I ntro du ctio n 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

more »

... tice 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 th at 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 th at it necessarily involves the crystal being in an inhomogeneous field, with the result th at the mea sured susceptibility is always an average over an appreciable range of fields. Thus if the susceptibility varies rapidly with field-as is particularly the case at low fields-the measured susceptibility-field curve is a greatly " smoothed-out " version of the true curve. To avoid these difficulties, we have adopted a different method in the present investigation, namely the measurement of the couple acting on a crystal suspended in a uniform magnetic field; this has the disadvantage th at it gives only differences of susceptibilities, but for purposes of comparison with theory this is not serious, and is outweighed by the great ease of measurement of a couple, and by the fact that no inhomogeneity of field is required. * Measurements were made also with crystals grown by other methods, which showed that the method of growing the crystal did not affect the results obtained. uses parameters a, which are related to these m's by the equation m0/a = m, where m0 is the ordinary electronic mass. on July 20, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from R e f e r e n c e s Blackman 1938 Proc. Roy. Soc. A, 166, 1. de Haas and van Alphen 1930 Commun. Lab. Univ. Leiden, no. 212a. --------I932 Commun. Phys. Lab. Univ. Leiden, no. 220d. Focke 1930 Phys. Rev. 36, 319. Landau 1938 Private communication (see Appendix).