Studies of the anisotropy of electron-impurity scattering in metals by the use of the de Haas—van Alphen effect: application to gold

Abstract

A general method is described for obtaining a map of the variation of the electronic lifetime over the Fermi surface using Dingle temperatures measured in the de Haas—van Alphen effect. The method requires a knowledge of the topography of the Fermi surface, and of the varia­tion of quasiparticle velocities over it. The local electronic lifetimes, Ƭ 8 ( k ), are deduced from the experimentally determined orbitally averaged values by means of an inversion procedure in which a general representation for Ƭ 8 ( k ) is used based, for example, on a Fourier series, harmonic expansion, or phase shift calculation, etc. In applying these ideas to gold we have employed a symmetrized Fourier series representation as used by Roaf (1962) and Halse (1969) in connexion with noble metal Fermi surfaces. Based upon studies of the dH—vA effect in dilute alloys of gold, results are presented in the form of topographic maps, showing the variation of Ƭ 8 ( k ) over the Fermi surface arising out of the presence of dilute concentrations of either Ag, Cu, Zn or Fe as impurity. The results reveal appreciable anisotropy in the electronic lifetime, which differs for different impurities, being most striking in Au(Ag) for which an extreme variation of 4.5:1 is observed, and least for Au(Fe) (at 1.2 K) in which the variation is only ca . 30% over the Fermi surface.