MODERN TECHNIQUES FOR CHARACTERIZING MAGNETIC

MATERIALS

MODERN TECHNIQUES FOR CHARACTERIZING MAGNETIC

MATERIALS

Edited by

YIMEI ZHU

KLUWER ACADEMIC PUBLISHERS Boston / Dordrecht / London

Library of Congress Cataloging-in-Publication Data

A C.I.P. Catalogue record for this book is available from the Library of Congress.

Modern techniques for characterizing magnetic materials / edited by Yimei Zhu. p. cm

Includes bibliographical references and index. ISBN 1-4020-8007-7 (alk, paper) -- ISBN 0-387-23395-4 (e-book)

1. Magnetic materials-Analysis. 2. Magnetic materials -Microscopy. 3. Electrons - Scattering, I. Zhu, Yimei.

O 2005 Kluwer Academic Publishers All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

Printed in the United States of America. (BSDH)

9 8 7 6 5 4 3 2 1 SPIN 11052838

Authors

Rolf Allenspach IBM Research Riischlikon, Switzerland

Ernst Bauer Arizona State University Arizona, USA

Marco Beleggia Brookhaven National Laboratory New York, USA

Matthias Bode University of Hamburg Hamburg, Germany

Byoung-Chul Choi University of Victoria British Columbia, Canada

Dan Dahlberg University of Minnesota Minnesota, USA

Michael Fitzsimmons Los Alamos National Laboratory New Mexico, USA

Mark Freeman University of Alberta Edmonton, Alberta, Canada

Paul Fumagalli Free University of Berlin Berlin, Germany

Daniel Haskel Argonne National Laboratory Illinois, USA

Burkard Hillebrands Technical University of Kaiserslautern Kaiserslautern, Germany

Joachim Kohlbrecher Paul Schemer Institute Villigen, Switzerland

Jeffery B. Kortright Lawrence Berkeley National Laboratory California, USA

Alexander Krichevsky Naval Research Laboratory Washington, DC, USA

Andre Kubetzka University of Hamburg Hamburg, Germany

Jonathan C. Lang Argonne National Laboratory Illinois, USA

Seung-Hun Lee National Institute of Standards and Technology Maryland, USA

Charles E Majkrzak National Institute of Standards and Technology Maryland, USA

Oswald Pietzsch University of Hamburg Hamburg, Germany

Roger Proksch Asylum Research California, USA

George Srajer Argonne National Laboratory Illinois, USA

Elio Vescovo Brookhaven National Laboratory New York, USA

Werner Wagner Paul Schemer Institute Villigen, Switzerland

Roland Wiesendanger University of Hamburg Hamburg, Germany

Igor Zaliznyak Brookhaven National Laboratory New York, USA

Yimei Zhu Brookhaven National Laboratory New York, USA

Preface

Magnetism and magnetic phenomena surround us. Magnetic materials pervade our lives far beyond just compasses and common household magnets. Magnetic materials and magnetism are used inconspicuously in many complex gadgets, ranging from magnetic recording disks and cellular phones, to magnetic resonance imaging instruments and spintronic devices. Understanding magnetic phenomena and developing new functional magnetic materials pose a big challenge, but also great opportunities, to our scientists and engineers. New characterization techniques help us to understand the fascinating behavior of newly discovered magnetic materials, while new materials stimulate the further development of novel methods.

We understand the physical and chemical behaviors of materials through directly or indirectly measuring a material's structure and properties. The field of structural characterization is often too wide; identifLing the most appropriate method to employ can be difficult. One objective of this book is to introduce the reader to various modem techniques in characterizing magnetic materials at different length scales, focusing on neutron, x-ray, electron, and laser-light scattering as well as proximal probes, their principles, applicability, limitations, and relationship to competing methods.

Neutrons, photons, and electrons are three major classes of modern probes for characterizing structures of materials. Since all materials absorb and emit electromagnetic radiation, the material's characteristics frequently manifest in the way it interacts with incident particles. Thus, the information gleaned not only depends on the wavelength of the radiation, but also on the nature of these interactions. Neutrons interact with atomic nuclei, x-ray photons with electron clouds, and electrons with electromagnetic potentials, i.e., both electrons and nuclei of the solid. For magnetic structural characterization, both electrons and nuclei in materials have a magnetic moment and, in principle, all the three sources can reveal magnetic information. In particular, because the neutron has spin %, the orientation of its spin is easily manipulated and when combined with scattering geometry, it yields an opportunity to measure the spatial dependence of the vector magnetization. However, neutrons are not handily and copiously produced. In contrast, x-rays are easy to generate, but due to their weak spin interaction with matter, magnetic scattering can only be observed using extraordinarily intense synchrotron radiation.

The past two decades have witnessed significant advancement in instrumentation and technique development in characterization of magnetic materials, especially in proximal probes and laser- light scattering, along with the newly constructed next-generation neutron and synchrotron photon sources. In domain imaging, for example, an important branch of the field, we see an ever-increasing spatial resolution. There is a multiplicity of techniques, ranging from magneto- optical imaging to spin polarized scanning tunneling microscopy, that have different mechanisms of image formation and are suitable, hence, for different measurements. For instance, magneto- optic microscopy is based on the contrast produced by Kerr rotation of linearly polarized light reflected off domains with different magnetization. It has a typical spatial resolution of 500- lOOOnm (which can be much improved by near-field optical microscopy), but superior time resolution of up to 10-9 sec for dynamic observations. Magnetic force microscopy (MFM), on the other hand, measures the force that the stray magnetic field of the surface exerts on a tiny magnetic tip attached to a flexible cantilever. Unlike other methods, it is mainly sensitive to field gradients and its resolution is on the order of 40-100 nm. Scanning electron microscopy with

polarization analysis (SEMPA) measures the spin polarization of secondary electrons emitted from a magnetized sample with resolution of about 30-200 nm. Spin polarized low energy electron microscopy (SPLEEM) is a surface-imaging technique using spin polarized electrons, and is sensitive to the interaction between the spins of the incident electron and the spins in the sample. Thus, surface magnetic behavior can be directly observed over a large area of view in real time with a resolution of 20nm. High-energy transmission electron microscopy techniques push resolution even further. A remarkable example is electron holography which is based on retrieving the phase shift of a coherent electron wave passing though the sample as encoded in a hologram, and provides a direct measure of the electrostatic and magnetic potentials of a local area of interest. Although a few nm resolution can be routinely achieved, separating magnetostatic potentials from electrostatic ones at the nanoscale can be challenging. To date, the most promising technique for attaining atomic resolution of local magnetic structure is spin-polarized scanning tunneling microscopy (SP-STM) that can reveal the magnetic lattice arrangement on an antiferromagnetic sample surface. This new breed of scanning tunneling microscopy measures the spin-polarized tunneling electrons between the tip and the sample.

Of course, the techniques for magnetic imaging exemplified here are not meant to be inclusive, as several others are available, notably the recently developed technique of synchrotron-based x-ray magnetic microscopy, i.e., the x-ray magnetic circular dichroism (XMCD). This method probes the transfer of the angular momentum of the x-ray photon to the photoelectron excited from a spin-orbit split core level with a spatial resolution of about 5 nm. The main advantage of the technique is its elemental specificity that derives from the process being tied to an absorption event at the core level, thus providing information on the spin orbital moments, site symmetry, and chemical state of the sample under study, which is not available from the desktop- or laboratory-instruments mentioned earlier. It is important to realize that these techniques are complementary; they all have their own advantages and drawbacks. Some are highly penetrating and non-destructive probes, while others require a high-quality surface or tedious sample preparation. If you are interested in these technologies and would like to know more about them, you will find this book, Modem Techniques for Characterizing Magnetic Materials, an invaluable tool for expanding your research capabilities.

This book is organized in the following way. The first three chapters deal with neutron scattering methods, including triple-axis spectrometry, small-angle scattering, and reflectometry. Chapter 4-6 focus on synchrotron-radiation based techniques, ranging from magnetic soft and hard x- ray scattering to photon-emission spectroscopy. Chapter 7-9 discuss electron scattering, with transmission electron microscopy focusing on Lorentz microscopy, electron holography and other phase-retrieval methods, and scanning electron microscopy with spin polarized analysis and spin polarized low energy electron microscopy. Chapter 10 and 1 1 describe proximal probes, covering spin-polarized scanning tunneling microscopy and magnetic force microscopy. The last three chapters deal with light scattering including the use of monochromatic laser light in magnetic imaging, such as scanning near-field optical microscopy, time-resolved scanning Kerr microscopy, and Brillouin light-scattering spectroscopy.

This book does not attempt to cover all aspects of magnetic structural characterization, but focuses on major modem techniques. Owing to the complexity of magnetic behavior, to tackle one single material problem often necessitates bringing to bear various characterization tools within our arsenal of techniques. Usually, this is not a trivial task. Different research communities employ different research techniques and, often, there is little communication between them. It is my hope that this book will bridge this gap, and make the combined use of various techniques in materials research a reality.

Although this book leans more toward the research laboratory than the classroom, it can serve as a methodological reference book for graduate students, university faculties, scientists and engineers who are interested in magnetic materials and their characterization. Expositions within individual chapters are largely self-contained without having been sequenced with any specific pedagogical thread in mind. Each chapter, therefore, has its own introduction, principle, instrumentation and applications, and references for fbrther study. The level of presentation is intended to be intermediate between a cursory overview and detailed instruction. The extent of coverage is very much dictated by the character of the technique described. Many are based on quite complex concepts and instrumentation. Others are less so, and can be based on commercial products. Researchers working on non-magnetic materials may also find this book useful since many techniques and principles described in the book can be used for characterizing other materials.

Finally, I would like to express my appreciation to the many expert authors who have contributed to this book. On the production side, special thanks go to Lisa Jansson, the type-setting editor at Brookhaven, for her significant role in finalizing the book format, and to my colleague Marco Beleggia, who spent significant amounts of time in helping Lisa on the technical aspects of type-setting, such as the conversion of equations and symbols, and to my student June Lau for checking the Appendices. I am also grateful to the staff at Kluwer Academic Publisher, especially senior editor Greg Franklin, for their help and advice.

Yimei Zhu

Brookhaven National Laboratory Long Island, New York

Table of Contents

List of Authors ............................................................................................................................................ v

................................................................................................................................ Preface vii

Table of Contents ............................................................................................................. xi

Neutron Scattering

Chapter I . Magnetic neutron scattering ............................................................................................ 3

I . I . Introduction ............................................................................................................................................ 3

1.2. Neutron interaction with matter and scattering cross-section ............................................... 5 1.2.1. Basic scattering theory and differential cross-section .................................................... 7 1.2.2. Neutron interactions and scattering lengths .................................................................... 9

1.2.2.1. Nuclear scattering length .......................................................................................... 9 1.2.2.2. Magnetic scattering length ...................................................................................... 10

1.2.3. Factorization of the magnetic scattering length and the magnetic form factors .... 14 1.2.3.1. Magnetic form factors for Hund's ions: vector formalism ................................ 16 1.2.3.2. Evaluating the form factors and dipole approximation .................................. 18 1.2.3.3. One-electron spin form factor beyond dipole approximation;

anisotropic form factors for 3d electrons ........................................................... 22

1.3. Magnetic scattering by a crystal .............................................................................................. 25 1.3.1. Elastic and quasi-elastic magnetic scattering .................................................................. 27 1.3.2. Dynarnical correlation function and dynamical magnetic susceptibility .................... 30 1.3.3. Magnetic Bragg scattering ................................................................................................. 31 1.3.4. Scattering from short-range nanoscale correlations .................................................... 34 1.3.5. Spin scattering and spin correlation function .......................................................... 37 1.3.6. Sum rules for the dynamic spin structure factor ........................................................... 38

1.3.6.1. Static structure factor and spectrum averaged energy ..................................... 40 1.3.6.2. First moment sum rule for Heisenberg spin

Hamiltonian with anisotropy and magnetic field ............................................. I

1.4. Measuring elastic and quasi-elastic magnetic scattering in experiment ............................... 42 1.4.1. Short-range magnetic order in La,,Sr,,CoO, .............................................................. 42 1.4.2. Temperature dependence of quasi-elastic magnetic fluctuations ............................... 45

1.5. Modern techniques in the triple axis neutron spectroscopy ................................................. 47 1.5.1. Inelastic neutron scattering setups with horizontally focusing analyzer .................. 47 1.5.2. Inelastic neutron scattering using the high count rate setups with the PSD .......... 48

1.5.2.1. Setup with a flat crystal analyzer ........................................................................... 50 1.5.2.2. Setup with consecutive analyzers .......................................................................... 52 1.5.2.3. Energy-integrating configuration in the two-axis mode ................................... 53

1.5.3. Experimental examples ........................................................................................................ 54 1.5.3.1. Spin excitation continuum in the Haldane spin chain ....................................... 54 1.5.3.2. Spin fluctuations in a geometrically frustrated magnet ..................................... 57

1.5.4. Neutron polarization analysis with PSD ....................................................................... 59

1.5.4.1. Nuclear and magnetic Bragg scattering in Las13Sr.13Ni0 ,. ................................. 60

Acknowledgements .................................................................................................................................. 62

References ................................................................................................................................................ 62

Chapter 2 . Small-angle neutron scattering ............................................................................................. 65

2.1. Introduction ....................................................................................................................................... 65

..................................................................................................................... 2.1.1. Neutron beams 66 2.1.2. Atomic scattering amplitudes ............................................................................................. 66

........................................................................................... 2.1.3. The classical SANS instrument 66

........................................................................................................................... Neutron scattering 67 2.2.1. Scattering potential ............................................................................................................... 68 2.2.2. Magnetic scattering ............................................................................................................... 68 2.2.3. Polarized neutron scattering .............................................................................................. 69

........................................................................................... 2.2.4. Small angle neutron scattering 70 .......................................................... 2.2.4.1. Scattering by individual magnetic particles 70

............................................................................ 2.2.4.2. Scattering by groups of particles 71 ............................................................. 2.2.4.3. SANS from superparamagnetic particles 72

2.3. Examples ............................................................................................................................................. 76 2.3.1. Ferrofluids ............................................................................................................................... 76

........................................................................ 2.3.2. Nanostructured ferromagnetic materials 80 ............................................................. 2.3.3. Magnetic nanostructure in Fe-Si-&based alloys 88

............................................................... 2.3.4. Micromagnetism in a two-phase CuNiFe alloy 93 . ............................................................................................................... 2.3.4.1 The material 93

.............................................................................. 2.3.4.2. Microstructural characteristics 94 ................................................................................. 2.3.4.3. Magnetic SANS from CuNiFe 95

............................................................................ 2.3.4.4. Modelling the 2D SANS pattern 97

............................................................................................................ 2.4. Summary and conclusions I O I

References ................................................................................................................................................ 103

CHAPTER 3 . Application of polarized neutron reflectometry to studies of ..................................................................................... artificially structured magnetic materials 107

3 . l . Introduction ..................................................................................................................................... 107

3.2. Neutron scattering in reflection (Bragg) geometry ................................................................ 109 ......................................................... 3.2.1 . Reflectometry with unpolarized neutron beams 109

3.3. Theoretical Example I : Reflection from a perfect interface surrounded by media of infinite extent .................... I I I

3.4. Theoretical Example 2: ......................................................................... Reflection from perfectly flat stratified media 113

3.5. Theoretical Example 3: .......................................................................... Reflection from "real-world" stratified media 116

3.5.1 . Reflectometry with polarized neutron beams .......................................................... 120

... Xlll

3.6. Theoretical Example 4: Reflection of a polarized neutron beam from a magnetic film ........................................ 123 3.6.1. Influence of imperfect polarization on the reflectivity ............................................... 124 3.6.2. "Vector" magnetometry with polarized neutron beams ............................................ 126

3.7. Theoretical Example 5: Reflection from a medium with arbitrary direction of magnetization in the plane of the sample .................................................................................. 126

3.8. A qualitative (and intuitive) understanding of "vector" magnetometry ............................ 129

3.9. Description of a polarized neutron reflectometer ................................................................. 132 3.9.1. Preparation of the cold neutron beam for a reflectometer

at a pulsed neutron source ......................................................................................... 132 3.9.2. Polarization of cold neutron beams ................................................................................ 135 3.9.3. Spin-flippers .......................................................................................................................... 138

3.10. Applications of polarized neutron reflectometry ................................................................. 142 3.10. I . Magnetic vs . chemical structures identified through x-ray and polarized

neutron reflectometry ................................................................................................ 143 3.10.2. Magnetic and chemical structures obtained from vector magnetometry using

neutron scattering ............................................................................................................ 148

3.1 1 . Summary and conclusions ................................................................................................... 151

Acknowledgments ................................................................................................................................... 152

References ................................................................................................................................................ 152

X-ray Scattering

CHAPTER 4 . Resonant sofi x-ray techniques to resolve nanoscale magnetism ........... 159

4 . l . Introduction .................................................................................................................................... 159

4.2. Core resonant magneto-optical properties ............................................................................. 160 ........................... 4.2.1. The resonant atomic scattering factors - theoretical description 161

4.2.2. The Fe scattering factors across the b*, edges ............................................................ 164

4.3. XMCD and related spectroscopies ............................................................................................ 166 4.3.1. XMCD sum rules and applications ................................................................................. 166

.............................................................. 4.3.2. Sensitivity of different absorption techniques 168 4.3.3. Polarizing optical elements ............................................................................................... 169 4.3.4. X-ray Faraday effect measurements ............................................................................... 170 4.3.5. Theoretical spectral calculations ...................................................................................... 170

................................... 4.4. X-ray magneto-optical Kerr effect (XMOKE) - specular reflection 171 4.4.1. Theoretical considerations ................................................................................................ 171 4.4.2. Exchange-spring heterostructures ................................................................................. 172 4.4.3. Opportunities ...................................................................................................................... 176

4.5. Diffuse scattering and diffraction ................................................................................................ 176 4.5.1 . Theoretical considerations ............................................................................................ 178

xiv

4.5.2. Perpendicular stripe domains in thin films .................................................................... 179 ............................... 4.5.3. Magnetic and chemical correlation lengths in recording media 184

4.5.4. Coherent magnetic scattering .......................................................................................... 188

...................................................................................................... 4.6. Direct magnetization imaging 191 4.6.1 . Photo-electron emission microscopes ....................................................................... 191 4.6.2. Imaging and scanning zone-plate microscopes ............................................................. 192 4.6.3. Zone-plate imaging of domain structure .................................................................... 193 4.6.4. Complementarity of microscopy and scattering .......................................................... 195

4.7. Summary ......................................................................................................................................... 195

Acknowledgements ............................................................................................................................ 196

References .............................................................................................................................................. 196

............ CHAPTER 5 . Hard x-ray resonant techniques for studies of nonomagnetism 201

5.1. Introduction ................................................................................................................................... I ......................................................................................... 5.1.1. X-ray scattering cross section 203

. . . . 5 I I I Nonresonant cross section ................................................................................... 203 .......................................................................................... 5.1.1.2. Resonant cross section 204

5.2. Diffraction techniques .................................................................................................................. 205 5.2.1. Site-specific magnetism in ferro- (ferri-) magnetic crystals ....................................... 205

..................................................................................... 5.2.2. Imaging spiral magnetic domains 208

5.3. Reflectivity techniques .................................................................................................................. 210 5.3.1 . Studies of interfacial magnetism with circularly polarized x-rays ............................ 210

5.4. Spectroscopy techniques .......................................................................................................... 214 5.4.1 . Magnetic domain mapping of buried nanostructures ................................................. 215

.................................................................................... 5.4.2. Biquadratic coupling in SmCoIFe 217 ................................................................................. 5.4.3. Magnetic reversal in antidot arrays 220

5.4.4. Inhomogeneous magnetic structures in magnetic multilayers .................................. 222

5.5. Conclusions and outlook ............................................................................................................... 225

References ................................................................................................................................................ 225

CHAPTER 6 . Spin-resolved photoemission studies of magnetic films ................................. 229

. 6.1 Introduction ..................................................................................................................................... 229

6.2. Experimental technique ................................................................................................................ 230

6.3. Simple magnetic films .................................................................................................................... 237 6.3.1. Spin-resolved photoemission as a spectroscopic tool:

the electronic structure of Fe surfaces .......................................................................... 237 6.3.2. Spin-resolved photoemission as a tool t o investigate magnetic properties:

.............................................. the magnetic reorientation transition in Fe(l 10) films 242

6.4. Metallic multilayers ......................................................................................................................... 247 6.4.1. The electronic origin of indirect exchange coupling ................................................... 248

...................................................................................................................... 6.5. Compound materials 254 6.5.1. Magnetic transition metal oxides .................................................................................... 255

................................................................................................................. 6.6. Future and perspectives 261

References ................................................................................................................................................ 263

Uectron Scattering

............. CHAPTER 7 . Magnetic phase imaging with transmission electron microscopy 267

7.1. Introduction ...................................................................................................................................... 267

7.2. Image formation in TEM ................................................................................................................ 269 7.2.1 . Image-formation theory .................................................................................................... 269 7.2.2. The transfer function ......................................................................................................... 271 7.2.3. The Schrodinger equation ................................................................................................ 273 7.2.4. Beam-object interaction .................................................................................................... 275

.............................................................................................................. 7.3. Magnetic Imaging by TEM 276 7.3.1. The electron microscope .................................................................................................. 276 7.3.2. Fresnel technique ................................................................................................................ 278 7.3.3. Defocus calibration ............................................................................................................. 279 7.3.4. Foucault technique ............................................................................................................. 282 7.3.5. In-situ magnetization .......................................................................................................... 283 7.3.6. Transport of Intensity ......................................................................................................... 286 7.3.7. Electron holography ........................................................................................................... 290 7.3.8. Holography vs.TIE ............................................................................................................... 293

7.4. Electrostatic and magnetic phase shifts ..................................................................................... 294 . .................................................................................................. 7.4.1 The mean inner potential 295

7.4.2. Magnetic induction mapping ............................................................................................. 297

7.5. Characterization of nanoscale magnetic structures ............................................................... 298 . ............................................................................................................... 7.5.1 Magnetic domains 299

................................................................................ . . 7.5.1 1 Model for magnetic domains 301 7.5.1.2. Measurement of domain wall widths .................................................................. 303 7.5.1.3. Measurement of magnetic potential in bulk magnets ...................................... 307

...................................................................................................... 7.5.2. Magnetic nanoparticles 308 7.5.2.1. Model for magnetic nanoparticles ....................................................................... 309 7.5.2.2. Basic shapes for nanoparticles .......................................................................... 310 7.5.2.3. The vortex state ................................................................................................... 312

................................................................................................ 7.5.2.4. Domain wall widths 313 7.5.2.5. Vortex state of nanoparticles ............................................................................. 314 7.5.2.6. Arrays of nanoparticles ...................................................................................... 316 7.5.2.7. Nanoparticles of arbitrary shapes ...................................................................... 317 7.5.2.8. Micromagnetic simulations .................................................................................... 319

7.6. Summary and future perspectives .............................................................................................. 322

Acknowledgements ................................................................................................................................ 324

References ................................................................................................................................................ 324

CHAPTER 8 . Spin-polarized scanning electron microscopy ....................................................... 32 7

..................................................................................................................................... 8.1. Introduction 327

8.2. Technique .......................................................................................................................................... 328 8.2.1. Principle ................................................................................................................................ 328 8.2.2. Instrumentation .................................................................................................................. 334

8.3. Magnetic domains ........................................................................................................................... 335 8.3.1. Bulk domains ........................................................................................................................ 335 8.3.2. Domains in ultrathin films ................................................................................................. 336 8.3.3. Domains in patterned structures .................................................................................... 337

................................................................................................................................... 8.4. Domain walls 341 8.4.1 . Surface termination of a bulk domain wall .................................................................... 341

........................................................................................ 8.4.2. Domain walls in ultrathin films 342 8.4.3 Domain walls in confined geometries ........................................................................... 343

8.5. Magnetic anisotropies .................................................................................................................... 344 8.5.1. Magnetization reorientation ............................................................................................. 345 8.5.2. Magnetic step anisotropies ............................................................................................... 347

8.6. Magnetization reversal ................................................................................................................... 350

8.7. Phase transitions and transformations ...................................................................................... 352

8.8. Exchange coupling .......................................................................................................................... 354

8.9. Concluding remarks ....................................................................................................................... 355

Acknowledgements ................................................................................................................................ 356

References ................................................................................................................................................ 356

CHAPTER 9 . Spin-polarized low energy electron microscopy (SPLEEM) ....................... 361

9.1. Introduction ..................................................................................................................................... 361

9.2. Physical basis ........................................................................................................................... : ........ 362

9.3. Instrumentation and methodic .................................................................................................... 364

9.4. Applications .................................................................................................................................... 368 9.4.1 . General comments ............................................................................................................. 368 9.4.2. Single layers .......................................................................................................................... 368 9.4.3. Double layers ....................................................................................................................... 375 9.4.4. Trilayers (sandwiches) ....................................................................................................... 376

9.5. Summary ........................................................................................................................................... 378

References ............................................................................................................................................ 378

Proximal Probe

CHAPTER I 0 . Spin-polarized scanning tunneling microscopy ................................................. 383

10 . I . Historical background ................................................................................................................. 383

10.2. Measurement principle ............................................................................................................... 384 10.2.1 . Planar junctions ................................................................................................................. 384 10.2.2. Spin-polarized tunneling with the STM ........................................................................ 385

10.3. Experimental ................................................................................................................................. 387 10.3.1. STM design-requirements ............................................................................................ 388 10.3.2. Tip design ........................................................................................................................... 388

10.4. Results ............................................................................................................................................ 392 .............................................................................. . 10.4.1 The local magnetoresistance mode 393

10.4.2. The differential conductance mode .............................................................................. 395 ......................................................... 10.4.2.1. Domain structure of mesoscopic islands 395

........ 10.4.2.2. Size-dependent reorientation transition of nanometer-scale islands 398 10.4.2.3. Superparamagnetic islands .................................................................................. 402

10.4.3. The constant current mode .......................................................................................... 405

10.5. Conclusions ................................................................................................................................... 408

Acknowledgements ................................................................................................................................ 409

References ............................................................................................................................................ 409

CHAPTER I I . Magnetic force microscopy ....................................................................................... 411

I I . I . Introduction ............................................................................................................................. 411 I I . I . I . Magnetic forces and force gradients ............................................................................. 414 1 1.1.2. Measuring the force or the force gradient with a cantilever .................................. 417

1 1.2. Sensing forces and force gradients ........................................................................................... 418 1 1.2.1 . DC forces ...................................................................................................................... 418 1 1.2.2. AC detection methods .................................................................................................... 419

1 1.2.2.1. Slope detection ...................................................................................................... 422 1 1.2.2.2. Phase detection ..................................................................................................... 423

...................................................................... 1 1.2.2.3. Phase locked loop (or FM mode) 425

........................................................................................................... 1 1.3. Characterizing the probe 426 ................................................................................................. 1 1.3.1. Cantilevers and coatings 426

1.3.2. Cantilever spring constants ............................................................................................ 427

Separating magnetic forces from others ................................................................................. 428 1.4.1. Electric field biasing .......................................................................................................... 428 1.4.2. Using short range interactions as a reference ........................................................... 429 1.4.3. Fourier methods in MFM ................................................................................................ 431

1 1.5. Imaging stability ............................................................................................................................. 432 1 1.5.1 . Imaging in an applied field ............................................................................................... 432

...................................................................................... 1 1.5.2. Quantifying tip magnetic fields 434

1 1.6. MFM resolution ............................................................................................................................ 436

xviii

1 1.6.1. Thin film coatings .............................................................................................................. 436 1 1.6.2. Nanofabricated tips: electron beam deposited. lithographically defined.

....................................................... focused ion-beam milled and carbon nanotubes 436

1 1.7. Modeling MFM response ............................................................................................................ 439 .................................................................................... 1 1.7.1. Sample magnetization modeling 439

1 1.8. Dissipative interactions ............................................................................................................... 439

............................................................................................... 1 1.9. High frequency MFM (HF-MFM) I 1 1.9.1. DC HF-MFM ...................................................................................................................... I

....................................................................................................................... 1 1.9.2. AC HF-MFM I

............................................................................... I 1.10. Combining MFM with other techniques 442 .................................................................... . 1 1 .I 0. 1 Combining MFM with Kerr microscopy 443

........................................................................... . 1 1 1 0.2. Vacuum and low temperature MFM 444

...................................................................................................... I I . I I . Other applications of MFM 444 I I . I I . I . Magnetic recording studies .......................................................................................... 444 I I . 1 1.2. Magnetite .......................................................................................................................... 445 I 1.1 1.3. Magnetostrictive materials ........................................................................................... 446

................................................................................................................................. 1 1 .I 2. Conclusions 447

References ................................................................................................................................................ 447

Light Scattering

CHAPTER 12 . Scanning near-field magneto-optic microscopy ................................................ 455

................................................................................................................................... 12.1. Introduction 455

....................................................................................................................... 12.2. Principle of SNOM 457 12.2.1. Classical limit of optical resolution ............................................................................... 457

12.2.1 . 1 . Rayleigh's criterion ................................................................................................ 457 12.2.1.2. Theory of microscopy .......................................................................................... 458 12.2.1.3. Optical diffraction limit and Heisenbergf uncertainty principle ................ 460 1 2.2.1.4. Evanescent waves ................................................................................................. 461

12.2.2. Aperture SNOM ............................................................................................................... 464 12.2.2.1. Simple theory of aperture SNOM .................................................................... 465 12.2.2.2. Experimental configurations of aperture SNOM ........................................... 469

1 2.2.3. Apertureless SNOM ......................................................................................................... 469

12.3. Technical realization of SNOM ................................................................................................. 470 1 2.3.1 . Fabrication of apertures .................................................................................................. 470

12.3.1.1. Apertures made by etching ................................................................................. 470 1 2.3.1.2. Apertures made by pulling ............................................................................... I 12.3.1.3. Forming an aperture by metallic coating ......................................................... I 12.3.1.4. Apertures made by nanostructuring ................................................................. 472

1 2.3.2. Shear-force distance control .......................................................................................... 473 12.3.2.1 . Detection of the shear-force signal ................................................................... 475 12.3.2.2. Experimental set-up of a SNOM in transmission and reflection mode .... 475

....................................................................................... 12.4. Magnetic imaging by magneto-optics 476 .............................................................................................. 12.4.1 . Theory of magneto-optics 476

. . ......................................................................................................... 12.4.1 I Faraday-effect 477 ............................................................................................................... 12.4.1.2. Kerr-effect 480

12.4.1.3. Atomic model of dispersion (Lorentz) ........................................................ I ........................................... 12.4.1.4. Origin of the magnetic-field-induced anisotropy 483

12.4.1.5. Relation between the off-diagonal conductivity and Faraday ...................................................................................................... and Kerr effect 484 .................................................................................................... 12.4.2. Magneto-optic imaging 486

. ........................................................................................................ 1 2.4.2.1 Sagnac SNOM 487 ...................... 12.4.2.2. Quantitative scanning near-field magneto-optic microscopy 488

................................................ 12.4.2.3 Contrast formation in magneto-optic imaging I

12.5. Characterization of magnetic materials by SNOM .............................................................. 492 . ............................................................................................................................... 12.5.1 History 493

12.5.2. Local magnetization measurements ............................................................................. 495 12.5.3. Quantitative magneto-optic measurements ............................................................... 498

12.6. Fundamental problems ................................................................................................................ 503 12.6.1 . Transmission mode versus reflection mode ............................................................... 503 1 2.6.2. Topographic cross talk ..................................................................................................... 506 12.6.3. Polarization effects ........................................................................................................... 506

......................................................................................................... 12.6.4. Polarization stability 508

12.7. Summary ........................................................................................................................................ 509

.................................................................................................................................................. Footnotes I 0

References ................................................................................................................................................ 511

CHAPTER 1 3 . Magnetization dynamics using time-resolved magneto- ........................................................................................................................................ optic microscopy 517

13.1. Introduction ................................................................................................................................ 517

................................................................................................................ 1 3.2. Experimental methods 518 1 3.2.1 . Pump-and-probe method ............................................................................................ 518 1 3.2.2. Experimental setup .......................................................................................................... 519

. .................................................................... 13.2.2.1 Optical setup and signal detection 519 13.2.2.2. Synchronization and magnetic field pulse generation ................................... 521 13.2.2.3. Sample preparation and magnetic field configuration ................................... 523

......................................................................................... 13.2.2.4. Crossed-wire element 523 13.2.3. Operation modes in TR-SKM experiments ................................................................ 524

13.3. Experimental results for magnetization reversal dynamics ................................................. 527 13.3.1. Domain nucleation vs . domain wall motion in nonequilibrium state .................... 527

.............. 13.3.2. Complex domain pattern formation : ............................................................. 529 13.3.3. Large amplitude precessional oscillations ................................................................... 532 13.3.4. Switching diagrams for crossed-wire devices ............................................................. 534 13.3.5. Precessional switching with the crossed-wire geometry ........................................ 536

1 3.4. Conclusions and prospects ........................................................................................................ 540

References ................................................................................................................................................ 540

CHAPTER 14 . Brillouin light scattering spectroscopy ..................................................................... 543

14.1 . Introduction ..................................................................................................................................... 543

14.2. The Brillouin light scattering technique .............................................................................. 544 14.2.1 . Experimental setup ........................................................................................................... 544 14.2.2. The Brillouin light scattering cross section ................................................................. 547

14.3. Spinwave basics .................................................................................................................................... 547 14.3.1 . Spin waves in magnetic films .......................................................................................... 549

14.3.1 . 1 . Procedure to determine anisotropy constants .............................................. 550 14.3.1.2. Standing spin waves .............................................................................................. 552

14.3.2. Spin waves in magnetic double layers and multilayers .............................................. 553 14.3.2.1. Enhancement and reduction of layer magnetizations,

................................................................................................ polarization effects 553 14.3.2.2. lnterlayer exchange coupling .............................................................................. 553

14.4. Determination of magnetic parameters ....................................................................................... 554 14.4.1 Magnetic anisotropies ........................................................................................................ 555

14.4.1 . 1. Epitaxial Co(l 10) films on a Cu(l 10) substrate ............................................. 555 14.4.1.2. Epitaxial Fe(O0 I) films with Pd cover layer ..................................................... 557 14.4.1.3. Comparison of Brillouin light scattering with magnetometry

for the determination of anisotropy constants ............................................... 558 14.4.2. The exchange constant ................................................................................................. 559 14.4.3. lnterlayer coupling ............................................................................................................ 560 14.4.4. Magnetic inhomogeneities .............................................................................................. 562

14.5. Patterned magnetic structures .................................................................................................. 563 14.5.1. Quantized spin-wave modes in magnetic stripes ...................................................... 564 14.5.2. Characterization of the spatial distribution of the spin-wave intensity

and localization of modes ............................................................................................... 567

.................................................................................................. 14.6. Wave propagation phenomena 568 14.6.1. Experimental setups ......................................................................................................... 568

.......................................................... 14.6.1.1. Space resolved Brillouin light scattering 568 ................................................. 14.6.1.2. Space-time resolved BriIIouin light scattering 568

14.6.2. Spin-wave radiation from an antenna and spin wave caustics ................................. 570 14.6.3. Spin wave tunnelling ......................................................................................................... 571 14.6.4. Magnetic solitons and bullets ......................................................................................... 573

14.7. Conclusions ................................................................................................................................... 575

Acknowledgements ................................................................................................................................ 575

................................................................................................................................................ References 575

Appendices ............................................................................................................................................... 579 Appendix I . Principal physical constants ...................................................................................... 579 Appendix 2 . Conversion between cgs units and SI units for magnetic quantities .............. 580 Appendix 3 . Conversion of energy related units ........................................................................ I Appendix 4 . Physical properties of some magnetic substances .............................................. 582

.......................................................................................................................................... Subject Index 583

Neutron Scattering