Space-time symmetry restrictions on the form of transport tensors. I. Galvanomagnetic effects

The transformation law for field-dependent tensors and the onsager reciprocity relations have been used to establish the form of the magnetoresistivity tensor rhoij(b) for all 32 crystallographic point groups. Each component of rhoij(b) is separated into even and odd terms in the magnetic induction b. The generality and simplicity of this formulation leads us to urge that the even components be defined as the magnetoresistance and the odd components as the hall effect. The form of rhoij(b) can also be obtained from restrictions imposed by band structure and transport theory, a procedure which can lead to results of higher symmetry than the phenomenological forms. The umkehr effect is shown to occur in any component of rhoij(b) which contains both even and odd terms in b and to be a direct result of crystal anisotropy.