1 Introduction to Magnetism .................................... 1
W. Weber
1.1 Introduction ............................................ 1
1.1.1 Definition of the Magnetic Moment ................ 1
1.1.2 Energy of the Moment in an External Magnetic
Field ............................................ 2
1.1.3 Further Definitions .............................. 3
1.2 Magnetism of Free Atoms and Electrons ................... 4
1.2.1 Diamagnetism of Free Atoms ....................... 4
1.2.2 Paramagnetism of Free Atoms ...................... 5
1.2.3 Pauli Paramagnetism of Free Electrons (in
Metals) .......................................... 9
1.3 Ferromagnetism ......................................... 10
1.3.1 Molecular Field ................................. 11
1.3.2 Exchange Interaction as Origin of the
Molecular Field ................................. 12
1.3.3 Mean Field Approximation (MFA) .................. 14
1.3.4 Spin Waves ...................................... 18
1.3.5 Itinerant Ferromagnetism ........................ 21
1.4 Magnetization Curves M(H) .............................. 22
1.4.1 Magnetostatic Energy or Shape Anisotropy ........ 23
1.4.2 Magneto-Crystalline Anisotropy .................. 24
1.4.3 Magnetization Curves in the "Uniform Rotation"
Model ........................................... 26
1.4.4 Domains and Domain Walls ........................ 28
1.5 Thin Film Magnetism .................................... 35
1.5.1 Surface Anisotropy .............................. 35
1.5.2 Indirect Exchange Coupling in Multilayers ....... 36
1.5.3 Giant Magnetoresistance ......................... 39
References .................................................. 40
2 Spintronics: Conceptual Building Blocks ..................... 43
J.-Ph. Ansermet
2.1 Spin Precession ........................................ 43
2.2 Spin Relaxation ........................................ 45
2.3 Spin-dependent Transport: The Collinear Case ........... 48
2.3.1 Collisions ...................................... 50
2.3.2 Calculation of the Currents ..................... 52
2.3.3 Diffusion Equation and the Spin Accumulation .... 55
2.4 Spin Relaxation of Conduction Electrons ................ 59
2.4.1 Spin-Lattice Relaxation Time for Conduction
Electrons ....................................... 59
2.4.2 The Bottleneck Regime ........................... 62
2.4.3 Spin-Orbit Scattering ........................... 63
2.4.4 Electron-Magnon Scattering ...................... 65
2.4.5 Spin Mixing by Collisions with Magnons .......... 67
2.5 Spin-dependent Transport: The Non-collinear Case ....... 70
2.5.1 Toward a Semi-classical Description of Spin
Dynamics in Transport ........................... 71
2.5.2 Constitutive Equations .......................... 71
2.5.3 Spin Diffusion in Non-collinear
Configurations .................................. 73
2.5.4 Domain Walls .................................... 74
References .................................................. 75
3 Interaction of Polarized Light with Matter .................. 77
Y. Joly
3.1 Introduction ........................................... 77
3.2 Experimental Observations of X-Ray Interaction
with Matter ............................................ 78
3.2.1 Absorption ...................................... 78
3.2.2 Dependence on Energy ............................ 78
3.2.3 Dependence on the Atomic Environment ............ 80
3.2.4 Dependence on the Light Polarization ............ 80
3.2.5 Diffraction Around Edges ........................ 81
3.3 The Light .............................................. 83
3.3.1 Definitions and Notations ....................... 83
3.3.2 Stokes Parameters ............................... 84
3.3.3 Quantization of the Electromagnetic Field ....... 85
3.4 Interaction of Light with an Electron in an Atom ....... 85
3.4.1 Linear and Nonlinear Interactions ............... 86
3.4.2 Interaction Hamiltonian ......................... 86
3.4.3 Absorption and Emission ......................... 88
3.4.4 Scattering ...................................... 88
3.4.5 Transition Matrix ............................... 93
3.4.6 Selection Rules ................................. 94
3.5 Dielectric Function or Macroscopic Point of View ....... 98
3.5.1 Complex Permittivity ............................ 99
3.5.2 Complex Refractive Index ....................... 101
3.6 X-Ray Spectroscopies .................................. 102
3.6.1 Characteristic Times ........................... 103
3.6.2 The Different Spectroscopies ................... 104
3.6.3 Fluorescence and Auger Spectroscopies .......... 106
3.6.4 XANES and RXS Formula .......................... 107
3.6.5 Multipole Analysis ............................. 112
3.6.6 X-Ray Magnetic Circular Dichroism .............. 118
3.7 Monoelectronic Simulations ............................ 120
3.7.1 The Potential .................................. 120
3.7.2 The Multiple Scattering Theory ................. 121
3.7.3 Available Codes ................................ 123
3.8 Conclusion ............................................ 123
References ................................................. 124
4 Synchrotron Radiation Sources and Optical Devices .......... 127
D. Cocco and M. Zangrando
4.1 Optics for UV and X-Ray ............................... 127
4.2 Sources, Beamlines, and Monochromators for Soft
X-Ray ................................................. 133
4.2.1 SR Sources and Prefocusing or Heat Load
Section ........................................ 133
4.2.2 Soft X-Ray Monochromators and Diffraction
Gratings ....................................... 138
4.2.3 Refocusing Optics .............................. 142
References ................................................. 143
5 X-Ray Magnetic Dichroism ................................... 145
H. Wende and C. Antoniak
5.1 Introduction .......................................... 145
5.2 X-Ray Absorption Spectroscopy ......................... 146
5.2.1 X-Ray Absorption Near-Edge Structure ........... 147
5.2.2 Dichroism in X-Ray Absorption Spectroscopy ..... 148
5.3 X-Ray Magnetic Circular Dichroism ..................... 149
5.3.1 Determination of Orbital and Spin Magnetic
Moments: Sum Rules ............................. 150
5.4 Experimental Setup .................................... 152
5.5 Data Analysis ......................................... 152
5.5.1 Self-absorption and Saturation Effects
in Electron Yield .............................. 152
5.5.2 Standard Analysis .............................. 154
5.6 Examples of Recent Research ........................... 155
5.6.1 Failure of Sum Rule-based Analysis for Light
3d Elements .................................... 156
5.6.2 Spin-dependence of Matrix Elements in Rare
Earths ......................................... 159
5.6.3 Paramagnetic Biomolecules on Ferromagnetic
Surfaces ....................................... 162
5.7 Conclusions and Outlook ............................... 165
References ................................................. 166
6 X-Ray Detected Optical Activity ............................ 169
A. Rogalev, J. Goulon, F. Wilhelm, and A. Bosak
6.1 Introduction .......................................... 169
6.2 X-Ray Detected OA Tensor Formalism .................... 171
6.3 Instrumentation and Experimental Considerations ....... 173
6.4 Natural Optical Activity Detected with X-Rays ......... 176
6.4.1 X-Ray Natural Circular Dichroism ............... 176
6.4.2 Vector Part of X-Ray-detected OA ............... 180
6.5 Nonreciprocal X-Ray-detected OA ....................... 182
6.5.1 Nonreciprocal X-Ray Linear Dichroism ........... 182
6.5.2 X-Ray Magnetochiral Dichroism: XM/D ............ 184
6.6 Effective Operators for X-Ray Detected OA ............. 186
References ................................................. 188
7 X-Ray Detected Magnetic Resonance: A New Spectroscopic
Tool ....................................................... 191
J. Goulon, A. Rogalev, F. Wilhelm, and G. Goujon
7.1 Introduction .......................................... 191
7.2 Precession Dynamics Probed with X-Rays ................ 193
7.2.1 Phenomenological Equation of Motion ............ 193
7.2.2 Precession Dynamics of Orbital and Spin
Magnetization Components ....................... 195
7.2.3 Precession Under High Pumping Power ............ 196
7.2.4 Nonuniform Eigen Modes of Precession ........... 199
7.2.5 Longitudinal and Transverse Relaxation Times ... 202
7.3 Experimental Results .................................. 203
7.3.1 Ferrimagnetic Iron Garnets ..................... 203
7.3.2 Modular XDMR Spectrometer ...................... 205
7.3.3 XDMR in Longitudinal Geometry .................. 207
7.3.4 XDMR in Transverse Geometry .................... 213
7.4 Facing New Challenges ................................. 220
References ................................................. 221
8 Resonant X-Ray Scattering and Absorption ................... 223
S.P. Collins and A. Bombardi
8.1 Absorption and Scattering: The Optical Theorem ........ 223
8.2 Symmetry and X-Ray Absorption ......................... 224
8.3 X-Ray Scattering and Multipole Matrix Elements ........ 226
8.4 Cartesian Tensors, Magnetism and Anisotropy ........... 228
8.5 Neumann's Principle and Symmetry-restricted Tensors ... 231
8.6 Scattering Matrix and Stokes Parameters ............... 232
8.7 Diffraction Intensity and the Unit-Cell Structure
Factor ................................................ 234
8.8 Magnetic Symmetry, Propagation Vector, and the
Magnetic Structure Factor ............................. 235
8.9 Crystal Coordinates and Azimuthal Rotations ........... 238
8.10 Spherical and Cartesian Tensors ....................... 239
8.11 Example: HoFe2 ........................................ 242
8.12 Example: ZnO .......................................... 248
8.13 Example: Ca3Co2O6 ..................................... 253
8.14 Conclusions ........................................... 261
References ................................................. 261
9 An Introduction to Inelastic X-Ray Scattering .............. 263
J.-P. Rueff
9.1 Introduction .......................................... 263
9.2 Theoretical Concepts .................................. 264
9.2.1 Overview of the IXS Process .................... 264
9.2.2 Interaction Hamiltonian ........................ 265
9.2.3 IXS Cross Sections and Fermi Golden Rule ....... 266
9.2.4 Nonresonant IXS ................................ 266
9.2.5 RIXS ........................................... 269
9.3 Applications of IXS ................................... 271
9.3.1 Extreme Conditions ............................. 271
9.3.2 Strongly Correlated Materials .................. 274
9.4 Conclusion ............................................ 277
References ................................................. 277
10 XAS and XMCD of Single Molecule Magnets .................... 279
R. Sessoli, M. Mannini, F. Pineider, A. Cornia, and
Ph. Sainctavit
10.1 Introduction .......................................... 279
10.2 Single Molecule Magnets ............................... 281
10.2.1 Building Up a Large Spin ....................... 281
10.2.2 Magnetic Anisotropy in Single Molecule \
Magnets ........................................ 284
10.2.3 The Dynamics of the Magnetization .............. 287
10.3 Deposition of Single Molecule Magnets on Surfaces ..... 292
10.4 XAS and XMCD of SMMs .................................. 295
10.4.1 XAS and XMCD to Investigate the Electronic
Structure of Mn12 Clusters ..................... 296
10.4.2 XAS and XMCD of Monolayers of Mn12 SMMs ........ 298
10.4.3 XMCD and Magnetic Anisotropy ................... 301
10.4.4 XMCD and the Dynamics of the Magnetization ..... 305
10.5 Conclusions ........................................... 307
References ................................................. 308
11 Magnetic Structure of Actiniae Metals ...................... 313
G. van der Laan and K.T. Moore
11.1 Introduction .......................................... 313
11.2 Volume Change Across the Actinide Series .............. 315
11.2.1 Photoemission Spectroscopy's Two Cents ......... 316
11.3 The Six Crystal Allotropes of Pu Metal ................ 317
11.3.1 Lowering the Electronic Energy Through
a Peierls-like Distortion ...................... 318
11.3.2 Comparison with Cerium ......................... 319
11.3.3 Stabilized δ-Plutonium ......................... 320
11.4 Revised View of the Periodic Table .................... 321
11.5 Actinide Magnetism .................................... 323
11.5.1 Experimental Absence of Magnetic Moments in
Plutonium ...................................... 323
11.5.2 Looking to Other Elements for Clues ............ 325
11.6 Experimental Complications of Plutonium ............... 325
11.7 One Man's Electron Energy Loss is Another's X-Ray
Absorption ............................................ 326
11.8 Theory ................................................ 327
11.8.1 Atomic Interactions ............................ 327
11.8.2 LS- and jj-Coupling Schemes .................... 330
11.8.3 Intermediate Coupling .......................... 332
11.8.4 Moments for ƒ2 ................................. 333
11.9 Spectral Calculations ................................. 335
11.10 Spin-Orbit Interaction and Sum Rule Analysis ......... 336
11.11 Validity of the Sum Rule ............................. 337
11.12 Experimental Results for the N4,5 Edges .............. 339
11.12.1 What Our Results Mean for Pu Theory ........... 341
11.13 Conclusions .......................................... 342
References ................................................. 342
12 Magnetic Imaging with X-rays ............................... 345
F. Nolting
12.1 Introduction .......................................... 345
12.2 Concepts of Magnetic Imaging Contrast ................. 347
12.2.1 XMCD Image ..................................... 348
12.2.2 XMLD Images .................................... 351
12.2.3 Polarization Control ........................... 354
12.2.4 Local Spectra .................................. 355
12.2.5 Spatial Resolution ............................. 356
12.3 Realization of the Magnetic Contrast with Different
Microscopes ........................................... 358
12.3.1 Photoemission Electron Microscope .............. 358
12.3.2 STXM/TXM ....................................... 359
12.3.3 "Lensless" Imaging ............................. 361
12.3.4 Combining Scanning Probes with X-Rays .......... 363
12.4 Summary ............................................... 364
References ................................................. 364
13 Domain Wall Spin Structures and Dynamics Probed by
Synchrotron Techniques ..................................... 367
M. Kläui
13.1 Introduction .......................................... 367
13.2 Techniques ............................................ 369
13.3 Domain Wall Types and Wall Phase Diagrams ............. 369
13.3.1 Theory of Head-to-Head Domain Wall Spin
Structures ..................................... 369
13.3.2 Experimental Determination of Head-to-Head
Domain Wall Spin Structures .................... 371
13.3.3 Further Head-to-Head Domain Wall Types ......... 373
13.4 Domain Wall Dynamics .................................. 376
13.4.1 Field-induced Domain Wall Propagation .......... 377
13.4.2 Current-induced Domain Wall Propagation ........ 377
13.4.3 Field- and Current-induced Domain Wall
Excitations .................................... 380
13.5 Summary ............................................... 382
References ................................................. 382
14 Dynamics of Mesoscopic Magnetic Objects .................... 385
C. Quitmann, J. Raabe, A. Puzic, K. Kuepper, and S. Wintz
14.1 Introduction .......................................... 385
14.2 Macroscopic vs. Mesoscopic Magnetic Objects ........... 386
14.2.1 Magnetic Interactions and Domains .............. 386
14.2.2 Magnetic Time Scales ........................... 388
14.2.3 Magnetic Length Scales ......................... 389
14.2.4 Landau-Lifshitz-Gilbert Equation ............... 389
14.2.5 Experimental Techniques ........................ 391
14.3 Dynamics in Simple Squares ............................ 392
14.3.1 Static Mesoscopic Structures ................... 392
14.3.2 Pulsed Field Excitations ....................... 394
14.4 Vortex Dynamics and Switching ......................... 399
14.4.1 Current Induced Resonant Vortex Core Motion .... 399
14.4.2 Bistable Configurations by Pinning the Vortex
Core ........................................... 401
14.4.3 Resonant Burst Switching ....................... 402
14.5 Summary ............................................... 403
References ................................................. 404
15 From Third- to Fourth-Generation Light Sources: Free-
Electron Lasers in the UV and X-ray Range .................. 407
M. Altarelli
15.1 Introduction .......................................... 407
15.2 The SASE Process and Short-wavelength Free-Electron
Lasers ................................................ 409
15.3 First Results at FLASH and the Science Case for
X-Ray FELs ............................................ 411
15.4 The Quest for Hard X-Ray FELs ......................... 414
15.5 Seeded Free-Electron Lasers ........................... 417
References ................................................. 418
Contributors .................................................. 421
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