Wave form of de Haas–van Alphen oscillations in a two-dimensional metal

Abstract

The effect of thermodynamical equilibrium transfer of electrons between closed (Landau) orbits and magnetic field independent states near the Fermi surface on the magnetoquantum oscillations in quasi-two-dimensional (2D) metals is investigated. The general relationship between magnetization and chemical potential oscillations in such a model is derived, and a variety of wave forms are obtained in the entire temperature--magnetic field region. It is shown quite generally that such an electron transfer suppresses the chemical potential oscillations, whereas the magnetization amplitude remains unchanged. A specific model of the relevant band structure in which the field independent (or reservoir) states correspond to quasiplanar energy surfaces is considered in detail. In this model, the chemical potential oscillations diminish when the bottom of the subband with the quasiplanar energy surfaces nearly coincides with the Fermi energy, and the corresponding one-dimensional van Hove singularity dominates the electron transfer. Similarly, the chemical potential may be pinned due to electrons in localized states near the Fermi energy. In both cases the de Haas--van Alphen oscillations are shown to have an inverse-sawtooth shape at sufficiently low temperatures. In the more common situation when the Fermi energy is relatively far from any sharp peak of the reservoir density of states, the wave form of the magnetization oscillations is symmetrized at all temperatures. All shapes of magnetization oscillations observed in the organic quasi-2D metals of the $(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F}{)}_{2}X$ type, from the rare sawtooth and inverse-sawtooth to the usual symmetrical ones, can be accounted for by this model.