Symmetry restrictions on field dependent tensors with application to galvanomagnetic effects

Abstract

The usual formalism for determining symmetry relations, due to macroscopic space symmetry, among the components of constant tensors, is shown to apply equally well to tensors that are a function of the applied fields. It differs only in two respects from the special case of constant tensors: (a) Only a subgroup, containing, in general, drastically fewer members than the entire group of symmetry operations, yields symmetry relations. (b) This subgroup contains elements other than the identity only for directions of the applied fields that are left invariant by the elements of macroscopic symmetry of the medium. Examples using first- and second-order tensors arising in electrical conductivity, with and without a magnetic field, are given and the even and odd parts of the tensor are separated.