Introduction to the Theory of Ferromagnetism

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.

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