Frequency Mixing of the de Haas-van Alphen Oscillations due to the Quantum Variation of the Fermi Energy in Bismuth

A frequency mixing of the de Haas-van Alphen oscillations in bismuth was found. The Fermi energy changes at magnetic fields where the Landau level crosses the Fermi energy, so that the Fermi energy shows a pseudo periodic variation with the fields. This variation is remarkable even at a low magnetic field in bismuth. The observed frequency mixing is ascribed to this effect.