Anisotropic Relaxation Times and Magnetoconductivity for Ellipsoidal Energy Surfaces: Onsager Reciprocity Restrictions and Jones-Zener Expansions

The magnetoconductivity is obtained using anisotropic relaxation-time tensors for materials having Fermi surfaces consisting of a group of ellipsoids. Each ellipsoid is described in terms of a number of carriers and a saturation field tensor. From crystal symmetry and Onsager reciprocity, it is proven in some cases and inferred for all other cases that all saturation field tensors must be symmetric. The anisotropic relaxation-time tensor is thereby restricted, but need not be symmetric itself. The saturation-field-tensor symmetry also requires the existence of ellipsoids of constant power density upon application of an electric field and no magnetic field. The Jones-Zener expansion of the conductivity in terms of magnetic field is simply derived, including anisotropic relaxation-time tensors. The Jones-Zener series diverges to infinity if a critical magnetic field Hc is reached. An expression for Hc is obtained and compared with past criteria for convergence.