General relations for transport properties in magnetically ordered crystals

In a previous paper [Grimmer (1991). Acta Cryst. A47, 226-232], general connections were given between the forms of tensors describing equilibrium properties in materials with point-group symmetry described by any of the 122 crystallographic Shubnikov point groups. In the present paper, it is shown how the results must be modified to include transport properties also. At least six different prescriptions for the treatment of transport properties in magnetically ordered crystals have been proposed in the literature. It is shown that the one due to Shtrikman & Thomas [Solid State Commun. (1965), 3, 147-150; erratum (1965), 3, civ] leads to a straightforward generalization of the results for equilibrium properties that seems to agree with experiment. Tensors describing transport properties generally consist of two contributions, T = Tⁱ+ T^s. The tensor Tⁱ is invariant under time reversal 1', whereas T^s changes sign under 1' and therefore vanishes for dia- and paramagnetic crystals, which are invariant under 1'. The form of the tensors describing electric and thermal conductivity, the thermoelectric Seebeck and Peltier effects and the Hall, Righi-Leduc, Nernst & Ettingshausen effect are given explicitly for all the 122 crystallographic and 21 limiting point groups.