Magnetism and Synchrotron Radiation (eBook)

Foreword 6
Preface 9
Contents 11
1 Introduction to Magnetism 22
1.1 Introduction 22
1.1.1 Definition of the Magnetic Moment 22
1.1.2 Energy of the Moment in an External Magnetic Field 23
1.1.3 Further Definitions 24
1.2 Magnetism of Free Atoms and Electrons 25
1.2.1 Diamagnetism of Free Atoms 25
1.2.2 Paramagnetism of Free Atoms 26
1.2.3 Pauli Paramagnetism of Free Electrons(in Metals) 30
1.3 Ferromagnetism 31
1.3.1 Molecular Field 32
1.3.2 Exchange Interaction as Originof the Molecular Field 33
1.3.3 Mean Field Approximation (MFA) 35
1.3.3.1 Curie Temperature in MFA 36
1.3.3.2 Curie–Weiss Law 37
1.3.3.3 The Behavior of M(T) Close to Tc 37
1.3.4 Spin Waves 39
1.3.4.1 Dispersion Relation of Spin Waves 40
1.3.4.2 Thermal Excitation of Spin Waves 41
1.3.5 Itinerant Ferromagnetism 42
1.4 Magnetization Curves M(H) 43
1.4.1 Magnetostatic Energy or Shape Anisotropy 44
1.4.2 Magneto-Crystalline Anisotropy 45
1.4.3 Magnetization Curves in the ``Uniform Rotation'' Model 47
1.4.3.1 =0 Case 48
1.4.3.2 =45 case 48
1.4.3.3 =90 case 49
1.4.4 Domains and Domain Walls 49
1.4.4.1 Why Do Domains Exist? 50
1.4.4.2 Domain Wall Width 51
1.4.4.3 Nucleation of Reversed Domains 52
1.4.4.4 Pinning of Domain Walls 52
1.4.4.5 Bloch or Néel Wall? 53
1.4.4.6 Why Small Particles are Always Mono-domain? 54
1.4.4.7 Superparamagnetism 54
1.5 Thin Film Magnetism 56
1.5.1 Surface Anisotropy 56
1.5.2 Indirect Exchange Coupling in Multilayers 57
1.5.3 Giant Magnetoresistance 60
References 61
2 Spintronics: Conceptual Building Blocks 63
2.1 Spin Precession 63
2.2 Spin Relaxation 65
2.3 Spin-dependent Transport: The Collinear Case 68
2.3.1 Collisions 70
2.3.2 Calculation of the Currents 72
2.3.3 Diffusion Equation and the SpinAccumulation 75
2.4 Spin Relaxation of Conduction Electrons 79
2.4.1 Spin-Lattice Relaxation Timefor Conduction Electrons 79
2.4.2 The Bottleneck Regime 82
2.4.3 Spin–Orbit Scattering 83
2.4.4 Electron–Magnon Scattering 85
2.4.5 Spin Mixing by Collisions with Magnons 87
2.5 Spin-dependent Transport: The Non-collinear Case 90
2.5.1 Toward a Semi-classical Descriptionof Spin Dynamics in Transport 91
2.5.2 Constitutive Equations 91
2.5.3 Spin Diffusion in Non-collinear Configurations 93
2.5.4 Domain Walls 94
References 95
3 Interaction of Polarized Light with Matter 97
3.1 Introduction 97
3.2 Experimental Observations of X-Ray Interaction with Matter 98
3.2.1 Absorption 98
3.2.2 Dependence on Energy 98
3.2.3 Dependence on the Atomic Environment 100
3.2.4 Dependence on the Light Polarization 100
3.2.5 Diffraction Around Edges 101
3.3 The Light 103
3.3.1 Definitions and Notations 103
3.3.2 Stokes Parameters 104
3.3.3 Quantization of the Electromagnetic Field 105
3.4 Interaction of Light with an Electron in an Atom 105
3.4.1 Linear and Nonlinear Interactions 106
3.4.2 Interaction Hamiltonian 106
3.4.3 Absorption and Emission 108
3.4.4 Scattering 108
3.4.4.1 Thomson Scattering 109
3.4.4.2 Compton Scattering 110
3.4.4.3 Resonant Scattering 111
3.4.4.4 Nonresonant Magnetic Scattering 112
3.4.5 Transition Matrix 113
3.4.6 Selection Rules 114
3.4.6.1 Final States 114
3.4.6.2 Initial States 115
3.4.6.3 Operator 116
3.4.6.4 The Transition Matrix 117
3.5 Dielectric Function or Macroscopic Point of View 118
3.5.1 Complex Permittivity 119
3.5.2 Complex Refractive Index 121
3.6 X-Ray Spectroscopies 122
3.6.1 Characteristic Times 123
3.6.2 The Different Spectroscopies 124
3.6.2.1 Real Absorption 124
3.6.2.2 Virtual Absorption 126
3.6.3 Fluorescence and Auger Spectroscopies 126
3.6.4 XANES and RXS Formula 127
3.6.4.1 Relation with the Density of States 130
3.6.5 Multipole Analysis 132
3.6.5.1 Cartesian Tensors 132
3.6.5.2 Spherical Tensors 134
3.6.5.3 m3m Symmetry (Oh) 136
3.6.5.4 4/mmm Symmetry (D4h) 136
3.6.5.5 4/m'm'm Symmetry 137
3.6.6 X-Ray Magnetic Circular Dichroism 138
3.7 Monoelectronic Simulations 140
3.7.1 The Potential 140
3.7.2 The Multiple Scattering Theory 141
3.7.3 Available Codes 143
3.8 Conclusion 143
References 144
4 Synchrotron Radiation Sources and Optical Devices 146
4.1 Optics for UV and X-Ray 146
4.2 Sources, Beamlines, and Monochromatorsfor Soft X-Ray 152
4.2.1 SR Sources and Prefocusing or Heat LoadSection 152
4.2.2 Soft X-Ray Monochromators and Diffraction Gratings 157
4.2.3 Refocusing Optics 161
References 162
5 X-Ray Magnetic Dichroism 164
5.1 Introduction 164
5.2 X-Ray Absorption Spectroscopy 165
5.2.1 X-Ray Absorption Near-Edge Structure 166
5.2.2 Dichroism in X-Ray AbsorptionSpectroscopy 167
5.3 X-Ray Magnetic Circular Dichroism 168
5.3.1 Determination of Orbital and Spin Magnetic Moments: Sum Rules 169
5.4 Experimental Setup 171
5.5 Data Analysis 171
5.5.1 Self-absorption and Saturation Effects in Electron Yield 171
5.5.2 Standard Analysis 173
5.6 Examples of Recent Research 174
5.6.1 Failure of Sum Rule-based Analysis for Light 3d Elements 175
5.6.2 Spin-dependence of Matrix Elements in Rare Earths 178
5.6.3 Paramagnetic Biomolecules on Ferromagnetic Surfaces 181
5.7 Conclusions and Outlook 184
References 185
6 X-Ray Detected Optical Activity 187
6.1 Introduction 187
6.2 X-Ray Detected OA Tensor Formalism 189
6.3 Instrumentation and Experimental Considerations 191
6.4 Natural Optical Activity Detected with X-Rays 194
6.4.1 X-Ray Natural Circular Dichroism 194
6.4.2 Vector Part of X-Ray-detected OA 198
6.5 Nonreciprocal X-Ray-detected OA 200
6.5.1 Nonreciprocal X-Ray Linear Dichroism 200
6.5.2 X-Ray Magnetochiral Dichroism: XMD 202
6.6 Effective Operators for X-Ray Detected OA 204
References 206
7 X-Ray Detected Magnetic Resonance: A New Spectroscopic Tool 209
7.1 Introduction 209
7.2 Precession Dynamics Probed with X-Rays 211
7.2.1 Phenomenological Equation of Motion 211
7.2.2 Precession Dynamics of Orbital and Spin Magnetization Components 213
7.2.3 Precession Under High Pumping Power 214
7.2.3.1 Foldover Effects 214
7.2.3.2 Suhl's Instability Thresholds 216
7.2.4 Nonuniform Eigen Modes of Precession 217
7.2.5 Longitudinal and Transverse RelaxationTimes 220
7.3 Experimental Results 221
7.3.1 Ferrimagnetic Iron Garnets 221
7.3.2 Modular XDMR Spectrometer 223
7.3.3 XDMR in Longitudinal Geometry 225
7.3.3.1 Detection Issues 225
7.3.3.2 Element-selective Measurements on YIG Films 225
7.3.3.3 Collective Effects in the Precession Dynamics of Orbital Components 228
7.3.3.4 Direct Estimate of the Longitudinal Relaxation Time T1 229
7.3.4 XDMR in Transverse Geometry 231
7.3.4.1 Super-Heterodyne Detection 231
7.3.4.2 Transverse XDMR Spectra of a YIG/GGG Thin Film Rotated at the Magic Angle 232
7.3.4.3 Transverse XDMR Spectra of a Ferrimagnetic Single Crystal of GdIG Above and Below the Compensation Temperature 235
7.4 Facing New Challenges 238
References 239
8 Resonant X-Ray Scattering and Absorption 241
8.1 Absorption and Scattering: The Optical Theorem 241
8.2 Symmetry and X-Ray Absorption 242
8.3 X-Ray Scattering and Multipole Matrix Elements 244
8.4 Cartesian Tensors, Magnetism and Anisotropy 246
8.5 Neumann's Principle and Symmetry-restrictedTensors 249
8.6 Scattering Matrix and Stokes Parameters 250
8.7 Diffraction Intensity and the Unit-Cell StructureFactor 252
8.8 Magnetic Symmetry, Propagation Vector, and the Magnetic Structure Factor 253
8.9 Crystal Coordinates and Azimuthal Rotations 256
8.10 Spherical and Cartesian Tensors 257
8.11 Example: HoFe2 260
8.12 Example: ZnO 266
8.13 Example: Ca3Co2O6 271
8.14 Conclusions 279
References 279
9 An Introduction to Inelastic X-Ray Scattering 281
9.1 Introduction 281
9.2 Theoretical Concepts 282
9.2.1 Overview of the IXS Process 282
9.2.2 Interaction Hamiltonian 283
9.2.3 IXS Cross Sections and Fermi Golden Rule 284
9.2.4 Nonresonant IXS 284
9.2.4.1 Cross Section 284
9.2.4.2 Expressions of the Dynamical Structure Factor 285
9.2.4.3 X-Ray Raman scattering: Equivalence with Absorption 286
9.2.5 RIXS 287
9.3 Applications of IXS 289
9.3.1 Extreme Conditions 289
9.3.1.1 Absorption Edge of Light Elements Under Pressure 289
9.3.1.2 Magnetic Collapse in Transition Metal 290
9.3.1.3 Valence Transition and Kondo Behavior 291
9.3.2 Strongly Correlated Materials 292
9.3.2.1 dd-excitations in Transition Metal Oxides 292
9.3.2.2 Phonons in Plutonium 294
9.4 Conclusion 295
References 295
10 XAS and XMCD of Single Molecule Magnets 296
10.1 Introduction 296
10.2 Single Molecule Magnets 298
10.2.1 Building Up a Large Spin 298
10.2.2 Magnetic Anisotropy in Single MoleculeMagnets 301
10.2.3 The Dynamics of the Magnetization 304
10.3 Deposition of Single Molecule Magnets on Surfaces 309
10.4 XAS and XMCD of SMMs 312
10.4.1 XAS and XMCD to Investigate the Electronic Structure of Mn12 Clusters 313
10.4.2 XAS and XMCD of Monolayers of Mn12SMMs 315
10.4.3 XMCD and Magnetic Anisotropy 318
10.4.4 XMCD and the Dynamics of the Magnetization 322
10.5 Conclusions 324
References 325
11 Magnetic Structure of Actinide Metals 329
11.1 Introduction 329
11.2 Volume Change Across the Actinide Series 331
11.2.1 Photoemission Spectroscopy's Two Cents 332
11.3 The Six Crystal Allotropes of Pu Metal 333
11.3.1 Lowering the Electronic Energy Through a Peierls-like Distortion 334
11.3.2 Comparison with Cerium 335
11.3.3 Stabilized -Plutonium 336
11.4 Revised View of the Periodic Table 337
11.5 Actinide Magnetism 339
11.5.1 Experimental Absence of Magnetic Moments in Plutonium 339
11.5.2 Looking to Other Elements for Clues 341
11.6 Experimental Complications of Plutonium 341
11.7 One Man's Electron Energy Loss is Another'sX-Ray Absorption 342
11.8 Theory 343
11.8.1 Atomic Interactions 343
11.8.1.1 Electrostatic Interactions 344
11.8.1.2 Spin–Orbit Interaction 345
11.8.2 LS- and jj-Coupling Schemes 346
11.8.2.1 LS Coupling 346
11.8.2.2 jj Coupling 346
11.8.2.3 Transformation Matrix 346
11.8.2.4 LS- vs. jj-Coupled Ground State: Example for f2 347
11.8.3 Intermediate Coupling 348
11.8.4 Moments for f2 349
11.8.4.1 Spin–Orbit Expectation Value 349
11.8.4.2 Orbital and Spin Magnetic Moments 350
11.9 Spectral Calculations 351
11.10 Spin–Orbit Interaction and Sum Rule Analysis 352
11.11 Validity of the Sum Rule 353
11.12 Experimental Results for the N4,5 Edges 355
11.12.1 What Our Results Mean for Pu Theory 357
11.13 Conclusions 358
References 358
12 Magnetic Imaging with X-rays 361
12.1 Introduction 361
12.2 Concepts of Magnetic Imaging Contrast 363
12.2.1 XMCD Image 364
12.2.2 XMLD Images 367
12.2.3 Polarization Control 370
12.2.4 Local Spectra 371
12.2.5 Spatial Resolution 372
12.3 Realization of the Magnetic Contrastwith Different Microscopes 374
12.3.1 Photoemission Electron Microscope 374
12.3.2 STXM/TXM 375
12.3.3 ``Lensless'' Imaging 377
12.3.4 Combining Scanning Probes with X-Rays 379
12.4 Summary 380
References 380
13 Domain Wall Spin Structures and Dynamics Probed by Synchrotron Techniques 383
13.1 Introduction 383
13.2 Techniques 385
13.3 Domain Wall Types and Wall Phase Diagrams 385
13.3.1 Theory of Head-to-Head DomainWall Spin Structures 385
13.3.2 Experimental Determination of Head-to-Head Domain Wall Spin Structures 387
13.3.2.1 Spin Structures in Ni80Fe20 (Permalloy) 387
13.3.3 Further Head-to-Head Domain Wall Types 389
13.3.3.1 Complex Wall Types in Permalloy 389
13.3.3.2 Domain Wall Spin Structures in Fe3O4 (Magnetite) 390
13.4 Domain Wall Dynamics 392
13.4.1 Field-induced Domain Wall Propagation 393
13.4.2 Current-induced Domain Wall Propagation 393
13.4.3 Field- and Current-induced Domain WallExcitations 396
13.4.3.1 Field-induced Dynamic Wall Deflection 397
13.5 Summary 398
References 398
14 Dynamics of Mesoscopic Magnetic Objects 401
14.1 Introduction 401
14.2 Macroscopic vs. Mesoscopic Magnetic Objects 402
14.2.1 Magnetic Interactions and Domains 402
14.2.2 Magnetic Time Scales 404
14.2.3 Magnetic Length Scales 405
14.2.4 Landau–Lifshitz–Gilbert Equation 405
14.2.5 Experimental Techniques 407
14.3 Dynamics in Simple Squares 408
14.3.1 Static Mesoscopic Structures 408
14.3.2 Pulsed Field Excitations 410
14.3.2.1 Sequence of Dynamics 410
14.3.2.2 Coherent Domain Precession 411
14.3.2.3 Tuning the Response of Mesoscopic Magnetic Objects using Defects 413
14.4 Vortex Dynamics and Switching 415
14.4.1 Current Induced Resonant Vortex CoreMotion 415
14.4.2 Bistable Configurations by Pinning the Vortex Core 417
14.4.3 Resonant Burst Switching 418
14.5 Summary 419
References 420
15 From Third- to Fourth-Generation Light Sources: Free-Electron Lasers in the UV and X-ray Range 422
15.1 Introduction 422
15.2 The SASE Process and Short-wavelengthFree-Electron Lasers 424
15.3 First Results at FLASH and the Science Casefor X-Ray FELs 426
15.4 The Quest for Hard X-Ray FELs 429
15.5 Seeded Free-Electron Lasers 432
References 433
Contributors 435