The oscillatory free energy for nearly free electrons in a magnetic field is expanded to second order in the periodic lattice potential. The result gives expressions for the de Haas-van Alphen oscillations corresponding to orbits on the Fermi surface involving at most two Bragg reflections, including magnetic breakdown. The result is a substantiation of the effective-mass approximation, with a field-dependent mass, in the case of a closed Fermi surface, and of Falicov and Stachowiak's semiclassical treatment.

• Received 6 February 1967

DOI:https://doi.org/10.1103/PhysRev.162.558