Symmetry Analysis of Magnetic Structures on the Basis of the Theory of Representations

Abstract

We develop in this chapter the general symmetry analysis method of magnetic structures of crystals on the basis of the theory of space group representations, wherein the magnetic structure is expanded in terms of the basis functions of irreducible representations of the space group of the crystal. The principal assumption of the symmetry theory of phase transitions, namely that a transition to a phase of lower symmetry takes place through an irreducible representation of the symmetry group of the initial phase, makes it possible to reduce the problem of magnetic structures which can exist in a given crystal to sorting versions of mixed basis functions of a single representation. We perform a symmetry analysis of the exchange Hamiltonian and show which information on possible magnetic structures of a crystal can be obtained from the eigenfunctions of this Hamiltonian. We establish a symmetry relation between the eigenstates of the exchange Hamiltonian and the basis functions of the irreducible representations of the space groups. This chapter expounds the principal method of using symmetry analysis in neutron diffraction and for the description of magnetic structures of crystals.