Use of Symmetry in the Determination of Magnetic Structures

Abstract

General symmetry considerations are used to determine what restrictions can be placed on the structure of the magnetic state in crystals. From the work of Landau and Lifshitz it is found that the following restrictions apply to those magnetic structures which can arise when a crystal undergoes a single second-order phase transition from the paramagnetic state to the magnetic state in question. In the immediate vicinity of the transition point the spin density of the magnetic state transforms as a basis function for a single irreducible representation of the symmetry group of the paramagnetic phase. At lower temperatures the spin density may change through the introduction of basis functions corresponding to odd order "harmonics" of the "fundamental" representation. This takes place in such a way that the symmetry of the spin density does not change. Other components may also be introduced in the spin density through other phase transitions at lower temperatures. It is further found that no such restrictions can be placed, in general, on the possible configurations of the magnetic ground state, and that definite information concerning the classical ground state cannot, therefore, be obtained by symmetry arguments alone. It is concluded that the use of symmetry in the determination of magnetic structures is restricted, in most cases, to the highest temperature magnetically ordered state exhibited by the crystal. The results are illustrated by a few examples.