualitative Summary of Results . . . . . . . . . . . . . . . . . 78

6.4.2 Tabulated Results . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.4.3 Consistency Checks . . . . . . . . . . . . . . . . . . . . . . . . 85

6.4.4 Iron Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.4.5 Time Evolution of Reaction Extent . . . . . . . . . . . . . . . 88

6.4.6 Precision and Absolute Error Bar . . . . . . . . . . . . . . . . 90

6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.5.1 Interface Structure . . . . . . . . . . . . . . . . . . . . . . . . 93

6.5.2 Application of XAS to Magnetic Systems . . . . . . . . . . . . 95

6.5.3 Implications for the Study of Exchange Anisotropy . . . . . . 95

6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7 Magnetic Structure of a NiO(100) Surface 98

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.2.1 Sample Growth and Characterization . . . . . . . . . . . . . . 100

7.2.2 Spectromicroscopy Experiments . . . . . . . . . . . . . . . . . 100

7.3 Review of XMLD Applied to NiO . . . . . . . . . . . . . . . . . . . . 101

7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.4.1 Magnetic Origin of the Image Contrast . . . . . . . . . . . . . 102

7.4.2 Quantification of Image Contrast . . . . . . . . . . . . . . . . 103

xii

7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8 Film Strain and AF Spin Orientation 107

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

8.2 XAS Microscopy Images of Annealed Polycrystalline NiO Films . . . 108

8.2.1 Sample Fabrication and AFM Images . . . . . . . . . . . . . . 108

8.2.2 Linear Dichroism and Topographical Images . . . . . . . . . . 110

8.3 Local Stress Explanation . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.3.1 Generation of Thermal Stress . . . . . . . . . . . . . . . . . . 113

8.3.2 Cracking to Relieve Stress . . . . . . . . . . . . . . . . . . . . 113

8.3.3 Island Stress Profile and Resulting Strain . . . . . . . . . . . . 115

8.4 Relationship between Antiferromagnetic

Ordering and Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8.4.1 Polycrystalline NiO Magnetostriction Constant . . . . . . . . 118

8.4.2 Explanation of Linear Dichroism Images . . . . . . . . . . . . 119

8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

9 Conclusion 122

A Normalization and Fitting Routines 124

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

A.2 XAS Spectrum Normalization . . . . . . . . . . . . . . . . . . . . . . 125

A.2.1 Element-Specific Information . . . . . . . . . . . . . . . . . . 125

A.2.2 The Standard Energy Profile . . . . . . . . . . . . . . . . . . . 126

A.2.3 Background Subtraction and Area Normalization . . . . . . . 126

A.3 Two-Layer XAS Spectrum Simulation and Fitting . . . . . . . . . . . 127

A.3.1 Relation to Oxidation/Reduction Experiment . . . . . . . . . 127

A.3.2 Element-Specific Information . . . . . . . . . . . . . . . . . . 129

A.3.3 Nominally-Metal and Nominally-Oxide Cases . . . . . . . . . 130

A.3.4 Simulation, Fitting, and Identifying the Best Fit . . . . . . . . 131

A.4 Main Routine Summary and Code . . . . . . . . . . . . . . . . . . . . 132

A.5 Function Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

xiii

Bibliography 146

xiv

List of Tables

2.1 Comparison of exchange anisotropy investigation methods . . . . . . 13

4.1 〈M〉 and 〈M2〉 at T = 0 and T = TN . . . . . . . . . . . . . . . . . . 29

5.1 Relative merits of XPS and total-electron-yield (TEY) XAS . . . . . 39

5.2 Thermally-averaged values 〈AqJ,J ′〉 of the 3j symbols . . . . . . . . . . 47

5.3 Zero-temperature values of (2J + 1)〈AqJ,J ′〉 . . . . . . . . . . . . . . . 47

6.1 Oxidation/Reduction of in-situ-prepared NiO/Fe sandwiches. . . . . . 83

6.2 Oxidation/Reduction of ex-situ-prepared sandwiches. . . . . . . . . . 84

6.3 Reduction of NiO single crystal and corresponding oxidation of de-

posited Co or Fe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.4 Effect of various errors on reported results. . . . . . . . . . . . . . . . 91

8.1 Residual strains in NiO film . . . . . . . . . . . . . . . . . . . . . . . 118

A.1 Normalization routine summary information . . . . . . . . . . . . . . 132

A.2 Simulation and fitting routine summary information . . . . . . . . . . 137

xv

List of Figures

2.1 Hysteresis Loops of exchange-biased and unbiased cobalt layers . . . . 4

2.2 Spin configurations and M-H loop of exchange-biased sample . . . . . 7

2.3 Exchange anisotropy model: F spin direction perpendicular to AF spin

axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Exchange anisotropy models: different AF domain wall orientations . 10

3.1 Spin directions of antiferromagnetically ordered NiO . . . . . . . . . . 16

3.2 NiO orthorhombic deformation . . . . . . . . . . . . . . . . . . . . . 17

3.3 NiO monoclinic deformation . . . . . . . . . . . . . . . . . . . . . . . 17

3.4 Distorted cubic structure of antiferromagnetically ordered NiO . . . . 18

3.5 Four-motif spin configuration resulting from 180◦ superexchange inter-

action only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1 Ideal uniaxial antiferromagnet susceptibilities . . . . . . . . . . . . . 30

4.2 Comparison of χfluct and χ‖ . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 Calculated NiO thermal average magnetizations . . . . . . . . . . . . 33

5.1 XAS photon absorption and electron emission process . . . . . . . . . 35

5.2 Initial electron transition of XPS, UPS, and XAS . . . . . . . . . . . 37

5.3 Relationship of XPS and XAS spectra . . . . . . . . . . . . . . . . . 38

5.4 XAS Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.5 NiO ligand field and consequent d-orbital splitting . . . . . . . . . . . 42

5.6 Multiplet effects for oxide XAS transitions . . . . . . . . . . . . . . . 43

5.7 Transition metal oxide versus transition metal XAS spectra . . . . . . 44

xvi

5.8 Nonmagnetic linear dichroism . . . . . . . . . . . . . . . . . . . . . . 49

5.9 Magnetic linear dichroism experiment on NiO . . . . . . . . . . . . . 53

5.10 The PEEM-2 microscope . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.11 Contrasts obtainable by x-ray absorption spectromicroscopy . . . . . 56

5.12 XAS microscopy images of correlated F and AF domains . . . . . . . 58

6.1 XAS spectra of NiO films of small thicknesses . . . . . . . . . . . . . 65

6.2 Nominal sample structure and possible actual structures . . . . . . . 67

6.3 Derivation of absorption coefficient spectrum from electron-yield spec-

trum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.4 Absolute absorption coefficient standard spectra for Fe, Co, and Ni

metals and oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.5 Total-electron-yield XAS metal and oxide spectra . . . . . . . . . . . 76

6.6 Normalization of experimental and calculated electron-yield spectra . 79

6.7 Ni and Fe L3 spectra of an in-situ-grown NiO/Fe sandwich . . . . . . 80

6.8 Cobalt L3 spectra of a CoO/Fe sample showing effects of anneal . . . 81

6.9 Ni L3 and L2 spectra for NiO/Fe and NiO/Co sandwiches . . . . . . . 82

6.10 Ni L2 and Co L3 spectra of an ex-situ-grown NiO/Co sandwich . . . . 87

6.11 Differing oxidation behaviors of iron films . . . . . . . . . . . . . . . . 89

6.12 Ni and Fe L-edge interpeak region spectra of an in-situ-grown NiO/Fe

sandwich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.1 AFM image of epitaxial NiO(100) film . . . . . . . . . . . . . . . . . 101

7.2 XMLD image of epitaxial NiO(100) . . . . . . . . . . . . . . . . . . . 103

7.3 Ni L2 resonance fine structure as a function of temperature . . . . . . 104

7.4 Antiferromagnetic image line scans as a function of temperature . . . 105

8.1 AFM images of NiO film, before and after anneal . . . . . . . . . . . 109

8.2 AFM images of annealed NiO films . . . . . . . . . . . . . . . . . . . 109

8.3 Average grain size of annealed NiO films . . . . . . . . . . . . . . . . 110

8.4 AF and topographical microstructure of annealed NiO films . . . . . 111

8.5 NiO spin axis orientation near and far from a crack . . . . . . . . . . 112

xvii

8.6 Estimated in-plane residual stress profile of a NiO island . . . . . . . 117

8.7 Polycrystalline NiO magnetostriction . . . . . . . . . . . . . . . . . . 120

A.1 Relation of Sample Stucture to Model Bilayers . . . . . . . . . . . . . 128

xviii

Chapter 1

Introduction

This chapter describes the organization of the thesis and the significance of the re-

search results. Chapters 2, 3, and 4 are background material. Chapter 2 is a brief

review of the phenomenon of exchange anisotropy. The message of this chapter—that

microstructurally-sensitive techniques such as x-ray absorption spectroscopy are es-

sential to continued progress in the investigation of exchange anisotropy—motivates

this thesis. Chapter 3 is a description of nickel oxide. Though the use of NiO in

magnetic hard drive read heads has declined1, it remains the subject of significant

academic interest, and is featured in the three experiments described in this thesis.

This chapter synthesizes a substantial amount of the early (1960–1975) literature on

the magnetic deformations in NiO. In addition a brief discussion of antiferromagnetic

domains is given, including a consideration of why antiferromagnets break up into

domains. Chapter 4 reviews the mean-field calculations which are necessary to the

discussion of magnetic linear dichroism spectroscopy. In this chapter two expressions

for the quantity 〈M2〉 are reconciled; to the author’s knowledge this has not been

considered previously.

Chapter 5 describes the main experimental techniques used in this work. In this

section, x-ray absorption spectroscopy (XAS) and microscopy, and their capabilities,

are discussed. Since readers outside the synchrotron community may be more familiar1Antiferromagnetic alloys of manganese are the focus of current technological efforts because of

their high blocking temperature.

1

CHAPTER 1. INTRODUCTION 2

with x-ray photoelectron spectroscopy (XPS), which is in some ways similar to XAS,

the two techniques are compared.

The experimental results of this work are described in Chapters 6, 7, and 8. In

Chapter 6 it is shown that at an oxide/metal interface, a reaction occurs which can

be modeled as the diffusion of oxygen atoms from the oxide layer to the metal layer.

The resulting reduced-oxide and oxidized-metal regions are 0.5–3 A thick. Existing

single-layer XAS formalism was extended to describe the spectra of two-layer samples,

and procedures to (a) create standard absorption spectra from available electron-yield

spectra, and (b) use these standard absorption spectra to model unknown electron-

yield spectra, were developed. The associated computer codes are displayed and

described in the Appendix.

Chapter 7, based on Ref. [1], was the first unambiguous determination of the

surface structure of an antiferromagnet. Chapter 8, as yet unpublished, describes a

study of the antiferromagnetic structure of thick polycrystalline NiO films, wherein

changes in spin axis orientation occur near cracks in the film. A plausible explanation

for this spin axis reorientation in terms of inhomogeneous strain in the film resulting

from annealing, cooling, and cracking is detailed.

Finally, Chapter 9 offers an assessment of x-ray absorption spectroscopy and mi-

croscopy applied to exchange anisotropy and suggests future experiments.

Chapter 2

Review of Exchange Anisotropy

2.1 Introduction

This thesis demonstrates the potential of x-ray absorption spectroscopy/microscopy

to investigate magnetic systems in general and exchange anisotropy in particular. In

early work, the author employed traditional magnetics methods to study exchange

anisotropy[2], but soon became convinced that the limits of these methods had been

reached and that a new approach was necessary. To justify this belief, a brief review

of exchange anisotropy is presented here. The interested reader is referred to both of

two recent review papers: Ref. [3], emphasizing theoretical treatments, and Ref. [4],

emphasizing the various exchange-biased systems, for comprehensive discussions and

extensive references.

2.2 Definition and Manifestations

Exchange anisotropy is a unidirectional interaction between an antiferromagnet (AF)

and an adjacent ferromagnet (F). This interaction creates a permanent preference

for the spins of the ferromagnet to order in a particular direction. The best-known

manifestation of exchange anisotropy is the shifted hysteresis loop of the ferromagnet,

depicted in Fig. 2.1. This figure shows the M–H loop of an unbiased ferromagnet (Co,

6 nm) and the corresponding loop of the ferromagnet adjacent to an antiferromagnet

3

CHAPTER 2. REVIEW OF EXCHANGE ANISOTROPY 4

Figure 2.1: Room temperature hysteresis loops of 6 nm cobalt, biased (on NiO) andunbiased (on Al2O3). The shifted hysteresis loop, or exchange bias, and increasedcoercivity in the biased case are apparent. The exchange bias of 45 Oe correspondsto an interfacial interaction energy of 0.04 erg/cm2.

(NiO, 40 nm) and suitably prepared. The shift of the loop, commonly known as the

exchange bias Hex, is apparent. Also apparent is the increased coercivity Hc which

usually accompanies the shifted loop.

Torque magnetometry reveals the unidirectional anisotropy Ku associated with

exchange anisotropy. These curves have a sin θ component, the minimum of which

denotes an easy direction. (As a counterexample, a free single crystal cobalt specimen

has a sin2 θ torque curve which characterizes a uniaxial anisotropy with an easy axis .)

The area between counterclockwise and clockwise torque curves represents the energy

lost in rotating the magnetization—the rotational hysteresis of the system. For a free

ferromagnet at high fields there is no energy loss, because the magnetization remains

parallel to the field. But for an exchange-biased ferromagnet, the rotational hysteresis


is nonvanishing even at high fields.

All of the above manifestations of exchange anisotropy decrease with increasing

temperature and disappear near the Neel temperature TN of the antiferromagnet—an

indication of the antiferromagnet’s importance to the phenomenon. The temperature

at which exchange anisotropy vanishes is known as the blocking temperature.

2.3 Preparation, Systems, and Applications

There are two common methods of creating the exchange anisotropy interaction.

First, an existing ferromagnet/antiferromagnet bilayer can be heated above the Neel

temperature of the antiferromagnet and then cooled in a field. Orientation of the fer-

romagnet is the important step; exchange anisotropy will result from a zero field cool

if the ferromagnet is oriented at remanence. Second, the ferromagnet can be deposited

on the antiferromagnet in a field sufficient to orient the deposited ferromagnet. This

deposition need not occur above TN.

Exchange anisotropy was discovered in a system of Co/CoO particles prepared

according to the former method[5, 6]. The phenomenon has since been seen in a

variety of systems, among them (F denotes ferromagnet, AF denotes antiferromagnet)

• F/oxide AF (such as CoO or NiO)

• F/metallic AF (FeMn,NiMn, IrMn, Cr)

• other nonmetallic AF/F (in particular FeF2/Fe, which has a simple uniaxial

spin structure)

• ferrimagnet substituted for AF or F (CoO/Fe3O4)

• spin glass and amorphous systems.

These systems can be multigrained or single-grained (single crystal), can possess a

multiplicity of crystal orientations or a single orientation (epitaxial), and can be

deposited by a variety of methods, such as sputtering and CVD.


In recent years the phenomenon of exchange anisotropy has taken on significant

technological importance. Exchange-biased layers have been important components

of two generations of magnetic hard disk read heads. Initially, exchange bias was

used to stabilize domains in heads based on the anisotropic magnetoresistance effect.

Currently, exchange bias is used to pin one of the two ferromagnetic layers in the

‘spin-valve’ read head structure, the transport properties of which are characterized

by the giant magnetoresistive (GMR) effect. GMR-based spin valves[7] and magnetic

tunnel junctions[8] (similar in structure to spin valves, but relying on spin-dependent

tunneling for their transport properties) have been proposed for use as magnetic

memory elements, or MRAM.

2.4 Simple and More Complicated Models

In this section a simple model[9] for exchange anisotropy will be presented and some

more complicated models will be quickly described. The simple model does not

accurately describe exchange anisotropy; it is presented to the reader unfamiliar with

exchange anisotropy as an aid to organizing his thoughts on the matter.

The model is depicted in Fig. 2.2 (taken from Ref. [4]). First the creation of

the exchange anisotropy interaction, in which the antiferromagnetic spin ordering is

modified by the oriented ferromagnetic layer, will be discussed. An antiferromag-

net/ferromagnet bilayer is heated above the Neel temperature TN of the antiferro-

magnet, disordering the AF spins, as shown in drawing (a)(i). The sample is then

cooled in an external field H sufficient to orient the ferromagnetic spins in a particular

direction. During cooling, the topmost (interfacial) layer of AF spins orients parallel

to the ferromagnetic spins. This ordering is frozen into the AF lattice—an exchange

bias in the direction of the topmost AF spins has been set.

Drawings (ii)–(v) of Fig. 2.2(a) describe the behavior of the exchange-biased sys-

tem as the external field H is swept from positive to negative and back. The (fixed)

AF ordering of the biased system modifies the F behavior. The ferromagnetic layer is

exchange-coupled to the uppermost AF spins, which establishes a preference for the F

spins to point in a particular direction. The resulting torque on the F spins helps the


Field Cool

(i)

(ii)

(iii)

(iv)

(v)

FAF

FAF

FAF

FAF

FAF

(a) (b)

T < T < TN C

T < TN

H

H

M

Hex

Figure 2.2: Spin configurations and associated M-H loop of an exchange-biased sam-ple. Part (a) is a simple picture of spin configurations at various points on thehysteresis loop (b) of an exchange-biased F/AF bilayer. Drawing (i) shows spin con-figurations above the AF ordering temperature TN but below the F ordering temper-ature TC; the AF spins are disordered while the F spins are macroscopically orientedby the external field H. After the field cool to T below TN the topmost layer of AFspins is oriented parallel to the F spins, depicted in drawing (ii). At drawing (iii),in a reversed external field, rotation of F spins away from the preferred direction isopposed by interaction with AF spins, as shown in drawing (iii). A large reversedfield, drawing (iv), rotates F spins away from the preferred direction. In drawing (v),rotation back to preferred direction is assisted by interaction with AF spins. The ex-change anisotropy interaction shifts the hysteresis loop from the origin by an amountknown as the exchange field Hex. Figure courtesy of J. Nogues.


spins rotate into this direction and hinders rotation away from this direction. The

external field required to rotate the F moment from antiparallel to parallel to this

direction is decreased, and the field required to rotate from parallel to antiparallel

to this direction is increased. The center of the resulting M-H loop (Fig. 2.2(b)) is

shifted from the origin by an amount known as the exchange bias or the exchange

field Hex.

It is instructive to note three significant assumptions of this simple model of

exchange anisotropy. First, the antiferromagnet is assumed to be in a single domain.

Second, the antiferromagnetic spin axis is assumed parallel to the ferromagnetic spin

direction. Third, the F/AF interface is assumed abrupt and smooth. All of these

assumptions will be considered briefly below; in Chapter 6 of this work it will be shown

that the interface of a metal/oxide F/AF system cannot be described as abrupt.

This simple model, proposed soon after the discovery of exchange anisotropy in

1956, yields values for the exchange field that are one to two orders of magnitude

larger than those observed[10]. Theoretical work since that time has consisted of

adding various complexities (roughness, domain structure, and so on) to the simple

model in an attempt to better reproduce the magnitude of the various manifestations

of the phenomenon. Current theories of exchange anisotropy are at right angles to

one another in two respects: the geometry of the antiferromagnetic-ferromagnetic cou-

pling, and the orientation of the domain walls in the antiferromagnet. In a model[11]

depicted in Fig. 2.3, the ferromagnetic spin direction is assumed to be perpendicular

to the antiferromagnetic spin axis. In other models, the ferromagnetic spin direction

is assumed parallel to the antiferromagnetic axis. Some models[12] assume that anti-

ferromagnetic domain walls form parallel to the AF-F interface. Other models[13] as-

sume that antiferromagnetic domain walls form perpendicular to the AF-F interface.

These two assumptions are compared in Fig. 2.4. There are in addition increasingly

sophisticated treatments[13, 14] of the effects of interface roughness on the magnetic

couplings of the layers.


Figure 2.3: Model of exchange anisotropyin which the ferromagnetic spin directionis perpendicular to the nominal antifer-romagnetic spin axis. The ferromagneticmoment (red) is coupled to the net mo-ment (pink) of the antiferromagnetic spins(blue), which are canted away from theirnominal (in this case collinear) orientation.The AF spin canting is ’frozen’ into the AFlattice during setting of the exchange bias.This model is from Ref. [11].

FM

AFM

2.5 Investigation Methods

This section will review some methods of investigating exchange anisotropy and com-

ment on their effectiveness. See Ref. [4] for a more complete discussion and extensive

references.

Traditional Methods Traditional methods of magnetics, such as plotting an M–H

loop and measuring torque curves, are ideal for demonstrating the manifestations of

exchange anisotropy. However, they give only macroscopic information and cannot

study the antiferromagnet directly (see Refs. [15, 14] for a notable exception.) Mag-

netoresistance measurements are of course crucial from a device point of view, but

perhaps too indirect for fundamental studies. Several established ferromagnetic do-

main observation techniques have been applied to the study of exchange anisotropy.

These methods yield the spatially-resolved ferromagnetic spin structure. While this

information is important, most competing theories of exchange anisotropy regard the

antiferromagnetic domain structure, inaccessible to these methods, as more impor-

tant.

Perturbative Methods An interesting class of methods move the magnetization

by only a small amount during the measurement, rather than fully switching it. These

perturbative methods include ferromagnetic resonance[16], AC susceptometry[17, 18],

and other methods. Because small (thermodynamically reversible) motions of the


F F

AFAF

(a) (b)

Figure 2.4: Models of exchange anisotropy differing in antiferromagnetic domain wallorientation. In drawing (a) (Ref. [12]), the antiferromagnetic domain wall is parallelto the F/AF interface. The F spins (red) couple to the topmost layer of AF spins(blue). In drawing (b) (Ref. [13]), the AF domain wall is perpendicular to the F/AFinterface. The F spins (red) couple to the small net moment (pink) of each AFdomain; there is an overall preponderance of AF moments in the biasing direction.The change of orientation of the black double arrows emphasizes the AF domain wallorientation. In both drawings, the dashed lines emphasize the relative orientation ofthe AF/F interface and AF domain wall. These models assume the antiferromagneticspin axis parallel to the ferromagnetic spin direction.

magnetization vector are significantly easier to model than the (thermodynamically

irreversible) switching process, they are expected to be more amenable to theoretical

analysis. See Ref. [16] for an introduction to this issue and Ref. [19] for a theoretical

treatment of the differences between reversible and irreversible results.

Ferromagnetic resonance, for example, studies the ferromagnet and changes in

ferromagnetic behavior when it is coupled to an antiferromagnet[16]. Studying the

antiferromagnet via antiferromagnetic resonance techniques requires applied fields

several orders of magnitude higher. Spatial resolution can be obtained by modulating

the resonance with heat from a scanning laser beam, or with a scanning probe[20].

Bulk v. interface information can be inferred from the results of thickness-dependent

measurements by identifying the portion of the result scaling as (1/thickness) as the


interface portion. This is a common method of extracting depth-dependent results

from measurements lacking this intrinsic sensitivity.

Neutron Diffraction Neutron diffraction is distinguished from other methods of

studying magnetic systems by its sensitivity to both ferro- and antiferromagnets. Cur-

rently it can be implemented as polarized neutron reflectivity[21, 22] (PNR) and high-

angle neutron diffraction[23, 24, 25, 26]. Two other implementations, neutron mag-

netic tomography[27, 28] and grazing-angle neutron diffraction are in earlier stages

of development.

PNR studies the vector magnetization as a function of field and temperature. As

an external field is swept, vector rotation and/or in-plane domain formation occur;

PNR can distinguish between these possibilities. The average size of in-plane domains

can be inferred. By monitoring the field dependence of the reflectivity near the critical

angle, the magnetic hysteresis loop can be plotted, determining any bias field and

anisotropy.

High-angle neutron diffraction is a versatile technique that can probe the magnetic

moment magnitude, direction and ordering region size as a function of field and tem-

perature. It can be applied to ferromagnets and antiferromagnets, and can measure

hysteresis loops and other bulk properties. This technique sees only sample-averaged

quantities. Neutron magnetic tomography[27, 28] can spatially resolve large (∼70

µm) antiferromagnetic domains at present and its spatial resolution should improve

with new neutron sources. Finally, grazing-angle neutron diffraction, a combination of

PNR and high-angle neutron diffraction, can in principle probe the antiferromagnetic

domain structure as a function of depth. It is currently in demonstration stages[29].

It is important to note that neutron diffraction experiments can be performed

in an external field. However, neutron diffraction requires moderate to large sample

thicknesses. This can be avoided by studying multilayers[23, 30], but one cannot

be sure whether the multilayer physics is identical to the physics of an exchange-

biased bilayer. In particular, the very different strain state of a multilayer probably

influences the antiferromagnetic ordering.


Mossbauer Spectroscopy Mossbauer studies of exchange-biased systems have the

potential to determine the chemical and magnetic states of the ferromagnetic and an-

tiferromagnetic atoms. It will be seen in this thesis that such information is expected

to be important, and perhaps fundamental, to exchange anisotropy. By concen-

trating the (radioactively) tagged atoms either near or far from the interface, some

depth-dependent information can be determined. In practice, Mossbauer spectra of

exchange-biased systems are complicated[31], though it may be possible to simplify

the situation by a suitable choice of compounds.

2.6 XAS Spectroscopy and Microscopy Techniques

The current understanding of exchange anisotropy can be summarized as follows:

“In common with most other magnetic phenomena in which surface and/or interfa-

cial properties are important, there exists no basic, generally applicable, predictive

theory/model [of exchange anisotropy]. The reason . . . is that the essential behav-

ior depends critically on the atomic-level chemical and spin structure at a buried

interface”[3]. This assessment is reflected in Table 2.1, which summarizes the suit-

ability of various experimental techniques for the investigation of exchange anisotropy.

The table shows that XAS spectromicroscopy is distinguished from the other tech-

niques by its combination of spatial resolution (SR in the table) and sensitivity to

both ferromagnets and antiferromagnets. In addition, as a spectroscopic, rather than

diffraction, technique, it can acquire meaningful data from very thin (Angstrom and

sub-Angstrom) layers. The surface and near-surface (∼20 A) sensitivity of XAS, cou-

pled with its intrinsic elemental specificity, makes possible the study of both sides

of a buried interface. The XAS signal is also sensitive to the chemical state of the

element—in fact, the magnetic ordering of different chemical (and in some cases,

structural[32]) phases of the same element can be distinguished. Given a favorable

sample construction, the various layers can be imaged by simply changing the x-ray

energy, thereby revealing the correlation of chemical regions or magnetic domains

across an interface.

An important weakness of XAS applied to magnetic problems is that its most


Method Ferromagnet AntiferromagnetTraditional MagneticMethods:VSM, SQUID, TorqueMagnetometry, MOKE

AVG (entire sample)M vs. H, Ms, Hex, Hc,Ku, rotational hysteresis

None

Traditional DomainObservation Techniques:Bitter, Kerr, SEMPA,Lorentz

SRSpin direction, domainsize

None

Anti & FerromagneticResonance

B/IHex, Ku, M

B/IHex, Ku

Neutron Diffraction:High Angle

AVGSpin direction, domainsize, Hex

AVGSpin axis, domain size,Hex

Neutron Diffraction:Polarized NeutronReflectometry

AVGSpin direction, domainsize, Hex, Ku

None

Mossbauer Spectroscopy B/Ichemical environment,magnetic environment

B/Ichemical environment,magnetic environment

X-Ray Absorption Spec-troscopy/Microscopy

SRchemical environment,spin direction, domains

SRchemical environment,spin axis, domains

Table 2.1: Comparison of exchange anisotropy investigation methods. The desig-nation AVG represents sample-averaged quantities, B/I represents bulk/interfacesensitivity, SR represents spatial resolution. Ms is the saturation magnetization;other quantities have been defined above.

common implementation, electron-yield detection, is difficult to realize in an applied

magnetic field. This problem is manageable for spectroscopy experiments but serious

for microscopy experiments, because the outgoing electrons must be carefully focused

to give a good image. Therefore one cannot, for example, directly follow changes in

magnetic microstructure in the presence of an external field.


2.7 Conclusion

XAS spectromicroscopy is well-suited to the investigation of exchange anisotropy.

In particular, it can access the microstructural magnetic and chemical information

expected to be crucial to a better understanding of the phenomenon. This thesis em-

ploys some of the unique strengths of x-ray absorption spectroscopy and microscopy

to gain significant new insight into the exchange anisotropy problem.

Chapter 3

Crystallographic, Electronic, and

Magnetic Structure of Nickel Oxide

3.1 Introduction

This chapter reviews the magnetic, electronic, and crystallographic structure of nickel

oxide. Sec. 3.2 describes the structure. In Sec. 3.3 the magnetic interactions and the

accompanying crystallographic distortions are discussed in more detail. In Sec. 3.4

the domain structure of a macroscopic sample of NiO is discussed and some general

comments on the formation of antiferromagnetic domains are presented.

3.2 NiO Structure

3.2.1 Crystallographic Structure and Magnetic Ordering

Above and Below TN

Nickel oxide crystallizes in the rocksalt structure, with nickel and oxygen ions in

interpenetrating fcc lattices. Above its magnetic ordering temperature TN=523 K,

NiO is paramagnetic. Below TN, NiO is antiferromagnetic (J=1), and the nominally-

cubic structure distorts slightly in concert with the magnetic ordering. In the ordered

15

CHAPTER 3. STRUCTURE OF NICKEL OXIDE 16

Figure 3.1: Spin directions of antiferro-magnetically ordered NiO. Spin orderingin the (111) plane (a single T-domain)and along the [112] axis (a single S-domain) is assumed. Shown are adjacent(111) sheets with spin direction of Ni2+

ions (ions not shown) indicated by ar-rows. In the front (red) sheet, spins pointin the [112] direction. In the rear (blue)sheet, spins point in the [112] direction.Three spins in the rear sheet are partiallyobscured by the front sheet. The figureshows the crystallographic unit cell, ap-proximate dimension 4.18 A.

4.18

Åz-axis, [001]

y-axis, [010]

x-axis, [100] direction

state, Ni2+ spins lie in one of the four sets of {111} planes1. Within each such plane,

the (111) plane for example, the spins are parallel to each other and parallel to one

of the three 〈112〉 directions. The spins in one plane are antiparallel to those in the

next. Adjacent (111) sheets of spins are shown in Fig. 3.1. Each sheet contains Ni2+

spins parallel to the [112] axis, with the spin directions reversed on adjacent sheets.

Several distortions associated with the magnetic ordering have been identified.

The largest, the rhombohedral deformation, is a contraction of about 0.15% along

the 〈111〉 axis perpendicular to the ordering planes[33, 34]. There are additional

deformations associated with the selection of one of the three 〈112〉 axes within the

ordering plane[35, 36]. These deformations are conveniently described within the

coordinate system (x′, y′, z′), where x′ is along the ordering axis, y′ is perpendicular to

the ordering axis in the ordering plane, and z′ is perpendicular to the ordering plane.

In the literature, the spin axis is usually assumed along [112] for these discussions,

in which case (x′, y′, z′) = ([112],[110],[111]). Two of the deformations act within the

ordering plane; they are ex′x′ = −2.7 × 10−4 and ey′y′ = +2.7 × 10−4. These strains

1Crystallographic notation: [111], specific direction; 〈111〉, family of equivalent directions; (111),specific plane; {111}, family of equivalent planes.


Figure 3.2: NiO orthorhombic distortionaccompanying magnetic ordering along oneof the three 〈112〉 axes. In this case,the spin axis (black double arrow) isalong [112]. Shown are the undistorted(dashed triangle) and distorted (solid tri-angle) (111) plane. The coordinate axesare (x′, y′, z′)=([112],[110],[111]). The in-dividual distortions (red arrows) are εx′x′ =−2.7 × 10−4, εy′y′ = +2.7 × 10−4.

x’

y’

z’ (out of page)

εy’y’ εy’y’

εx’x’

εx’x’

z’

x’

x’

z’

Figure 3.3: NiO monoclinic distortion ac-companying magnetic ordering along oneof the three 〈112〉 axes. In this case, thespin axis (black double arrow) is along[112]. The original (undistorted) axesx′, z′ (dashed lines) are at right angles andare within and perpendicular to the (111)plane (shaded triangle) respectively. Themonoclinic distortion, εz′x′ = −0.91×10−4,results in the distorted axes x′, z′ (blue ar-rows and text) at an angle of slightly lessthan 90◦.

are often expressed together as the orthorhombic deformation ex′x′ −ey′y′ , depicted in

Fig. 3.2. There is finally a monoclinic deformation ez′x′ = 0.91 × 10−4 [36], depicted

in Fig. 3.3.

The resulting structure is a slightly deformed cube. At room temperature, and

assuming the (111) ordering plane and [112] spin axis throughout the sample, the

lattice basis vectors are of length a = b = 4.177 A, c =4.175 A, and the associated

angles are α = β = 90.055◦, γ = 90.082◦ [36]. This structure is shown in Fig. 3.4.

In general, spins will not order uniformly throughout a macroscopic sample; the

formation of domains will be discussed in Sec. 3.4.


α=90.055°

γ=90.082°

β=90.055°

a=4.177 Å

b=4.177 Å

c=4.

175

Å

Figure 3.4: Distorted cubic structure of antiferromagnetically ordered NiO. Thedouble-headed arrow (red) denotes the [112] spin axis assumed for these distor-tions. The lattice constants at room temperature are a = b = 4.177 A, c =4.175A. The angles are α = β = 90.055◦, γ = 90.082◦. Lattice constants and angles fromRef. [36]. Without magnetic ordering, at room temperature, the values would bea = b = c =4.183 A (estimated), α = β = γ = 90◦.

3.2.2 Electronic Structure

Free Ni2+ Ion

The electronic configuration2 of a free Ni2+ ion is 2p63d8; it is simpler and equivalent

(except where noted) to consider the 3d2 case. Each of the two equivalent d-electrons

has an angular momentum l = 2 and spin s = 1/2. Since the spin-orbit coupling

in the 3d level is relatively weak, LS coupling is appropriate. An overall L =∑

i li,

L = L1 +L2, L1 +L2 − 1, . . . , |L1 −L2| (assuming two electrons) and S =∑

i si, S =

S1 +S2, S1 +S2 −1, . . . , |S1 −S2| are determined, and then coupled to give J = L+S,

|L+S| ≥ J ≥ |L−S|. An LS-coupled state is described by the term symbol 2S+1LJ ,

where capital letters S, P,D, F,G, . . . represent L = 0, 1, 2, 3, 4, . . . respectively. The2Part I of Ref. [37] is a concise review of elementary theory of atomic spectra.


allowed3 states for the 3d2 configuration are 1S0,1D2,

1G4,3P0,1,2,

3F2,3,4 .

Hund’s rules enable one to guess the lowest-energy or ground state configuration.

For equivalent electrons, the lowest-energy configuration with respect to electrostatic

splitting will be the state of the highest S having (for this S) the highest L. The

ground-state value of J may be established as well. For a shell that is more than half

full, such as the 3d8 configuration of Ni2+, the multiplet with the greatest possible

value of J has the lowest energy. Therefore the ground state electronic configuration

for the free Ni2+ ion is 3F4 (S = 1,L = 3,J = 4).

Solid-State Effects

In NiO, the Ni2+ ion is in the (nearly) cubic crystal field of the six surrounding O2−

ions. This crystal field has a significant effect on the electronic configuration. It splits

the state of 3F4 symmetry into the states 3T2g and 3A2g, the latter having the lower

energy for two holes. Within the 3A2g state, the five d-orbitals are grouped into two

representations of different energy. The T2g representation consists of the dxy, dyz, dzx

orbitals which point toward the cube corners and therefore have less repulsive in-

teraction with the ligand (oxygen) electrons. The Eg representation consists of the

dz2 , dx2−y2 orbitals which point toward the cube faces and therefore have more repul-

sive interaction with the ligand electrons. The consequent nickel oxide ground state

electronic configuration is (2p6)3d8(t62ge2g;

3A2g), with a spin S = 1 and a strongly

quenched L = 0.

Final State of the Electric Dipole Transition

X-ray absorption spectroscopy, the principal experimental technique of this thesis,

involves an electric dipole transition. The electronic configuration of the final state of

this transition will be considered here. One of the 2p electrons is promoted to the 3d

level as a result of the photon absorption; the resulting final state is 2p53d9 ∼= 2p13d1.3There are 2(2L1 + 1)2(2L2 + 1)=100 combinations of two d-electrons (L1 = L2 = 2). Since

two 3d electrons are equivalent, the Pauli principle allows only 45 of these combinations. The sum∑(2J + 1) over the J levels of all terms in the NiO ground state configuration above is 45, as

expected.


Then the configurations of the possible final states (setting aside the nature of the

transition) are 1P1,1D2,

1F3,3P0,1,2,

3D1,2,3,3F2,3,4 . The electric dipole transition

selection rules ∆S = 0,∆L = ±1,∆J = 0,±1 plus the ordering of the final state

configurations given by Hund’s rules, predicts that the XAS final state for nickel

oxide is 3D3.

Section 5.2.4 gives a qualitative discussion of the influence of electronic structure

and other factors on the NiO XAS spectrum. A detailed description of the XAS

electronic transition and lineshape is beyond the scope of this thesis. L edge (2p → 3d)

absorption spectra of d transition metals and compounds, such as NiO, are discussed

in Refs. [38] and [39]. A comprehension review of the topic can be found in Ref. [40].

3.3 Magnetic Interactions

In this section the various magnetic interactions in NiO will be discussed in more

detail.

3.3.1 180◦ Superexchange and the Multi-Axis Structure

The starting point is the interaction which couples NiO spins antiferromagnetically.

This is the 180◦ superexchange interaction of 〈001〉 neighbor (next-nearest-neighbor)

nickel ions, via the intervening oxygen ion. The energy associated with this inter-

action is J2=+221 K (+19 meV)[41]. This interaction divides the crystal into four

independent magnetic submotifs[42, 43, 44]. Within each submotif there is antiferro-

magnetic long range order, but the submotifs are not correlated to one another—the

multi-spin-axis situation. The magnetic structure resulting from this interaction is

depicted in Fig. 3.5. The four magnetic submotifs are denoted 1(1’), 2(2’), 3(3’),

4(4’), where the primed spins are antiparallel to the unprimed spins. An ordering

plane (shown in the lower part of the figure) contains spins from all four submotifs.

The 180◦ superexchange interaction does not correlate the submotifs.


z=0

1

1’

1

2

2’

1’

1

1’

2’

2

1

1’

1

3’

z=1/4

4’ 4

3

4’4

3

3’33’

44’

1 1’1’

z=1/2

2’ 2

1’ 11

2’2

1’11’

z=3/4

4’4

3 3’3’

4’ 4

3’

4’4

33

z=0

z=1/4

z=1/2

z=3/4

8.35

Å

1

34

12

1 43

4 13 2

12

1

Figure 3.5: NiO Spin Configuration resulting from 180◦ superexchange interactiononly. Bottom, the (111) plane; top, (001)-type planes at the specific height withinthe unit cell z. There are four simple cubic submotifs. Within each submotif, theprimed spins are antiparallel to the unprimed spins. There is no correlation amongsubmotifs. The figure shows the magnetic unit cell of approximate dimension 8.35 A,twice the crystallographic unit cell parameter. Figure from Ref. [43].


3.3.2 Confinement to a Single Spin Axis

NiO spins are confined to one of the four sets of {111} planes and to a single axis

within this plane by a mechanism described in this section. A nickel ion is coupled to

its twelve near neighbors (along 〈011〉 directions, where at this point a cubic structure

is assumed so [110] and [110], for example, are equivalent) by various interactions, in-

cluding a 90◦ superexchange interaction and direct exchange. The overall interaction

depends on internuclear distance and on the relative spin orientation. This provides a

mechanism for the crystal to lower its energy by adjustment of these two parameters.

It is found[45] that the total energy of the crystal is lowest if

• all spins lie in one of the four sets of {111}-type planes, say the set of (111)

planes, and

• the distance between adjacent (111) planes is slightly decreased (relative to the

cubic case) with spins on adjacent planes antiparallel, and

• the spins within the (111) plane are oriented parallel to a single axis (to be

determined).

Therefore, to reach the lowest energy state, the crystal contracts perpendicular to the

ordering planes, the spins within an ordering plane become parallel to one another,

and successive ordering planes are antiparallel. This contraction is the rhombohe-

dral distortion mentioned above. The twelve nearest neighbors, which in a cubic fcc

structure would be at equal distances, are divided into two sets. The distance to the

six nearest neighbors of opposing spin (in the adjacent (111) planes) is slightly less

than the distance to the six nearest neighbors of the same spin (in the same (111)

plane). The energies associated with these interactions, evaluated at the equilibrium

distances, are J+1 =-15.7 K, J−

1 =-16.1 K, where J+1 denotes the coupling to the six

antiparallel near neighbors, and J−1 denotes the coupling to the six parallel near neigh-

bors. These values for J±1 correspond to about -1.4 meV. The difference between the

two values can be successfully predicted from the rhombohedral distortion and the

dependence of J1 on internuclear distance[41].


3.3.3 Orientation of the Spin Axis Within The Plane

Within the (111) plane, the (parallel) spins are oriented along one of the three 〈112〉axes[35, 46, 47]. This is a consequence of the cubic crystalline anisotropy energy, and

the allowance of a slight departure of the spins from the (111) plane. Assuming spins

are along the [112] axis, the orthorhombic and monoclinic deformations described in

Sec. 3.2 follow from minimization of the elastic and magnetoelastic energies. This

completes the description of the magnetic interactions in NiO and the accompanying

deformations from the (cubic) rocksalt structure.

To summarize: The 180◦ superexchange interaction determines that next-nearest-

neighbors are antiparallel. Confinement of spins in {111} planes, contraction along the

〈111〉 axis perpendicular to the ordering planes, parallel orientation of spins within

ordering plane, and antiparallel orientation of adjacent ordering planes, taken to-

gether, lowers the crystal’s energy. Then, assuming a very small deviation from the

ordering plane, minimization of the cubic magnetic anisotropy energy determines the

single spin axis 〈112〉 within the plane. Smaller deformations result from this in-plane

orientation.

3.3.4 Note on Terminology

In the literature, the terms magnetostriction and exchange striction are used in de-

scribing the interrelationship of magnetic ordering and crystal structure in NiO. It

may be helpful to distinguish these terms. Exchange striction is a deformation result-

ing from ∂J/∂r, the dependence of the value of the exchange integral J on internuclear

distance, and on relative spin orientation. The rhombohedral contraction in NiO is an

exchange striction. It is sometimes described as isotropic, which means that it does

not depend on the orientations of the spins relative to the crystal lattice, but only on

the orientations of the spins relative to each other. There are also magnetostrictive

deformations. These deformations depend on anisotropy energies, which result from

the coupling of the spin orientation to the crystal lattice, and may be described as

anisotropic. The deformations ex′x′ − ey′y′ and ez′x′ are magnetostrictive in origin.


3.4 Antiferromagnetic Domains

3.4.1 NiO Domain Structure

In the above it has been assumed that all spins in the crystal order along a single

axis, with spins within the ordering plane oriented in one direction and spins on

adjacent planes in the opposite direction. This is not the case on a macroscopic

scale; a crystal of NiO, unless carefully prepared, will contain many magnetic or-

dering regions—antiferromagnetic domains—each with a different spin axis. Regions

differing in their spin plane and compression axis are called T-domains, and denoted

by the compression axis. Thus there are four possible T-domains, corresponding to

the four members of the 〈111〉 family of directions. Regions differing in the spin axis

within each T-domain are called S-domains, and denoted by the particular 〈112〉 axis.

There are three possible S-domains, corresponding to the three possible 〈112〉 axes

within each (111) plane. There are in total 12 different S-domains and (since spins

on adjacent (111) planes are antiparallel) 24 possible spin directions.

The domain configuration of a crystal of NiO can be modified. If a bulk crystal is

annealed and slowly cooled to remove imperfections, a single T-domain can be chosen

by applying a modest stress to the appropriate compression axis[34]. The S-domain

configuration of NiO platelets designed to be free of imperfections and strain can be

modified by applied fields of about 2 kOe[48].

3.4.2 Origin of Multidomain Configurations in Antiferromag-

nets

In a ferromagnet, domain formation is driven by magnetostatic energies, i. e., dipo-

lar interactions. These energies do not exist for collinear antiferromagnets (such

as NiO) because there is no net moment. Therefore, one might assume that the

thermodynamically-stable configuration for such an antiferromagnet is a single do-

main. In practice, antiferromagnets usually adopt multidomain configurations for

a variety of reasons. Antiferromagnetic crystals can be prevented from attaining


single-domain configurations by crystalline imperfections and kinetic factors. Crys-

tal imperfections or boundaries resulting from the film crystallographic structure (a

polycrystalline film, or an epitaxial film built from multiple growth regions) interrupt

the long-range magnetic ordering, allowing a change of spin axis, e. g., an antiphase

boundary. Some domain configurations, while not representing global free-energy

minima, may be stable because of kinetic considerations[49]. A four-wall (four T

domains) configuration in NiO[34, 50] is such a configuration[51]; once formed, it is

essentially stable. Finally, in a perfect crystal, the lowering of free energy accom-

panying an increase in entropy can lead to an equilibrium multidomain structure.

For an S-domain wall, the absence of demagnetization energies allows the wall some

flexibility of configuration, with a consequent increase in entropy. This entropy in-

crease can be greater than the energy cost of forming the domain wall, in which case

the multidomain configuration is thermodynamically favored[52]. The temperature

range in which domain formation is favored for NiO has been estimated to be 100

K < T < TN=523 K [53]—in other words, this mechanism will favor domain forma-

tion over a wide temperature range. As was mentioned in the previous section, the

equilibrium domain configuration can be modified by external forces: stresses and/or

applied fields, for example.

Chapter 4

Mean-Field Calculation of

Magnetization Thermal Average

Quantities

4.1 Introduction

A magnetic linear dichroism XAS (XMLD) experiment measures the local 〈M2〉, the

axial projection of the local magnetization vector. Since the temperature dependence

of the XMLD signal is evidence of its magnetic origin[54, 55], an expression for the

temperature dependence of 〈M2〉 is necessary for linear dichroism experiments. Two

such expressions are derived and compared in the present chapter. The connection

to XMLD spectra follows in Chapter 5.

For a collinear antiferromagnet (such as NiO) the sample-averaged moment van-

ishes. However, XAS is a local probe, so the symbol 〈M〉 refers here to the local

magnetic moment. This quantity is nonzero for any magnetic substance. Both an-

tiferromagnets and ferromagnets have nonzero 〈M2〉 locally and within a magnetic

domain.

26

CHAPTER 4. MEAN-FIELD CALCULATIONS 27

4.2 Temperature Dependence of 〈M〉At zero temperature, a magnetic system is in a single ground state, but at finite

temperatures, the system occupies higher-energy states to an extent described by the

partition function Z. The partition function for a quantum spin J in a magnetic field

H is

Z =J∑

MJ=−J

eMJx

where x = gµBH/kT , H is the local field, and MJ is the component of the spin in

the field direction. In this chapter the constants have the following values:

• J = 1, appropriate for the 3d8, 3A2g electronic ground state of NiO

• g = 2, appropriate for a pure spin moment

• µB = 0.927 × 10−20 emu/Oe, the Bohr magneton, a positive quantity

• k = 1.38 × 10−16 erg/K, the Boltzmann constant.

T is the temperature in Kelvins.

Then the average local magnetization in the direction of the field is

〈M〉 = Z−1J∑

MJ=−J

gMJµBeMJx. (4.1)

After some manipulation, the expression

〈M〉 = gµB

{(J +

12

)coth

[(J +

12

)x

]−(

12

)coth

[(12

)x

]}(4.2)

is obtained. Note that variations of density with temperature have been ignored.

[The expression on the right is sometimes written in terms of the Brillouin function

B(J, a′) =2J + 1

2Jcoth

(2J + 1

2Ja′)

− 12J

coth(a′

2J

)


as 〈M〉 = gµBJB(J, a′), where a′ = gJµBH/kT = Jx.] Equation 4.2 must be evalu-

ated by numerical methods because, within mean-field theory, the field H, and there-

fore the quantity x, are functions of M . Such an evaluation yields the temperature

dependencies of H and x in addition to 〈M〉.

4.3 Temperature Dependence of 〈M 2〉Two expressions for the quantity 〈M2〉 will be obtained in this section. In Sec. 4.5

these expressions will be shown to be equivalent if properly interpreted.

Taking the derivative of Eq. 4.1 with respect to x, and multiplying by gµB, the

following expression is obtained:

gµB∂〈M〉∂x

= Z−1J∑

MJ=−J

g2M2Jµ

2BeMJx −

(Z−1

J∑MJ=−J

gMJµBeMJx

)2

.

This may be recognized as

gµB∂〈M〉∂x

= 〈M2〉 − 〈M〉2. (4.3)

Equation 4.3 will be used to derive two expressions for 〈M2〉.First an expression involving a susceptibility χ is derived. In Eq. 4.3, the term

∂〈M〉/∂x can be replaced by (∂〈M〉/∂H)(∂H/∂x). Writing χ for (∂〈M〉/∂H), the

expression

〈M2〉 = 〈M〉2 + kTχ (4.4)

is obtained[56]. Thus 〈M2〉 can be calculated if χ is known.

Another way to use Eq. 4.3 is to substitute for 〈M〉 the specific functional form

given in Eq. 4.2. Performing the indicated mathematical operations, and with the


help of the identity (coth2u− csch2u = 1) the following result

〈M2〉 = g2µ2BJ(J + 1) − gµB〈M〉 coth

[(12

)x

](4.5)

is obtained[57]. This expression involves only quantities that have been calculated

(by numerical methods) above, 〈M〉 and x. The two expressions for 〈M2〉, Eqs. 4.4

and 4.5, will be compared in Sec. 4.5.

4.4 〈M〉 and 〈M 2〉 at T = 0 and T = TN

As T approaches TN, the molecular field H becomes small. Therefore x = gµBH/kT

and the hyperbolic cotangent arguments of Eqs. 4.2 and 4.5 become small as well. As

T approaches zero, x and consequently the hyperbolic cotangent arguments become

large. The resulting values for 〈M〉 and 〈M2〉 are listed in Table 4.1. [Note for the

Temperature u cothu 〈M〉〈M2〉0 K large 1 −J J2

TN small 1/u+ u/3 0 (1/3)J(J + 1)

Table 4.1: Values of 〈M〉 and 〈M2〉 at T = 0 and T = TN. Included for convenienceis the behavior of cothu in the appropriate limit. The variable u represents theargument of the hyperbolic cotangent function in its occurrences in Eq. 4.2 (for 〈M〉)or Eq. 4.5 (for 〈M2〉).

student new to magnetics and/or quantum mechanics: The operator S2 acting on an

eigenstate ψ yields S(S + 1)ψ, where√S(S + 1) is the length of the vector ~S. The

square of the quantum number MJ takes on values M2 = 0, . . . , (J − 1)2, J2.] The

value of 〈M2〉 at T = TN, (1/3)J(J + 1), is the contribution to 〈M2〉 that does not

depend on long range magnetic ordering, the isotropic contribution. In Chapter 5 it

will be shown that the magnetic linear dichroism spectrum is proportional to 〈M2〉less this isotropic contribution (Eq. 5.3).


Figure 4.1: Calculated (J = 1) susceptibilities for ideal uniaxial antiferromagnet inan applied external field from T = 0 to TN. Red, parallel susceptibility χ‖; black,perpendicular susceptibility χ⊥; blue, susceptibility of a powder sample χpowder.

4.5 Equivalence of the Two Expressions for 〈M 2〉In Eq. 4.4 one might be tempted to employ the experimentally-obtained susceptibility

χ for the given substance. This quantity χ = ∂〈M〉/∂Happlied, which measures the

change in the magnetization upon application of an external field, is described briefly

here. Antiferromagnets have two distinct susceptibilities. The parallel susceptibility

χ‖ measures the change in magnetization when a field is applied parallel to the spin

axis. The perpendicular susceptibility χ⊥ measures the change in magnetization

when a field is applied perpendicular to the spin axis. These susceptibilities can be

calculated within mean-field theory; Fig. 4.1 shows χ‖ and χ⊥, plus the spatially-

averaged susceptibility χpowder appropriate for a powder sample. These χ, displayed

here for completeness, are not appropriate for calculation of 〈M2〉.Equation 4.4 is a specific case of the linear response theorem[56], 〈X2〉 − 〈X〉2 =

kT (∂〈X〉/∂Y ), which relates fluctuations in X to the (linear) response of 〈X〉 to the


parameter Y . Applying this theorem to an XMLD experiment, X becomes M , the

local magnetization, and Y becomesH, the molecular field (assuming that no external

field is applied during the experiment). Therefore the susceptibility (∂〈X〉/∂Y ) in

the linear response theorem is appropriately expressed as χfluct = ∂〈M〉/∂H, where

the quantity ∂H denotes fluctuations in the molecular field. The experimentally-

obtained χ‖, χ⊥, and χpowder characterize the response of the system to an external

applied field, rather than to fluctuations in the molecular field, and therefore should

not be used in the calculation of 〈M2〉 via Eq. 4.4.

The temperature dependence of χfluct can be derived within mean-field theory;

the derivation is similar to but simpler than the derivation of χ‖. In the derivation

of χ‖ in [58] set the applied field Ha to zero and replace (−γρ|∆σB|) with ∆Hm,A,

the fluctuation in the molecular field at (the sublattice) A. For σ0,A use the local

saturation magnetization gJµB. Then

χfluct = (∂σA/∂Hm,A) = (g2J2µ2B/kT )(∂B(J, a′)/∂a′).

The slope of the Brillouin function with respect to its argument a′ is a byproduct of

the numerical calculation of 〈M〉. The temperature dependence of χfluct is shown in

Fig. 4.2. Also shown is χ‖ calculated for NiO within mean-field theory.

When 〈M2〉 is calculated via Eq. 4.4 using χfluct, the result is identical to the

calculation of Eq. 4.5, demonstrating the equivalence of the two expressions. Figure

4.3 displays 〈M〉, 〈M〉2, and 〈M2〉. The curves have been divided by gµB or g2µ2B

as appropriate, and 〈M2〉 has been normalized to (1, 0), to facilitate comparison of

the temperature dependencies. It is evident that 〈M2〉 is ‘flatter’ than the other

quantities.


Figure 4.2: Comparison of χfluct (black) and χ‖ (red). χfluct describes the changesin magnetization resulting from fluctuations in the molecular field. χ‖ assumes anexternal field applied along the direction of one of the sublattice magnetizations. Thedifferent shape is evident.


. .

Figure 4.3: Calculated thermal average magnetizations for NiO (J = 1) versus re-duced temperature T/TN. Black, 〈M〉; blue, 〈M2〉; red, 〈M2〉 normalized to (1, 0)at T/TN = (0, 1). Also shown is the quantity 〈M〉2 (black dots) for reference. AtT = TN, 〈M2〉=J(J + 1)/3, the isotropic value.

Chapter 5

XAS, Linear Dichroism, and

SpectroMicroscopy

5.1 Introduction

In this chapter the main experimental technique used in this work, x-ray absorption

spectroscopy (XAS), is discussed. Section 5.2 gives the general background of the

technique. Section 5.3 concentrates on linear dichroism, and Sec. 5.4 discusses the

implementation of XAS as a microscopy technique. Unless otherwise stated, this

chapter (and thesis) refers to the total-electron-yield (TEY) mode of XAS.

5.2 X-Ray Absorption Spectroscopy

This section discusses first the photon-absorption, electron-emission process of electron-

yield XAS. Then a comparison is made to another photon-in, electron-out technique,

x-ray photoelectron spectroscopy or XPS. After a brief exposition of XAS capabili-

ties, the XAS lineshape is considered. Finally the multiplet description of the photon

absorption process is given.

34

CHAPTER 5. XAS, LINEAR DICHROISM, AND SPECTROMICROSCOPY 35

Photoelectrons

Auger electrons

4

EF

Low-energy

secondary electrons

Electron KE

em

itte

de

lec

trons

Add all electrons

3

Auger energyLow energy (<20 eV)

Auger electron either escapes orsets off inelastic cascade

XAS signal is total number of emittedelectrons.

2

EF

Core hole decays via Auger processPhoton absorption creates core hole

Figure 5.1: XAS photon absorption and electron emission process. Panel 1, absorp-tion of photon/creation of core hole; panel 2, decay of core hole; panel 3, escape ofhigh-energy (Auger) electron or low-energy electron cascade; panel 4, energy distri-bution of electrons contributing to total-electron-yield signal.

5.2.1 Photon-In, Electron-Out

Figure 5.1 shows the steps by which the photon absorption process results in the

ejection of secondary electrons from the sample. In Panel 1, the absorption of a photon

promotes an electron to the valence band, thereby creating a core hole. The photon

absorption cross section σ, discussed further in Sec. 5.2.5, measures the probability of

photon absorption. This core hole decays via an Auger process1, depicted in Panel 2.

Panel 3 shows two possible fates of the Auger electron. If it originates from an atom

within ∼5 A of the surface it escapes. Such (high-energy) emitted electrons are called

1At transition metal L edge photon energies, ∼1 keV, the Auger process dominates other decayprocesses like fluorescence decay.


primary electrons. If the Auger electron originates from deeper within the sample it

will set off a series of inelastic collisions. The resulting cascade process increases the

number and decreases the energy of the electrons; the resulting secondary electrons

escaping the sample have energies of only a few electron volts. Panel 4 shows a

schematic energy distribution of the emitted electrons.

The depth-sensitivity of the measurement is determined by the range of elec-

tron energies that the experimenter chooses to count; for example, counting only the

highest-energy photoelectrons gives an extremely surface-sensitive measurement. In

this thesis, the experimentally-convenient total-electron-yield (TEY) implementation

of XAS was used. The TEY signal at a given photon energy is simply the sum of all the

ejected electrons—the total area under the curve in Panel 4. In this implementation

of XAS, the depth-sensitivity is characterized by a material-dependent (1/e) depth of

10–50 A. Atoms as deep as ∼3× the (1/e) depth can be ‘seen’ by total-electron-yield

XAS.

The emitted electron signal is only a proxy for the more fundamental quantity,

the photon absorption cross section. The total-yield signal is often assumed to be

proportional[59] to the absorption cross section. This important assumption is con-

sidered in detail in Ref. [60] and will be revisited in Chapter 6.

5.2.2 Comparison of XAS to XPS

Figure 5.2 compares three spectroscopies. In all three techniques, a photon is ab-

sorbed and an electron is excited. In x-ray photoelectron spectroscopy (XPS), a core

electron is excited to the vacuum, escaping the sample. In ultraviolet photoelec-

tron spectroscopy (UPS), a valence electron is excited to the vacuum. The escaping

electrons are collected, giving information about the core or filled valence level, as

appropriate. In x-ray absorption spectroscopy, a core electron is excited to an unfilled

valence level, as described above. The decay of the core hole thus created eventually

leads to ejection of low-energy secondary electrons.

Although both XPS and (electron-yield) XAS are photon-in, electron-out tech-

niques, the experimental differences can confuse the novice. In XPS, the incoming


}Unfilled

Valence

Band

XPS

UPS

Filled

Core Levels

Atomic Positions

Vacuum

XAS

Figure 5.2: Comparison of initial electron transition of XPS, UPS, and XAS. In XPS,a core electron is ejected from the sample as a photoelectron. In UPS, a valenceelectron is similarly ejected. For XAS, the initial electron transition is from a corelevel to an unfilled valence level.

photon energy is fixed (at 750 eV for this spectrum), the spectrum abscissa repre-

sents a scan over the (kinetic) energy of the emitted electrons, and the ordinate is

the number of electrons having that energy. In XAS, the spectrum abscissa is a

scan over the incident photon energy (from 250 to 750 eV for this spectrum), and

the ordinate is sum of the electrons emitted when the sample is illuminated with a

photon of the given energy. Each point of an XAS spectrum can be thought of as an

energy-integrated XPS spectrum. Figure 5.3 shows that the integrated intensity of

the XPS spectrum (left-hand plot) taken with (fixed) photon energy 750 eV, is the

ordinate of the point with abscissa 750 eV of the XAS spectrum (right-hand plot).

This correspondence holds for all points of the XAS spectrum, not just the highest

energy point highlighted in Fig. 5.3. The XAS intensity at incident photon energy 475

eV, for example, represents an energy-integrated XPS spectrum taken with photon

energy 475 eV.


Emitted Electron Energy Incident Photon Energy

XAS SpectrumXPS Spectrum

Add all emitted electrons... ...to get one point of XAS spectrum

ValenceBand

0 200 400 600 800

C

F

O

NC

OF

Secondary electrons(x 1/100) Photon Energy

750 eV

Auger peaks

250 350 450 550 650 750

NN

O O

O O

nCO

NH

C

F

F

F

C

N

O

F

Figure 5.3: Relationship of XPS and XAS spectra. The XAS intensity at a givenincident photon energy is equivalent to the energy-integrated (up to the given energy)XPS spectrum.

Table 5.1 summarizes the relative merits of XAS and XPS. Because the techniques

probe core-to-valence(XAS)/core-to-vacuum(XPS) transitions, they yield element-

specific information. XPS requires x-rays of only a single energy, whereas XAS uses

a monochromating device to step through a range of x-ray energies, provided by a

synchrotron. The photoelectrons that are the XPS signal must be selected by en-

ergy, thus an energy-analyzer is required. For XAS in total-electron-yield mode, the

measured quantity is actually not the emitted electrons but the replacement current

to the sample. Therefore the total-electron-yield detection device is simply a wire

from ground to the sample, and a picoammeter. XPS is extremely surface-sensitive,

whereas XAS can ‘see’ atoms up to 3× the (1/e) depth of the material below the sur-

face. This gives XAS the important ability to probe both sides of a buried interface.

XAS gathers magnetic information by using the unfilled 3d-orbitals, which are

the orbitals responsible for the magnetization of the transition metals and their com-

pounds, as magnetically-sensitive detectors[61]. A corresponding XPS (actually UPS)

experiment would excite electrons from the (filled) 3d orbitals to the vacuum and then

attempt to detect their spins. The required external apparatus, a Mott detector, is


XPS TEY XASX-ray source Single Energy Range of Energies

Detection Apparatus Energy Analyzer Ground Wire + picoammeterSignal Strength low high

Probes . . . filled core level unfilled valence levelSurface Sensitivity ∼5 A ∼50 A

Magnetic Information difficult yesChemical Information yes (via peak shift) yes (via symmetry)

Best at . . . electronic configuration local symmetry

Table 5.1: Relative Merits of XPS and total-electron-yield (TEY) XAS.

not trivial. The sensitivity of XAS to local bonding symmetry (whether of chemi-

cal, structure, or magnetic origin) comes from the fact that the transition is between

states of definite symmetry, which imposes symmetry-dependent limitations on the

spectrum. The XPS final state couples to initial states of any symmetry, so the XPS

spectrum is, loosely speaking, an average over all symmetry information. This dif-

ference between 2p XAS and XPS can be summarized as follows: “XPS is sensitive

to . . . the electronic configuration of the ground state, while XAS is sensitive to the

symmetry of the ground state with its characteristic multiplet”[40]. Further discus-

sion of the differences between XPS and XAS in the general case can be found in

Ref. [40]; the specific case of NiO is discussed in Ref. [62].

5.2.3 XAS Capabilities

Figure 5.4 shows spectra exemplifying some of the capabilities of XAS applied to

magnetic systems. First, XAS is element-specific, which makes possible the study

of the individual behavior of the separate components of a complex system. If a

sample is constructed appropriately, this element-specificity can be translated into

layer specificity. The near-surface sensitivity of XAS enables the study of the buried

interfaces commonplace in magnetic devices. XAS is sensitive to both ferromagnetic

and antiferromagnetic ordering, to the chemical environment of the atom, and in some

cases to crystallographic structure (not shown in the Figure). As will be discussed

below, the combination of XAS with electron microscopy enables the gathering of all


700 800 900

Photon Energy (eV) Photon Energy (eV)

Co

NiFe

Fe E

Norm

aliz

ed

Ele

ctro

nY

ield

720 722 724

Photon Energy (eV)

4

1

2

3

S

690 700 710 720 730 740

0

4

8

Photon Energy (eV)

L3

L2

No

rma

lize

dE

lect

ron

Yie

ld

LaFeO3

774 776 778 780 782

CoO

Co

1. Elemental Specificity

4. Linear Dichroism (antiferromagnets)3. Circular Dichroism (ferromagnets)

2. Chemical Sensitivity

Norm

.E

lectr

on

Yie

ld

Norm

.E

lectr

on

Yie

ld

Figure 5.4: Spectra exemplifying some of the capabilities of XAS. 1: Elemental speci-ficity, exemplified by a portion of the spectrum of a MgO(001)/NiO (600 A)/CoO(10A)/Fe (15 A)/Ru (15 A) sample. The Fe, Co, and Ni signals are distinct. 2: Chemicalspecificity, showing the Co L3 edge multiplet structure which distinguishes CoO fromcobalt metal. 3: Circular dichroism—a measure of 〈M〉—in Fe; the spectra are takenwith the photon spin axis parallel and antiparallel to the magnetization vector. 4:Linear dichroism—a measure of 〈M2〉—in LaFeO3; the antiferromagnetic spin axis isperpendicular and parallel to the electric field vector of the linearly-polarized x-rays.


of the above information with spatial resolution. This last capability is expected to

be crucial to the study of interfacial phenomena such as exchange anisotropy.

5.2.4 Lineshape of X-Ray Absorption Spectra

The XAS lineshape of transition metals and oxides is dominated by the large (∼10 eV)

2p core-hole spin-orbit coupling, which splits the L (2p to 3d) absorption spectrum

into two portions. The lower-energy L3 region is associated with transitions to a 2P3/2

final state; the higher-energy L2 region is associated with transitions to a 2P1/2 final

state. Unfortunately, this is the only spectral feature that is easy to understand in the

general case. The more detailed spectral features result from a complicated interplay

of interactions of similar strengths. Two of the most important for transition metal

oxides are crystal field and multiplet effects. These effects split the relatively simple

peaks of the metal spectrum into several smaller subpeaks.

XAS is sensitive to chemical bonding as expressed in the symmetry of the crystal

field. Figure 5.5 shows the octahedral arrangement of O2− ions around the central

Ni2+ ion in NiO. The electrostatic effects of these ions constitute a cubic crystal (or

ligand) field at the Ni2+ ion. For rocksalt NiO (and CoO, FeO), d-orbitals pointing

directly toward the ligands (d3z2−r2 , dx2−y2 , of Eg symmetry) interact more strongly

with the ligand field than the orbitals which do not (dxy, dyz, dzx, of T2g symmetry).

Electronic transitions involving these orbitals are at slightly different energies, split-

ting the XAS peaks. Thus the peak splitting is in part a fingerprint of the local

chemical environment of the absorbing atom.

Another source of peak definition is multiplet splitting. A multiplet is a group

of electronic states with coupled spin and angular momenta, e. g., the LS-coupled

state 2S+1LJ forms a multiplet of differing MJ = −J . . . J . Multiplets are important

when the electronic configuration has more than one electron2. The left-hand side of

Fig. 5.6 compares the 3d9 configuration of nickel metal, for which multiplets are not

important, to the 3d8 configuration of nickel oxide, for which multiplets are important.

The two final states for the nickel metal 2p → 3d XAS transition were described2Whether multiplets exist for metals is a matter of debate, but it is safe to say that any multiplet

effects are obscured by band structure effects.


O2-

O2-

O2-O

2-

O2-

O2-

Ni2+

d

d

d xy

yz

xz

d

d3z -r

x -y

2

22

2

Eg T2g

Octahedral (cubic) crystalfield

orbitalsplitting

Figure 5.5: NiO ligand field and consequent d-orbital splitting. The octahedral co-ordination of the Ni2+ ion by oxygen atoms creates a cubic ligand field. The ligandfield splits the five d-orbitals into two groups—those pointing toward and interactingstrongly with the ligands, of Eg symmetry, and those which do not point toward theligands, of T2g symmetry.

above; the spectrum has only two peaks, corresponding to transitions to the 2P3/2

(L3 transition), and 2P1/2 (L2 transition) final states. In the case of NiO, however,

the eight d electrons (or alternatively two d holes) interact, giving rise to a number of

states with energies depending on (J,M) due to exchange and Coulomb interactions.

Therefore the transitions between different multiplets have slightly different energies

and the peaks are split by multiplet effects.

The overall effect of the crystal field, multiplets, and other factors is shown in

Fig. 5.7. The Figure shows XAS spectra for Fe, Co, and Ni metal, and for the

oxides LaFeO3, CoO, and NiO. As mentioned above, the metal spectra have only

two main peaks—the core-hole spin-orbit split L3 (lower energy, higher intensity)

and L2 resonances. For the oxide spectra, the crystal field and multiplet effects split

these resonances into several peaks. The initial separation of the spectrum by the 2p


2D

2P1/2

2P3/2

groundstate

excitedstate

d pd2d p

groundstate

excitedstate

3F1P

1S

1D

1G1D3F

3P

3P1F 3D

∆S = 0∆L = +1-

∆J= 0, +1-

Ni metal: Ni , d1+ 9NiO: Ni , d2+ 8

Figure 5.6: Multiplet effects for oxide XAS transitions. In the left-hand panel, theinitial and final states of the photon absorption for nickel metal, well described by aone-electron model, are shown. There are only two final states (2P1/2 and 2P3/2) sothe metal spectrum has two peaks. The right-hand panel displays the possible levelsof the two-electron (actually two-hole) configuration appropriate for NiO. Electroncorrelations give rise to many possible initial and final states and allowed transitions.The oxide XAS spectrum will be more complex than the metal spectrum.


0

5

10

15

20

700 710 720 730 770 780 790 800 850 860 870 880

LaFeO3 CoO NiO

Fe Co Ni

Photon Energy (eV)

No

rm.

Ele

ctr

on

Yie

ld

Figure 5.7: Transition metal oxide versus transition metal XAS spectra. Shown areXAS spectra for the metals Fe, Co, and Ni, and the oxides LaFeO3, CoO, and NiO.In every case, the spectrum of the oxide, for which electron correlation or multipleteffects are important, has a richer structure than the metal spectrum.


core-hole spin-orbit coupling, a significantly stronger effect than the others, is still

evident. Comparison of the NiO and CoO spectra shows immediately the importance

of multiplet effects because these substances have a similar crystal field but different

electronic configurations (d8 for Ni2+, d7 for Co2+) and therefore very different spectra.

Returning to the discussion of multiplet effects, the sublevels of different M are

nondegenerate in the presence of a magnetic field—either an externally-applied field

or the molecular field governing spontaneous ordering in ferromagnets and antifer-

romagnets. This might be expected to lead to further peak splittings in the XAS

spectrum, but in fact these splittings are small and individual M → M ′ transitions

cannot be observed. However, the thermally-averaged quantity 〈M〉, the local magne-

tization (and the associated quantity 〈M2〉 characterizing an antiferromagnet) does

contribute to the linestrength of a given J → J ′ transition. Thus the XAS peak

heights contain magnetic information and XAS is sensitive to magnetic quantities.

Unfortunately, this significant capability of XAS comes at a price—it complicates the

determination of the ‘true’ chemical signature of a magnetic substance.

5.2.5 Multiplet Description of the Electric Dipole Transition

of a Magnetic System

This section introduces the multiplet description of the XAS photon absorption and

relates the resulting absorption cross section to quantities characterizing the magnetic

ordering of the sample.

In L edge XAS, an electron absorbs a photon and is promoted from the 2p to an

empty 3d level. The photon absorption cross section σ can be written

σ(αJM ;α′J ′M ′) ∝∑

q

| < αJM |C(1)q |α′J ′M ′ > |2

where unprimed quantities denote the initial state and primed quantities denote the

final state. C(1)q is Racah’s electric dipole operator, J is the total angular momentum,

M is the component of J along the quantization axis of the system, and α represents

all other quantum numbers. The photon polarization is denoted by q, where q = 0 for


the electric field vector linearly polarized parallel to an axis of interest, E‖, and q = ±1

for circularly polarized light. Light linearly polarized perpendicular to the axis, E⊥,

is represented by 12((q = +1) + (q = −1)). This expression can be decomposed into

a radial and angular portion via the Wigner-Eckart theorem:

σ(αJM ;α′J ′M ′) ∝ SαJα′J ′∑

q

(J 1 J ′

M q −M ′

)2

. (5.1)

In Eq. 5.1, SαJα′J ′ is the line strength of the transition, containing the radial matrix

element and a factor depending on the specific J → J ′ transition. The matrix in

parenthesis is the 3j symbol, which describes the angular momentum relationship

inherent in the transition. It gives the distribution of the line strength of the J → J ′

transitions over their various M → M ′ components for a given polarization. Selection

rules3 found in evaluation of the 3j symbol are ∆J = 0,±1 (characterizing an electric

dipole transition) and ∆MJ = −q, which reflects the transfer of angular momentum

from the photon to the electron.

Via the 3j symbol in Eq. 5.1, the absorption cross section σ can be expressed in

terms of the quantum number M and its square, M2. However, an expression for the

absorption cross section in terms of the observable quantities 〈M〉, the thermal average

of the local magnetization, and 〈M2〉, the thermal average of the axial projection of

the local magnetization, is desired. Therefore, in lieu of values for the 3j symbols,

values for the thermally-averaged quantities

〈AqJJ ′〉 = Z−1

∑MJ

(J 1 J ′

M q −M ′

)2

e−MJx

are presented in Table 5.2 (Ref. [63]). The 〈AqJJ ′〉 describe each J,M → J ′,M ′

transition in terms of the magnetic expectation values 〈M〉 and/or 〈M2〉. In Sec. 5.3.2

the zero-temperature limit of the linear dichroism spectrum will be discussed. The

resulting zero-temperature 〈AqJJ ′〉 are given in Table 5.3 (Ref. [63]).

3the p → d transition considered in this thesis obeys the additional selection rule ∆l = ±1


q = 0 q = ±1〈Aq

J,J+1〉 (J+1)2−〈M2〉(2J+3)(J+1)(2J+1)

(J+1)(J+2)±(2J+3)〈M〉+〈M2〉2(2J+3)(J+1)(2J+1)

〈AqJ,J〉〈M2〉

J(J+1)(2J+1)J(J+1)∓〈M〉−〈M2〉

2J(J+1)(2J+1)

〈AqJ,J−1〉 J2−〈M2〉

J(2J−1)(2J+1)J(J−1)∓(2J−1)〈M〉+〈M2〉

2J(2J−1)(2J+1)

Table 5.2: Thermal Average Values 〈AqJ,J ′〉 of the 3j symbols expressed in terms of

〈M〉 and 〈M2〉. Table from Ref. [63].

∆M = −q∆J -1 0 +1-1 1 0 00 1

(J+1)J

(J+1) 0+1 1

(2J+3)(J+1)(2J+1)

(2J+3)(J+1)(2J+1)(2J+3)

Table 5.3: Zero-temperature values of (2J + 1)〈AqJ,J ′〉. At T = 0, 〈M〉 = −J and

〈M2〉 = J2. Table from Ref. [63].

Substitution of the 〈AqJJ ′〉 into Eq. 5.1 yields

σ(αJM ;α′J ′M ′) ∝ SαJα′J ′∑

q

〈AqJJ ′〉. (5.2)

Equation 5.2 expresses the photon absorption cross section in terms of the magnetic

expectation values 〈M〉 and 〈M2〉. This is the basis for extracting magnetic infor-

mation from XAS via the techniques of circular dichroism (sensitive to 〈M〉) and

linear dichroism (sensitive to 〈M2〉). In Sec. 5.3, linear dichroism will be consid-

ered. The reader desiring information on circular dichroism in particular, and a more

comprehensive discussion of the photon absorption process in general, is referred to

Ref. [64].

Note on the Calculation of 〈AqJJ ′〉 Derivation of the thermally-averaged values

〈AqJJ ′〉 from the 3j symbols is similar to the derivation of 〈M〉 from M described in

Chapter 4. Here the specific 〈A0J,J〉, corresponding to (∆J, q) = (0, 0), is derived.

The value of the appropriate 3j symbol is required. The general expression for these


values is complicated, but simpler expressions can be found for some special cases[65].

The square of this particular 3j symbol is

(J 1 J

M 0 −M

)2

=M2

(2J + 1)(J + 1)J.

Then the thermal-averaging expression becomes

〈A0J,J〉 = Z−1

∑M

(M2

(2J + 1)(J + 1)J

)e−MJx.

The denominator, which does not depend on M , can be taken out of the summation,

and the terms remaining within the summation are simply the definition of 〈M2〉.Thus M and M2 in the 3j symbol can be replaced by their thermal averages 〈M〉and 〈M2〉 to yield the 〈Aq

J,J〉. This particular result is

〈A0J,J〉 =

〈M2〉(2J + 1)(J + 1)J

as is seen in Table 5.2.

5.3 Linear Dichroism Theory and Experiment

This section defines the linear dichroism spectrum in terms of the quantity 〈M2〉 and

its geometrical relationship to the electric field vector ~E. In addition it is shown

that the linear dichroism spectrum is strong when multiplets can be distinguished.

A representative linear dichroism experiment on nickel oxide is described. Finally,

an appropriate method of comparing the experimentally-obtained measure of linear

dichroism (for NiO the L2 peak ratio) to the calculated 〈M2〉 is described.

5.3.1 Linear Dichroism Theory

A linear dichroism spectrum is the difference between spectra taken with the incident

x-ray electric field vector perpendicular and parallel to a system axis of interest. A


p bonds

s bond 280 290 300 310 320

0

1

2

3

Polyimide XAS Spectra

p s

Photon Energy

Nor

m.E

lect

ron

Yie

ld

Figure 5.8: Use of linear dichroism to detect preferential bond orientations due tononmagnetic effects. The polyimide molecule has inherently highly nonspherical σand π bonds attached to the carbon ring. XAS spectra are taken with the electricfield vector of the linearly-polarized x-rays parallel and (nearly) perpendicular tothe surface plane. Peaks corresponding to an orbital are larger when the electric fieldvector is oriented along the orbital. The spectra show that the σ bond and the carbonring lie in the surface plane, while the π bonds are perpendicular to the surface plane.

non-zero linear dichroism spectrum can result from both magnetic and non-magnetic

effects. In the latter case, linear dichroism can be used to, for example, establish

that a particular orbital is predominantly aligned in the plane of the sample surface.

Figure 5.8 shows the use of linear dichroism to establish the orientation of an aligned

polyimide film[66]. This thesis considers linear dichroism of a magnetic origin, specif-

ically, the distortion of electron orbitals accompanying antiferromagnetic ordering. In

this case, the axis of interest is↔A, the antiferromagnetic spin axis. Linear dichroism

measures the projection M2 of the magnetization vector ~M on↔A.

The absorption intensities for the |αJM〉 → |α′J ′M ′〉 transitions calculated in

Sec. 5.2.5 can be related to the physical quantity of interest in a linear dichroism

experiment, 〈M2〉. Light linearly-polarized parallel to the spin axis, E‖, excites the

transitions described by 〈A0J,J ′〉. Light polarized perpendicular to the spin axis, E⊥,

excites the transitions described by (1/2)(〈A−1J,J ′〉 + 〈A+1

J,J ′〉). The linear dichroism

spectrum is defined as the difference spectrum, (E‖ spectrum-E⊥ spectrum). It can


be shown that for any one of the ∆J channels from Table 5.2,

LD spectrum ≡ (E‖ spectrum − E⊥ spectrum) ∝(

〈M2〉 − 13J(J + 1)

). (5.3)

(Note that throughout this thesis, a small spin-spin contribution[67] to the linear

dichroism signal has been neglected.) Since the quantity (1/3)J(J + 1) was shown in

Chapter 4 to be an isotropic contribution to 〈M2〉, Eq. 5.3 expresses the proportion-

ality of the linear dichroism signal to long range magnetic ordering.

Equation 5.3 defines the maximum possible linear dichroism signal because it

assumes that ~E has been oriented exactly parallel and perpendicular to↔A. In practice,

since the orientation of↔A may not be known, ~E will usually be oriented relative to

a sample axis—parallel or perpendicular to the sample surface, for example. It is

therefore desireable to express the linear dichroism contribution to the spectrum in

terms of the angle θ between ~E and↔A. Defining 〈A‖

J,J ′〉 = 〈A0J,J ′〉 and 〈A⊥

J,J ′〉 =

(1/2)(〈A−1J,J ′〉 + 〈A+1

J,J ′〉), one obtains[63]

〈AθJ,J ′〉 = 〈A‖

J,J ′〉 cos2 θ + 〈A⊥J,J ′〉 sin2 θ

which expresses 〈AqJJ ′〉 in terms of an arbitrary angle θ. This equation can be rewritten

as

〈AθJ,J ′〉 =

13(〈A‖

J,J ′〉 + 2〈A⊥J,J ′〉) − (

13

− cos2 θ)(〈A‖J,J ′〉 − 〈A⊥

J,J ′〉)

or finally as[63]

I(θ, J) = I(0) + (3 cos2 θ − 1)I(2)(J), where (5.4)

I(0) ≡ (1/3)(〈A‖J,J ′〉 + 2〈A⊥

J,J ′〉), and

I(2)(J) ≡ (〈A‖J,J ′〉 − 〈A⊥

J,J ′〉).

Equation 5.5 expresses the absorption coefficient spectrum as the sum of an isotropic

portion I(0) and a portion I(2)(J) sensitive to the angle θ between ~E and the spin

axis↔A. It may be checked that for any J → J ′ transition the isotropic portion I(0)


is independent of magnetic ordering 〈M〉, 〈M2〉, and equals the statistical value4

(1/3)(1/(2J + 1)) as expected. The linear dichroism term I(2)(J) goes to zero at TN,

when 〈M2〉→ (1/3)J(J + 1), or at the magic angle θ = 54.7◦. The maximum linear

dichroism signal will be obtained from the θ = 0 and θ = 90◦ measurements.

5.3.2 Importance of Multiplet Splitting

It is often said that a strong magnetic linear dichroism spectrum can be obtained

when the experimental resolution permits the x-ray absorption to be resolved into

the separate J → J ′ components[57, 63]. Conversely, when multiplet splitting cannot

be distinguished, as in ferromagnetic materials, linear dichroism is small (though

still measurable[68]). These statements will be considered here, using the zero-

temperature limit for simplicity. First the case that the separate J → J ′ components

of the spectrum cannot be distinguished will be treated. The 3j-related contribution

to the spectrum for the case E ‖↔A corresponds to entries in Table 5.3 with q = 0.

Since the separate J → J ′ components cannot be resolved, they must be added to

give a combined signal5:

E‖ spectrum =∑

J ′=J−1,J,J+1

〈A0J,J ′〉 =

2J2 + 5J + 1(2J + 3)(2J + 1)(J + 1)

.

The E⊥ spectrum is written as a combination of the two q = ±1 cases as mentioned

above. First the J → J ′ components are combined for each q:

〈A+1〉 =∑

J ′=J−1,J,J+1

〈A+1J,J ′〉 =

2J2 + 3J + 1(2J + 3)(2J + 1)(J + 1)

〈A−1〉 =∑

J ′=J−1,J,J+1

〈A−1J,J ′〉 =

2J2 + 7J + 7(2J + 3)(2J + 1)(J + 1)

.

4For each J there are (2J +1) different M = −J . . . J . Therefore each transition M has a weightof (1/(2J + 1)) in the isotropic situation.

5In this purely-pedagogical example, the J-dependent prefactor has been ignored.


Then these expressions are added to give the signal

E⊥ spectrum =12(〈A+1〉 + 〈A−1〉) =

2J2 + 5J + 4(2J + 3)(2J + 1)(J + 1)

.

Finally, the magnitude of the T = 0 linear dichroism signal, as a proportion of the

total signal, in the case that the multiplet structure cannot be resolved is

LD(all ∆J) =E‖ − E⊥

E‖ + E⊥ =3

4J2 + 10J + 5.

This result is to be compared to the situation if multiplet splitting can be resolved.

Here a simple inspection of Table 5.3 reveals the advantage of the multiplet-resolved

case. Any of the J → J ′ transitions may be separately observed. The J → (J − 1)

transition is particularly advantageous for this purpose, because the transition does

not exist in the E ‖↔A spectrum. In this case, the linear dichroism is 100% of the

observed signal. It is evident that resolution of the multiplet components greatly

facilitates the observation of the linear dichroism signal. A specific case which parallels

the calculation above is described in Ref. [54].

5.3.3 A Linear Dichroism Experiment on NiO

In Fig. 5.9 the experimental geometry and results of a linear dichroism experiment

on NiO are shown. Two spectra, with ~E in the sample plane (blue) and ~E nearly

perpendicular to the sample plane (red) are shown. The spectra are taken with the

same x-ray incidence angle to eliminate differences caused by saturation effects. The

spectra are clearly different, but in the absence of additional information, conclusions

about the magnetic ordering cannot be drawn. First it is necessary to know that the

cubic crystal field of NiO cannot cause magnetic linear dichroism[69, 70]. Therefore

the observed orientational dependence of the spectrum must be of magnetic origin.

Next it is necessary to know exactly how the geometrical relationship of the electric

field vector ~E and the antiferromagnetic spin axis↔A affects the spectrum. This must

be determined by explicit calculation of the spectrum. For NiO, this calculation has

been performed, and it is known that the higher-energy peak of both the L3 and L2


0

1

2

3

868 870 872 874

0

2

4

6

8

845 850 855 860 865 870 875 880

Ni L2

Ni L3

Ni L2

A B

A

20°

E

90°

E

Photon Energy (eV)

Photon Energy (eV)N

orm

.Ele

ctro

nY

ield

Nor

m.E

lect

ron

Yie

ld20°

20°

Figure 5.9: Linear dichroism experiment on 105 A NiO (001) on MgO. Left-handdrawings show the orientation of the electric field vector of the linearly-polarized x-rays relative to the sample normal. X-ray incidence angle of 20◦ in both (red andblue) cases. Upper drawing, ~E in plane (90◦ from sample normal); middle drawing, ~Enearly perpendicular to plane (20◦ from sample normal). Bottom drawing, orientationof antiferromagnetic spin axis

↔A inferred from spectra, experiment geometry, and

calculations. Right-hand plots: upper, Ni L edge. Blue spectrum taken with ~Ein plane, red with ~E nearly perpendicular to the plane. Lower, Ni L2 resonance,including the dichroism (difference) spectrum (black, ×2). L2 peak energies A=870.3eV, B=871.5 eV.


double-peak structures (peak B of the lower plot of Fig. 5.9) is higher when the electric

field vector is parallel to the antiferromagnetic spin axis[55]. From consideration of

the experimental geometry and the resulting spectra it can be concluded that the

spin axis of this sample is more perpendicular than parallel to the sample surface, as

indicated in the bottom drawing of Fig. 5.9.

Note that magnetic information is expressed in each of the two (~E in plane and~E out of plane) spectra, but to ensure removal of non-magnetic effects, and to enable

the comparison to 〈M2〉 (Eq. 5.3) it is useful to calculate the dichroism (difference)

spectrum, shown in black. Also, since saturation effects (Chapter 6) can be important

for the intense lower-energy peak of the L3 resonance, it is better to study the linear

dichroism of NiO at the L2 resonance.

5.3.4 Comparison of Experimental NiO L2 Peak Ratio and

〈M 2〉The temperature dependence of the NiO L2 peak ratio is known to follow that of the

long range magnetic ordering[67, 55]. Accordingly the right-hand plots of Figs. 7.3

and 7.4, Chapter 7, demonstrate the magnetic origin of the observed linear dichroism

by comparing the temperature dependence of the NiO L2 peak ratio to that of 〈M2〉.The dual y-axes of the plots facilitate the comparison; this treatment of the data is

explained here.

The left-hand y-axis, the L2 peak ratio, is straightforward; the T = 520K value

of 1.055 is the high-temperature limit of the peak ratio, as discussed in the text. In

other words, this is the peak ratio in the absence of magnetic effects. The right-

hand y-axis is the result of two normalization processes. First, 〈M2〉 is divided by

its zero-temperature value g2µ2BJ

2 (= 4µ2B for NiO.) Second, the quantity J(J + 1)/3

is subtracted, removing the isotropic contribution to 〈M2〉. What remains is the

quantity (〈M2〉−J(J +1)/3) to which the linear dichroism signal (the L2 peak ratio)

is proportional, as shown in Eq. 5.3.


MonochromaticX Rays

-10 kV

0 V

0 V

Sample

Objective

Lens

Aperture

Lens

PhosphorScreen

Magnified

Image

Projection

-10 kV

-10 kV

Photoelectrons

Figure 5.10: The PEEM-2 microscope at beam-line 7.3.1.1 at the Advanced Light Source, LBNL,Berkeley, CA. Monochromatic x-rays incident onthe sample at an angle of 30◦ excite electron emis-sion from a spot size of ∼30 µm. Electrons are ac-celerated by a bias voltage of 10–20 kV, then de-celerated as they enter the microscope. An aper-ture behind the focus of the first lens removeselectrons of energies >2 eV, reducing chromaticaberrations. The electrons are projected onto aphosphor screen read by a CCD camera; lateralresolution can be 20 nm.

5.4 XAS SpectroMicroscopy

5.4.1 PhotoEmission Electron Microscopy (PEEM)

In Chapter 2, it was emphasized that exchange anisotropy is thought to depend on

the magnetic microstructure of the ferromagnetic/antiferromagnetic interface. XAS

combined with photoemission electron microscopy (PEEM) is uniquely able to provide

this information. The microscope, shown in Fig. 5.10, spatially resolves and images

the electrons emitted from a sample as a result of an XAS experiment. A high-flux-

density x-ray beam focused to a spot size of ∼30 µm is incident on the sample at an

angle with the surface of 30◦. Low-energy secondary electrons are emitted from the

entire illuminated surface. PEEM’s electrostatic lenses focus these electrons onto a

phosphor screen read by a CCD camera, achieving a lateral resolution of ∼20 nm.

This lateral resolution considerably exceeds that of neutron diffraction topography

(70 µm), x-ray diffraction topography (1-2 µm)[71], and the fundamental resolution

limit (0.2 µm) of optical[72, 48] and nonlinear optical[73] techniques.

The contrast of the image thus obtained is the difference in the number of electrons


(a) ferromagnetic (b) antiferromagnetic

(c) topographic

Figure 5.11: Types of contrast obtainable by x-ray absorption spectromicroscopy.Upper left: ferromagnetic (spin direction) contrast of stripe domains. Upper right:Antiferromagnetic structure of cracked polycrystalline NiO films. Lower: Drawing oftopographical contrast (above, image plan view) and source of the contrast (below,sample cross-section). Variation in electric field intensity near corners lead to vari-ations in electron emission, thus imaging topographical features. Antiferromagneticand topographical contrast are discussed in Chapter 8.

emitted from different areas of the sample surface. This contrast can be of elemental,

chemical, magnetic, or topographical origin. Some of these effects are displayed in

Fig. 5.11. The upper-left image is a typical example of the use of XAS microscopy,

via circular dichroism techniques, to image ferromagnetic domains. The upper-right

image is a linear dichroism experiment on the antiferromagnet NiO. Bright areas

denote a spin axis preferentially oriented in the sample plane; the dark area spin axis

is preferentially oriented perpendicular to the surface plane. Topographical imaging

is based on the effect depicted in the bottom half of the lower drawing. The biasing

electric field is modified at surface topographical features such as corners and edges,


leading to variation in intensity of emitted electrons. The consequent topographical

contrast is sketched in the top half of the lower drawing. Thus electron-emission-based

microscopy images topographical features. Both antiferromagnetic and topographical

images will be discussed in Chapter 8.

An important additional capability of PEEM applied to certain samples is its

ability to reveal local correlations across an interface. If each elemental constituent

of a several-layer sample appears in only one layer, the elemental-specificity of XAS

translates to layer-specificity. Then different layers can be independently imaged by

a simple change of the incident x-ray energy. A recent study[74] of Co deposited on

LaFeO3 is a beautiful example. Figure 5.12 shows the domains of a thin cobalt layer

(right image) deposited atop a thick layer of LaFeO3 (left image). The (ferromagnetic)

Co domain boundaries follow the (antiferromagnetic) LaFeO3 domain boundaries.

The cobalt spin direction is parallel to the in-plane projection of the LaFeO3 spin

axis.

PEEM can be used in spectromicroscopy mode to collect the XAS spectrum of a

particular region of any size (between the resolution limit of ∼20 nm and the x-ray

spot size ∼30 µm). This is done by defining on an initial image the area of interest,

scanning the energy of the incoming x-rays, and collecting all electrons originating

from the defined area at each x-ray energy. In this manner, all of the information

contained in the XAS spectrum, the chemical composition, magnetic ordering, and

so on, can be determined for the area of interest.

5.4.2 Linear Dichroism Imaging via PEEM

The geometrical relationship of the x-ray beam and the sample is significantly con-

strained for a PEEM experiment. The beam is always incident at an angle of 30◦ to

the sample surface, and the electric field vector of linearly-polarized x-rays is always

in the plane of the synchrotron, which is the sample plane. (The sample can be

rotated around its normal, providing sensitivity to azimuthal variations). The angle

θ in Eq. 5.5 is the angle between the electric field polarization ~E and the antiferro-

magnetic spin axis↔A, so the absorption intensity describes the orientation of the spin


ES

LaFeO (AF) domains3 Co (F) domains

Figure 5.12: Images of ferromagnetic (Co) and antiferromagnetic (LaFeO3) domains.Because the separate images were acquired by a change of incident x-ray energy, withno motion of the sample, the images are of the same sample region (dimension ∼10µm) and reveal correlations of the domain structures in the two layers. Left image:Antiferromagnetic domain structure of 40 nm LaFeO3 on SrTiO3(001); the contrastdistinguishes parallel (light) from perpendicular (dark) orientation of the Fe3+ spinaxis relative to the linearly-polarized electric field vector. The spin axis is inclined 45◦

to the sample plane; ~E is in the sample plane so the experiment detects the in-planeprojection of the spin axis. Right image: Ferromagnetic domain structure of a 1.2nm cobalt layer deposited on the LaFeO3 layer. Contrast denotes orientation of spindirection relative to the polarization direction of the (circularly-polarized) incidentx-rays. Light areas, spin direction 0◦ from polarization direction; grey, 90◦; dark,180◦. Consideration of the highlighted correlated areas (and other areas) shows thatthe ferromagnetic spin direction is always parallel to the antiferromagnetic spin axis.Images and drawings from Ref. [74].


axis relative to the sample plane. Specifically, after subtraction of the isotropic por-

tion, the image contrast due to antiferromagnetic ordering is proportional to cos2 θ

× 〈M2〉. The definition of the linear dichroism spectrum as the difference of two

spectra (Sec. 5.3) implies that a reorientation of the electric field vector relative to

the sample magnetization axis is required to gather the second of the two spectra.

This would be difficult, because neither the PEEM nor the synchrotron can be readily

rotated, but fortunately it is not necessary. Inspection of Table 5.2 shows that every

entry—every multiplet peak—contains information about 〈M2〉. If the absorption

spectrum is familiar to the investigator, the 〈M2〉 information can be obtained from

measurement of one peak height. In practice, it is experimentally advantageous to

acquire images at two different x-ray energies, corresponding to spectral peaks with

opposite polarization dependence. The two-image method minimizes non-magnetic

and emphasizes magnetic effects relative to a single image; see Chapter 7 for more

details. In summary, from two images taken at differing x-ray energies in the same

experimental geometry, a dichroism image describing the orientation of the spin axis

with respect to the sample surface is obtained.

Chapter 6

Chemical Effects at Metal/Oxide

Interfaces Studied by X-Ray

Absorption Spectroscopy

6.1 Introduction

Exchange anisotropy—the unidirectional coupling of a ferromagnet to an adjacent

antiferromagnet—is of interest both technologically and academically. Technologi-

cally, magnetic disk drive read heads incorporating exchange anisotropy are essential

to the attainment of data densities beyond ∼1 Gb/in2 (the 1997 industry standard).

Academically, 45 years after its discovery[5] and 22 years after it was proposed for

use in magnetic sensors,[75] a fundamental description of exchange anisotropy re-

mains elusive. Recent reviews [4, 3] describe the current state of understanding of

exchange anisotropy and explain why its investigation is difficult:“[I]n common with

most other magnetic phenomena in which surface and/or interfacial properties are

important, there exists no basic, generally applicable, predictive theory/model [of

exchange anisotropy]. The reason . . . is that the essential behavior depends critically

on the atomic-level chemical and spin structure at a buried interface.”[3] The impor-

tance of the ferromagnetic/antiferromagnetic interface to exchange anisotropy is a

specific example of the importance of interfaces to a variety of magnetic phenomena.

60

CHAPTER 6. INTERFACIAL CHEMICAL EFFECTS 61

For example, the giant magnetoresistance effect, spin tunneling, and spin injection

are phenomena to which the exact nature of the associated interface is crucial. Tech-

niques that can distinguish interface from bulk properties, and furthermore study

the interface with spatial resolution, are therefore expected to become increasingly

important.[8]

Synchrotron-based x-ray absorption spectroscopy (XAS) is well-suited to the in-

vestigation of exchange anisotropy and other interfacial magnetic phenomena. The

surface and near-surface (∼20 A) sensitivity of XAS, coupled with its intrinsic ele-

mental specificity, makes possible the study of both sides of a buried interface. As will

become apparent below, the XAS signal is sensitive to the chemical state of the ele-

ment, and therefore to any departures from a nominal configuration. Judicious sample

construction can help avoid the problem of an interfering bulk signal. The linear and

circular polarization of synchrotron light enables one to study the spin configuration of

both antiferromagnets and ferromagnets. The inherently local nature of spectroscopy

enables XAS-based microscopy techniques to study interfaces with spatial resolution,

thereby imaging AF and F domains and deducing their couplings.[76, 74]

In this work, the interface sensitivity of x-ray absorption spectroscopy was used

to obtain clear, quantitative evidence of oxidation/reduction reactions at as-grown

metal/oxide interfaces. These results were obtained from a variety of samples, differ-

ent in preparation method and in elemental constituents, and therefore are expected

to be generally valid. Different elements are shown to have different degrees of re-

activity, an anneal is shown to increase the amount of reaction, and evidence for a

time dependence of the reaction is described. The implications of our results for the

understanding of the exchange anisotropy phenomenon are considered.

6.2 Experiment

6.2.1 Sample Design

The sample design, and the particular mode of XAS used in this work, were dic-

tated by the need to study a buried interface. The total-electron-yield mode of XAS


spectroscopy was chosen for its surface to near-surface sensitivity and experimental

convenience. Sample layers were thin, 10–20 A, to obtain adequate weighting of the

interfacial region in the total signal, and adequate overall signal intensity. Through-

out this report, samples containing an interface between metal and oxide layers will

be called ‘sandwiches’. Samples grown for comparison purposes, consisting of thicker

films of pure metal or oxide, will be called ‘standards.’ Three different methods of

sample preparation are described below.

6.2.2 Samples Prepared Ex Situ

A set of sandwich samples (‘ex-situ-grown’ sandwiches) was prepared in a molecular

beam epitaxy synthesis chamber at Stanford University. The sandwiches were of

the form MgO(001)/oxide(10 A)/metal(10 A)/Ru(20 A), where oxide=NiO or CoO

and metal=Fe, Co, or Ni. A given element occurred in only one layer of any given

sandwich, ensuring that the element-specificity of XAS could be translated to layer-

specificity. The sandwiches were fabricated by electron-beam evaporation from pure

metal sources at a base pressure of 4 × 10−8 torr. The oxide and metal thickness was

monitored during deposition by a quartz crystal monitor, which had been calibrated

by x-ray reflectivity analysis of previous samples. MgO substrates were degreased by

an ultrasound soak in 111-trichloroethane, acetone, and methanol (twenty minutes,

twice per solvent), rinsed with isopropanol, and loaded into the chamber.[77] They

were then heated to 600◦C in an atmosphere of 1×10−5 torr molecular oxygen for ∼12

hours to remove carbon deposits.[78] Oxide growth took place in a molecular (CoO)

or ECR-microwave-activated[77] (NiO) oxygen atmosphere of approximately 1×10−5

torr. Oxides were grown at 300◦C at a typical rate of 0.3–0.5 A/sec; the samples were

then cooled to room temperature, and the metals were deposited at similar rates. Note

that the metal/oxide interface was created at room temperature and never annealed,

unless otherwise specified. Samples were capped with ruthenium to protect the metal

from oxidation during transport to the synchrotron radiation facility. RHEED images

of the MgO substrate prior to deposition, and of the (001) NiO and CoO oxides,

confirmed clean, flat, well-ordered surfaces. High-angle symmetric and asymmetric


x-ray diffraction scans on thick samples confirmed the growth of single-phase epitaxial

NiO and CoO(100).

The ex-situ-grown sandwiches present two complications: limited base pressure

during metal deposition and the presence of a capping layer. The growth chamber,

optimized for growing complex oxides, did not attain a base pressure typically required

for growing clean metal layers. Spectra of thick metal layers, grown at a fast rate

(3–5 A/sec, or several hundred times a typical surface science growth rate), were very

similar to the spectra of in-situ-grown metal samples (see below) and did not exhibit

signs of oxidation. However, the 10 A metal layers of the sandwiches were grown

more slowly (0.3–0.5 A/sec) to enable thickness monitoring. Test samples of the form

MgO/Ru(50 A)/Fe or Co(10 A)/Ru(20 A) were analyzed to determine the extent of

metal oxidation during growth. It was determined that for iron, ∼0.5 A of metal was

oxidized during growth; cobalt oxidation was less than 0.5 A. The ruthenium capping

layer was found to effectively prevent oxidation of the underlying metals, as indicated

by repeated scans of pure metal samples kept in air for a period of months. However,

ruthenium has absorption structure underlying the L-edge region of the transition

metals. This background structure complicates data analysis, as will be discussed in

Sec. 6.4.6. A disadvantage of any capping layer is the reduced intensity of electron

yield signals from the layers below.

6.2.3 Samples Prepared In Situ and on NiO Single Crystal

A second set of sandwiches (‘in-situ-grown’ sandwiches) was prepared to confirm

that any metal oxidation seen for the ‘ex-situ-grown’ sandwiches was the effect of

proximity to an oxide, and to check for a time dependence of the reaction. These

samples were grown on silicon substrates dipped in HF to remove any oxides before

insertion into a preparation chamber. The samples were of the form Si/NiO(5–30

A/Fe(1–10 A). The NiO was deposited in a molecular oxygen atmosphere of 1× 10−6

torr in a preparation chamber. The samples were then transferred through a small

aperture to the main chamber with a base pressure of about 1 × 10−10 torr for metal

deposition and XAS analysis. Both nickel and iron were evaporated by electron beam


bombardment of pure metal sources at typical rates of 1 A/minute. After deposition

of each layer, scans of the nickel and iron absorption edges were performed, and

then repeated to check for a time dependence of the oxidation/reduction reaction.

The x-ray absorption as well as Auger measurements were used to estimate the layer

thicknesses during growth. The Auger signal was independently calibrated against ex

situ x-ray reflectivity measurements on test samples. We estimate error bars of about

20% for our quoted thicknesses. For these sandwiches the absence of a capping layer

avoided the problems of an interfering absorption structure and signal reduction.

A third set of sandwiches (‘single crystal’ sandwiches) of the form NiO bulk sin-

gle crystal/metal(2–10 A), where metal=Fe or Co, was studied in conjunction with

XAS microscopy experiments.[79] Nickel oxide single crystals (Mateck GmbH) were

cleaved to expose the (001) surface and immediately introduced into the XAS analysis

chamber. Thin layers of iron or cobalt were then deposited under ultra-high vacuum

conditions as described above.

6.2.4 Standard Samples

Pure metal and oxide standard samples were prepared for each element. These stan-

dards consisted of a thicker (200–600 A) film to enable x-ray diffraction analysis and

to obtain bulk-like XAS spectra. Standards grown ex situ were capped by 20 A of

ruthenium (Ni metal, NiO, CoO), 20 A platinum (Fe3O4), or 30 A CNx (α-Fe2O3).

Other standards (Fe metal, Co metal) were grown and analyzed in situ. An FeO

standard spectrum was prepared in situ according to a recipe in the literature.[80]

It is known that a thin NiO layer has a lower antiferromagnetic ordering tem-

perature than a bulk layer.[55] The XAS spectrum contains information about the

magnetic ordering, therefore the spectrum of a thin layer is different from the bulk

spectrum. In addition, the thin layer antiferrmagnetic spin axis orientation may differ

from that of the bulk. Also, for thinner samples a possible reduction of the surface in

vacuum will have a larger effect on the XAS spectrum which samples only the near

surface region. For these reasons, it is desirable to use a NiO standard of the same

thickness as the NiO layer of the experimental sandwiches. Two thin NiO standards


Ni L2

NiO bulkNiO 30 ÅNiO 5 Å

Figure 6.1: Ni L2 resonance XAS spectraof bulk (black), 30 A(dark gray), and 5 A(light gray) nickel oxide standards. Themultiplet structure is less defined for thethinner films. The spectra are normalizedto zero before the L3 peak and to an L-edgeintegrated intensity of 100 units.

(5 A and 30 A, in-situ-grown) were available and were employed in the analysis where

noted. The Ni L2 edge spectra of these thin standards, and the bulk NiO standard,

are shown in Fig. 6.1; the L2 peaks of the thinner layers are less defined.

6.2.5 XAS Experiments

X-ray absorption spectroscopy experiments were performed on beamline 10-1 at the

Stanford Synchrotron Radiation Laboratory. This wiggler/spherical grating monochro-

mator beamline produces soft x-rays in the range 200–1200 eV with an intrinsic reso-

lution of about 100 meV at 800 eV. A typical set of measurements included extended

energy scans for identification of the major absorption edges and high resolution

scans over the L-absorption edges of the oxide and metal layers. In order to accu-

rately determine the relative energy positions of the L3 and L2 fine structure for the

sandwiches and the corresponding standards we recorded sequential calibration spec-

tra. We estimate the relative energy accuracy of our sandwich and metal spectra to

be about 50 meV. The absolute energy was calibrated by referencing our pure metal

spectra to those of Chen et al.[81] All scans were performed at normal incidence us-

ing linearly polarized light and in total-electron-yield mode. We simply measured the

photocurrent of the samples with a picoammeter (typical signal 10−10A), which was


flux-normalized by the photocurrent of a gold grid reference monitor.[59]

6.3 XAS Analysis

6.3.1 Sample Structure Assumed for Analysis

The goal of this work is to determine the chemical structure of metal/oxide sand-

wiches near the interface by use of high resolution x-ray absorption spectroscopy.

The nominal sandwich structure is illustrated in Fig. 6.2(a), where each layer is typi-

cally 10 A thick and the capping layer and the substrate are omitted. Drawing (b) is

discussed in Sec. 6.3.3. Fig. 6.2(c) illustrates a structure that would be the result of

oxygen diffusion, driven by thermodynamic considerations, from a portion of the NiO

to a portion of the Co. The darkness of the shading represents the concentration of

nickel atoms. The depicted formation of a thin ferromagnetic Ni metal layer atop NiO

would have significant implications for the study of exchange anisotropy. Drawing (d)

represents another possibility, the formation of a mixed Co-Ni-O compound at the

interface region, and shows, via shading, a transition from nickel-rich to cobalt-rich.

Such a structure would result from metal ion and oxygen diffusion. In the following

we will derive expressions for the x-ray absorption spectra of the Fig. 6.2(c) struc-

ture, utilizing both the element specificity and the chemical sensitivity of the x-ray

absorption technique. The former enables XAS to separately probe the Co and Ni

containing layers in Fig. 6.2, the latter allows it to distinguish between metal and

oxide components of the same element.

6.3.2 XAS Formalism

Single-Film XAS Formalism

Our x-ray absorption studies were performed in total-electron-yield (TEY) mode by

collecting the electrons created by photon absorption events in a sample. Here we

give the relevant expressions for the TEY signal from a single film or a sandwich that

consists of films composed of different elements as shown in Fig. 6.2(a). Since x-ray


(a) (b)

NiO

Co

NiO

NiO (i)

Co

*Co (i)

(c)

NiO

*Ni

CoO

Co

(d)

NiO

Co Ni Ox y

Co

Figure 6.2: Nominal experimental sample structure and possible actual structures.Shading represents the concentration of nickel atoms. Drawing (a), the nominal struc-ture, assumes an abrupt interface and no interface reactions. Drawing (c), the modelconfiguration for generation of test spectra, is the result of an interfacial reaction inwhich oxygen diffuses across the metal/oxide interface. It retains abrupt interfaces.The Ni-rich layer at the interface is a possible source for the interfacial uncompen-sated spin moments responsible for exchange anisotropy. Drawing (d), resulting fromboth oxygen and metal ion diffusion, and assumes graduated interfaces. Drawing(b) describes the structure before the interfacial reaction; ‘(i)’ denotes the regions oneither side of the initial interface which will take part in the reaction. The thicknessesof the starred metal regions are reported in the data tables. The change of interfaceregion thickness resulting from oxygen transfer is qualitatively represented in drawing(c).

absorption is element specific we obtain separate spectra from the Co and NiO films

in Fig. 6.2(a). The Co spectrum will contain some small background from the NiO

and the NiO TEY signal will be attenuated by traversing the Co film, but otherwise

the respective spectra can be treated as if originating from a single film. At normal

x-ray incidence, the total-electron-yield dNe from a layer of thickness dz at a depth

of z is given by [64]

dNe = I0µ(E)G(E)e−zµ(E)e−z/λdz . (6.1)


Here I0 is the number of photons striking the sample surface, µ(E) is the absorption

coefficient representing the probability of photon absorption [the x-ray absorption

length is 1/µ(E)], and G(E) is the number of electrons produced per absorbed photon

(see Sec. 6.3.3 below). The first exponential denotes the probability of a photon

penetrating to depth z, and the second exponential denotes the probability of an

electron created at depth z escaping from the sample. The quantity λ is the material-

dependent electron escape depth.

Integrating this expression over the thickness of a slab composed of many differ-

ential layers dz gives the TEY XAS signal from a single film of thickness t:

Ne(E) = I0G(E)

1 + 1µ(E) λ

(1 − e−t[µ(E)+1/λ]) , (6.2a)

or from a semi-infinitely thick sample:

Ne(E) = I0G(E)

1 + 1µ(E) λ

. (6.2b)

It is useful to consider the general Eqs. 6.2 in certain limits with respect to the

relative magnitudes of the lengths t, λ, and 1/µ(E). The x-ray absorption length

1/µ(E) is a strong function of photon energy E. It is longest below the absorption

edge and is long compared to the electron sampling depth λ ∼ 2.5 nm at energies both

below and well above the edge. However, at resonance energies at the L3 edge, 1/µ(E)

may become as short as 15 nm.[82] At the resonance peak energies, the photon flux

that reaches deeper layers in the sample is then significantly reduced by absorption

in the upper layers. This gives rise to a reduced electron-yield contribution from the

lower layers to the peak intensity in the measured electron yield spectrum which is

said to be “saturated.”[82] Saturation is avoided when λ � 1/µ(E). In this limit,

Eqs. 6.2 become

Ne(E) = I0G(E)λµ(E)(1 − e−t/λ

), (6.3a)


Ne(E) = I0G(E)λµ(E). (6.3b)

These equations represent the unsaturated TEY XAS signal for finite and semi-infinite

sample thicknesses, respectively. The unsaturated electron-yield signal is proportional

to the absorption coefficient spectrum µ(E).

If the signal is unsaturated (µλ � 1) and in addition t � λ, Eq. 6.3a becomes

Ne = I0Gµt

(1 − t

2λ

)

and the signal is proportional to the layer thickness, to first order. In this limit the

XAS signal can be used for relative thickness determinations of ultra thin films. For a

typical value of λ ∼2.5 nm the above equation applies only to layers with thicknesses

up to a few monolayers.

Bilayer XAS Formalism

In the following we shall develop a formalism to calculate x-ray absorption spectra of

the model structure shown in Fig. 6.2 (c). Since x-ray absorption is element specific,

a given XAS spectrum will represent either the Co or Ni portions of the sandwich.

The Co spectrum will contain Co and Co-oxide components and the Ni spectrum Ni

and Ni oxide components. In the following we shall derive an expression for the total-

electron-yield signal from such effective bilayer samples, extending the treatment by

O’Brien and Tonner.[83] For simplicity we shall treat the case of a partially-reduced

nickel oxide layer, modeled as a thin layer of nickel metal (reduced oxide) atop the

remaining nickel oxide. The upper layer (Ni), thickness tNi = z1, extends from the

surface (z = 0) to depth z1; the lower layer (NiO), thickness tNiO = z2 − z1, extends

from depth z1 to z2. Eq. 6.2a describes the signal from the upper layer:

Ne,Ni = I0GNi(E)

1 + 1µNi(E) λNi

(1 − e−tNi[µNi(E)+1/λNi]

).


To obtain an expression for the signal from the underlying NiO, Eq. 6.1 must be

modified to account for the effect of the Ni overlayer. The resulting expression is

dNe,Ni = I0e−z1µNie−(z−z1)µNiOµNiOGNiOe−(z−z1)µNiOe−z1µNidz

Terms have been added to account for the signal attenuation by the Ni layer, i. e.,

the reduction of the number of photons into and the number of electrons out of the

sample. The argument of the NiO exponentials has been changed from z to (z − z1)

to correctly reflect the distance traveled in the NiO. When the above equation is

integrated over the NiO layer the result is

Ne,NiO = I0e−tNi[µNi(E)+1/λNi] GNiO(E)1 + 1

µNiO(E) λNiO

(1 − e−tNiO[µNiO(E)+1/λNiO]) .

Now the total signal can be formed:

Ne,Ni +Ne,NiO = I0

(GNi(E)

1 + 1µNi(E) λNi

(1 − e−tNi[µNi(E)+1/λNi]

)

+ e−tNi[µNi(E)+1/λNi] GNiO(E)1 + 1

µNiO(E) λNiO

(1 − e−tNiO[µNiO(E)+1/λNiO])) .

(6.4)

The first term of Eq. 6.4 is the Ni metal overlayer signal; the second term is the NiO

layer signal, attenuated by the factor e−tNi[µNi(E)+1/λNi] representing the effect of the

Ni metal overlayer.

6.3.3 Quantitative Analysis of Electron-Yield Spectra

The Need for Standard Absorption Spectra

Electron-yield detection is the preferred mode for recording soft x-ray absorption spec-

tra because it offers near-surface sensitivity, few restrictions on sample or substrate

preparation and ease of signal detection by means of a picoammeter. The electron


yield spectrum Ne(E) is a byproduct of the more fundamental x-ray absorption pro-

cess, quantitatively characterized by the x-ray absorption coefficient µ(E)). Values

for µ(E) can be found in the literature[84] and on the Internet1 for all common mate-

rials. However, these tabulations are based on additive atomic x-ray absorption cross

sections; they do not describe the important spectral regions near absorption edges,

since these regions are dominated by chemical bonding effects. On the other hand, the

measured electron-yield spectra are typically concerned with the rich fine structure

near the absorption edges that provides chemical sensitivity, but is only a relative, not

absolute, measure of the x-ray absorption coefficient. In this paper we are concerned

with the determination of chemical processes at metal/oxide interfaces. In order to

obtain quantitative thickness information from x-ray absorption for the thickness of

a metal relative to its oxide in a sandwich, one must first obtain the absolute x-ray

absorption coefficients of standards for the metal and oxide components. By use of

linear combination of the absorption standards one can then model the measured

spectrum of the sandwich and obtain the relative contribution, i. e. thickness, of the

metal and oxide components. This procedure therefore requires that the measured

electron yield spectra be converted into absolute x-ray absorption coefficients µ(E)

according to Eqs. 6.2. The methods of this conversion are not well established and

in the following Section we shall outline a suitable procedure.

Derivation of Standard Absorption Spectra from Electron-Yield Spectra

In this section the equations of Sec. 6.3.2 will be used to derive the absorption spectra

from the total-electron-yield spectra. We start by ignoring saturation effects. The

relevant Equations 6.2b and 6.3b for a semi-infinitely thick sample can be rewritten

as

Ne(E) = T −1[

µ(E)1 + λµ(E)

], (6.5a)

1http://www-cxro.lbl.gov


Ne(E) = T −1[µ(E)], (6.5b)

where T −1 ≡ I0G(E)λ has been introduced as an inverse transformation for later

convenience. The important portion of the transformation is the term G(E) which

describes the conversion of absorbed photons into electrons.[59, 60] We will assume

that over a single absorption edge, i. e. a spectral range of about 150 eV, G(E) can be

represented adequately as a linear function of E, and we will not distinguish between

G(E) of the metal and oxide(s).

To derive µ(E) from Ne(E), Eq. 6.5b is inverted to yield µ(E) = T [Ne(E)],

which is valid in the pre- and post-edge regions where electron yield saturation ef-

fects are unimportant since λ << 1/µ(E). The (linear) tranformation T corre-

sponds to commonly-performed spectrum manipulations—subtraction of a pre-edge

background and scaling by a constant or energy dependent factor. Experimentally

obtained total-yield spectra are manipulated such that they overlay the tabulated

off-resonance absorption coefficients, thereby determining T . The left-hand plot of

Fig. 6.3 gives an example of the overlay of the renormalized electron yield spectrum

of Ni metal, referred to as the “overlay spectrum”, with the tabulated absorption

coefficient. Identification of the best overlay on the (smooth) tabulated absorption

coefficient is complicated by the significant post-edge extended x-ray absorption fine

structure (EXAFS) in the measured spectra.

The electron yield overlay spectrum is an intermediary in the analysis since it

still needs to be corrected for saturation effects. Equation 6.5a, valid in all regions,

is inverted to yield µ(E) =(

1T [Ne(E)] − λ

)−1. Since the linear transformation T is

known, it is only necessary to know the value for the electron escape depth λ, which

will be discussed below. The result, the saturation corrected overlay spectrum which

corresponds to the absorption coefficient spectrum µ(E), is shown in the right-hand

plot of Fig. 6.3 along with the overlay spectrum to clarify the effects of saturation.

Similar analyses were performed on all electron yield spectra of the standard samples

to yield the metal and oxide standard absorption spectra used for analysis of the

sandwich spectra.

In summary, deriving the absorption coefficient spectrum from the electron-yield


unsaturatedoff-resonancescaled TEY

Ni L3

Ni L2Ni L3

Figure 6.3: Derivation of absorption coefficient spectrum from electron-yield spec-trum. Tabulated absorption coefficient spectrum, dark gray; Scaled (saturated)electron-yield spectrum, light gray; saturation-corrected (absorption coefficient) spec-trum, black. Left plot: pre- and postedge region of the nickel L-edge, emphasizingthe overlay of the electron-yield spectrum on the calculated off-resonance spectrum.Right plot: Ni L3 region, emphasizing the correction for saturation. The higher ofthe two spectra is the (derived) standard nickel metal absorption coefficient spectrum.The lower of the two spectra is the overlaid electron-yield spectrum.

spectrum requires two steps. First, the electron-yield spectrum is overlaid on tabu-

lated off-resonance absorption spectra, and second, the overlay spectrum is corrected

for saturation effects. Similar procedures have previously been described by Hunter

Dunn et al.[85]and Gota et al.[86]

The Standard Metal and Oxide Absorption Spectra

In the derivation of the absorption spectra from the measured electron yield spectra

we proceeded as follows. First, a background was subtracted from the measured TEY

spectra. We either subtracted a linear background or a background that included the

EXAFS structure from lower energy edges, measured on suitably prepared samples.

This important issue will be revisited in Sec. 6.4.6.

The background subtracted electron yield spectrum has zero intensity below the

absorption edge and can be conveniently rescaled. A common practice has been to


scale spectra to a fixed edge jump.[59, 85] This procedure normalizes spectra to the

same relative number of absorbing atoms. It requires spectra that extend to energies

well above the edge where the spectra become smooth and a linear step function can

be fitted. We have used here a different procedure justified by an empirical sum rule

that states that for a given element the x-ray absorption intensity, integrated from

below the edge to an energy of about 100 eV above the edge is remarkably constant,

independent of sample orientation and chemical structure.[87] Such a normalization

to constant intensity is less sensitive to differences in spectral shape than the nor-

malization to a constant edge jump. For the electron yield spectra in this paper we

have chosen an integration interval 100 eV above the edge and have set the integrated

intensity arbitrarily to a value of 100.

For the conversion of the electron yield overlay spectra to absorption coefficients,

and in use of Eq. 6.4, we have used electron escape depths from the literature: Fe 15

A[88, 64], FeO 30 A, Fe3O4 50 A[86], α-Fe2O3 35 A[86], Co 22 A[88, 82], CoO 30 A,

Ni 22 A[88, 82], NiO 30 A. To our knowledge, the monoxide electron escape depths

have not been determined and we shall use a value of 30 A. The effect of uncertainty

in this value will be discussed in Sec. 6.4.6.

The absorption coefficient spectra for the standards are shown in Fig. 6.4 and the

normalized TEY spectra from which they were derived are shown in Fig. 6.5.

The absorption coefficient spectra of the standards will be used to calculate model

spectra of the sandwiches which can then be compared to the measured spectra. The

TEY spectra of the standards are not used for quantitative analysis, but appear in

several figures to aid in the interpretation of the TEY spectra for the sandwiches.

Fig. 6.4 illustrates the inherent element-specificity of XAS. The spectra for each

element cover different energy ranges. The additional sensitivity to the chemical state

of the metal atom (for example, an oxide environment) is manifested in the richer

fine structure in the oxide spectra. The L3 region of each compound is shown in the

right-hand plots on an expanded scale.

The TEY oxide spectra in Fig. 6.5 differ from the corresponding metal spectra

because of the constant-intensity normalization procedure. They exhibit an increased

L3 peak intensity, a decrease in intensity between the L3 and L2 peaks, and a splitting


Fe metal

FeO α-Fe O2 3

Fe O3 4

CoO

NiO

Co metal

Ni metal

Figure 6.4: Absolute absorption coefficient standard spectra for iron, cobalt, andnickel metals and oxides. Upper plots: Fe metal, black; FeO, dark gray; Fe3O4, lightgray; α-Fe2O3, dashed black. Middle plots: Co metal, black; CoO, gray. Lower plots:Ni metal, black; NiO, gray. The L absorption edge (2p → 3d transition) is shown.The absolute absorption coefficient, units (1/µm), is the reciprocal of the photonpenetration length. Left-hand panels, L3 and L2 regions; right-hand panels, expandedL3 regions. The L3 region displays the multiplet structure which is a fingerprint ofthe oxide.


Fe L3

Co L3

Ni L3

Ni L2

Co L2

Fe L2

Fe metal

FeO α-Fe O2 3

Fe O3 4

CoO

NiO

Co metal

Ni metal

Figure 6.5: Total-electron-yield XAS metal and oxide spectra. Upper plot: Fe metal,black; FeO, dark gray; Fe3O4, light gray; α-Fe2O3, dashed black. Middle plot: Cometal, black; CoO, gray. Lower plot: Ni metal, black; NiO, gray. All spectra arenormalized to zero before the L3 region and to an L-edge integrated intensity of 100.Relative to the metal spectra, the oxide spectra show an increase in L3 peak intensity,a decrease in intensity between the L3 and L2 peaks, and multiplet splitting of thepeaks. The experimentally-determined quantities ∆L3(= oxide L3 maximum - metalL3 maximum) are, in eV, FeO ∼0, Fe3O4 1.4, α-Fe2O3 1.7, CoO -0.25, NiO 0.4.


of each of the L3 and L2 peaks into several multiplet peaks. The height changes of

the L3 peak and the valley between the L3 and L2 peaks (the ‘interpeak’ region) is

particularly characteristic of oxidation and we shall use this fact below. The shift

of the L3 peak intensity ∆L3 (oxide L3 maximum minus metal L3 maximum) was

experimentally determined for each case and we obtained the following values: FeO

∼0eV, Fe3O4 1.4eV, α-Fe2O3 1.7eV, CoO -0.25eV, NiO 0.4eV. In general, the larger L3

intensity for the oxides reflects their more-localized d bands, and the multiplet struc-

ture arising from crystal field and electron-electron correlation effects is unobscured

by band structure effects as discussed in detail by de Groot.[40] This has important

implications for the application of XAS to magnetic systems, as will be discussed in

Sec. 6.5.2.

Analysis and Normalization Procedures

Once the standard metal and oxide absorption spectra were established, data analysis

proceeded as follows. The partially-reduced oxide (or partially-oxidized metal) was

modeled with a pure metal/pure oxide bilayer template [either the top two (cobalt-

containing) layers, or the bottom two (nickel-containing) layers, of Fig. 6.2(c)]. A

range of model bilayers was created from the bilayer template by varying the layer

thicknesses, keeping a constant amount of the absorbing species (e. g. Co2+ ions

+ Co metal atoms = constant). A TEY spectrum for each model bilayer was cal-

culated from the absorption coefficient spectra of the standards via Eq. 6.4. The

model and experimentally-obtained TEY spectra were normalized for comparison,

by subtraction of a linear background (or a suitable reference spectrum, if available)

and overall scaling. For each model spectrum, the goodness-of-fit was calculated by

simply summing the squares of the difference between the model datum and actual

datum at each energy point, and dividing by the number of points. The best-fitting

model spectrum was identified, thereby determining the thicknesses of the two layers

of the best-fitting model bilayer. Typically, a separate best fit was identified for three

energy regions: the L3 resonance, the L2 resonance, and the region between L3 and

L2 (the interpeak region). The reported thicknesses were either an average of the

results from the three regions (if within 20%), or the result from the region judged to


be least affected by background or other uncertainties.

Drawing (b) of Fig. 6.2 notes the interfacial regions of the nominally-pure oxide

and metal layers that will take part in the oxidation/reduction reaction. In principle,

for each sample, four best thicknesses could be reported: the thicknesses of the inter-

facial regions that will react [Co (i) and NiO (i) in drawing (b)] and the thicknesses

of the interfacial regions resulting from the reaction [CoO and Ni in drawing (c)].

To facilitate consideration of the consistency of the results, we report the two metal

thicknesses: the thickness of metal that results from oxide reduction and the thickness

of metal that becomes oxidized; the corresponding regions are starred in Fig. 6.2. If

the final configuration of the sandwich is desired, the latter quantity can be converted

to an oxide thickness. Via the appropriate molecular weights and densities, it is found

that 1 A of iron corresponds to 1.78 A FeO, 2.11 A Fe3O4, and 2.14 A α-Fe2O3; 1 A

Co corresponds to 1.75 A CoO; 1 A Ni corresponds to 1.69 A NiO.

The results of the normalization and fitting procedure for the cobalt absorption

edge of a CoO/Fe sandwich are shown in Fig. 6.6. The top plot shows the measured

TEY spectrum and the middle plot shows the optimum model TEY spectrum, cal-

culated via Eq. 6.4 with Co and CoO parameters. The bottom plot, showing the

normalized experimental spectrum and the best-fitting model spectrum, displays the

quality of the fit. For this sandwich, the best-fitting test spectrum is calculated from

a hypothetical structure of 2.2 A Co metal atop 6.2 A CoO. This indicates that in

such a structure the top 3.8 A of CoO was reduced to 2.2 A Co metal (same number

of cobalt atoms) by the adjacent iron metal.

6.4 Results

6.4.1 Qualitative Summary of Results

At an as-grown metal/oxide interface, an interfacial reaction occurs which reduces up

to two atomic layers of oxide and oxidizes a similar amount of metal. An anneal in-

creases the amount of oxide reduction, and the relative extent of reaction of elemental

combinations is in accord with thermodynamic considerations.


Experimentally-obtained spectrum

Calculated test spectrum

Normalized experimental spectrumNormalized test spectrum

Co L3

Co L2

Figure 6.6: Normalization procedure for experimental and calculated electron-yieldspectra. Upper plot: experimentally-obtained total-electron-yield spectrum of thecobalt edge of an ex-situ-grown MgO(001)/CoO (10 A)/Fe (10 A)/Ru (20 A) sand-wich. The TEY spectrum is obtained by dividing the sample photocurrent by thephotocurrent of a gold grid reference monitor. Middle plot: test spectrum calculatedvia Eq. 6.4, using Co and CoO in place of Ni and NiO, and assuming 2.2 A of Co atop6.2 A of CoO. Lower plot: normalized spectra. The experimentally-obtained spec-trum (black) has been normalized by subtracting an NiO/Fe reference spectrum andscaling to attain an L-edge integrated intensity of 100. The test spectrum (gray) hasbeen normalized by subtracting a linear pre-edge and scaling to an L-edge integratedintensity of 100.


NiONiO/FeFitNi metal

FeONiO/FeFitFe metal

Ni L3 Fe L3

Figure 6.7: Ni and Fe L3 spectra of an in-situ-grown NiO (5 A)/Fe (5 A) sandwichshowing reduction of NiO and oxidation of Fe. Pure metal, dark gray; pure oxide,light gray; sandwich layer, black; best fit to sandwich layer spectrum, dashed black.The fit to the Ni L-edge spectrum of the sandwich is of a model structure of 1.5 ANi atop 2.5 A NiO—at the interface, 2.5 A NiO has been reduced to Ni. The fit tothe Fe L-edge spectrum of the sandwich is of a model structure of 3.4 A Fe atop 2.9A FeO—at the interface, 1.6 A Fe has been oxidized to FeO.

Figure 6.7 shows, for example, the L3 resonance of both the oxide and metal for

an in-situ-grown NiO (5 A)/Fe (5 A) sandwich. Considering first the Ni L3 resonance

(left-hand plot), the spectrum of NiO adjacent to Fe (solid black) is in between

the spectra of pure NiO (light gray) and pure Ni metal (dark gray). This suggests

that the nominally-pure NiO layer is in fact a mixture of nickel oxide and nickel

metal. Similarly, the right-hand plot (Fe L3 resonance) shows that the spectrum of

Fe adjacent to NiO is in between the spectra of pure iron metal (dark gray) and pure

FeO (light gray), suggesting that the nominally-pure iron layer is in fact a mixture

of Fe and FeO. Each plot displays also a fit spectrum (dashed) which quantifies the

mixtures: the sandwich can be modeled as NiO (2.5 A)/Ni (1.5 A)/FeO (2.9 A)/Fe

(3.4 A).

The oxidation/reduction reaction occurs at interfaces created at room temperature

and never annealed. To determine the effect of an anneal, one sandwich [ex-situ-grown

MgO(001)/NiO (600 A)/CoO (10 A)/Fe (15 A)/Ru (15 A)] was measured before and


Co L3

CoOas-grownannealedCo

Figure 6.8: Cobalt L3-edge XAS spectra of aMgO(001)/NiO (600 A)/CoO (10 A)/Fe (15A)/Ru (15 A) showing the increased CoO re-duction caused by annealing. Pure Co metal,dark gray; pure CoO, light gray; as-grownCoO/Fe, black; CoO/Fe after a one hour,230◦C anneal, dashed. The increased reduc-tion of CoO after the anneal is evident inthe lessening of the multiplet structure def-inition and in the overall decrease of the L3

peak height. The anneal increases by 1 A theamount of Co metal produced by oxide reduc-tion.

after a 1 hour, 230◦C anneal. Figure 6.8 displays the cobalt L3 resonance for the

sandwich sample before (solid black) and after (dashed) the anneal, in addition to

the spectra of pure CoO (light gray) and Co metal (dark gray) standard samples.

The decrease of overall resonance height and the loss of definition of the multiplet

structure of the resonance, relative to pure CoO, shows that the CoO layer adjacent

to Fe was somewhat reduced as-grown, and was additionally reduced by the anneal.

This anneal, typical of that employed in magnetic device fabrication, increased the

amount of cobalt metal (reduced cobalt oxide) by about 1 A.

An elemental trend in reaction extent is evident from Fig. 6.9, which compares

the spectrum of NiO adjacent to Fe (solid black), to the spectrum of NiO adjacent to

Co (dashed). The spectra of pure NiO (light gray) and pure Ni metal (dark gray) are

included for reference. Oxide reduction (increase of metallic character) is indicated

by a decrease of resonance height (at both the Ni L3 and L2 resonances) and loss of

definition of multiplet structure (at the Ni L2 resonance), relative to the pure NiO

spectrum. The spectrum of NiO adjacent to iron is more metallic than that of NiO

adjacent to cobalt, showing that the NiO/Fe interface reacts more than the NiO/Co

interface.


NiONiO/CoNiO/FeNi metal

Ni L2Ni L3

Figure 6.9: Nickel L3 and L2 spectra for Ni, NiO, MgO(001)/NiO (10 A)/Fe or Co(10 A)/Ru (20 A) sandwiches, showing the reduction of nickel oxide by the adjacentmetal. Ni metal, dark gray; NiO, light gray; NiO/Fe, solid black; NiO/Co, dashedblack. Relative to pure nickel oxide, NiO adjacent to both Co and Fe has a lowerL3 peak intensity (left-hand plot), higher intensity between L3 and L2 (below 870eV in the right-hand plot), and less multiplet definition (L2 peak in the right-handplot). These differences indicate reduction of the nominally nickel oxide layer by theadjacent metal. The spectrum of NiO adjacent to iron is more metallic than thatof NiO adjacent to cobalt, showing that the NiO/Fe interface reacts more than theNiO/Co interface.

6.4.2 Tabulated Results

The metal and oxide layers of each sandwich sample were analyzed as described in

Sec. 6.3.3; the results are given in the following three tables. Table 6.1 displays the

extent of oxidation and reduction of in-situ-grown NiO/Fe sandwiches. In analysis

of the nickel edge spectra we used the 30 A or 5 A NiO standards, as appropriate.

For very thin iron layers deposited on NiO (upper portion of Table 6.1) it is evident

that deposition of additional iron increases the amount of interfacial reaction. For

example, after deposition of 1 A of Fe, NiO reduction produces 1.2 A of Ni and 0.7 A

of Fe is oxidized to FeO. After deposition of an additional 1 A of Fe (2 A tabulated

Fe thickness), the amount of nickel produced has increased to 1.7 A and the amount

of iron oxidized has increased to 0.8 A. This suggests that the extent of reaction is

limited by amount of reactant, for small quantities of reactant.


Table 6.1: Oxidation/Reduction of in-situ-prepared sandwiches consisting of either 5or 30 A NiO plus successive depositions of Fe. Entries represent either the thicknessof Ni that results from NiO reduction, or the thickness of Fe that is oxidized to FeO.The designation ‘+ time’ denotes the passage of about one hour between scans ofthat edge.

Sandwich (grown in situ) Amount Reacted (A)

Ni from NiO Fe to FeO

30 A NiO +1 A Fe 1.2 0.7

+time 1.2 0.6

+2 A Fe 1.7 0.8

+time 1.8 0.7

+3.5 A Fe 2.6 0.9

5 A NiO +5 A Fe 1.5 1.6

+time 1.5 1.3

+10 A Fe 2.0 1.5

+time 2.0 1.4

Table 6.2 summarizes the extent of oxidation/reduction for the ex-situ-grown sand-

wiches. Elemental trends are evident: iron metal is a stronger reducing agent than

nickel or cobalt, a NiO/Co pair reacts somewhat more strongly than a CoO/Ni pair,

and iron reduces nickel oxide more than cobalt oxide. These results are in qualitative

agreement with thermodynamic considerations2 which predict that iron metal will

be a significantly stronger, and cobalt metal a slightly stronger, reducing agent than

nickel metal. In this ex-situ-grown set of sandwiches, iron spectra were not express-

ible as a combination of the pure metal and the associated monoxide (FeO) only. The

total amount of iron oxidized, listed in the table, was established from the interpeak

region of the iron edge spectrum, which is sensitive to ‘amount of oxidation’ rather

than to the specific oxide. The shape of the iron L3 edge showed that both the NiO/Fe

2Standard Gibbs Free Energies of Formation: FeO -58.1, CoO -51.5, NiO -50.6 kJ/mol


Table 6.2: Oxidation/Reduction of ex-situ-prepared sandwiches. Entries represent ei-ther the thickness of metal that results from oxide reduction, or the thickness of metalthat is oxidized. The entry 3.3∗ denotes [3.0 A Fe→FeO and 0.3 A Fe→higher oxide(Fe3O4 or α-Fe2O3)]. The entry 2.9∗∗ denotes [2.4 A Fe→FeO and 0.5 A Fe→higheroxide].

Sandwich (grown ex situ) Amount Reacted (A)

Ni from NiO Co to CoO

10 A NiO +10 A Co 1.4 2.2

Co from CoO Ni to NiO

10 A CoO +10 A Ni 1.3 1.0

Ni from NiO Fe to FexOy

10 A NiO +10 A Fe 3.2 3.3∗

Co from CoO Fe to FexOy

10 A CoO +10 A Fe 2.2 2.9∗∗

and CoO/Fe sandwiches contained some iron atoms in environments characteristic of

the higher iron oxides3, and enabled an estimation of the amounts.

Table 6.3 gives the oxidation/reduction results for the ‘single crystal’ sandwiches,

which consist of layers of iron or cobalt deposited on ex-situ-cleaved NiO(001). The

single-crystal results are similar to those for the entirely in-situ-grown sandwiches.

At the cleaved NiO/metal interface, a thin layer of NiO reduces to nickel metal, and

a thin layer of the metal is oxidized. Spectromicroscopy studies of a cleaved NiO/Co

interface[89] identify the reduced-NiO layer as the origin of the interfacial spins crucial

to exchange anisotropy.3Since the unit cells of Fe3O4 and α-Fe2O3 are larger than a few atomic layers, we distinguish

between formation of the atomic environment characteristic of the oxide, and formation of the oxideitself.


Table 6.3: Reduction of NiO Single Crystal (SC), and corresponding oxidation ofmetal, upon deposition of Co or Fe metal layers. Entries represent either the thicknessof Ni that results from NiO reduction, or the thickness of cobalt or iron that isoxidized. The entry ‘x’ means that the data was inadequate for analysis.

Sandwich (grown in situ) Amount Reacted (A)

on ex-situ-cleaved NiO)

Ni from NiO Co to CoO

NiO +10 A Co 0.7 0.9

Ni from NiO Fe to FeO

NiO +1.6 A Fe x 0.8

+time 0.6 0.7

+3.4 A Fe 1.4 1.0

+time 1.3 1.0

+9.0 A Fe 2.8 x

+time 2.5 1.2

6.4.3 Consistency Checks

Consistency Within Spectrum

As discussed in Sec. 6.3.3, and illustrated in Fig. 6.5, normalized TEY oxide L edge

spectra differ from the corresponding metal spectra in three ways: the resonances

(especially the L3 resonance) are higher, the interpeak region is lower, and the reso-

nances are split by multiplet effects. Therefore, a useful check of our normalization

and analysis procedures is whether all features of the spectrum imply the same ex-

tent of oxidation or reduction. This was qualitatively true for all samples studied,

and quantitatively true (within 20%) to the extent that background effects could be

removed.

For example, Fig. 6.9 displays the Ni L3 and L2 resonances for an NiO/Fe sandwich

in comparison with pure Ni metal and NiO. The spectra were normalized to zero below

the L3 edge and intensity normalized above the edge as discussed earlier. Note that


the intensity of both the L3 and L2 resonances has been reduced relative to pure

nickel oxide (light gray). In addition, the multiplet splitting of the L2 resonance is

less defined for NiO/Fe than for pure NiO. Finally, the low-energy (less than 870

eV) region of the right-hand plot is a portion of the interpeak region, where metal is

expected to be higher than oxide. It is evident that the spectrum of NiO adjacent to

Fe is higher than that of pure NiO in this interpeak region. That the three spectrum

features—resonance height, interpeak height, and multiplet definition—tell the same

story gives us confidence that the observed effect (oxide reduction) is real, and not

an accident of normalization or analysis.

Consistency Within Sample

We have modeled the interfacial reaction as a transfer of oxygen atoms across an

abrupt interface. Therefore the metal and oxide layers of our sandwich samples

should show complementary results. This was qualitatively true for all samples, as

demonstrated by Fig. 6.7 above, which shows that the reduction of NiO adjacent to

Fe is accompanied by the expected iron oxidation. Similarly, Fig. 6.10 shows the

oxide reduction and the corresponding metal oxidation for an ex-situ-grown NiO (10

A)/Co (10 A) sandwich.[!tb] NiO reduction is seen in the left-hand plot as a lessening

(relative to pure NiO) of L2 resonance multiplet definition, and in the right-hand plot,

oxidation of cobalt is evident from the beginnings of L3 resonance multiplet definition.

In principle, the oxygen transfer hypothesis can be tested quantitatively. Keep-

ing the number of oxygen atoms constant, consideration of the densities, molecu-

lar weights, and stoichiometries of the constituents predicts that 1 A of Ni metal

formed will correspond to 1.1/0.8/0.7 A Fe oxidized, if the iron oxide is respectively

FeO/Fe3O4/α-Fe2O3. The densities and molecular weights of both cobalt and nickel

metal, and CoO and NiO, are nearly identical so a one-to-one relationship is expected

in the case of CoO/Ni or NiO/Co sandwiches. Therefore it is expected that in Tables

6.1 and 6.3, the iron entries will be 1.1× the associated nickel entries. In Tables

6.2 and 6.3, the cobalt entries should equal the nickel entries for the NiO/Co and

CoO/Ni sandwiches. It is found, for example, that for the ex-situ-grown CoO/Ni

sandwich, 1.O A of nickel metal is oxidized to NiO, and 1.3 A of cobalt metal results


CoONiO/CoFitCo metal

NiONiO/CoFitNi metal

Ni L2 Co L3

Figure 6.10: Ni L2 and Co L3 spectra of an ex-situ-grown MgO(001)/NiO (10 A)/Co(10 A)/Ru (20 A) sandwich showing reduction of NiO and corresponding oxidationof Co. Pure metal, dark gray; pure oxide, light gray; sandwich layer, black; best fitto sandwich layer spectrum, dashed black. The fit to the Ni L-edge spectrum of thesandwich is of a model structure of 1.4 A Ni atop 7.7 A NiO—at the interface, 2.3 ANiO has been reduced to Ni. The fit to the Co L-edge spectrum of the sandwich is ofa model structure of 7.8 A Co atop 3.9 A CoO—at the interface, 2.2 A Co has beenoxidized to CoO.

from reduction of CoO. Since the absolute error bar (∼1 A, Sec. 6.4.6) exceeds the

difference between the Ni and Co values, we conclude that the present experiment is

not a quantitative test of the oxygen transfer hypothesis.

Notwithstanding the large error bar, we would like to comment on particular

deviations from the expected relationships. Iron oxidation is consistently less than

(rather than 1.1×) NiO reduction. For the NiO/Fe sandwiches, the most likely source

of the disagreement is the sensitivity of the iron signal to errors in subtraction of the

oxygen absorption background. This normalization is difficult in some cases [NiO

(30 A)/Fe (1–3.5 A)] because of the relative magnitudes of the iron and oxygen

signals, and in all cases because of the proximity of the oxygen absorption edge (∼530

eV) to the iron edge (∼710 eV). Finally, for the ex-situ-grown CoO/Fe and NiO/Fe

sandwiches of Table 6.2 a mix of iron oxides is formed so no simple relationship of the

table entries is expected. Calculation of the number of oxygen atoms involved in the


reactions reveals that in both cases the number of oxygen atoms associated with iron

oxidation is greater than the number available from oxide reduction, for the NiO/Fe

sandwich, by 13%, and for the CoO/Fe sandwich, by 77%. If it is assumed that the

higher iron oxides are formed during growth of the Fe layer (due to the limited base

pressure) rather than by reaction with the oxide, the magnitude of the discrepancy is

the same for the NiO/Fe sandwich but significantly reduced, to 12%, for the CoO/Fe

sandwich. This ‘missing’ oxygen corresponds to a monoxide thickness of 0.6 A.

6.4.4 Iron Oxidation

Figure 6.11 displays differing oxidation behaviors of iron films. Shown are the iron L3

edge spectra of two oxidized iron films. The spectrum of in-situ-grown Fe on NiO is

intermediate between Fe metal and FeO, showing that only the lowest oxide of iron

was formed. A thick iron layer was grown in situ and post-oxidized by repeated doses

of molecular oxygen. Shown is the spectrum after exposure to 65 Langmuirs of O2.

The strong shoulder at ∼709 eV reveals the presence of a higher oxide, either Fe3O4

or α-Fe2O3 (not shown). The evolution with oxygen dose of the peak associated with

Fe and FeO, at 707.36 eV, was particularly interesting. This peak initially increased,

reached a maximum at 15 Langmuirs O2, and then decreased. The higher-oxide peak

at ∼709 eV was evident as a shoulder after 35 Langmuirs O2 and thereafter increased.

We conclude that the formation of the lowest oxide FeO occurs only when oxygen is

available in limited quantities. This was the case for the in-situ-grown NiO/Fe: the

only source of oxygen was the adjacent NiO layer. When oxygen is present in large

quantities, the higher oxides are formed. The ex-situ-grown MgO/NiO or CoO/Fe/Ru

sandwiches were an intermediate case: oxygen was present in limited quantity at the

NiO/Fe interface and in larger quantities during iron growth in the 4×10−8 base

pressure.

6.4.5 Time Evolution of Reaction Extent

Table 6.1 and Fig. 6.12 include scans retaken after about one hour on the in-situ-grown

NiO/Fe sandwiches. Iron oxidation decreases with time. For example, of the 1 A Fe


Fe L3 Fe OFeOFeNiO/FeFe + O

3 4

2

Figure 6.11: Oxidation behavior of iron films. In-situ-grown NiO/Fe, dark gray; in-situ-grown Fe with subsequent oxygen dosing (65 Langmuirs shown), light gray; Femetal, black; FeO, dashed; Fe3O4, dotted. The NiO/Fe spectrum represents a limitedoxygen situation—oxygen only available from the adjacent NiO film. The lowest oxideof iron, FeO, is the result. The higher oxides of iron, represented here by Fe3O4, areformed when larger amounts of oxygen are available. The peak at ∼709 eV (in thepost-oxidized Fe spectrum, the strong shoulder) signals the presence of the higheriron oxides.

deposited on 30 A NiO, 0.7 A initially oxidizes to FeO. After ∼1 hour, the amount

of oxidation has decreased to 0.6 A Fe. When an additional 1 A of iron is deposited,

initially 0.8 A of the 2 A total is oxidized, but after ∼1 hour this has decreased to 0.7 A.

(Note that the monotonic increase in the height of the Fe spectrum interpeak region,

shown in the right-hand plot of Fig. 6.12, does not contradict the non-monotonic trend

of the iron entries in Table 6.1. The spectral height reflects the relative metal/oxide

proportion of the iron layer, whereas the entries in the Table are the absolute amounts

of iron oxidized to FeO.) On the basis of the Fe L-edge interpeak region alone, we

cannot exclude the possibility that a long-wavelength EXAFS feature of the combined

NiO+FeO oxygen K edge can have the opposite effect as that originating from iron


oxidation. However, analysis of the iron layer L3 and L2 peaks agrees with the initial

conclusion from the interpeak region—that the iron layer reduces slightly with time.

Iron layers deposited on ex-situ-cleaved NiO (Table 6.3) also show a lessening of

oxidation with time. This surprising situation obtained for five of the six pairs of

iron spectra (taken immediately after iron deposition, and after 1 hour elapsed time)

included in Tables 6.1 and 6.3.

Evolution of reaction extent as evidenced by reduction of the NiO layer was not

consistent. In some cases, NiO reduction increased with time. For example, when a

total of 2 A Fe has been deposited on 30 A NiO (Table 6.1, upper portion), 1.7 A of

nickel metal results from NiO reduction. After one hour, the amount of reduction has

increased to 1.8 A Ni metal. In other cases, NiO reduction decreased with time. The

change of interfacial reaction extent as seen in the NiO spectrum did not necessarily

correlate to the change deduced from the Fe spectrum. In the example just given,

NiO (30 A)/Fe (2 A), NiO reduction increases with time while Fe oxidation decreases.

6.4.6 Precision and Absolute Error Bar

Precision

The relative precision of ±0.1 A implied by the Tables deserves comment. Comparison

of the results for the nominally 30 A thick NiO sandwich in Table 6.1 to the associated

spectra in Fig. 6.12 allows an estimate of the sensitivity of the spectra to small changes

in extent of reaction. In the NiO spectra displayed in the left-hand plot, the reduction

to Ni metal of thicknesses in the 1.2 to 1.7 A range upon addition of iron is clearly

resolved. However, the very small change with time is not easily visible in this region.

(A small change in the L3 peak height, not shown here, causes the change of reaction

extent from 1.7 to 1.8 A Ni metal displayed in the Table.) For the iron spectra

displayed in the right-hand plot, a decrease in oxidation is evident with time and with

deposition of additional iron metal. These spectral changes correspond to changes in

reaction extent as small as 0.1 A Fe. We conclude that the relative precision of this

experiment reaches ±0.1 A for very thin layers, and ±0.5 A for thicker layers.


Table 6.4: Effect of various errors on reported results. First column, source of error;second column, quantified amount of error. The third column reports the change inthe reported result (metal thickness) caused by the error. The linear v. referencespectrum comparison refers to the cobalt edge of an MgO(001)/CoO (10 A)/Fe (10A)/Ru (20 A) sandwich.

Source of Error Amount of Error Change of Result

electron escape depth λNiO: 30 A→40 A 1 A at L3, 0.3 A at L2

overlay 10% change of slope 0.1 A

finite thickness effect bulk v. 30 A NiOstandard spectrum

0.3 A at L3, 1 A at L2

background subtraction linear v. referencespectrum

1 A

in-situ-grownlayer thickness

±20% 0.5 A

ex-situ-grown metallayer contamination

N/A 0.5 A

ex-situ-cleaved NiOsurface contamination

N/A unknown

Absolute Error Bar

The effect of various sources of error on the reported results are summarized in Table

6.4. The error sources are listed in the first column and quantified in the second

column. The third column gives the effect of the error on the results of the analysis;

an absolute error bar of 1 A is a reasonable description of the experiment. This is a

substantial proportion of typical reported results (metal thicknesses) which are in the

of range 0.5–3 A. Combining the magnitudes of all the effects listed in the right-hand

column yields a worst-case error bar of 2–3 A, or about one monolayer.

The first two sources of error in Table 6.4, uncertainty of electron escape depth

λ and the slope of the overlay, can in principle be reduced by future XAS experi-

mentation. The overlay procedure was necessitated by the lack of standard absorp-

tion spectra for all the metals and oxides investigated in this work and it could be


eliminated by recording transmission spectra that can directly yield the absorption

coefficients.[81, 88] The analysis required a value for λ at two points: in construction of

the standard absorption spectra (by correcting the overlay for saturation, Sec. 6.3.3)

and in calculating test total-yield spectra from the standard absorption spectra (via

Eq. 6.4). Therefore λ would appear in the analysis even if the required absorption

coefficient spectra were available. The electron escape depth has been determined

for relatively few substances, and there is substantial disagreement among even these

values. The sensitivity of our analysis to variations in λ is stated for the example

of NiO. Given a 33% change in λNiO, the result of the analysis (Ni layer thickness)

performed at the L3 region changes by 1 A.

The third source of error, the finite thickness effect on the spectrum of NiO thin

films, can be easily removed by gathering spectra of films of various small thicknesses.

The only caution is that these reference standard spectra should be identical to the

thin NiO layer under investigation, to eliminate any other effects on the magnetic axis

orientation (and thus the spectrum). For example, in this work we used the initial

bare 5 A and 30 A NiO on Si films, as the nickel oxide standards in analyzing the

eventual Si/NiO (5 or 30 A)/Fe sandwiches. But these thin NiO spectra were not

used to analyze the MgO(001)/NiO (10 A)/metal (10 A)/Ru (20 A) sandwiches, as

we could not be sure that the magnetic axis orientation of the (epitaxial) NiO on

MgO was the same as for the (presumably polycrystalline) NiO on Si.

The fourth source of error is background subtraction. Table 6.4 compares two

methods of performing this task on the cobalt edge of a CoO/Fe sandwich. The

first method is simply fitting the pre-edge region to a straight line and subtracting

this line from the entire spectrum. The second method subtracts a background that

contains the EXAFS structure of lower energy absorption edges. For the CoO/Fe

sandwich a NiO/Fe sandwich measured through the region of the Co edge can be

used as a suitable reference spectrum since the O K-edge EXAFS of NiO and CoO

are nearly identical. Subtracting such a reference spectrum removed any CoO and

Fe EXAFS structure from the Co edge spectrum of the CoO/Fe sandwich. The Ni L

absorption edge, located at a higher energy than that of Co, did not interfere with

this process. In general, the normalization and fitting procedure is quite sensitive to


the background subtraction method. Analysis after a linear background subtraction

gave 1.3 A cobalt metal, significantly less than the reported result (2.2 A Co) after

subtraction of the reference spectrum.

Subtraction of a reference spectrum is preferable, but one must plan carefully to

ensure availability of appropriate reference samples. For example, we were unable to

remove the effect of iron background at the Ni L edge of the NiO/Fe sandwich because

an appropriate reference spectrum (perhaps CuO/Fe in this case) was not available.

In such a case, one can fit the peak shape independently of the peak height. Fitting

only the shape of the L3 absorption edge (by varying an additional scaling parameter)

was successful in the case of the CoO/Fe sandwich—it yielded the same result, 2.2 A

cobalt metal, as that obtained from the subtraction of the reference spectrum.

The ex-situ-grown metal layers and the ex-situ-cleaved NiO surface may have

suffered from contamination. As discussed in Sec. 6.2.2, we were able to determine

that the former problem contributed only about 0.5 A of the reported amount of Fe

oxidized, and less than 0.5 A of the reported Co oxidized. We are unable to estimate

the effect of contamination of the cleaved NiO surface.

In principle, the experimental and analysis methods described in this work enable

the identification of interfacial metal layers as thin as 0.1 A. A reasonable error bar

for the absolute thicknesses reported in this work is 1 A or one-half monolayer of

interfacial metal.

6.5 Discussion

6.5.1 Interface Structure

In this section the assumptions behind the possible sample structures illustrated in

Fig. 6.2 will be evaluated. The first assumption, used in deduction of the thickness

of the oxidized/reduced region, is that the border between reacted and unreacted

material is abrupt. This is of course unlikely. Consider as an example the thin layer

that in the absence of an adjacent oxide would be a pure metal. We believe that one

or at most two atomic layers adjacent to the interface are fully oxidized, the layers far


(10 A) from the interface are pure metal, and the mixed-phase region between these

regions transitions gradually from oxide-rich to metal-rich. This belief is supported

by a recent study[90] which finds that when permalloy is deposited at 100◦C on γ-

Fe2O3, the thickness of the resulting interfacial layer, measured by change in oxygen

concentration, is ∼10 A. The abruptness of the transition is governed by the interplay

of thermodynamic forces and kinetic considerations.

A second assumption is that the resulting intermixed region can be described as a

two-phase combination (of the pure metal and associated monoxide). This assumption

resulted in satisfactory fits in almost all of the cases in this work. The exceptional

cases—ex-situ-grown iron layers, which contained several different iron oxides—have

been noted in Sec. 6.4.2. The oxygen K-edge XAS spectrum is in principle a clear

signature of the various iron oxides.[91, 92] However, interpretation of the oxygen

spectrum will be more complicated if it contains contributions from additional sources

of oxygen (NiO, CoO in our samples; surface oxygen on ex-situ-grown samples). There

is the further possibility that, if kinetic considerations preclude the attainment of

thermodynamic equilibrium, an atom may be in a non-equilibrium oxide coordination.

It may be difficult to establish a standard absorption spectrum in this case.

A third assumption is that the two reacted regions (reduced oxide and oxidized

metal) remain distinct as shown in Fig. 6.2 (c) rather than mix as shown in drawing

(d). In fact, there is experimental evidence that in some cases these two regions

mix to form a single interfacial compound. For example, a Mossbauer spectroscopy

study [31] of the CoO/Fe interface found a complicated mix of iron and iron/nickel

environments. Determining the precise reaction mechanism or exact nature of the

product formed is challenging, but some progress has been made: recent works have

identified the product of reactions at a NiO/α-Fe2O3[93] or NiO/γ-Fe2O3[90] interface

as nickel ferrite. To investigate this possibility using the methods of the present work,

a standard spectrum of the interfacial species—CoxNiyO in the case of Fig. 6.2(d)—is

needed.


6.5.2 Application of XAS to Magnetic Systems

This study has focused solely on the chemistry of the metal/oxide interface. An

important additional capability of XAS is its sensitivity to magnetic ordering. The

magnetic information is contained in the same multiplet structure that is a signature

of the various chemical species—antiferromagnetic ordering, for example, is seen as

an increase of some peaks, and a decrease of others, within a particular multiplet.[55]

Therefore, extraction of magnetic information from XAS spectra of complex system

requires knowledge of both the chemical signatures of the component species, and

the modifications of those signatures that accompany magnetic ordering. Once this

information is known, XAS can determine the magnetic ordering not only of each

element, but of different chemical phases of the same element. The present study is

significant not only for its expected general applicability, but as a necessary foundation

for the study of magnetic interfaces using XAS.

6.5.3 Implications for the Study of Exchange Anisotropy

It has long been recognized that exchange anisotropy is an interface phenomenon

which depends on the existence of uncompensated interfacial spin moments. Much

work has been devoted to finding the origin of these interfacial spins. The present work

provides evidence that the interfacial spins are of chemical origin. More specifically,

at the interface of an NiO/Co exchange-biased sandwich, there exists a nickel-metal-

like layer that is the source of the uncompensated interfacial spins. Such a model[94]

of exchange anisotropy receives strong support from spectromicroscopic imaging of

the spin moment of this interfacial layer.[89]

6.6 Conclusion

The present study demonstrates the existence of chemical reactions at metal-oxide

interfaces. Such an interface can be described as a reduced-oxide region adjacent to an

oxidized-metal region. The metal regions involved (either oxide that has been reduced

or metal that will be oxidized) are 0.5–3 A thick. The metal-like layer resulting from


oxide reduction is a possible origin for the interfacial magnetic moments giving rise

to exchange anisotropy.


NiO

Fe metal

Ni metal

FeO

3.5 Å Fe2 Å Fe + time2 Å Fe1 Å Fe + time1 Å Fe

Figure 6.12: Interpeak region spectra of the nickel L-edge (left-hand plot) and ironL-edge (right-hand plot) for an in-situ-grown 30 A NiO/1–3.5 A Fe sandwich. Pureoxide and metal, black; 1 A Fe as-grown, solid dark gray; after 1 hour, dashed darkgray; 2 A Fe as-grown, solid light gray; after 1 hour, dashed light gray; 3.5 A Fe,black (between metal and oxide spectra). In each plot, the highest spectrum is themetal standard and the lowest spectrum is the monoxide standard. Left-hand plot:As successive thin iron layers are deposited, NiO reduction increases, but very smallchanges with time are indistinct. For example, the spectra taken immediately afterdeposition of 1 A Fe (solid dark gray) and after 1 hour elapsed time (dashed darkgray) cannot be distinguished in the left-hand (Ni L edge) plot. Right-hand plot: Ironoxidation lessens with time. For example, the spectrum taken 1 hour after depositionof 1 A Fe (dashed dark gray) is higher than (less oxidized than) the spectrum takenimmediately after iron deposition (solid dark gray). The proportion of iron metalrelative to iron oxide increases with successive deposition of thin iron layers.

Chapter 7

Images of the Antiferromagnetic

Structure of a NiO(100) Surface

via XMLD Spectromicroscopy

This chapter is based on Ref. [1]. The text has been modified to follow the detailed

discussion of 〈M2〉 in Chapter 4. In the right-plots of Figs. 7.3 and 7.4, the right-hand

axis label has been changed to (〈M2〉T/〈M2〉0 − J(J + 1)/3). References have been

updated.

7.1 Introduction

In the last decade the ability to atomically engineer magnetic structures with reduced

dimensions, such as thin film sandwiches and multilayers, has created new interest in

the study of magnetism and magnetic materials[8]. While an abundance of work exists

for ferromagnetic thin films, the study of antiferromagnetic thin films has been im-

peded by their magnetically compensated nature. The study of antiferromagnetic sur-

faces and interfaces has posed an even larger challenge because conventional optical, x-

ray and neutron techniques[72, 71, 30] are bulk sensitive. This limitation is overcome

by use of x-ray magnetic linear dichroism (XMLD) spectroscopy[57, 62, 95, 54, 55]

carried out by means of surface sensitive electron yield detection[96, 82]. In contrast

98

CHAPTER 7. MAGNETIC STRUCTURE OF A NIO(100) SURFACE 99

to the x-ray magnetic circular dichroism (XMCD) technique[97, 98, 99] which directly

measures the magnetic moment 〈M〉 through transfer of the x-ray angular momentum

vector in the absorption process, XMLD spectroscopy measures the expectation value

of the square of the magnetic moment, 〈M2〉 because linearly polarized photons only

have axiality. In principle, XMCD can only be used for unidirectional magnetic sys-

tems, i.e. ferro- or ferrimagnets, while XMLD can be applied for all uniaxial magnetic

systems, e.g. antiferromagnets, as well.

It has been suggested that, in principle, XMLD spectroscopy in conjunction with

a photoelectron emission microscope (PEEM) should be capable of imaging the de-

tailed antiferromagnetic domain structure of a surface or interface[96], similar to

XMCD-PEEM spectro-micrososcopy of ferromagnets[100]. In comparison to other

imaging techniques of antiferromagnetic domains such as neutron and x-ray diffrac-

tion topography[72, 47, 71], and optical[72, 48], and non-linear optical[73] techniques,

XMLD-PEEM spectromicroscopy offers elemental specificity, surface sensitivity (∼2

nm sampling depth[82]) and improved spatial resolution (∼20 nm). In practice, how-

ever, it has been difficult to obtain reliable, meaningful antiferromagnetic images by

XMLD microscopy as demonstrated by a recently published first attempt[101].

This chapter reports the first unambiguous surface images with antiferromagnetic

contrast. These images were obtained with XMLD microscopy for NiO(100) grown

on MgO(100) and were made possible by a new spectromicroscopy facility at the

Advanced Light Source (ALS) in Berkeley that combines a high flux-density soft x-

ray beam line with a high spatial resolution PEEM[102]. The images reveal striking

antiferromagnetic contrast which through atomic force microscopy images is linked

to crystallographic line defects. From the temperature dependence of the surface

integrated XMLD absorption spectra a NiO(100) surface Neel temperature indistin-

guishable from the bulk (523 K) is determined. Detailed analysis of the antiferromag-

netic images reveals a different temperature dependence of the defect regions. This

is attributed to a temperature dependent magnetic (spin) component of the XMLD

contrast which vanishes at the reduced Neel temperature of the line-defects (455 K),

and a constant crystallographic (charge) component arising from a lower than cubic

symmetry in the defects.


7.2 Experiment

7.2.1 Sample Growth and Characterization

The 10–80 nm thick NiO(100) films on MgO(100) were grown by electron beam evap-

oration of elemental nickel in an activated oxygen atmosphere. Molecular oxygen was

fed into the chamber (base pressure 4 × 10−8 torr) to a pressure of 2 × 10−5 torr,

confined with a magnetic field, and activated with an electron cyclotron resonance

microwave source[77]. A typical growth rate was 0.3 A/sec. Reflection high-energy

electron diffraction patterns monitored during and after growth showed almost no

change from the pattern of the MgO substrate, indicating that the NiO grew epitax-

ially in the desired MgO rocksalt structure. High-angle symmetric and asymmetric

x-ray diffraction scans confirmed the growth of single-phase epitaxial NiO(100). The

NiO thickness was determined by small-angle x-ray diffraction. Bare NiO(100) sur-

faces were characterized with atomic force microscopy (AFM). The surfaces were

generally smooth and composed of square growth regions of dimension 30–50 nm, as

shown in Fig. 7.1. Linelike structures, arranged in a crisscross pattern, consisting of

raised bars having cross-sections 1–3 nm high and 30–1000 nm wide were also ob-

served. Corresponding images of MgO(100) substrates, taken soon after polishing,

suggested that imperfections in the substrate could be the source of the NiO surface

features.

7.2.2 Spectromicroscopy Experiments

Spectromicroscopy studies were carried out using the PEEM2 facility on beam line

7.3.1.1 at the ALS[102]. Linearly polarized x-rays are obtained by the use of an

aperture that selects the central horizontal fan of radiation from a bending magnet

source[96]. The sample is located in the focal plane of a slitless spherical grating

monochromator and a horizontally focusing elliptical mirror with a 30 µm focal spot.

The monochromatic photon flux density at the sample is (3 × 1012 photons/sec)/(0.4

eV/30 µm2) at 800 eV and a ring current of 400 mA. The x-rays are incident on the

sample at an angle of 30◦ from the surface with the electric field vector ~E oriented


1 µm 100nm

Figure 7.1: Atomic force microscopy image of a 80 nm thick NiO(100) film grown onMgO(100). The inset shows a magnified part of the image.

parallel to the surface. The all electrostatic PEEM2 microscope collects low-energy,

secondary photoelectrons from the sample. In order to avoid charging effects the

NiO(100) sample was coated with a 2 nm Cu layer in the PEEM preparation chamber.

The photoelectrons are imaged with magnification onto a phosphor screen which is

read by a CCD camera. The spatial resolution of PEEM2 is limited by chromatic

aberrations to 20 nm. The resolution for our studies was about 50 nm.

7.3 Review of XMLD Applied to NiO

The resonant absorption intensity of linearly polarized x-rays may be written as[55,

99],

I(ϑ, θ, T ) = a+ b (3 cos2 ϑ− 1)〈Qzz〉+ c (3 cos2 θ − 1)〈M2〉T + d

∑i,j

〈si · sj〉T . (7.1)


The constant first term is independent of the x-ray polarization and the sample tem-

perature T , the second term expresses the x-ray polarization dependence due to the

presence of a quadrupole moment of the charge, 〈Qzz〉, where ϑ is the angle of ~E with

the crystallographic z axis, assuming higher than twofold symmetry about z. This

term gives rise to the conventional linear dichroism effect in x-ray absorption[99]. The

third term is responsible for the XMLD effect[55]. It depends on the x-ray polarization

through the angle θ between ~E and the magnetic axis↔A and on temperature through

〈M2〉T . This term reflects the temperature dependence of the long range magnetic

order and attains a limiting, isotropic value of (1/3)J(J + 1) above the Neel temper-

ature. Finally, the last term expresses the dependence on the short range magnetic

order through the temperature dependent spin-spin correlation function 〈si · sj〉T [67].

In NiO the charge-only linear dichroism effect vanishes because of cubic sym-

metry (〈Qzz〉 = 0)[99, 70]. However, the alignment of the Ni spins along the an-

tiferromagnetic axis↔A[48] leads to a pronounced XMLD effect whose angular and

temperature dependence has been studied in detail for ultrathin NiO(100) films on

MgO(100)[55, 67]. In particular, the Ni L2 resonance exhibits two multiplet peaks of

which the lower energy peak A is larger for ~E ⊥↔A and the higher energy peak B is

larger for ~E ‖↔A[55]. The peak intensity ratio and its temperature dependence is dom-

inated by the XMLD effect[55]. The smaller spin-spin correlation term was found to

exhibit a similar temperature dependence as the 〈M2〉T term[67, 55]. The L2 multi-

plet peak intensity ratio can therefore be used as spectroscopic contrast when imaging

the magnetic configuration of the antiferromagnetically ordered NiO surface[101, 96].

7.4 Results

7.4.1 Magnetic Origin of the Image Contrast

Figure 7.2 shows an antiferromagnetic image with a 40 µm field of view for a 10

nm thick NiO(100) film. The image was generated by dividing an image acquired at

871.5 eV, peak B, by one recorded at 870.3 eV, peak A. This procedure eliminates

topographical and produces antiferromagnetic contrast. The image exhibits straight


290 K

425 K

520 K

5 mµ

Figure 7.2: XMLD antiferromagnetic image of a 10 nm thick NiO(100) film onMgO(100) recorded at room temperature, and the temperature dependence of a regionwithin the image.

bright lines or stripes with typical widths between 400 nm and 2000 nm on a darker

background. Such features are observed at other locations on the same sample and

on other samples with different NiO thicknesses in the 10–80 nm range. The lines

are several 100 µm long, and the fact that similar structures are also observed by

AFM indicates that the lines in our image are correlated with the structure of the

surface. However, the contrast in Fig. 7.2 is of antiferromagnetic and not of topo-

graphic nature. This is demonstrated by the temperature dependence evident from

Fig. 7.2. Images recorded at 290, 425, and 520 K, respectively, are shown. The con-

trast disappears gradually as the Neel temperature of the film is approached. The

temperature dependence is reversible and the XMLD contrast is fully restored upon

returning to room temperature (see Fig. 7.4 below). This indicates that the linelike

antiferromagnetic regions are pinned by the surface structure of the film.

7.4.2 Quantification of Image Contrast

Figure 7.3 shows temperature dependent absorption spectra obtained with PEEM

from a large region of ∼20 µm diameter, dominated by dark areas. The ratio of

peak A (870.3 eV) to peak B (871.5 eV) intensities is plotted versus temperature. At


868 870 872 874

Tem

pera

ture

(K)

290325410425445465490500520

Inte

nsity

(a.u

.)

Photon Energy (eV)

1.05

1.1

1.15

1.2

1.25

0

0.2

0.4

0.6

0.8

280 320 360 400 440 480 520P

eak

A/

Pea

kB

<M

>/<

M>

-J(J+

1)/32

2

T0

Temperature (K)

Figure 7.3: Ni L2 resonance fine structure as a function of temperature for 10 nmNiO(100)/MgO(100). The spectra were obtained by averaging over a 20 µm area ofthe sample, dominated by “dark” regions in the corresponding image. On the rightthe temperature dependence of the peak A (870.3 eV) to peak B (871.5 eV) intensityratio is shown. The solid line is a superimposed theory curve as discussed in the text.

room temperature, peak A is larger than peak B indicating, on average, a preferred

orientation of↔A perpendicular to the surface[55]. At higher temperatures the peak

ratio decreases to 1.055 at T=520 K, the same value found by Alders above the

Neel temperature for thinner NiO films[55]. [This value is identified as the isotropic

contribution, (1/3)J(J + 1), to 〈M2〉. Accordingly the quantity (1/3)J(J + 1) is

subtracted from 〈M2〉T (Chapter 4, calculated with the bulk value of TN) to yield

the right-hand axis of the right-hand plot of Fig. 7.3.] Thus the disappearance of

magnetism goes hand in hand with the reduction in image contrast.

Bright stripes on a dark background are always observed when the sample is

rotated about the surface normal. The stripes therefore do not correspond to az-

imuthally oriented antiferromagnetic domains. Close inspection of the XMLD images

reveals a superstructure of light speckles which we believe to originate from the true

antiferromagnetic domains. Their size is probably comparable to the square growth


0

2

4

6

8

10

12

14

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

280 320 360 400 440 480 520

290

320

355

390

420

460

500

290

Tem

pera

ture

[K]

Temperature (K)

<M

>/<

M>

-J(J+

1)/32

2

T0

Lin

eC

ontr

ast

(%)

Lin

eP

rofi

le(a

.u.)

Figure 7.4: Line scans across antiferromagnetic images of a 10 nmNiO(100)/MgO(100) sample as a function of temperature. The peaks in the linescans are due to a “white” line in Fig. 7.2 and the peak intensity reflects the contrast.On the right are shown the temperature dependence of the “white” line contrast anda theory curve (solid line) as discussed in the text.

regions shown in the inset in Fig. 7.1 (≤50 nm) which is at the resolution limit of

these experiments. A bright area in the XMLD contrast image corresponds to an

increased intensity of peak B relative to peak A. The stripes may thus be caused by

a more in-plane orientation of↔A or, in accordance with Fig. 7.3, by a reduced value

of 〈M2〉 associated with individual or an agglomeration of surface defect lines.

The temperature dependent antiferromagnetic contrast in the XMLD images can

be quantified by direct comparison of the intensity of the stripes and the intensity of

the darker areas. Figure 7.4 shows consecutive temperature dependent line profiles

through the same image. Also shown is a temperature dependent plot of the line

contrast defined as the difference of the line intensity (area) and the background

intensity, normalized to the background intensity. This curve therefore reflects the

true line defect signal, with any underlying nondefect background subtracted out.

The signal shows a characteristic 〈M2〉T temperature dependence with a reduced

Neel temperature TN = 455 ± 10 K, indicated by the solid line theory curve. This

is attributed to a finite size effect [55] associated with the reduced dimension of the


line defects. At higher temperatures the signal remains constant at a small but finite

value. We attribute this to a temperature independent crystallographic (charge)

contribution to the linear dichroism signal, i. e. a finite 〈Qzz〉 term in Eq. 7.1, caused

by a crystallographic distortion in the surface line defects.

7.5 Conclusion

This chapter demonstrates the use of XMLD spectromicroscopy for obtaining detailed

mesoscopic information on the antiferromagnetic structure of epitaxial thin films and

their surfaces. Contrast in images of a NiO(100) surface was shown to be of magnetic

origin. Surface line defects were found to have a reduced Neel temperature (455 K)

relative to the rest of the film surface and the bulk (523 K). The separate spin and

charge components of the linear dichroism effect were obtained. More generally, it is

clear that the technique can be extended to the study of polycrystalline surfaces (see,

for example, Chapter 8) and to interfaces between thin films.

Chapter 8

Relationship of Film Strain and

Antiferromagnetic Spin Axis

Orientation in Polycrystalline NiO

Films

8.1 Introduction

This chapter describes a new application of XAS microscopy—investigation of the

relationship of local film strain and antiferromagnetic spin axis orientation. Large-

grained polycrystalline films were thought to be good candidates for the imaging of

antiferromagnetic domains. As described in Section 8.2, XAS microscopy images of

these films did not reveal individual AF domains, and the observed AF spin reorien-

tation followed cracks in the film. An explanation of the spin orientation in terms of

the inhomogeneous strain state of the film was sought. Section 8.3 estimates the inho-

mogeneous stress in the film resulting from annealing, cooling, and cracking. Section

8.4 describes the consequences this stress for the antiferromagnetic spin orientation.

107

CHAPTER 8. FILM STRAIN AND AF SPIN ORIENTATION 108

8.2 XAS Microscopy Images of Annealed Polycrys-

talline NiO Films

8.2.1 Sample Fabrication and AFM Images

Early attempts to image antiferromagnetic domains in NiO were unsuccessful or

ambiguous[101]. For example, in Ref. [1] (Chapter 7), it was thought that the true

domain structure was just beyond the experiment’s resolution limit of 50 nm. The

boundaries of the square NiO growth regions may have interrupted magnetic order-

ing, limiting domain size to the (30–50 nm) size of the growth region. To avoid this

possibility, large-grained films were prepared as described below, in the hope that the

grains would become large (single) antiferromagnetic domains. Polycrystalline films

were chosen to improve the odds of the grains being magnetically decoupled, yielding

AF contrast.

Polycrystalline NiO films of thickness 100 nm, 200 nm, and 400 nm were sputter-

deposited on Si substrates and annealed to increase their grain size. The grain size of

the as-grown films was small—15–20 nm. The films were annealed at 1100◦C for one

hour, in an oxygen atmosphere to prevent NiO reduction. Figure 8.1 shows atomic

force microscopy images of the 200 nm sample taken before and after the anneal.

Evidently the anneal dramatically increased the grain size. Images of the three films,

after anneal, are shown in Fig. 8.2. Post-anneal average lateral grain dimensions are:

80 nm for the 100 nm thick film, 140 nm for the 200 nm thick film, 180 nm for

the 400 nm thick film, as shown in Fig. 8.3. The NiO grains were randomly oriented

before and after the anneal; both (200) and (111) peaks (the two strongest reflections)

were visible in symmetric x-ray scans, and asymmetric scans showed no preferential

orientation.


1m

m

Figure 8.1: AFM images of 200 nm thick polycrystalline NiO film on Si, before (left)and after (right) a one hour anneal to 1100◦C in oxygen. Both images are 1 µmsquare. Full vertical color scale: left 10 nm, right 100 nm. Grain size before anneal,15–20 nm; after anneal, ∼140 nm.

100 nm 200 nm 400 nm

2 mm

Figure 8.2: AFM images of 100 nm, 200 nm, and 400 nm thick polycrystalline NiOon Si, after annealing to 1100◦C in O2. Images are 2 µm square. Estimated grainsizes: 100 nm thickness, 80 nm grain size; 200 nm thickness, 140 nm grain size; 400nm thickness, 180 nm grain size.


Figure 8.3: Average grain size of an-nealed polycrystalline NiO films. Post-anneal average lateral grain dimensions80 nm (100 nm thick film), 140 nm (200nm thick film), 180 nm (400 nm thickfilm). The solid curve is proportional tothe square root of film thickness.

Film Thickness (nm)G

rain

Siz

e(n

m)

100 200 300 400

100

50

00

150

200

8.2.2 XAS Microscopy Linear Dichroism and Topographical

Images

X-ray absorption spectromicroscopy images of the antiferromagnetic structure and

topography of the samples are shown in Fig. 8.4. On the left is a magnetic linear

dichroism (antiferromagnetic structure) image. Image contrast reflects a change in

the NiO spin axis orientation relative to the (in-plane) electric field vector ~E; bright

regions have a greater, and dark regions a lesser, projection of the spin axis on the

horizontally-oriented vector ~E. The image dimension is ∼20 µm so the bright regions

are approximately 1 µm wide and separated by 2–4 µm; a contiguous dark region will

be referred to as an island. On the right is an image of the sample topography in

which the light lines were determined (by optical microscopy) to be cracks. The light

lines in the right image match up perfectly with the bright regions of the left image.

Specifically, each light line (right image) is flanked on both sides by a bright region

(left image). Note that the vertical flanking regions are brighter than the horizontal

flanking regions. Since the left and right image are of the same sample location, it

can be concluded that near the cracks, the NiO spin axis is oriented in the sample

plane, while away from the cracks, the spin axis is out of plane. Individual grains

are not clearly distinguished. Upon close inspection, the dark regions are seen to be


20m

µ

Figure 8.4: Correlation of antiferromagnetic and topographical microstructure of an-nealed polycrystalline NiO. Left: AF spin axis information gathered by x-ray ab-sorption spectroscopy magnetic linear dichroism. Bright region denotes a spin axisrotated towards an in-plane orientation. Right: topographical information. Brightlines are cracks extending through the film. Left and right are images of the samesample area, which is 20 µm square. The electric field vector ~E is in the plane of thefilm and oriented horizontally in the figure.

small spots of red (some intensity intermediate between dark and bright) on a dark

background. These small spots do represent magnetically different regions and may

be the desired single-domain grains. Nonetheless, the correlation of the magnetic

structure with the cracks strongly suggests that domain contrast is not the overriding

mechanism in these films.

Figure 8.5 schematically depicts the in-plane (near a crack) and out-of-plane (far

from a crack) spin axis orientations. The figure is drawn to match the experimental

geometry of Fig. 8.4. The upper drawing shows the spin axes of the NiO grains in

a single island. In addition, the electric field vector, which is in the sample plane, is

shown. The lower region shows a cross-sectional view of two islands and the crack

separating them.

This chapter suggests an explanation for the NiO antiferromagnetic spin axis

reorientation: as the result of inhomogneous film strain resulting from the anneal and

cool. In Sec. 8.3, the stresses and consequent strains resulting from the anneal, cool,


E

Si

NiO

Figure 8.5: Drawing of NiO spin axis orientation near and far from a crack, planview (upper) and cross-sectional view (lower). The upper drawing shows also theelectric field vector, in the sample plane and oriented horizontally in the figure. Theexperimental geometry depicted is the same as for Fig. 8.4.

and cracking are estimated. In Sec. 8.4, the response of the NiO spin axis orientation

to the strain is described.

8.3 Local Stress Explanation

In this section, the lateral stress profile, and the resulting strain, in the annealed NiO

film is estimated. First the thermal stress upon cooling from the anneal temperature

is calculated. It is then shown that this (tensile) stress is sufficient to crack the NiO

film, and that the observed crack spacing can be successfully predicted from this stress

and the relevant mechanical quantities. Then an expected residual stress profile—

stress as a function of lateral distance from the crack—in a NiO island is estimated.

Finally, the strains at important points in the island are calculated.

Elastic Constants There is substantial variation in the literature values of elastic

constants. Here the following values are used:


• Young’s modulus ENiO = 191 GPa, Poisson ratio νNiO = 0.32

• Mode I fracture toughness1 for NiO KIc = 1.2 × 106 Pa√

m

• Young’s modulus ESi = 130 GPa, Poisson ratio νSi = 0.28

• Thermal expansion coefficients αNiO = 10.2 × 10−6/K, and αSi = 2.6 × 10−6/K.

• NiO elastic constants c11=270 GPa, c12=125 GPa, c44=105 GPa.

The values[103] of E, ν, and KIc for nickel oxide are appropriate for a polycrys-

talline (assumed isotropic) film; the values for silicon are calculated from compliance

constants[104], also assuming isotropic behavior. The thermal expansion coefficient

values[105] are for room temperature; their temperature dependencies do not affect

the conclusions significantly. The NiO elastic constants[106] will be employed in

Sec. 8.4.1. Throughout this chapter, the randomly-oriented polycrystalline NiO film

will be assumed isotropic; a departure from this assumption will be considered in

Sec. 8.4.2.

8.3.1 Generation of Thermal Stress

The NiO/Si samples were annealed to high temperatures and then cooled. Because

of the difference in thermal expansion coefficient between NiO and Si, this cooling

resulted in a biaxial tensile stress σth in the nickel oxide. The magnitude of this

stress can be calculated from the equation σth = −(ENiO/(1 − νNiO))(αNiO − αSi)∆T .

The anneal and cool resulted in ∆T= 293 K - 1373 K = -1080 K; the resulting

thermal stress expected in the NiO film is +2.3 GPa. Qualitatively, the nickel oxide

is prevented from contracting by the silicon, and therefore is in biaxial tension after

cooling.

8.3.2 Cracking to Relieve Stress

Here it is shown that the expected thermal stress in the NiO film exceeded the NiO

fracture toughness, cracking the film. In addition, it is shown that this cracking1The designation ‘Mode I’ is used when stresses are normal to the crack.


mechanism predicts the observed crack spacing. The argument is presented in two

steps.

The critical stress for film cracking is σc =√

2/π (KIc/√h); a stress exceeding

σc is expected to crack the film. The particular film thickness h=400 nm=0.4 µm

will be used throughout this chapter. For this film, σc = 1.5 GPa, so the expected

thermal stress of 2.3 GPa is sufficient to crack the NiO film.

Next the analysis in Ref. [107] is employed to decide if cracking due to thermal

stress predicts the observed crack spacing. For the analysis to apply, the relationship

ENiOε20h/Γf ≥ 0.5 must hold. It is necessary to determine the component of film

strain normal to the crack, ε0, which here is the strain ε11 = ε22 resulting from the

biaxial thermal stress. This quantity, and in addition ε33, are determined via Hooke’s

Law:

ε11(22) =σ11(22)

ENiO− νNiO

ENiO(σ22(11) + σ33)

ε33 =σ33

ENiO− νNiO

ENiO(σ11 + σ22). (8.1)

The component σ33, the out-of-plane stress, is zero, and the cross components σa 6=b

are zero for pure biaxial stress. For σ11 and σ22 the thermally-induced stress of +2.3

GPa is used. The expected in-plane strains are found to be ε11, ε22 = +0.0082. The

expected out-of-plane strain is ε33=-0.0077. (The signs of these two quantities signify

that the film is in tension in-plane and compression out-of-plane, as expected.) Next

the Mode I fracture resistance Γf = K2Ic/ENiO is calculated; the result Γf=7.5 Pa m

is obtained. With ε0 = ε11,22 = 0.0082, the inequality above is 0.68 ≥ 0.5, so the

analysis of Ref. [107] is applicable here.

The equilibrium crack spacing λequil is determined by a compromise between the

strain energy relieved by cracking and the energy cost of the surfaces created. It is

found that λequil/h = 5.6√

Γf/(Eε20h). The resulting equilibrium crack spacing of

λequil=6.8 h, or 2.7 µm, is a lower bound, as it assumes that crack propagation is not

arrested by imperfections. In addition, the analysis assumes that the cracks occur

parallel to a single direction in the film, and that the elastic properties of the film are

identical to those of the substrate.


[In fact nickel oxide and silicon do not have identical elastic properties. In

Ref. [108], cracking of films bonded to substrates in considered, allowing for a differ-

ence in elastic properties, for the case of plane strain. The relative stiffnesses of the

film and substrate is represented by the parameter α. For identical elastic properties,

α=0; if the film is stiff relative to the substrate, α > 0; in the extreme case of an in-

finitely rigid film (or infinitely compliant substrate), α=1. Using the elastic constants

given above, the NiO/Si system is characterized by α ∼ 0.2, meaning that the NiO

film is somewhat stiff relative to the Si substrate. Given α, a value for the param-

eter g, which characterizes the energy released during cracking, is found. The value

obtained, g=1.46, is about 16% greater than g=1.26 which characterizes the identical-

elastic-properties situation. This means that cracks, once started, are somewhat more

likely to propagate across the film than in the identical-elastic-properties case. This

might be expected to assist the crack network in achieving the lower-bound crack

spacing (2.7 µm) given above. Modification of the plane strain argument of Ref. [108]

to suit the plane stress situation of this chapter is beyond the scope of this thesis.]

Figure 8.4 shows that the estimated crack spacing of 2.7 µm is in good agreement

with the observed spacing of 2–4 µm, or 5–10 times the film thickness.

This section departed from the chapter’s main argument to consider a plausible ex-

planation of the cracking and the crack spacing. It was found that the cracking shown

in the right-hand image of Fig. 8.4 can be satisfactorily explained as a consquence

of the stresses induced by the anneal and cool. The left-hand image of Fig. 8.4, the

antiferromagnetic structure of the NiO films, has yet to be explained. One result of

Sec. 8.3.2 is used below: the critical stress for cracking of 1.5 GPa. In addition, the

observed crack spacing of 2–4 µm is used.

8.3.3 Island Stress Profile and Resulting Strain

Experiments[109, 110] indicate that cracking does not relieve all film stress, and mod-

els predict that the residual strain profile is inhomogeneous. This section estimates

the residual strain profile in the NiO islands. The technical importance of silicon

substrates has motivated an extensive literature on substrate stress caused by an


overlayer. An early work[111] derives (in addition to the substrate stresses) the over-

layer stress profile by a relatively simple analysis, which will be employed here.

Estimation of the Residual Stress Profile

Reference [111] determines stresses in a silicon substrate resulting from an overlayer.

A ‘built-in’ stress σ0 in a cracked film (the overlayer) is modified by interaction with

the substrate. If the film is compliant relative to the substrate, the resulting film

stress profile rises rapidly with increasing distance from the crack. If the film is stiff

relative to the substrate, interaction with the substrate spreads out the film stress

profile. The parameter characterizing the NiO film/Si substrate stiffness relationship

in Ref. [111] isK = ESi(1−ν2NiO)/ENiO(1−ν2

Si)=0.66. This value signifies that the NiO

film is somewhat stiff relative to the Si substrate. Assuming a lateral island dimension

of ∼3 µm=7.5h, the resulting film stress profile is estimated by interpolating by eye

between the curves calculated for K = 1 and K = 0.2 in Figure 3 of Ref. [111]. It is

found that the maximum residual stress at the center of the island is ∼0.65 σ0, where

σ0 = σc=1.5 GPa, the critical stress for cracking. The resulting residual stress at the

island center is ∼1 GPa. The stress increases from zero at the crack to ∼0.45 σ0, or

∼0.7 GPa, at a distance of 0.5 µm ≈ h (the bright/dark boundary) from the crack.

The estimated stress profile is depicted in Fig. 8.6.

More sophisticated treatments of the substrate-overlayer stress relationship are

found in Refs. [112, 113, 114, 108].

Resulting Strains in an Island of NiO

The values for the stress at three (lateral) locations are particularly important: in the

center of the island (σ=1 GPa), at the bright/dark boundary (σ=0.7 GPa), and at the

crack (σ=0). The strains resulting from these stresses, determined via Eqs. 8.1, are

displayed in Table 8.1. At this point the lateral residual stress profile in the annealed

polycrystalline NiO film, and the resulting strains, have been determined. It remains

to consider the consequences for the NiO spin axis orientation.


island dimension 3 mµ

film thickness 0.4 mµ

bright regionwidth 1 mµ

1.0

0.5

in-plane stress(GPa)

severalgrains

1 GPa

0.7 GPa

Figure 8.6: Estimated in-plane residual thermal stress in an island of NiO. The stressis 1 GPa at the center of the island and diminishes to zero at the crack. At theboundary between the bright and dark regions in the AF image (Fig. 8.4, left image),the in-plane stress is approximately 0.7 GPa.

8.4 Relationship between Antiferromagnetic

Ordering and Strain

The connection between magnetic spin axis orientation and dimension changes is

given by the magnetostriction constant λsi, which measures the change in dimen-

sion when the specimen is brought from the ideal unmagnetized state to magnetic

saturation[115]. For a cubic substance, λsi is a function of the orientation of the spin

axis, the orientation of the strain, and the magnetostriction constants λ111 and λ100.

The latter two quantities relate a magnetization orientation along 〈111〉 (〈100〉) to a

strain applied along 〈111〉 (〈100〉). Since the NiO film considered here is polycrys-

talline, the relevant quantity is λsi, the spatially-averaged magnetostriction appropri-

ate for an isotropic polycrystalline sample, which is determined next.


lateral position σ ε11,22 ε33crack 0 0 0

boundary 0.7 GPa 0.0025 -0.0023island center 1 GPa 0.0036 -0.0034

Table 8.1: Residual strains in the NiO film at important lateral locations. Stresses σwere estimated as described in the text. Resulting strains ε from Eqs. 8.1. The word‘boundary’ refers to the lateral position of the boundary between the bright and darkregions of Fig. 8.4, left image.

8.4.1 Polycrystalline NiO Magnetostriction Constant

A value for the magnetostriction constant of NiO was not available2 and was deter-

mined as follows. In Ref. [46] a general expression for the magnetic anisotropy energy

and magnetoelastic energy of NiO is obtained. The magnetoelastic energy is written

in the customary fashion as

Eme = B1(exxα2 + eyyβ

2 + ezzγ2) +B2(exyαβ + eyzβγ + ezxγα)

where the direction cosines (α, β, γ) express the direction of the spin axis relative

to the (assumed cubic) basis vectors (a,b,c)=([100],[010],[001]), the strain compo-

nents eij express the lattice deformation, and B1, B2 are the magnetoelastic coupling

constants[118]. However, given the magnetic structure of NiO (Chapter 3) it is sim-

pler to calculate the energies in the basis (a′,b′,c′)=([112],[110],[111]). The coeffi-

cients of the magnetoelastic energy in the primed basis are A′1 = 6.9 × 108 erg/cc,

A′4 = −3.0 × 108 erg/cc, from which B1 = 2.2 × 109 erg/cc, B2 = 9.6 × 108 erg/cc are

obtained[46]. Then the magnetostriction constants can be determined via[118]

λ100 = −23

B1

c11 − c12,

λ111 = −13B2

c44.

2Refs. [116] and [117] measure the strain in NiO as a function of large external field. Thisphenomenon is properly termed forced magnetostriction[115].


The results are λ100 = −1.0 × 10−3, λ111 = −0.30 × 10−3. The next task is to form

the average quantity λsi. Assuming that the true situation is intermediate between

uniform stress and uniform strain3, the appropriate expression is[119]

λsi = λ111 + (25

− ln c8

)(λ100 − λ111),

where c = 2c44/(c11 − c12). Via the elastic compliances given in Sec. 8.3, the result is

λsi = −5.5 × 10−4.

The above results are significantly larger than commonly-encountered magne-

tostriction constants. For example, λ111 and λ100 for iron and nickel metal are of

order 10−5, one-tenth to one-hundredth of the values derived above for NiO. How-

ever, the experimentally-obtained magnetostriction constant of polycrystalline cobalt

ferrite (λsi = −1.1 × 10−4) is of the same order of magnitude as the calculated nickel

oxide value. This unusually large value is a consequence of the large spontaneous

distortion (cubic to tetragonal) of the cobalt ferrite unit cell upon magnetic order-

ing. Since NiO experiences a similar distortion (from cubic to rhombohedral, see

Chapter 3), NiO magnetostriction constants similar to those of cobalt ferrite are not

unreasonable.

8.4.2 Explanation of Linear Dichroism Images

As mentioned above, λsi measures the change in dimension when a specimen is

brought from the ideal demagnetized state to saturation. This is a tolerable de-

scription of our situation: the NiO film was demagnetized during the anneal, and the

sublattice magnetization has reached over 90% of the saturation magnetization at

room temperature. Therefore λsi measures the change in dimension of the polycrys-

talline NiO film along an axis when the magnetization goes from zero to saturation

along that axis. Its negative value implies that the crystal will contract along the

magnetization axis, as sketched in Fig. 8.7. Furthermore, it explains the out-of-plane

spin axis orientation at the center of the NiO islands considered in this chapter. At

the island center, there is significant out-of-plane compression and in-plane tension,3Assuming uniform strain yields λsi = −5.8 × 10−4


surface plane

surface normal

Figure 8.7: Schematic representation of the magnetostriction of polycrystalline NiO.Compression along the surface normal coupled with in-plane tension (red arrows)distorts the unstrained spherical grain (dashed) into a flattened ellipse (solid). Sincethe magnetostriction constant is negative, the spin axis (blue double arrow) orientsperpendicular to the plane. This is what is observed at the island interior, where thecompression and tension are relatively large.

and the negative magnetostriction constant dictates that the spin axis parallels the

compression axis.

[Similarly, the negative values obtained above for λ111 and λ100 are in accord

with the observed spin axis orientation of epitaxial NiO films. NiO(100) (lattice

constant 4.18 A) grown epitaxially on MgO(100) (lattice constant 4.21 A) may be

expected to be under out-of-plane compression and in-plane tension, and in fact this

has been verified by x-ray diffraction experiments[120]. Therefore the spin axis would

be expected to be out-of-plane, as has been observered[67, 55, 1]. Conversely, the

spin axis is in the sample plane4 for NiO(100) films on Ag(100) (lattice parameter

4.09 A), which may be expected to be under in-plane compressive stress.]

This argument can be quantified using the entries in Table 8.1. Reverse the

causal arrow and assume that a NiO film will orient its magnetization parallel to a

(compressive) strain of at least −5.5×10−4. Clearly this situation obtains at the island

center, where ε33=-0.0034. At the boundary between the bright and dark regions,

ε33=-0.0023, which is still much larger than the threshhold strain for magnetization4Wei Zhu, private communication.


reorientation λsi = −5.5 × 10−4. At the crack, of course, ε33=0.

Far from the crack, the local strain model predicts that the NiO spin axis will

be oriented out of plane, as observed. Within the bright region, but away from the

crack, the model still predicts an out-of-plane spin axis, contrary to observation.

However, it might be expected that the argument developed in this chapter would

fail near the crack, since two assumptions do not hold there. First, the bright region

contains only a few grains (and therefore only a few crystal orientations), so it is

unrealistic to expect that the NiO can be modeled as an isotropic material. Second,

a region consisting of a few discrete grains cannot be described with a continuum

stress model. Description of this region requires knowledge of the local strain and

local crystallographic orientations, so that the appropriate λsi can be calculated and

applied.

8.5 Conclusion

In this chapter, the NiO antiferromagnetic spin orientation has been explained as

a consequence of the inhomogeneous stresses and strains generated from annealing,

cooling, and cracking. The explanation applies to the majority of the film, where

there is an out-of-plane compressive strain sufficient to orient the NiO spin axis per-

pendicular to the film plane. Description of the regions near the cracks will require

spatially-resolved crystallographic and strain information.

Chapter 9

Conclusion

This thesis describes important new results in the investigation of magnetic mate-

rials via x-ray absorption spectroscopy and microscopy techniques. The significance

of the major discovery, the existence of interfacial oxidation/reduction reactions at

metal/oxide interfaces described in Chapter 6, has already been demonstrated: a

recent investigation[89] of cleaved NiO/Co has mapped the domain structure of the

reduced-NiO region at the NiO/Co interface. This interfacial region may well be the

source of the uncompensated interfacial spins at the heart of exchange anisotropy.

The results of Chapter 7, while groundbreaking, have (happily) already been super-

seded by the long-awaited imaging of antiferromagnetic domains by our group and

others[76, 74, 121, 79]. It is a good bet that x-ray absorption spectroscopy and

microscopy will soon yield further discoveries in the imaging of antiferromagnetic

domains and exchange anisotropy.

Here two other aspects of this work will be discussed—the results of Chapter 8,

and an issue relating to dealing with XAS standard spectra and spectral analysis

apparent from Chapter 6.

It is hoped that the results of Chapter 8 will inspire the collaboration of spatially-

resolved techniques of imaging magnetic microstructure and local strain. The new

technique of x-ray microdiffraction offers the ability to obtain spatially-resolved crys-

tallographic orientation and strain information. Given the x-ray intensity available

at synchrotrons and powerful analysis software, the orientation of individual grains,

122

CHAPTER 9. CONCLUSION 123

and the strain state of these grains, is extracted from the diffraction pattern. In

combination with x-ray absorption spectromicroscopy, the local strain state could

be correlated to the local spin axis orientation. If the x-ray microdiffraction exper-

iment were performed on cracked epitaxial films, where only one crystal orientation

is seen, the task of identifying the local strain would be much simplified. The x-ray

microdiffraction technique is currently in development stages[122].

A preliminary XMLD spectroscopy (not microscopy) experiment would directly

measure the response of the NiO (or other suitable material) spin axis orientation to

applied stresses. This experiment would require a sample stage capable of applying

(and reporting) stresses to a substrate in the spectroscopy chamber, under UHV

conditions.

Chapter 6 describe the normalization and analysis of XAS spectra. These tasks

require (a) standard spectra, (b) accepted methods of normalization, and (c) computer

codes to perform the normalization and analysis. Unfortunately, none of the above

were readily available. Chapter 6 describes, for example, construction of the required

absorption spectra (which were not available) from total-electron-yield spectra. It is

desirable for the convenience of XAS as an experimental tool to keep pace with its

increasing applicability.

To this end, the author proposes that easily-accessed libraries of standard spectra

(both absorption spectra and total-electron-yield spectra) and analysis routines be

established. This would free future researchers (many of whom will be from outside

the synchrotron community, and unfamiliar with these issues) to concentrate on their

results rather than on data analysis.

Appendix A

XAS Spectrum Normalization and

Fitting Routines

A.1 Introduction

The XAS spectrum normalization and analysis routines employed in Chapter 6 are

presented and described in this appendix. Physical assumptions inherent in the rou-

tines are highlighted. Section A.2 describes the XAS spectrum normalization routine.

Section A.3 describes the simulation and fitting routine, emphasizing the connection

to the experiment of Chapter 6. Section A.4 provides tables summarizing both rou-

tines and displays the code. In Sec. A.5, functions called by the routines are presented

and described.

The routines are coded in Matlab. Matlab variables are arrays: a scalar variable

is a 1× 1 array; a vector variable is a 1×N (or N× 1) array. A text string is an array

of characters. The code represents an XAS spectrum as two (vector) variables, one

for the abscissae (the energy points) and one for the ordinates (the XAS intensities).

Arrays of the same dimension can be combined element-by-element with the operators

+, - . Matrix multiplication and division are performed on arrays of compatible

dimensions with the operators * and /. The operators .*, ./ perform element-by-

element multiplication/division on arrays of (any) identical dimension. The operator

ˆ raises a (square) array to a power; the operator .ˆ raises each element of an array

124

APPENDIX A. NORMALIZATION AND FITTING ROUTINES 125

(of any dimension) to a power. Matlab ignores lines beginning with %.

Routines to import the original data into Matlab are specific to the software of

the particular beamline and are therefore not included. The code is presented as it

was used, except that, to fit thesis formatting, lines that extended beyond the right

margin were broken. The continued line begins with LINE.

A.2 XAS Spectrum Normalization

Routine sssa removes a linear background from the spectrum, scales the integrated

absorption area to 100 units, and sets the spectrum to a standard energy profile

appropriate for the absorption edge. The inputs are the spectrum to be normalized

(abscissae and ordinates) and pure metal and oxide standard spectra. The output is

the normalized ordinates, which are paired with the standard abscissae to yield the

normalized spectrum.

A.2.1 Element-Specific Information

The routine first selects the appropriate element-specific information via the variable

WHICH_ELEMENT. The variable bounds contains energy values to use as boundaries

for the pre-edge linear fit and the area normalization. For iron and cobalt, the user

may select (in the code) a modified bounds to avoid the following cobalt and nickel

absorptions, respectively, which should not be included in the edge-area calculation.

[If our nickel-containing samples had contained in addition copper (for example) a

modified bounds would have been required for nickel as well.]

The routine finds the energy of the L2 maximum within the energy range L2_region.

A range of 10 or 15 eV should easily account for normal beamline calibration errors.

The L2_region variable is used for iron and cobalt compounds, all of which are as-

sumed to have a well-defined L2 maximum. This variable is not used, however, for

nickel oxide, because either of the two L2 peaks can be higher depending on mag-

netic linear dichroism effects. Therefore the NiO L2 lower-energy peak is determined

manually, later in the program.


The abscissae of all normalized spectra are referenced to the results of Chen et

al. [81] from transmission experiments on pure metal films. Specification of two

energies (L3 and L2 maxima) determines the correct energy scale and dispersion.

The appropriate standard abscissae are contained in the variables en_XX_std, where

XX=fe, co, or ni.

A.2.2 The Standard Energy Profile

Setting the spectrum to the standard abscissae requires several steps. First a correct

energy scale must be constructed.

Correct energy scales for the pure metals are taken from Ref. [81] as mentioned

above. The correct energy scale for the spectrum to be normalized is determined as

follows. The original energy scale is shifted and stretched such that the L3 and L2

maxima (or the lower-energy NiO L2 peak) have the correct energies. The correct L3

maximum is determined by the fast scans mentioned in Chapter 6, which established

the energy difference between the L3 maximum of the substance under consideration

and that of a pure metal standard sample. Fast scans to determine the correct L2

peak relationships were not performed. It was assumed that the (energies of the)

L2 maxima of different phases of a given element coincide. (In the case of NiO, it

was assumed that the lower-energy oxide peak is at the same energy as the metal L2

peak.) This was true to within the variance in energy calibration of our beamline,

∼1 eV, but experimental confirmation is clearly desirable.

Once a correct energy scale, temp_energy, has been determined, the spectrum

ordinates are splined to the standard energy profile (standard abscissae). Though

this step is not necessary—it does not modify a plot of the spectrum, for example—

it greatly facilitates comparison or combination of two spectra. Matlab’s ‘spline’

command performs cubic spline interpolation.

A.2.3 Background Subtraction and Area Normalization

Routine sssa performs two simple normalization tasks.

The line that best fits the pre-L3-region of the spectrum is subtracted. This is the


simplest method of removing the EXAFS (extended x-ray absorption fine structure)

of any preceding (lower-energy) absorptions. Unfortunately, only the farthest EXAFS

(at least 200 eV above the absorption edge) is close to linear and can be removed by

this simple procedure. Given the proximity of the absorption edges of the constituents

of our multicomponent samples (e. g. the cobalt absorption is only 70 eV below the

nickel absorption) the pre-edge region of our spectra (which is the EXAFS of preceding

edges) was in general not linear. As a quick method of partially compensating for this

difficulty, a optional second linear subtraction was performed. A line with fulcrum just

prior to the L3 maximum was subtracted, tilting the spectrum. This step, combined

with the area normalization, was used to locate the ordinate of the L2 maximum of

the normalized spectrum at a reasonable position with respect to the L2 maxima of

the pure metal and oxide standard spectra.

The area of the entire absorption edge, from just before the L3 absorption to as

far above the edge as possible, was arbitrarily set to 100 units. As discussed in Ch. 6,

division by total edge area results in a ‘per atom’ spectrum that can be compared to

similarly-normalized spectra of the same absorption edge.

A.3 Two-Layer XAS Spectrum Simulation and Fit-

ting

Routine tlfit constructs model bilayers, calculates the electron-yield XAS spec-

trum of each, and finds the model sample which best fits an experimentally-obtained

spectrum. The model bilayers are of the form metal layer atop oxide layer. The

experimental spectrum must have been normalized in the fashion of routine sssa.

A.3.1 Relation to Oxidation/Reduction Experiment

Figure A.1 shows that the experiment described in Chapter 6 required only one model

bilayer template: metal region atop oxide region. Drawing (a) shows a nominal

sample structure, specifically the ex-situ-grown sample MgO(001)/NiO (10 A)/Co

(10 A)/Ru (20 A). Two XAS spectra (cobalt and nickel L edges) of this sample were


lower: NiO (? Å)

upper: Ni (? Å)NiO (10 Å)

MgO(001)

MgO(001)

lower: CoO (? Å)

(a) (b)

upper: Co (? Å)

Co (10 Å)

Ru

Ru

{{

Figure A.1: Relation of sample structureinvestigated in Chapter 6 to model bilayersemployed in routine tlfit. Drawing (a):typical nominal sample structure. Drawing(b): Sample structure assumed after ox-idation/reduction reaction at metal/oxide(in this case Co/NiO) interface. Portionsof the sample are separated to empha-size that their spectra are studied indepen-dently. Routine tlfit replaces ‘? A’ withthe thicknesses that best reproduce the ex-perimental spectrum.

acquired. Though the sample nominally contained pure cobalt metal and pure nickel

oxide, each of the two spectra resembled a mixed spectrum (either Co + CoO or

Ni+NiO), and quantification of the mixture was desired. Model bilayers resulting

from the assumed interfacial oxidation/reduction reaction and used by routine tlfit

are shown in drawing (b). Note that each of the two (cobalt-containing and nickel-

containing) bilayers fits the metal-atop-oxide template. The sample is broken into

four pieces to emphasize that the routine considers only either the cobalt-containing

bilayer or the nickel-containing bilayer. The effects of the other three pieces are

assumed to be removed by the normalization procedure. For example, analysis of

the cobalt-containing regions of the sample uses a Co/CoO model bilayer in routine

tlfit; effects of the MgO, Ru, and Ni-containing regions are assumed to have been

removed in the normalization routine sssa. The designations ‘upper’ and ‘lower’

are a reminder that the electron-yield spectrum of the bilayer is affected by the

relative depths of the layers. Routine tlfit finds the thicknesses of oxide and metal

that best reproduce the experimentally-obtained spectrum. Drawing (b) qualitatively

represents the increase of nominally-metal (Co) layer thickness, and the decrease of

nominally-oxide (NiO) layer thickness, resulting from oxygen transfer.


A.3.2 Element-Specific Information

As for normalization routine sssa, element-specific information is built into routine

tlfit.

The element (Fe, Co, or Ni) is chosen via the variable WHICH_ELEMENT. As was

mentioned in Chapter 6, the absorption coefficient spectra and electron escape depths

are not well established, therefore different versions/values were used to estimate the

effect on the results. In the case of nickel, for example, there are several choices for

the variable mu2, the NiO standard absorption spectrum. Since calculation of the

absorption coefficient spectra required a value for the electron escape depth (Chapter

6), a particular line of code specifies both the absorption spectrum mu2 and corre-

sponding electron escape depth le2a. (Note that it is important to keep straight

whether thicknesses, electron escape depths, and absorption coefficient spectra are

given in Angstroms or microns. In routine tlfit, these parameters are entered in

the code as Angstroms and converted to microns for calculations. The standard ab-

sorption spectra are in units of µm−1 as is customary.) The only choice for mu1, the

metal standard absorption coefficient spectrum, is that from Ref. [81]. (Exploring the

effects of different escape depths for iron metal necessitated the calculation of slightly-

modified iron metal standard absorption spectra.) The electron escape depths (le1a

and le2a) given in the routine are referenced in Chapter 6.

Densities and molecular weights of the metals and oxides are included in the

element-specific information. In the case of iron, the user must manually choose a

particular oxide of iron in the code. [Note: although element-specific data is provide

for three common oxides of iron, the code displayed here only works for the monoxide

FeO. As is noted in Chapter 6, the amounts of higher oxides present in our samples

were manually estimated from the peak shape, without recourse to routine tlfit. To

employ the higher oxides of iron, the fraction (1/1) (appropriate for a monoxide) in

the line

oxtomet=(rho_ox/mw_ox)*(1/1)*(mw_met/rho_met);

must be replaced by a fraction expressing the stoichiometry of the particular oxide.

The fractions (3/4), for Fe3O4, and (2/3), for Fe2O3, are appropriate for the line of


code above.]

The variable bounds is used in normalization of simulated two-layer spectra for

comparison to the (normalized) experimental spectrum. The program calculates the

entire simulated spectrum, but establishes a goodness of fit for only a smaller energy

region: the L3 absorption, the L2 absorption, both absorptions, or the region between

the two absorptions. The desired fitting region (variable fit_region) is chosen via

the variable fr prior to running the program.

A.3.3 Application to Nominally-Metal and Nominally-Oxide

Cases

The spectrum-simulation function mutotey (described in Sec. A.5) requires the layer

thicknesses t1,t2 of the model bilayer. These thicknesses are determined as follows.

The nominally-pure layer is conceptually divided into two regions, the region to be

changed (either oxidized or reduced) by the interfacial reaction, and the region which

will remain unchanged. (The sum of these regions’ thicknesses is the thickness of

the nominally-pure layer, tnoma.) The thickness ttbc of the region-to-be-changed

is multiplied by the factor oxtomet (in the case of reduction) or mettoox (in the

case of oxidation) to find its thickness after the interfacial reaction. The routine

determines which of the two (changed and unchanged) regions is the upper, and

which the lower, layer of the resulting bilayer, via the variable WHICH_MODIFIED. The

upper layer thickness is assigned to the variable t1 and the lower layer thickness is

assigned to the variable t2.

For example, suppose it is desired to analyze the cobalt-edge spectrum of the sam-

ple MgO substrate/NiO (10 A)/Co (10 A)/Ru cap (20 A). The upper (closest to Ru)

portions of cobalt remain metallic; the lower portions are oxidized to CoO by the adja-

cent NiO layer. The variable WHICH_MODIFIED is set to bot to signify that the changed

(in this case, oxidized) region of the nominally-pure-metal layer will be the bottom

layer of the model structure. The thickness of this bottom layer is t2=ttbc*mettoox,

and the thickness of the upper (unchanged) region is t1=tnom-ttbc.

The above discussion implies that one model bilayer, created from a single pair


of thicknesses (t1,t2), is employed by routine tlfit. Actually spectra from a num-

ber numt of model bilayers are simulated. Variable ttbc is a 1 × numt array, from

which the (also 1 × numt) arrays t1 and t2 are determined. The for i=1:numt loop

steps through the numt thickness pairs (t1(i),t2(i)), creating a model bilayer and

simulating the bilayer’s spectrum for each pair, as described in the next section.

A.3.4 Simulation, Fitting, and Identifying the Best Fit

The heart of routine tlfit is the for i=1:numt loop which simulates and normalizes

the electron-yield spectrum of each model bilayer, and compares this spectrum to the

(normalized) experimentally-obtained spectrum. The electron-yield spectrum sim-

ulation is performed by function mutotey. The normalization process—pre-edge

line subtraction and area normalization—is described in Sec. A.2. The simulated

spectrum and the experimental spectrum are compared as follows. The difference

spectrum ordinates are calculated; this can be done by simple subtraction because

the spectra have been set to the same energy profile. Each ordinate is squared. These

squares are summed in the specified fit region, and this sum is divided by the number

of points in the fit region to get a ‘goodness of fit’ for each simulated spectrum.

After completion of the for loop, the model spectrum with the best ‘goodness

of fit’ is identified as the best-fitting spectrum. This spectrum is recalculated and

normalized. The routine reports, in addition to other information, the variable

best_thicks. This variable contains three thicknesses: the thickness ttbc(b) of the

region-to-be-changed, and the resulting thicknesses t1(b) (metal) and t2(b) (oxide),

of the best-fitting model bilayer, all in Angstroms. The data tables of Chapter 6

display only one thickness: either the thickness of metal that will be oxidized, or the

thickness of metal resulting from oxide reduction. In analysis of a nominally-metal

layer, such as the cobalt layer of the example of the previous section, the thickness

ttbc(b) is the tabulated value. In analysis of a nominally-oxide layer, the thickness

t1(b) is tabulated.


A.4 Main Routine Summary and Code

Table A.1 summarizes information pertaining to sssa. The code is displayed following

the table.

Functions Called areanorm,linesub, addaslopeVariables in Memory original spectrum (en_orig,data_orig); total-yield

equivalents of metal and oxide standard spectra(data1_int,data2_int,en_XX_std)

Choose Manually normalization boundary energies (bounds)Choose Global elemental region to be analyzed (WHICH_ELEMENT)Choose Prompt L3 shift from pure metal (shift_L3); optional slope

(routine addaslope); for Ni, click on lower-energy L2

peakOutput normalized ordinates (data_new)

Table A.1: Summary information for normalization routine sssa.

%%%%% sssa %%%%%

%original name ssa_all

% sssa: shifts, splines,slopes, renormalizes to area

% uses functions linesub, areanorm, addaslope and

% (global) WHICH_ELEMENT

% must type "global WHICH_ELEMENT; WHICH_ELEMENT=Fe or Co or Ni"

% upon first running this program

% note: spline doesn’t work if en_orig doesn’t start close to 730

% or end close to 900

%%% data in memory

% en_orig (the energy profile)

% data_orig

% data1_int & data2_int, the standards (just for some plots)

%%% returns

% data_new


help sssa;

global WHICH_ELEMENT;

%%% Begin element-specific information

if WHICH_ELEMENT==’Fe’%% Iron Edge Scan

%bounds=[670 695 734 800];

bounds=[670 695 734 770]; % avoid cobalt region

% to avoid fluorine contamination see ’addaslope’ call below

L2_region=[715 725];

metal_L3_en=707.36; % for fe metal via CTC

metal_L2_en=720.46;

metal_delta=metal_L2_en-metal_L3_en;

ens=en_fe_std;

elseif WHICH_ELEMENT==’Co’%% Cobalt Edge Scan

bounds=[730 770 810 900];

%bounds=[730 770 810 840];

% 840 eV is to avoid the nickel edge

%bounds=[760 770 810 840];

% for very old scans, but then spline screws up

L2_region=[785 800];

metal_L3_en=777.72; % for Co metal via CTC

metal_L2_en=793.11;


ens=en_co_std;

elseif WHICH_ELEMENT==’Ni’%% Nickel Edge Scan

bounds=[801 840 876 950];

L2_region=[870 871]; %we don’t do it this way for nickel

metal_L3_en=852.85; % for nickel metal via CTC

metal_L2_en=870.66;


ens=en_ni_std;

else

fprintf(’Your entry was wrong!\n’);

% should stop execution


end;

%%% will use WHICH_ELEMENT again below

%%% End element-specific information

%%% Determine indices corresponding to bounds energies

% This time, original energy; below, standard energy profile

for i=1:length(bounds)

d=en_orig-bounds(i);

[a b]=min(abs(d));

bound_index(i)=b;

end;

bound_index_orig=bound_index; % save just in case

%%%

data_in=data_orig;

% make it more modular by using fewer intermediate vars

%%% Subtract pre-edge line from unknown

[data_out,lineparams]=linesub(en_orig,data_in,

LINE bound_index(1),bound_index(2));

%data_out=addaslope(ens,data_in,685);

% this is to avoid fluorine with iron scans (also below)

data_in=data_out;

data_linsub=data_out;

%%% Spline unknown data to standard energy profile

% (here, en_xx_std)

%% L3 shift: want unknown L3 = metal L3 + desired L3 ABBA shift

plot(ens,data1_int,’b’,ens,data2_int,’g’,en_orig,data_in,’r’);

shift_L3=input(’Enter the desired L3 shift from metal L3 (eV): ’);

%% need this info to construct the temporary energy

[current_L3_height b]=max(data_in(bound_index(2):bound_index(3)));

%should be L3 peak, save height for later


current_L3_ind=-1 + b + bound_index(2);

current_L3_en=en_orig(current_L3_ind);

%% Find L2 max and calculate L2 shift. Element-specific methods!

if WHICH_ELEMENT==’Ni’ % nickel

plot(en_orig, data_in,’b’);

axis([869 873 0 current_L3_height/3]);

fprintf(’click on first (leftmost) unknown L2 peak (blue)\n’);

[current_L2_en a]=ginput;

else % iron or cobalt

for i=1:length(L2_region)

d=en_orig-L2_region(i);

[a b]=min(abs(d));

L2_region_index(i)=b;

end;

[a b]=max(data_in(L2_region_index(1):L2_region_index(2)));

current_L2_ind= -1 + b + L2_region_index(1);

current_L2_en=en_orig(current_L2_ind);

end

shift_L2=metal_L2_en-current_L2_en;

%% L2 shifts calculated

%% temporary energy scale

current_delta=current_L2_en-current_L3_en;

desired_delta=metal_delta-shift_L3; % desired L2s coincide

temp_energy=(metal_L3_en+shift_L3)+(desired_delta/current_delta)*

LINE (en_orig-current_L3_en);

%% current L3 & L2 should be in desired (temp_energy) positions

%% spline so unknown & standards share the same energy profile

data_out=spline(temp_energy, data_in,ens);

%% now set to standard energy profile

%% recalculate boundary energies using standard energies


d=ens-bounds(i);

[a b]=min(abs(d));


bound_index(i)=b;

end;

%%% End splining

data_in=data_out;

plot(ens,data1_int,’b’,ens,data2_int,’g’,ens,data_in,’r’,

LINE en_orig,data_orig,’k’);

%%% Add a slope

data_out=addaslope(ens,data_in,bounds(2));

%data_out=addaslope(ens,data_in,685);

% this is to avoid fluorine with iron scans (also above)

data_in=data_out;

%%% Recalculate area and divide by it

[data_out,edgearea]=areanorm(ens,data_in,bounds(2),bounds(4));

data_new=data_out;

plot(ens,data1_int,’b’,ens,data2_int,’g’,ens,data_new,’r’,

LINE en_orig,data_orig,’k’);

fprintf(’To process the output data, type en_orig=ens;

LINE data_orig=data_new then rerun sssa\n’);


Table A.2 summarizes information pertaining to routine tlfit. The code is dis-

played following the table.

Functions Called mutotey,areanorm,linesubVariables in Memory all standard absorption spectra; standard abscissae

(en_XX_std); spectrum to be fit (data_unk); fitting re-gion (fr)

Choose Manually metal and oxide standard absorption spectra (mu1 andmu2); associated electron escape depths (le1a,le2a);nominal layer thickness (tnoma); number of simulatedspectra (numt); reacting thickness range (via low_thickand delta_thick); iron oxide densities and molecularweights (must choose a specific oxide)

Choose Global elemental region to be analyzed (WHICH_ELEMENT);position of reacting region of the nominal layer(WHICH_MODIFIED)

Choose Prompt noneOutput thickness of region-to-be-changed, metal thickness, and

oxide thickness of best-fit bilayer (best_thicks) andother information

Table A.2: Summary information for simulation and fitting routine tlfit.

%%%%% TLFIT %%%%%

%original name tey2c

%tlfit: calculates the electron-yield signal from a two-layer sample

% given the absorption spectrum, thickness, and electron escape depth

% of the layers

% uses functions mutotey, areanorm, and linesub

%chooses top-modified or bottom-modified with

% global variable WHICH_MODIFIED=’top’ or ’bot’

%chooses element with global variable

% WHICH_ELEMENT=’Fe’ or ’Co’ or ’Ni’

%must type "global WHICH_MODIFIED; WHICH_MODIFIED=’top’ or ’bot’ "


% and "global WHICH_ELEMENT; WHICH_ELEMENT=’Fe’ or ’Co’ or ’Ni’ "

% upon first running this program

%the two layers are the same element

%thickness and electron escape depth of each layer in program

%appropriate absorption spectra must be in memory

%unknown,normalized electron-yield spectrum must be in memory

% (data_unk)

%densities and molecular weights in program---

% must choose correct line of code

%note that the mus were created with a specific escape depth!

%sample structure:

% No Cap/(possible metal)/layer 1/layer 2/(possible oxide)

help tlfit;

global WHICH_MODIFIED; WHICH_ELEMENT;

%%%%% Get element-specific info

if WHICH_ELEMENT==’Ni’

mu1=ni_mu422; le1a=22; %Angstroms

%mu2=nio_mu230; le2a=30;

%mu2=nio30a_mu130; le2a=30; % 30 AA NiO standard

%mu2=nio30a_mu140; le2a=40; % 30 AA NiO, change elect.esc.depth

%mu2=nio30a_mu230; le2a=30; % overlay slope +10percent

%mu2=nio30a_mu330; le2a=30; % overlay slope -10percent

%mu2=nio5a_mu130; le2a=30; % 5 AA NiO standard, 0.40 eV shift

mu2=nio5ap30_mu130; le2a=30; % 5 AA NiO standard, 0.30 eV shift

%mu2=nio_mu240; le2a=40;

if fr==’L3’

fit_region=[850 856];

elseif fr==’L2’


elseif fr==’in’


else



end;

%fit_region=[840 874];

ens=en_ni_std;

rho_ox=6.67;mw_ox=74.69;mw_met=58.69;rho_met=8.9;

bounds=[801 840 876 950];

elseif WHICH_ELEMENT==’Co’

mu1=co_mu422; le1a=22;

mu2=coo_mu130; le2a=30;

if fr==’L3’


elseif fr==’L2’


elseif fr==’in’


else


end;

ens=en_co_std;

rho_ox=6.45;mw_ox=74.93;mw_met=58.93;rho_met=8.9;

bounds=[730 770 810 900];

%bounds=[730 770 810 840]; % avoids Ni edge

elseif WHICH_ELEMENT==’Fe’

%mu1=fe_mu210; le1a=10;

%mu1=fe_mu217; le1a=17;

mu1=fe_mu215; le1a=15;

mu2=feo_mu230; le2a=30;

%mu2=fe304_mu350; le2a=50;

%mu2=fe203_mu335; le2a=35;

ens=en_fe_std;

mw_met=55.85;rho_met=7.86;

rho_ox=5.7;mw_ox=71.85; % for FeO

%rho_ox=5.18;mw_ox=231.54; % for Fe3O4

%rho_ox=5.24;mw_ox=159.69; % for Fe2O3


if fr==’L3’


elseif fr==’L2’


elseif fr==’in’

fit_region=[];

else


end;

bounds=[670 695 734 800];

%bounds=[670 695 734 770]; % avoid Co edge

end;

%%%%% Use the element-specific info

oxtomet=(rho_ox/mw_ox)*(1/1)*(mw_met/rho_met);

% (1/1) reminds of monooxide assump

mettoox=1/oxtomet;


d=ens-bounds(i);

[a b]=min(abs(d));

bound_index(i)=b;

end;

[a b]=min(abs(ens-fit_region(1)));

low_fit_index=b;

[c d]=min(abs(ens-fit_region(2)));

high_fit_index=d;

%change electron escape depths to microns

le1=le1a/1e4;

le2=le2a/1e4;

%%%%%% done with element-specific info

G1=1; G2=1; I0=1; A0=1;

vars=[le1 le2 G1 G2 I0 A0];


% these are passed to the spectrum calc function mutotey.m

%%% make the vectors of test thicknesses

numt=41; % number of test spectra

varmat=ones(length(numt));

%tnoma=1e5; tnom=tnoma/1e4;

%10 microns; approximates infinite sample

tnoma=10; tnom=tnoma/1e4;

%nominal thickness (a scalar, Angstroms)

low_thick=0;

delta_thick=4;

high_thick=delta_thick+low_thick;

ttbc=1e-4*(low_thick:(delta_thick/(numt-1)):high_thick);

%thicknesses to be changed

if WHICH_MODIFIED==’top’

fprintf(’top-modified: reduction of nominally-oxide layer\n’);

t1=ttbc*oxtomet; % resulting thicknesses of changed layer

t2=tnom-ttbc; % thicknesses of remaining original material

elseif WHICH_MODIFIED==’bot’

fprintf(’bottom-modified: oxidation of nominally-metal layer\n’);


t2=ttbc*mettoox; % resulting thicknesses of changed layer

else

fprintf(’Wrong entry, assuming top-modified (nominally oxide)\n’);

t1=ttbc*oxtomet; % resulting thicknesses of changed layer


end;

for i=1:numt

%%% make the test absorption spectrum

sig=mutotey(t1(i),t2(i),mu1,mu2,vars);

%%% normalize the test spectrum


data_in=sig; en_orig=ens;

[data_out,lineparams]=linesub(en_orig,data_in,bound_index(1),

LINE bound_index(2));

data_in=data_out;


sig_norm=data_out;

%%% compare to unknown spectrum and record result

differ=data_unk-sig_norm;

diffsq=differ.ˆ2;

s1=sum(diffsq(low_fit_index:high_fit_index));

v1=s1/(high_fit_index-low_fit_index-1);

varmat(i)=v1;

end % done making & testing all thicknesses

%%% reconstruct the best-fitting spectrum

[a b]=min(varmat);

best_thicks=1e4*[ttbc(b) t1(b) t2(b)]; % Angstroms

best_fit_unnorm=mutotey(t1(b),t2(b),mu1,mu2,vars);

data_in=best_fit_unnorm; en_orig=ens;

[data_out,lineparams]=linesub(en_orig,data_in,bound_index(1),

LINE bound_index(2));

data_in=data_out;


best_fit_norm=data_out;

fprintf(’Fit region (eV): [%g\t%g], nominal thickness (AA):

LINE %2.2g\r’,fit_region(1),fit_region(2),tnoma)

fprintf(’Best thicks (AA): to-be-changed %1.2g,

LINE Resulting upper(metal) %1.2g, lower(oxide) %1.2g \r’,

LINE best_thicks(1),best_thicks(2),best_thicks(3));

fprintf(’Upper(metal) thickness percent %2.1f%% ’,

LINE ( 100*best_thicks(2)/(best_thicks(2)+best_thicks(3)) ) );

fprintf(’Lower(oxide) thickness percent %2.1f%%\r’,


LINE ( 100*best_thicks(3)/(best_thicks(2)+best_thicks(3)) ) );

plot(ens,data_unk,’b’,ens,best_fit_norm,’r’);

ang=setstr(hex2dec(’c5’));

A.5 Function Code

This section displays the functions called by routines sssa and tlfit.

Function mutotey calculates the total-electron-yield spectrum of a bilayer given

the absorption spectra, electron escape depths, parameter G, and thickness for each

layer, and incident x-ray beam parameters I0 and A0. Normal incidence is assumed.

The function notes which layer is on top by the designations ‘1’ and ’2’ for the various

quantities. The contribution of (lower) layer 2 to the spectrum is attenuated (by the

factor exp(arg1)) by (upper) layer 1. In standard mathematical notation,

sig1 is(

GNi(E)1+ 1

µNi(E) λNi

)(1 − e−tNi[µNi(E)+1/λNi]

), and

sig2 is e−tNi[µNi(E)+1/λNi]

(GNiO(E)

1+ 1µNiO(E) λNiO

)(1 − e−tNiO[µNiO(E)+1/λNiO]

)as is evident from comparison to Eq 6.4.

%%%%% MUTOTEY %%%%%

function y=mutotey(a1,a2,x1,x2,params)

% all inputs must be in microns (or inverse microns)

%a1, a2 thicknesses

%x1,x2 absorption spectra (so this function determines a full spectrum)

%params: escape depth 1, escape depth2, G1, G2, I0, A0

% layer 2 is beneath layer 1.

Gfact2=params(4)./(1+1./(params(2)*x2));

Gfact1=params(3)./(1+1./(params(1)*x1));

arg2=-a2*(x2+1/params(2));

arg1=-a1*(x1+1/params(1));

sig2=Gfact2.*exp(arg1).*(1-exp(arg2));


sig1=Gfact1.*(1-exp(arg1));

y=params(5)*params(6)*(sig1+sig2);

The following three functions perform simple normalization tasks. Function are-anorm normalizes the absorption edge to an integrated area of 100 units.

%%%%% AREANORM %%%%%

function [y,area_under]=areanorm(x,y_orig,a,b)

% a and b are energies of the area region

temp=x-a;

[c d]=min(abs(temp));

low_index=d;

temp=x-b;

[c d]=min(abs(temp));

high_index=d;

x_area=x(low_index:high_index);

y_area=y_orig(low_index:high_index);

area_under=trapz(x_area,y_area);

y=y_orig/area_under;

Function linesub subtracts a linear pre-edge from the spectrum. (For consis-tency with the other functions, this function should be rewritten to accept boundaryenergies, rather than boundary energy indices.)

%%%%% LINESUB %%%%%

function [y, theline]=linesub(x,y_orig,x1,x2);

% a and b are indices of the fit region

x_fit=x(x1:x2);

y_fit=y_orig(x1:x2);

theline=polyfit(x_fit,y_fit,1);

y=y_orig-(theline(2)+theline(1).*x);


Function addaslope adds an optional slope to the spectrum. The fulcrum of theslope is immediately prior to the L3 absorption.

%%%%% ADDASLOPE %%%%%

function y=addaslope(x,y_orig,a);

% adds a slope to the data

% a is the fulcrum of the slope, in eV

fprintf(’Post-edge value will change by approx delta-y\n’);

fprintf(’Fulcrum is %g\t eV\n’,a);

slope_input=input(’Enter delta-y: ’);

slope_line=(slope_input/100)*(x-a);

y=y_orig+slope_line;

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