Quantum Theory of Magnetism

 

Lecture # 1                   28.10.05

 

Introduction. Spin. Various magnetic states. Connection between spin and statistics. Fermions and Bosons. Pauli principle. Paramagnetism. Pauli susceptibility.

 

Lecture # 2                   04.11.05

 

Classical and quantum ferromagnetism. Classical magnetic moments. Langevin function. Curie susceptibility. Molecular (Weiss) field. Curie-Weiss susceptibility. Atomic magnetic moments. Russell-Saunders coupling scheme. Brillouin  function.

 

Lecture # 3                   11.11.05

 

Spin exchange models. Ising model. XY model. Heisenberg model. Mean field approach. Static susceptibility. Ornstein-Zernike function. Susceptibility of Heisenberg ferromagnets. Curie temperature. Heisenberg antiferromagnets. Neel temperature. Susceptibility of ferrimagnets.

 

Lecture # 4                   18.11.05

 

Bloch equations (I).  Dynamic susceptibility of weakly interacting local moments. Macroscopic description: equations of motion. Density matrix approach.

 

Lecture # 5                   25.11.05

 

Bloch equations (II).  Calculation of dynamic susceptibility: local moments in transverse magnetic field. Transverse and longitudinal relaxation times.

 

Lecture # 6                 02.12.05 *)

 

Phase transitions. Examples of magnetic phase transitions. Classification of phase transitions. Phase transitions of 1st order.  Landau theory of 2nd order phase transitions. Critical exponents. Fluctuations. Ornstein-Zernike theory. Ginzburg number. Scaling equations.

 

Lecture # 7                 09.12.05 *)

 

Quantum phase transitions. Excitations in 1D Ising model in transverse magnetic field. QPT in local and itinerant magnets: Millis-Hertz theory.

 

Lecture # 8                   16.12.05

 

Landau-Lifshitz equations. Excitations in magnets: macroscopic description. Magnons in ferromagnets. Magnons in antiferromagnets. Thermodynamics of ferro- and antiferromagnets.

 

Lecture # 9                   23.12.05 (facultative)

 

Causality. Karmers-Kronig relations. Fluctuation-dissipation theorem (FDT). Onsager symmetry relations.

 

Lecture # 10                 13.01.06

 

Microscopic description of local magnetism. Excitations in magnets: microscopic description. Holstein-Primakoff representation. Dyson-Maleev representation. Bogoliubov transformation. Spin waves in ferromagnets. Spin waves in antiferromagnets. Magnon-magnon interaction.

 

Lecture # 11                 20.01.06

 

Ferromagnetism in metals. Stoner model. Hubbard model. Anderson model. Spin Density Waves. Magnetism in strongly correlated systems. Neutron scattering.

 

Lecture # 12                 27.01.06

 

Magnetism of electronic systems. Electron in magnetic field (level quantization). Landau levels. Degeneracy. Diamagnetism. Oscillations. De Haas –van Alphen effect.

 

Lecture # 14                 03.02.06

 

Magnetic correlations. Magnetic impurities in non-magnetic metals. Kondo effect. Calculation of resistivity. RKKY interaction. Oscillation of exchange integral. Magnetic orderings. Spin glasses.

 

Lecture # 15                 10.02.06

 

Magnetism in mesoscopic systems. Quantum dots. Magnetotransport. Spintronics.

 

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,
Cambridge, 1979)

 

 

*) Lectures will be cancelled due to my travel to US. Printouts of the lecture notes for these lectures will be available.