Introduction ................................................... ix
1 Localized and itinerant electrons in solids .................. 1
1.1 Itinerant electrons, band theory ........................ 1
1.2 Hubbard model and Mott insulators ....................... 5
1.3 Magnetism of Mott insulators ........................... 11
1.4 Interplay of electronic motion and magnetism in Mott
insulators ............................................. 14
1.5 Doped Mott insulators .................................. 19
S.l Summary of Chapter 1 ................................... 22
2 Isolated transition metal ions .............................. 25
2.1 Elements of atomic physics ............................. 25
2.2 Hund's rules ........................................... 28
2.3 Spin-orbit interaction ................................. 31
S.2 Summary of Chapter 2 ................................... 35
3 Transition metal ions in crystals ........................... 37
3.1 Crystal field splitting ................................ 37
3.2 Jahn-Teller effect for isolated transition metal ions .. 57
3.3 High-spin vs low-spin states ........................... 65
3.4 Role of spin-orbit coupling ............................ 71
3.5 Some general principles of the formation of typical
crystal structures of transition metal compounds ....... 78
S.3 Summary of Chapter 3 ................................... 91
4 Mott-Hubbard vs charge-transfer insulators .................. 94
4.1 Charge-transfer insulators ............................. 94
4.2 Exchange interaction in charge-transfer insulators .... 103
4.3 Systems with small or negative charge-transfer gap .... 105
4.4 Zhang-Rice singlets ................................... 108
S.4 Summary of Chapter 4 .................................. 118
5 Exchange interaction and magnetic structures ............... 120
5.1 Superexchange in insulators and Goodenough-Kanamori-
Anderson rules ........................................ 120
5.2 Double exchange ....................................... 136
5.3 Role of spin-orbit interaction: magnetic anisotropy,
magnetostriction, and weak ferromagnetism ............. 142
5.4 Systems with unquenched orbital moments ............... 156
5.5 Singlet magnetism ..................................... 159
5.6 Magnetic ordering in some typical situations .......... 163
5.7 Frustrated magnets .................................... 173
5.8 Different magnetic textures ........................... 191
5.9 Spin-state transitions ................................ 194
S.5 Summary of Chapter 5 .................................. 198
6 Cooperative Jahn-Teller effect and orbital ordering ........ 204
6.1 Cooperative Jahn-Teller effect and orbital ordering
in eg systems ......................................... 205
6.2 Reduction of dimensionality due to orbital ordering ... 221
6.3 Orbitals and frustration .............................. 225
6.4 Orbital excitations ................................... 227
6.5 Orbital effects for t2g-electrons ..................... 228
6.6 Quantum effects in orbitals ........................... 231
S.6 Summary of Chapter 6 .................................. 234
7 Charge ordering in transition metal compounds .............. 238
7.1 Charge ordering in half-doped systems ................. 240
7.2 Charge ordering away from half-filling ................ 244
7.3 Charge ordering vs charge density waves ............... 253
7.4 Charge ordering in frustrated systems: Fe304 and
similar ............................................... 255
7.5 Spontaneous charge disproportionation ................. 259
S.7 Summary of Chapter 7 .................................. 265
8 Ferroelectrics, magnetoeiectrics, and multiferroics ........ 269
8.1 Different types of ferroelectrics ..................... 269
8.2 Magnetoelectric effect ................................ 282
8.3 Multiferroics: materials with a unique combination
of magnetic and electric properties ................... 288
8.4 "Multiferroic-like" effects in other situations ....... 303
S.8 Summary of Chapter 8 .................................. 307
9 Doping of correlated systems; correlated metals ............ 310
9.1 Nondegenerate Hubbard model at arbitrary band
filling ............................................... 311
9.2 Representative doped transition metal oxides .......... 319
9.3 Doped Mott insulators: ordinary metals? ............... 331
9.4 Magnetic properties of doped strongly correlated
systems ............................................... 338
9.5 Other specific phenomena in doped strongly
correlated systems .................................... 341
9.6 Superconductivity in strongly correlated systems ...... 350
9.7 Phase separation and inhomogeneous states ............. 357
9.8 Films, surfaces, and interfaces ....................... 363
S.9 Summary of Chapter 9 .................................. 371
10 Metal-insulator transitions ................................ 378
10.1 Different types of metal-insulator transitions ........ 378
10.2 Examples of metal-insulator transitions in systems
with correlated electrons ............................. 384
10.3 Theoretical description of Mott transitions ........... 404
10.4 Insulator-metal transitions for different electronic
configurations ........................................ 408
10.5 Insulator-metal transitions in Mott-Hubbard and
charge-transfer insulators ............................ 415
10.6 Formation of molecular clusters and "partial" Mott
transitions ........................................... 420
10.7 Mott transition: a normal phase transition? ........... 426
S.10 Summary of Chapter 10 ................................. 428
11 Kondo effect, mixed valence, and heavy fermions ............ 433
11.1 Basic features of/-electron systems ................... 433
11.2 Localized magnetic moments in metals .................. 436
11.3 Kondo effect .......................................... 438
11.4 Heavy fermions and mixed valence ...................... 442
S.11 Summary of Chapter 11 ................................. 448
Appendix A Some historical notes ............................. 452
A.l Mott insulators and Mott transitions .................. 452
A.2 Jahn-Teller effect .................................... 456
A.3 Peierls transition .................................... 456
Appendix В A layman's guide to second quantization ........... 459
Appendix С Phase transitions and free energy expansion:
Landau theory in a nutshell ................................ 462
C.l General theory ........................................ 462
C.2 Dealing with the Landau free energy functional ........ 464
C.3 Some examples ......................................... 466
References .................................................... 469
Index ......................................................... 481
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