de Haas-van Alphen Effect and Fermi Surface in Antimony

Abstract

The Fermi surface of antimony has been completely determined by the de Haas-van Alphen (dHvA) effect using the field-modulation measuring technique, modified to give strong dHvA period spectrometer action. The Fermi surface is found to consist of two sets of warped ellipsoids, the $\ensuremath{\alpha}$ set having a tilt angle of 53.0\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}0.1\ifmmode^\circ\else\textdegree\fi{} defined by the period maximum in the mirror plane, and the $\ensuremath{\beta}$ set having a tilt angle of 87.7\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}0.1\ifmmode^\circ\else\textdegree\fi{} (angles are measured from $\ensuremath{\Gamma}T$ in the sense toward $\ensuremath{\Gamma}X$). Carrier compensation has been established with the $\ensuremath{\alpha}$ set of carriers consisting of 6 pockets and the $\ensuremath{\beta}$ set of 3 pockets. When the present results are compared with the recent band-structure calculations it is clear that the $\ensuremath{\alpha}$ carriers are the holes and the $\ensuremath{\beta}$ carriers the electrons. This is the reverse of the conventional assumption for the signs of the carriers in antimony. The deviation of each set of pockets from ellipsoids has been accurately determined From the ellipsoidal approximation, the carrier concentration was found to be ${n}_{e}=(5.54\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{19}$ electrons/${\mathrm{cm}}^{3}$ and ${n}_{h}=(5.49\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{19}$ holes/${\mathrm{cm}}^{3}$. This new model removes the necessity for postulating a third band of carriers and is in agreement with all the previous experimental data. Comparison of the observed spin splitting with the electron-spin-resonance data of Datars gives new information on the angular variation of the $g$ factor. Extra period branches have been observed along almost every field direction, but these have all been shown to arise from nonlinear mixing of strong dHvA period components.