Quantum theory of magnetism
Introduction
Lecture 0. About the lecture course [slides]
Lecture 1. Introduction, Magnetic susceptibility; Dia-, para-, ferro- and antiferromagnetism [slides]
Lecture 2. Dia-, para-, ferro- and antiferromagnetism, dipole-dipole interaction, Bohr-van Leeuwen theorem [slides]
Magnetism of free ions
Lecture 3. Spin, orbital, and total moments. Hund's rules, spin-orbit coupling, atomic diamagnetism [slides]
Lecture 4. Atomic diamagnetism, Pascal constants, Van Vleck paramagnetism [slides]
Magnetism of ions in a crystal
Lecture 5. Spherical and cubic harmonics, crystal-field splitting in a nut shell, the Jahn-Teller effect [slides]
Lecture 6. Intra-atomic exchange interaction, spin-state transitions, orbital moment quenching [slides]
Lecture 7. Curie law, Brillouin function, imprtance of orbital moment quenching [slides]
Correlation effects
Lecture 8. Second quantization. Tight-binding approximation [slides]
Lecture 9. Mott insulators. Hubbard model. Metal-insulator transitions. Spectral function in Hubbard model. Phase diagram of non-degenerate Hubbard model on the square lattice. Different types of insulators (band, Mott, Slater, charge-transfer). [slides]
Heisenberg-like models
Lecture 10. Derivation of the Heisenberg model, symmtric and antisymmetric exchanges, Dzyaloshinskii-Moriya vector. Heisenberg's misperception. Different spin models. [slides]
Lecture 11. Exchange due to tunneling of electrons. Goodenough - Kanamori - Anderson rules. [slides]
Lecture 12. Kugel-Khomskii model. Superexchange interaction. Double exchange. [slides]
Different approaches to Heisenberg model
Lecture 13. Magnetic spirals, Luttinger-Tizsa method for classical Heisenberg model. [slides]
Lecture 14. Mean-field approximation to Heisenberg model. Curie-Weiss law. Critical indexes. [slides]
Lecture 15. Spin-wave theory for ferromagnets.