Theory
of Magnetism
Lecture
# 1
Introduction. Spin.
Various magnetic states. Connection between spin
and statistics. Fermions and Bosons. Pauli principle. Fermi sphere.
Lecture
# 2
Magnetism of itinerant electrons. Pauli paramagnetism. Electron in a magnetic field. Landau
levels. Landau diamagnetism.
Lecture
# 3
Semi-classical theory of local ferromagnetism. Classical magnetic moments. Langevin function. Spins and orbital moments. Brillouin function.
Curie
susceptibility. Molecular (Weiss) field. Curie-Weiss susceptibility.
Lecture
# 4
Quantum theory of local magnetism. Microscopic models of magnetism.
Ising model. XY model. Heisenberg model. Random Phase approximation.
Static
susceptibility. Ornstein-Zernike
function. Susceptibility of Heisenberg ferromagnets.
Lecture
# 5
Microscopic description of local ferromagnetism. Excitations in magnets:
microscopic description. Holstein-Primakoff representation. Goldstone theorem.
Magnons.
Transverse and longitudinal susceptibilities.
Lecture
# 6
Microscopic description of local antiferromagnetism. Antiferromagnetic magnons.
Transverse and longitudinal susceptibilities. Mermin-Wagner theorem.
Lecture
# 7
Spin impurities in Fermi liquids. Magnetic impurities in non-magnetic metals. Kondo effect.
Basics of scattering theory. Resistivity in Kondo regime.
Lecture
# 8
Spin dynamics. Dynamic
susceptibility of weakly interacting local moments. Macroscopic description:
equations of motion.
Calculation
of dynamic susceptibility: local moments in transverse magnetic field.
Transverse and longitudinal relaxation times. Bloch equation.
Lecture
# 9
Magnetism of nano-systems. Quantum dots. Carbon nano-tubes. Molecular transistors.
Quantum transport. Kondo effect in nano-structures. Magnetotransport. Spintronics.
Lecture
# 10
Spin impurities in Fermi liquids. Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction.
Oscillation of exchange integral. Magnetic orderings. Spin glasses.
Lecture
# 11
Magnetism of strongly correlated systems I. Stoner model. Hubbard model.
Anderson model. Spin Density Waves. Strongly Correlated Systems.
Lecture
# 12
Magnetism of strongly correlated systems II. Resonance Valence Bonds.
Magnetism in low-dimensional systems. Heavy Fermions. Organic compounds: spin chains and ladders.
Lecture
# 13
Magnetism: summary.
Examples of dia- para - ferro and antiferro- magnetic systems. Magnetisation.
Hysteresis. Magnetic domains.
Experimental techniques: Neutron scattering, Torque magnetometry, MuSR.
Application of magnetism
Tutorial
# 1
Basics
of Fermi - liquid theory.
Tutorial
# 2
Quantum
oscillator.
Tutorial
# 3
Basics
of Scattering theory.
Tutorial
# 4
Fluctuation
to Dissipation Theorem. Kramers - Kronig relations.
Recommended literature:
|
1.
|
R. White. Quantum Theory of Magnetism. (Springer-Verlag, 1983) |
|
2.
|
A. Auerbach. Interacting Electrons and
Quantum Magnetism. (Springer-Verlag,1994) |
|
3.
|
T.Moria. Spin Fluctuations in Itinerant
Electron Magnetism. (Springer-Verlag, 1985) |
|
4.
|
C.Kittel. Quantum Theory of Solids.(John Wiley and Sons, New
York 1987) |
|
5.
|
J. M. Ziman. Principles of the Theory of
Solids. (Cambridge University Press, |