Quantum theory of magnetism
Внимание. Билеты, полученные на экзамене, - затравка для разговора с преподавателем. Оцениваться будет знание всего курса, а не конкретных попавшихся тем.
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 4. Spherical and cubic harmonics, crystal-field splitting in a nut shell [slides]
Lecture 5. Group theory in a nutshell, its application for crystal-fields (not for exam) [slides]
Lecture 6. The Jahn-Teller effect, txE and txT problems [slides]
Lecture 7. Intra-atomic exchange interaction, spin-state transitions, orbital moment quenching [slides]
Lecture 8. Curie law, Brillouin function, imprtance of orbital moment quenching [slides]
Correlation effects
Lecture 9. Second quantization. Tight-binding approximation [slides]
Lecture 10. Mott insulators. Hubbard model. Metal-insulator transitions. Spectral function in Hubbard model. Phase diagram of non-degenerate Hubbard model on the square lattice. [slides]
Lecture 11. Different types of insulators (band, Mott, Slater, charge-transfer). [slides]
Heisenberg-like models
Lecture 11. Derivation of the Heisenberg model, symmtric and antisymmetric exchanges, Dzyaloshinskii-Moriya vector. Heisenberg's misperception. [slides]
Lecture 12. Classical Heisenberg, Ising, XY models. Connection between Hubbard and Heisenberg models. [slides]
Lecture 13. Exchange due to tunneling of electrons. Goodenough - Kanamori - Anderson rules. Kugel-Khomskii model [slides]
Lecture 14. Superexchange interaction. Double exchange. [slides]
Different approaches to Heisenberg model
Lecture 15. Magnetic spirals, Luttinger-Tizsa method for classical Heisenberg model. [slides]
Lecture 16. Mean-field approximation to Heisenberg model. [slides]
Lecture 17. Curie-Weiss law. Critical indexes. Spin-wave theory for ferromagnets. [slides]
Lecture 18. Mermin-Wagner theorem and why our world is 3D. Spin-wave theory for antiferromagnets. [slides]
Low-dimensional magnetism
Lecture 19. Dimers, spin gaps, Schottky anomaly. AFM chains in Ising model. AFM chain in Heisenberg model [slides]
Lecture 20. Spinons, Haldane chains. 2D Ising. Frustrations, spin liquids. Berezinskii-Kosterlitz-Thauless transiton. Frustration [slides]
Lecture 21. Kitaev model. Single-ion anisotropy. Spin ice. Magnetic monopoles. Order-by-disorder [slides]
Magnetism of itinerant (metallic) electrons
Lecture 22. Fermi gas. Pauli susceptebility. Screening of Coloumb interavtion in metals. Fermi-liquid [slides]
Lecture 23. Linear response theory, Lindhard's formula [slides]
Lecture 24. RKKY exchange. Nesting of the Fermi surface. Peierls transition, spin and charge density waves (SDW and CDW) [slides]
Lecture 25. Susceptibility of interacting electronic "gas". Generalized Stoner criterium. Mechanism of spin density waves (SDW) formation [slides]
Strong correlations in metallic systems
Lecture 26. Periodic and impurity Anderson models, Vonskovskii s-d and Kondo models [slides]
Lecture 27. Kondo problem, Abrikosov-Suhl resonance. Heavy fermions [slides]
Lecture 28. Mixed-valence compounds. Hybridization gap, Kondo insulators. Doniach phase diagram [slides]
Experimental methods in magnetism
Lecture 29. Elastic and inelastic neutron scattering [slides]
Lecture 30. Resonance methods: ferromagnetic, antiferromagnetic, electron spin and nuclear resonance