Topology of the Fermi Surface of Gallium

Abstract

High-field magnetoresistance, Hall effect, planar Hall effect, and transverse even effect have been measured on gallium single crystals at 4.2\ifmmode^\circ\else\textdegree\fi{}K with the current along the crystallographic axes and the magnetic field in the major crystallographic planes. The results are interpreted in terms of the Lifshitz, Azbel', and Kaganov theory. The magnetoresistance is quadratic in the magnetic field except when both the current and the field are in the $\mathrm{ab}$ plane, where it saturates. These results are attributed to a surface which permits open orbits along the ${k}_{c}$ axis and to compensation between the number of holes and electrons. In addition, subsidiary minima are observed in the magnetoresistance rotation curves, but the field dependence remains quadratic at these points. The Hall and planar Hall data are highly dependent upon the magnetic field direction and show some features similar to the magnetoresistance. The nearly-free-electron (single-orthogonalized-plane wave) Fermi surface has been constructed for gallium and it is found that, after certain modifications, the sixth band predicted by this model has the basic topological features required by these data. The origin of the transverse even voltage is discussed in terms of the Lifshitz theory.