The magnetic properties of bismuth, III. Further measurements on the de Haas-van Alphen effect

Abstract

As was'first shown by de Haas and van Alphen (1932), the susceptibility of bismuth single crystals at low temperatures depends in a peculiar periodic fashion on the magnetic field, and later this effect was studied in greater detail by Shoenberg and Zaki Uddin (1936), especially as regards the influence of temperature and impurities. The general features of the effect were found to agree qualitatively with Peierls’ theory (Peierls 1933), but since this theory was for a cubic lattice it could take no account of the directional features of the effect, and no detailed comparison could be made between the theory and the experiments. Since then, however, the theory has been developed by taking into account the actual crystal symmetry of bismuth (Blackman 1938; Landau 1938), and Landau has shown that the theory assumes a relatively simple analytical form at low field strengths, thus making desirable measurements at fields rather lower than those used in the previous experiments. With the ordinary Faraday method, it is not easy to make accurate susceptibility measurements at field strengths below about 4000 gauss, and this indeed was roughly the lowest field used in the previous work, but an even more serious disadvantage of this method is that it necessarily involves the crystal being in an inhomogeneous field, with the result that the measured susceptibility is always an average over an appreciable range of fields.