Influence of Impurities on the de Haas-van Alphen Effect

Abstract

The influence of impurities, or solute atoms, upon the de Haas-van Alphen effect associated with a metal having a Fermi surface of arbitrary shape is investigated. It is shown that the well-known result of Dingle for the decrease in amplitude of the oscillations in the magnetic susceptibility may be derived without recourse to the additional phenomenological assignment of a specific line shape to each Landau level. The relaxation parameter used by Dingle is shown to be twice the lifetime of a state at the Fermi energy. This is compared with the relaxation time for electrical conduction for a class of impurity potentials of variable range in real space. The derivation of the Dingle result presented here depends only upon certain continuity arguments related to the effect of impurities on the electronic band structure. These are investigated in detail for the free-electron model. Simultaneously, the method yields the change in period of the oscillations upon alloying. The conditions under which the rigid-band model is applicable to this problem are derived and a possible generalization is suggested to account for the changes in period which are observed when the solute and solvent have the same valency. The information which can be obtained from experiment concerning the change in amplitude and period is correlated with previous theoretical studies.