6 Magnetism and Conduction ............................. 1 7 7
6.1 Electron Hopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.2 Double Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
6.3 A Quantum Chemical Approach to Magnetic Interactions
in the Solid State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.3.1 Embedded Cluster Approach . . . . . . . . . . . . . . . . . . . . . 190
6.3.2 Periodic Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.4 Goodenough–Kanamori Rules . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.5 Spin Waves for Ferromagnets . . . . . . . . . . . . . . . . . . . . . . . . . 204
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Appendix A: Effect of the ^ l Operator and the Matrix Elements
of the p and d Orbitals ......................... 2 1 3
Appendix B: Effect of the ^
S Operator and the Matrix Elements
for
1
2 ≤ S ≤
5
2 ................................. 2 1 5
Appendix C: Matrix Representation of the ZFS Model
Hamiltonian ................................. 2 1 7
Appendix D: Analytical Expressions for χðTÞ ................... 2 1 9
Appendix E: Solutions .................................... 2 2 3
Index ................................................ 2 4 3
Contents
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