Chapter 8 - Itinerant antiferromagnetism

Abstract

This chapter focuses on the simple model of itinerant Antiferromagnetism. In the antiferromagnetic state, the nearest-neighbor magnetic moments are opposite to each other. The crystal lattice of an antiferromagnet can be divided into two interpenetrating sub-lattices with opposite magnetic moments. The new lattice constant, after transforming by which we return to the atom with the same magnetic moment, will be twice the original constant. The unit cell is doubled by this operation and correspondingly, the Brillouin zone is reduced by one half. The simple examples of the lattice that can be divided into two interpenetrating sub-lattices are the simple cubic (sc) and body-centered cubic (bcc) lattices. The general model of itinerant antiferromagnetism is based on the extended Hubbard quasi-single-band Hamiltonian. In this Hamiltonian, the dominant on-site Coulomb correlation U and the on-site Hund's field F are also included. The on-site Hund's field, F, can exist only as the interaction between different orbitals in a multi-orbital band, as is the case of the d-type band. The single band, composed from identical orbitals, is fully degenerate. In such a band, the effective exchange field can be expressed as F = (p−1)jin where Jin is the exchange interaction between different orbitals within the same atomic site and p is the number of orbitals within the band.