Shubnikov-de Haas type oscillations have been studied in bismuth in magnetic fields up to 88 kG. Oscillations are observed which have been attributed to the hole band in bismuth. A machine calculation of the density of states and of the Fermi level as a function of magnetic field is used to fit the data. The calculation is based on the nonparabolic (two-band) model of the electron band, and includes the possibility of spin splitting for both electrons and holes. It correctly predicts the observed change in Fermi energy with magnetic field. We find that the hole Landau levels are indeed split by spin. The spin splitting is almost twice the Landau level spacing along the trigonal axis and is extremely small perpendicular to the trigonal axis. Spin splitting is also observed for electrons. We find that the spin splitting is about one-third the orbital splitting in the heaviest mass direction and about 10% larger than the orbital splitting in the light mass direction. Our observations imply that there are important states both above and below the hole band. This is in direct contradiction to the Abrikosov and Falkovskii model which considers only one set of states (either above the hole band or below) with which the hole band interacts.

• Received 11 March 1964

DOI:https://doi.org/10.1103/PhysRev.135.A1118