Magnetism

Abstract

This chapter discusses various types of magnetic order in materials and underscores the importance of electronic interactions in inducing ferromagnetic and antiferromagnetic order in magnetic solids. Different theoretical spin Hamiltonians, such as the Ising model, quantum XY model, Heisenberg model, etc., are introduced and the corresponding solutions, for example, the transfer matrix method, linear spin wave theory, etc., are hence discussed with a view to obtaining the magnetization and the ground state energy of a magnetic system. Since magnetism is intrinsically an electronic phenomenon, and that the electronic interactions are indispensable, a jellium model is introduced and solved within a mean field approximation to ascertain the magnetic properties, and the inadequacies therein for such a model. Subsequently, the Hubbard model is introduced and the corresponding symmetries are discussed. The model is further solved within a Hartree-Fock approximation to explain the ferromagnetic and antiferromagnetic orderings in crystal lattices.