The low-field galvanomagnetic transport coefficients of cubic metals: General formulae and experiments on the hall coefficient in Al(Ge)

Abstract

The scattering of conduction electrons by defects is described by a low-field transport relaxation timeτ ^x _k . It depends on the electron wavevectork and on the direction of the electric fieldE/E, but not on the magnetic fieldH. From a discussion of Kohler's rule written in terms of the exact relaxation timeτ ^*_k it follows that this approximation is very good for low values ofH/ρ, withρ being the resistivity forH=0. Assumingτ ^x _k to be known, the linearized Boltzmann equation is solved by a Jones-Zener expansion up to termsH ³. 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 coefficientR(H)=R ₀+R ₂(H/ρ)². Simplifications occur for aτ _k with cubic symmetry and for metals with special Fermi surfaces.

These formulae are used to interpret experimental results of the magnetic field dependence ofR(H) in Al(Ge) at 4 K. In this dilute aluminium alloyR ₀ is highly positive andR ₂ 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 bothR ₀ and |R ₂|. This is discussed in a three-group model of the Fermi surface of aluminium.