The thermodynamic potential and magnetization are calculated for a system of electrons interacting with phonons in the presence of a magnetic field. The results are used for a numerical evaluation of the de Haas-van Alphen amplitude of the oscillations of the magnetization as a function of temperature in mercury. The calculated results show that although we are dealing with a strong-coupling system, the experimental observations of the de Haas-van Alphen effect should be very similar to that expected for free particles. We also apply the techniques used in the derivation to the case of nearly ferromagnetic electron systems and calculate the enhancement of the argument of the spin-splitting factor. The analysis for nearly ferromagnetic systems leads to the prediction that the cyclotron frequency which enters the amplitude of the oscillations is reduced by the same mass-enhancement factor as that which enters the specific heat.

• Received 2 March 1970

DOI:https://doi.org/10.1103/PhysRevB.2.1657