1 One-dimensional Magnetism: An Overview of the Models ......... 1
1.1 Introduction ............................................ 1
1.2 Quantum-spin Heisenberg Chains: Numerical Models ........ 4
1.2.1 General Method ................................... 4
1.2.2 Linear Ferrimagnetic Chains ...................... 5
1.2.3 Complex Quantum-spin Heisenberg Chains ........... 8
1.3 Classical-spin Heisenberg Chains ....................... 12
1.3.1 Fisher's Model .................................. 12
1.3.2 Linear Ferrimagnetic Chains and Related
Random Systems .................................. 14
1.3.3 Complex Classical-spin Heisenberg Chains ........ 20
1.4 Quantum-classical Heisenberg Ferrimagnetic Chains ...... 23
1.4.1 Alternation of Quantum and Classical Spins:
Uniform and Alternating Quantum-classical
Chains .......................................... 23
1.4.2 Alternation of a Classical Spin with a
Quantum System .................................. 27
1.4.3 Other Complex Quantum-classical ID Systems ...... 28
1.5 Ising Chains ........................................... 30
1.5.1 The Transfer-matrix Method ...................... 30
1.5.2 Ferrimagnetic Ising Chains and Related Random
Systems ......................................... 32
1.5.3 Exotic Chains Showing Ising Coupling ............ 37
1.6 Spin Chains with Anisotropic Exchange Interactions ..... 41
1.7 Conclusion ............................................. 43
2 Haldane Quantum Spin Chains ................................. 49
2.1 Introduction ........................................... 49
2.2 Theoretical Survey ..................................... 50
2.2.1 The Hamiltonian ................................. 50
2.2.2 Isotropic Case: the Haldane Conjecture .......... 50
2.2.3 Effect of Anisotropy and Interchain
Interactions on the Haldane Gap ................. 54
2.2.4 Haldane-gap Antiferromagnet in Applied Fields ... 57
2.2.5 S = 1/2 Spin Chains with Alternating F and AF
Interactions .................................... 57
2.3 Quasi-ID Antiferromagnets for Haldane Gap
Experiments ............................................ 58
2.3.1 Conditions for Obtaining Haldane Systems ........ 58
2.3.2 Fulfilling the Structural and Electronic
Conditions for Obtaining Haldane Systems ........ 60
2.3.3 Some Haldane Gap Systems ........................ 65
2.4 Static Magnetic Properties of Haldane Gap Systems ...... 67
2.4.1 Magnetic Susceptibility ......................... 67
2.4.2 Magnetic Specific Heat .......................... 69
2.4.3 High-field Magnetization ........................ 70
2.4.4 Long-range Order ................................ 71
2.5 Dynamic Properties of Haldane Gap Systems .............. 71
2.5.1 Spin Dynamics at Intermediate Energy (Ј ≈ Д) .... 74
2.5.2 Spin Dynamics at Low Energy (Ј << Д) ............ 83
2.6 Effect of Chain Breaking by Impurities ................. 85
2.7 Conclusion ............................................. 87
3 Spin-Peierls Materials ...................................... 95
3.1 Introduction ........................................... 95
3.2 Inorganic SP Materials ................................. 96
3.2.1 CuGeO3 .......................................... 96
3.2.2 Impurity-doped СuGеО3 Systems .................. 105
3.2.3 α'-NaV2O5 ...................................... 108
3.2.4 Doping in the α'-NaV2O5 System ................. 113
3.3 Organic SP Materials .................................. 114
3.3.1 (TTF)M(BDT): M = Cu, Au ........................ 115
3.3.2 MEM(TCNQ)2 ..................................... 116
3.3.3 DAP(TCNQ) ...................................... 117
3.3.4 (TMTTF)2PF6 .................................... 117
3.3.5 (BCPTTF)2X ..................................... 119
3.3.6 α'-(ET)2 Ag(CN)2 ............................... 120
3.3.7 β'-(ET)2SF5CF2SO3 ............................... 121
3.3.8 Perylene ....................................... 121
3.3.9 ζ-(ET)PF6 ...................................... 123
3.4 Summary ............................................... 123
4 Magnetic Measurements at the Atomic Scale in Molecular
Magnetic and Paramagnetic Compounds ........................ 131
4.1 XAS and XMCD .......................................... 131
4.1.1 X-Ray Absorption Spectroscopy .................. 131
4.1.2 X-Ray Magnetic Circular Dichroism .............. 133
4.2 Sum Rules for XMCD .................................... 134
4.2.1 The Magnetic Sum Rules ......................... 134
4.2.2 Validity of the Sum Rules ...................... 135
4.2.3 The Contribution from the Magnetic Dipole
Operator ....................................... 136
4.2.4 Checking the Theory with the Theory ............ 136
4.3 Chemical Bond and Magnetism Explored by XMCD
in Prussian Blue Analogs .............................. 137
4.3.1 Chemical Bond in CsI[NiIICrIII(CN)6]-2H2O ........ 137
4.3.2 Local Magnetic Moments by XMCD in
CsI[NiIICrIII(CN)6]-2H2O ......................... 140
4.3.3 Magnetic Anisotropy in
CsI[NiIICrIII(CN)6]-2H2O ......................... 141
4.3.4 Application of One-electron Theory to XMCD ..... 142
4.4 Local Magnetic Structure in Room-temperature
Molecule-based Magnets ................................ 144
4.5 Paramagnetic Complexes ................................ 147
4.5.1 Instrumentation ................................ 147
4.5.2 High-spin Paramagnetic Heptanuclear
Chromicyanides ................................. 148
4.5.3 XMCD in Metal Clusters of Metalloproteins ...... 150
4.6 Conclusion ............................................ 150
5 Magnetic Properties of Mixed-valence Systems: Theoretical
Approaches and Applications ................................ 155
5.1 Introduction .......................................... 155
5.2 Double-exchange Mechanisms ............................ 156
5.3 Classical Spin Model for the Double Exchange .......... 158
5.4 Mixed-valence Dimers .................................. 160
5.4.1 Electronic Interactions ........................ 160
5.4.2 Vibronic Interactions in Dimers ................ 166
5.4.3 Examples ....................................... 179
5.5 Mixed Valence Trimers ................................. 180
5.5.1 Electronic Interactions ........................ 180
5.5.2 Vibronic Interactions in Trimers ............... 185
5.5.3 Examples ....................................... 189
5.6 Mixed Valence Tetramers ............................... 190
5.6.1 Electronic Interactions ........................ 190
5.6.2 Vibronic Interactions in Tetramers ............. 194
5.7 Higher Nuclearity Mixed Valence Clusters .............. 197
5.7.1 Electronic Interactions in Polyoxometalates .... 199
5.7.2 Vibronic Interactions in Polyoxometalates ...... 201
5.7.3 Other High Nuclearity Mixed-valence Systems .... 203
5.8 Final Remarks ......................................... 206
5.8.1 Role of the Electron Transfer .................. 207
5.8.2 Role of the Second-order Electronic
Processes ...................................... 207
5.8.3 Role of the Vibronic Coupling .................. 208
6 Magnetocrystalline Anisotropy of Transition Metals:
Recent Achievements in X-ray Absorption Spectroscopy ....... 211
6.1 Introduction .......................................... 211
6.2 The X-ray Magnetic Circular Dichroism Technique ....... 211
6.2.1 An Historical Survey ........................... 212
6.2.2 Theoretical Background ......................... 212
6.2.3 The Sum Rules .................................. 214
6.2.4 Conclusion ..................................... 215
6.3 The Anisotropy of the Orbital Magnetic Moment ......... 216
6.3.1 Probing the Magnetocrystalline Anisotropy
Energy ......................................... 216
6.3.2 A Perturbation Approach ........................ 217
6.3.3 XMCD Measurements in Collinear and Transverse
Geometries ..................................... 220
6.4 Magnetocrystalline Anistropy of CoxPtl-x Thin Film
Alloys ................................................ 224
6.4.1 Experimental ................................... 224
6.4.2 XMCD at the Co L2,3 Edges ....................... 225
6.4.3 MCA in 3d/5d Systems ........................... 229
6.4.4 XMCD at the Pt L2,3 Edges ....................... 230
6.4.5 Discussion ..................................... 231
6.5 Conclusion ............................................ 232
7 Muon-spin Rotation Studies of Molecule-based Magnets ....... 235
7.1 Introduction .......................................... 235
7.2 The Principles of the Experimental Technique .......... 237
7.3 Experimental Results .................................. 246
7.3.1 Nitronyl Nitroxides ............................ 246
7.3.2 Other Molecular Magnets ........................ 249
7.3.3 Organic Salts .................................. 251
7.3.4 Nanomagnets .................................... 253
7.4 Conclusions ........................................... 253
8 Photomagnetic Properties of Some Inorganic Solids .......... 257
8.1 Introduction .......................................... 257
8.2 Technical and Practical Aspects ....................... 259
8.2.1 Magnetic and Reflectivity Measurements:
Twofold Access to the Behavior under
Photoexcitation ................................ 260
8.2.2 An Unavoidable Side-effect: Heating of the
Sample ......................................... 263
8.2.3 The Problem of Bulk Absorption of Light ........ 264
8.3 Cooperative Effects ................................... 264
8.3.1 The Intensity Threshold Effect ................. 268
8.4 Magnetic Properties of Prussian Blue Analogs .......... 270
8.4.1 Light-stimulated MAE of Cs0.83 [Cr2.10(CN)6]
• 3.9H2O ....................................... 273
8.4.2 The Photo-induced Ferrimagnetic State of
Rb0.52Co[Fe(CN)6]0.84-2.31H20 .................... 280
8.4.3 The Magnetic Properties of the Photo-induced
State .......................................... 283
8.5 The Valence Tautomeric Solid Co-semiquinone ........... 288
8.6 Conclusion and Perspectives ........................... 291
9 Colossal Magnetoresistance and Charge-ordering in Rare
Earth Manganites ........................................... 297
9.1 Abstract .............................................. 297
9.2 Introduction .......................................... 297
9.3 From Hole-doped to Electron-doped CMR Manganites ...... 298
9.4 Key Factors Controlling the CMR Properties-Magnetic
Phase Diagrams ........................................ 301
9.5 Structural Transitions ................................ 307
9.6 Charge-ordering ....................................... 308
9.7 Effect of Mn-site Doping .............................. 320
10 Neutron Scattering and Spin Densities in Free Radicals ..... 325
10.1 Introduction .......................................... 325
10.2 Measurement and Reconstruction of Magnetization
Distributions ......................................... 325
10.2.1 Experimental Technique ......................... 325
10.2.2 Methods of Analysis ............................ 327
10.2.3 Ab-initio Calculations of the Spin Density ..... 329
10.3 Spin Densities in Isolated Radicals ................... 330
10.3.1 The Spin Derealization Effect .................. 331
10.3.2 The Spin Polarization Effect ................... 333
10.3.3 The Shape of the Spin Density .................. 337
10.4 Spin Densities in Interacting Molecules ............... 339
10.4.1 Positive Coupling Between Neighboring
Molecules ...................................... 339
10.4.2 Hydrogen Bonds ................................. 345
10.4.3 Strongly Interacting Spin Carriers ............. 348
10.5 Conclusions ........................................... 353
11 Spin Distributions in Molecular Systems with Interacting
Transition Metal Ions ...................................... 357
11.1 Introduction .......................................... 357
11.2 Antiferromagnetic Intramolecular Coupling
in Heterometallic Dimers .............................. 359
11.2.1 Short Bridge in a CuIINiII Dimer ................ 359
11.2.2 Extended Bridge in a MnIICuII Dimer ............. 361
11.3 From a Molecule to a Chain of Antiferromagnetically
Coupled MnnCunIons .................................... 364
11.4 Ferromagnetic Coupling in Copper(II) Dimers ........... 367
11.4.1 Di-μ-hydroxo Bridged Dimer Cu(OH)2Cu ........... 367
11.4.2 Di-μ-azido Bridged Copper Dimer Cu(N3)2Cu ...... 369
11.5 Ferromagnetic Chain Bimetallic Compound ............... 370
11.6 Clusters .............................................. 372
11.6.1 Mn12 Cluster ................................... 372
11.6.2 Мп10 Cluster ................................... 373
11.6.3 Fe8 Cluster .................................... 374
11.7 Conclusion ............................................ 375
12 Probing Spin Densities by Use of NMR Spectroscopy .......... 379
12.1 Introduction .......................................... 379
12.2 The Spin Density and its Sign ......................... 381
12.3 Relating Spin Density to Magnetic Resonance ........... 381
12.4 The NMR Method: Effects of Unpaired Electrons ......... 383
12.4.1 Experimental Hints ............................. 383
12.4.2 Relaxation Constraints ......................... 385
12.4.3 Contact, Dipolar, and Experimental Signal
Shifts ......................................... 388
12.4.4 Signal Assignment Strategy ..................... 390
12.5 Spin Derealization Mechanisms ......................... 392
12.5.1 Spin Distribution in π Orbitals ................ 392
12.5.2 Spin Delocahzation into σ Orbitals ............. 399
12.5.3 Spin Delocahzation from π Orbitals to Nuclei
of Substituents ................................ 401
12.6 Experimental Examples ................................. 405
12.6.1 Organic Radicals ............................... 405
12.6.2 Organometallic Radicals ........................ 408
12.6.3 Paramagnetic Coordination Compounds of
Organic Ligands ................................ 415
12.6.4 Inorganic Compounds ............................ 419
12.7 Concluding Comments (Knight Shifts, Evaluation of
the NMR Method) ....................................... 421
Subject Index ................................................. 431
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