### 你将学到什么

The classification of materials by their magnetic properties

Mean-field approach to calculation of various magnetic characteristics

Summary of the phenomenological Landau model

Antiferromagnetism

### 课程概况

This course focuses on the phenomenon of ferromagnetism. Ferromagnetism is a magnetically ordered state of matter in which atomic magnetic moments are parallel to each other, so that the matter has a spontaneous magnetization. Owing to ferromagnetism, some materials (such as iron) can be attracted by magnets or become the permanent magnets themselves. The phenomenon of ferromagnetism plays an important role in modern technologies. It is a physical basis for the creation of a variety of electrical and electronic devices, such as transformers, electromagnets, magnetic storage devices, hard drives, spintronic devices, etc. However, in the absence of external magnetic field ferromagnetism does not occur at any temperature. It occurs only below some critical temperature, which is called the Curie temperature. For different ferromagnetic materials, the Curie temperature has its own value. It should be noted that the phenomenon of ferromagnetism arises due to the exchange interaction, which tends to set the magnetic moments of neighboring atoms or ions parallel to each other. The exchange interaction is a purely quantum effect, which has no analogue in classical physics. In this course we shall try to understand the microscopic origin of ferromagnetism, to learn about its experimental appearing, magnetizing field, magnetic anisotropy, and quantum mechanical effect. We try to build a quantum mechanical theory of ferromagnetism. The course is aimed to graduate students wishing to improve their level in the field of theoretical physics.

### 课程大纲

First week

Opening lecture. Classification of phase transitions

Second week

Atomic magnetic moment

Physical quantities characterizing the magnetic properties of matter

Classification of materials for their magnetic properties

Third week

Isolated local magnetic moment in an external magnetic field

A system of noninteracting local magnetic moments in an external magnetic field

Curie law

Effective Weiss field

Exchange interaction

Interaction of two local magnetic moments

Fourth week

Heisenberg model and Ising model

Mean-field approximation in the Ising model

Curie-Weiss equation and Curie-Weiss law

Ferromagnetic transition in the Ising model. Curie temperature. Order parameter

Temperature dependence of the ferromagnetic order parameter in the Ising model

Ground and excited states of a ferromagnet in the Ising model

Fifth week

Free energy of a ferromagnet in the Ising model. Free energy of a ferromagnet near the critical temperature

Spontaneous symmetry breaking at the paramagnetic-ferromagnetic transition

Phenomenological Landau theory of second-order phase transitions

Heat capacity and magnetic susceptibility of the Ising ferromagnet in the mean-field approximation

Critical exponents

Sixth week

Exact solution of the Ising model in one dimension

Ising model for antiferromagnets. Mean-field approximation. Neél temperature

Magnetic susceptibility of the Ising antiferromagnet in the mean-field approximation

Seventh week

Problems solving. Concluding remarks

### 预备知识

Basic knowledge of vector calculus, theory of functions of a complex variable, theory of differential equations, probability theory, statistical physics, and quantum mechanics is required.

### 常见问题

1. How difficult is the course?

The course is designed for graduate students. Thus, basic knowledge of quantum mechanics is obligatory.

2. What resources shall I need for this class?

All you need is time to study with video lectures. In addition, you will need a pen and paper to reproduce the most complex calculations made during the lectures yourself.

3. What is the main thing I shall learn if I take this course?

As a result of the course you will understand in detail the physical principles and mechanisms of the ferromagnetism phenomenon.