Magnetism and superconductivity

The lecture aims in presenting the basics of magnetism: fundamental magnetic quantities, the nature of magnetism, magnetism of isolated magnetic ions and collective properties of interacting magnetic centers. In contrast to typical electromagnetic courses, this course focuses on microscopic phenomenas and mechanisms yielding magnetism of condensed matter, in particular of crystals and nano materials.

The lecture is addressed to the students with no knowledge of magnetism. Lecture aims in providing the basic knowledge about problems of modern magnetism. After the course the student is able to follows the actual literature of modern magnetism.

Outline of the lecture:

Fundamental magnetic quantities

Magnetic moment; Paramagnetic and diamagnetic behavior; Magnetization; Magnetic field in a magnetized matter; Work and energy in magnetic field;

Ideal, noninteracting magnetic moments

Hamiltonian in magnetic field; Magnetic moment and angular momentum; Energy and magnetic moment of a quantum state; Brillouin-type paramagnetism; Curie law; Van Vleck - type paramagnetism; Diamagnetism.

Free ions and atoms

Magnetic moments of ions and atoms; Hund’s rules; Electronic configuration of Transition Metals and Rare Earths metals; Atomic terms of TM and RE.

Magnetic ions in matter - Crystal Field

An ion in a crystal lattice; Crystal Field Model (CF); d-states in an octahedral and tetrahedral crystal field; Kramers theorem; Jahn-Teller effect; Experimental observation of CF induced energy splittings; CF quenching of orbital momentum - difference between TM and RE; Effective spin; Anisotropy of magnetization; Isotropic magnetic ions.

Interaction between magnetic ions

Interaction between magnetic moments; Heisenberg exchange interaction; The nature of Heisenberg-type interaction; Exchange interaction between to electrons; Kinetic exchange interaction; Superexchange; Double exchange; RKKY exchange; Anisotropic exchange; Dipolar interaction.

Long range magnetic order (ferromagnetic and antiferromagnetic systems)

Long range order of magnetic moments - ferromagnets; Spontaneous magnetization; Magnetic phase transition; Antiferromagnets; Typical antiferromagnetic structures; Ferrimagnets; Other ordered magnetic systems

Mean Field Approximation of paramagnetic and ferromagnetic phases

The idea of Mean Field Approximation (MFA); Exchange field; Magnetization in MFA; Paramagnetic phase in MFA; Curie-Weiss law; Ferromagnetic phase in MFA; Limitations of MFA; Corrections to MFA - Magnons; Corrections to MFA - Critical Point Approximations

Magnetic domains - the role of anisotropy

Formation of magnetic domains in ferromagnets; Domain walls; Single domain objects; Superparamagnets; Stoner-Wohlfarth model; Magnetic hysteresis; Applications of ferromagnets

Spin glasses

Random interacting magnetic systems; RKKY interaction; Frustration of magnetic system; Characteristic features of spin-glass system; Microscopic picture of a spin-glsss

Magnetic semiconductors

Semiconductors with implemented magnetic moments (DMS); Exchange interactions in magnetic semiconductors - d-d and s,p-d exchange; Modification of band structure of magnetic semiconductors; Mn-based DMS; Fe-based DMS; III-V Mn based DMS; Ferromagnetism of DMS.

Magnetism of metals

Degenerate electron gas in magnetic field; Total energy of degenerate electron gas; Pauli paramagnetism; Exchange interaction in electron gas; Ferromagnetic phase of electron gas; Stoner criterion; Ferromagnetic metals.

C. Kittel, Introduction to Solid State Physics.

A.H. Morrish, The Physical Principles of Magnetism.

S.Blundell, Magnetism in Condensed Matter

R.M. White, Quantum Theory of Magnetism

D.C. Mattis, Theory of magnetism