The low field Hall-effect of poly-valent metals in the nearly free electron approximation. I: Al, In and Pb

Abstract

The formula by Tsuji for the low field Hall-coefficient is applied for tri- and tetra-valent metals in thefcc structure. Under the assumption of sufficient small pseudopotential the evaluation of the Tsuji formula is rather simple. The Fermi-surface can be divided into different parts; the free electron sphere and the ring shaped distorted parts at the intersection circles with the Bragg-planes. The latter represent electron-like and hole-like carriers; the Bragg-particles. The actual Hall coefficient is a sum of the free electron Hall-coefficientRo and the contribution of the Bragg-particles. The latter is of the same order of magnitude asRo. Its sign depends on the actual scattering potential and on the sign of the pseudopotential. A successful comparison with experimental results for Al, In and Pb is given for impurity scattering. thermal scattering and temperature dependence. A measurement of the Hall-effect under pressure is suggested to prove the dominant role of the sign of the pseudopotential for the Hall-effect.