LOW-FIELD GALVANOMAGNETIC TRANSPORT-COEFFICIENTS OF CUBIC METALS - GENERAL FORMULAS AND EXPERIMENTS ON THE HALL-COEFFICIENT IN AL(GE)

The scattering of conduction electrons by defects is described by a low-field transport relaxation time τkx. It depends on the electron wavevector k and on the direction of the electric field E/E, but not on the magnetic field H. From a discussion of Kohler's rule written in terms of the exact relaxation time τk* it follows that this approximation is very good for low values of H/ρ, with ρ being the resistivity for H=0. Assuming τkx to be known, the linearized Boltzmann equation is solved by a Jones-Zener expansion up to terms H3. For metals with cubic symmetry we derive simple formulae for the coefficients of transverse and longitudinal magnetoresistance and for the two leading terms of the Hall coefficient R(H)=R0+R2(H/ρ)2. Simplifications occur for a τk with cubic symmetry and for metals with special Fermi surfaces. These formulae are used to interpret experimental results of the magnetic field dependence of R(H) in Al(Ge) at 4 K. In this dilute aluminium alloy R0 is highly positive and R2 strongly negative. By irradiating a 3,000 ppm Al(Ge) sample with reactor neutrons at 4 K, an increasing concentration of self-interstitials and vacancies is added to the germanium impurities resulting in a decrease of both R0 and |R2|. This is discussed in a three-group model of the Fermi surface of aluminium. © 1979 Springer-Verlag.