The forms of tensors describing magnetic, electric and toroidal properties

Abstract

The forms of tensors describing properties of a magnetically ordered crystal depend on its Shubnikov point group according to the Neumann principle. Taking the example of a third rank tensor, symmetric in two of its indices, it is shown explicitly how the form of the tensor for a point group in a given orientation with respect to a Cartesian coordinate system depends on the behaviour of the tensor under the inversions of space and time. It is shown how this behaviour differs for magnetic, electric and toroidal properties. Failure to state and use well defined orientation conventions has often led to conflicting results in the literature. The treatment of non-equilibrium properties in magnetically ordered crystals has been the object of a long-lasting controversy after the initial proposal by Birss in 1964. It is shown that a proposal by Shtrikman and Thomas made as early as 1965 gives the basis for a treatment not only of transport but also of optical properties.

Key Words:

• property tensors
• transport properties
• optical properties
• magnetically ordered materials
• toroidal moments