Magnetic interaction in the de Haas-van Alphen effect in lead

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Abstract
The frequency modulation of the high-frequency de Haas-van Alphen oscillation from the second-band hole sheet of the Fermi surface with the period of the low-frequency oscillation from the third-band electron network along the [110] crystalline direction in Pb has been examined in ellipsoidal samples. Within the framework of the Shoenberg conjecture that the magnetic induction is the relevant field in the Lifshitz-Kosevich theory and the assumption that the induction is uniform over the sample, the analysis of the frequency modulation should yield an absolute determination of the magnetic induction oscillation amplitude. This determination in each of our samples was found to be inconsistent for two crystallographically equivalent directions. The results can most easily be interpreted as implying that the induction averaged over the cyclotron orbit has an oscillation amplitude about 25% larger than that averaged over the sample. Several mechanisms which could cause an inhomogeneous magnetic induction are considered.

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