Phenomenological theory of anisotropic isothermal galvanomagnetic effects

Abstract

The isothermal galvanomagnetic tensor components associated with the Hall effect and the magnetoresistance effect are analyzed for arbitrary orientation of the crystal axes in the sample, arbitrary orientation of the magnetic field B, and arbitrary crystal symmetry. The conductivity components in suitable co-ordinates are expanded in powers of the components of B. The coefficients are the galvanomagnetic material constants, called “brackets”. By means of O nsager's relations, it is shown that the magnetoresistance effect is always even in B, whereas the Hall effect is odd in B only with special geometry. Further, the Hall effect is even or zero for some geometric and crystallographic conditions. The effects of the crystal symmetry on the brackets are covered by a theorem. The resultant dependencies between the brackets are tabulated completely for all powers of B for the crystal classes other than trigonal and hexagonal. For the latter, the bracket relations are given up to the sixth power of B. Formulae for the number of independent brackets up to any power of B are given for all crystal symmetries. The significance of the results obtained is pointed out.