Theory of the de Haas-van Alphen Effect in a System of Coupled Orbits. Application to Magnesium

A Green's-function formulation for the calculation of amplitudes of the de Haas-van Alphen effect is developed. The theory can be applied to the case of metals in which magnetic breakdown takes place. The exact theory is presented and then approximated by a wave-packet approach susceptible of a simple physical interpretation; this approximation is proved to involve no error for the free-electron gas. The method is then applied to a hexagonal network corresponding to the case of magnesium for magnetic fields parallel to the hexad axis. Curves are presented for the magnetic-field dependence of the amplitude of various important periods at $T=1$^∘{}K; they are in agreement with preliminary experimental data. The method is also proved to give a density of states which agrees with that obtained from Pippard's model for the hexagonal network of coupled orbits.