Landau-level widths, effective masses, and magnetic-interaction effects in lead

Abstract

The amplitudes of the de Haas-van Alphen effect in lead have been studied in detail using large impulsive magnetic fields and employing a narrow-band filtering system. Crystals of high purity were grown, cut, and mounted in a manner which was essentially strain-free, and the Dingle broadening temperatures $T_D$ for many of these crystals were found to be less than 0.1°K, corresponding to Landau-level widths of less than 1% of the level spacing $\hslash {\omega }_c$ in a field of about ${10}^5$ G. These findings strongly suggest that the large level widths ($T_D\approx 1-2$°K) frequently reported in the past for many pure metals arise from destruction of phase coherence by dislocations. Accurate effective mass values have been determined for the extremal orbits at symmetry directions, and these results are compared with the data obtained directly from cyclotron resonance. The temperature dependences of the amplitudes for the harmonic and combination tones provide yet further detailed evidence for the correctness of Shoenberg's proposal that the Lifshitz-Kosevich theory must be modified when the magnetic interaction between conduction electrons is important. The absolute amplitudes of the fundamental oscillations are compared with the theoretical predictions, and the harmonic content is also discussed.