Low-field magnetoresistance in metals

Low-field magnetoresistance and Hall coefficient are calculated in the anisotropic-relaxation-time approximation. Simple results are obtained for Fermi-surface models which can be composed of spherical, cylindrical, and planar surfaces. Influences of the Fermi-surface geometry and the scattering anisotropy on the low-field magnetoresistance are discussed. With small modifications the method is applied to polyvalent metals with nearly-free-electron Fermi-surfaces. Simultaneous magnetoresistance and Hall-coefficient measurements combined with a three-group model calculation for the electronic mean free path are suggested as a means to determine the anisotropy of the electronic scattering in nearly-free-electron-like polyvalent metals. In an Appendix the results are extended to the longitudinal magnetoresistance.