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In this paper the semiclassical condition for the quantization of magnetic energy levels of Bloch electrons is extended to one order higher in the magnetic field. The result enables us to make a calculation of the magnetic susceptibility of Bloch electrons which includes both the de Haas-van Alphen effect and the steady susceptibility. While the basic calculation is made for fairly simple closed orbits, the results have been extended to include spin splitting, self-intersecting orbits, and open orbits, but omitting consideration of banding of magnetic levels and magnetic breakdown. Possible new oscillations due to self-intersecting orbits are discussed.
Laura M. Roth (1966) studied this question.