ELECTRONIC STRUCTURE, CORRELATION EFFECTS AND PHYSICAL PROPERTIES OF d- AND f-TRANSITION METALS AND THEIR COMPOUNDS
By V.Yu.Irkhin and Yu.P.Irkhin
Contents
1 INTRODUCTION 11
1.1 Partly filled atomic shells and electron localization in transition metals . . . . . . . . . . . . . . . . . 11
1.2 Atomic and band approaches in the transition element theory 15
1.3 Crystal field and orbital momenta in solids . . . . . . . . . . . 19
2 BAND THEORY 23
2.1 Orthogonalized plane wave method and pseudopotential . . . 27
2.1 Orthogonalized plane wave method and pseudopotential . . . 27
2.2 Augmented plane wave (APW) and Korringa-Kohn-Rostoker (KKR) methods . . . . . . . . . . 30
2.3 The Hartree-Fock-Slater and density functional approaches to the problem of electron correlations . . . . . . . . . . . . . . . 34
2.4 Discussion of band calculation results . . . . . . . . . . . . . . 43
2.5 Experimental investigations of band structure: spectral data . 48
2.6 Band calculations of rare earths and actinides . . . . . . . . . 54
2.7 Fermi surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.7.1 Methods of Fermi surface investigation and de Haasvan Alphen effect . . . . . . . . . . . . . . . . 59
2.7.2 Experimental and theoretical results on the Fermi surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 63
3 THERMODYNAMIC PROPERTIES 71
3.1 Cohesive energy and related properties . . . . . . . . . . . . . 71
3.2 Crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3 Specific heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.1 Lattice specific heat . . . . . . . . . . . . . . . . . . . 82
3.3.2 Electronic specific heat . . . . . . . . . . . . . . . . . . 85
3.3.3 Specific heat of magnetic metals . . . . . . . . . . . . . 90
4 MAGNETIC PROPERTIES 93
4.1 Exchange interactions and the Heisenberg model for localized spins . . . . . . . . . . . . . . . . . . . . 94
4.2 Magnetic susceptibility of paramagnetic transition metals . . . 98
4.3 Itinerant electron ferromagnetism and the Stoner theory . . . 102
4.4 Spin-fluctuation theories . . . . . . . . . . . . . . . . . . . . . 108
4.5 Electronic structure and properties of half-metallic ferromagnets114
4.6 Magnetism of highly-correlated d-systems . . . . . . . . . . . . 121
4.7 Magnetism of rare earths and actinides . . . . . . . . . . . . . 128
4.8 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . 133
4.8.1 Quenching of orbital momenta by periodic lattice potential and magnetic anisotropy of d-metals . . . . . . 135
4.8.2 Magnetic anisotropy of rare earths . . . . . . . . . . . 138
5 TRANSPORT PROPERTIES 143
5.1 General classification of transport phenomena . . . . . . . . . 144
5.2 Calculation of transport coefficients . . . . . . . . . . . . . . . 148
5.3 Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.3.1 Electron-electron scattering . . . . . . . . . . . . . . . 153
5.3.2 Mott s-d scattering mechanism . . . . . . . . . . . . . 157
5.3.3 Resistivity of magnetic metals . . . . . . . . . . . . . . 158
5.3.4 Resistivity of transition metal alloys . . . . . . . . . . 163
5.3.5 Two-current model of ferromagnetic metals . . . . . . . 164
5.4 Thermoelectric power . . . . . . . . . . . . . . . . . . . . . . . 169
5.5 The Hall effect . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.6 Magnetoresistivity . . . . . . . . . . . . . . . . . . . . . . . . 177
5.7 Anomalous transport effects in ferromagnetic metals . . . . . . 181
5.7.1 The extraordinary Hall effect . . . . . . . . . . . . . . 181
5.7.2 Magnetoresistivity in the presence of spontaneous magnetization . . . . . . . . . . . . . . . . . . . . . . . . . 190 5.7.3 Magnetooptical effects . . . . . . . . . . . . . . . . . . 192
5.7.4 Thermomagnetic effects . . . . . . . . . . . . . . . . . 196
6 THE KONDO EFFECT AND PROPERTIES OF ANOMALOUS d- AND f-COMPOUNDS 199 6.1 The one-centre Kondo effect . . . . . . . . . . . . . . . . . . . 201
6.2 The Kondo temperature for d-impurities . . . . . . . . . . . . 205
6.3 Spin dynamics and electronic properties of Kondo lattices . . . 208
6.4 Ground state of the Kondo lattices . . . . . . . . . . . . . . . 212
6.5 Intermediate valence systems . . . . . . . . . . . . . . . . . . . 216
6.6 Magnetic ordering in Kondo lattices and heavy-fermion compounds . . . . . . . . . . . . . . . . . 224
6.7 Current carriers in a two-dimensional antiferromagnet . . . . . 234
6.8 Spin-liquid state in systems with spin and charge degrees of freedom . . . . . . . . . . . . . . . . . . . 240
CONCLUSIONS 247
APENDIXES
A Many-electron creation operators for atomic configurations and Hubbard’s operators 251
B Angular momentum operators and double irreducible tensor operators 259
C Hamiltonian of a crystal with many-electron atoms 267
D Interatomic electrostatic interaction and derivation of the Heisenberg Hamiltonian 275
E Spin waves in Heisenberg magnets and the Green’s function method 283
F Hubbard operator approach in the Heisenberg model 291
G Electron-magnon interaction in magnetic metals 297
G.1 Ferromagnets . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
G.2 Antiferromagnets . . . . . . . . . . . . . . . . . . . . . . . . . 310
H The Hubbard model with strong correlations 321
I Narrow-band s-d exchange model and t-J model 327
J APPENDIX J Electron states and spin waves in the narrowband Hubbard ferromagnet 331
K s − f exchange model and indirect exchange interaction in rare earths 337
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