Open Orbits and the Fermi Surface of Gallium by an Induced-Torque Method

An investigation of the open-orbit structure in gallium at 1.4°K using the induced-torque technique has yielded direct information on the connectivity of the sixth-band hole surface. This surface supports a $k_c$ trajectory for all field directions in the $\mathrm{ab}$ plane, except within 0.1° of the $a$ axis. A smaller-amplitude $k_a$ trajectory is reported, existing over a 10° range of field direction centered (32±2)° from the $b$ axis in the $\mathrm{bc}$ plane. These data, in addition to the highly anisotropic amplitude and field dependence of the $k_c$ trajectory, require that this surface contact the Brillouin-zone boundary at both the $k_a$ and the $k_c$ faces. The present data are compared with available models of the sixth-band hole surface and are found to be in excellent agreement with the predictions of Reed's pseudopotential calculations. The possibility of magnetic breakdown in the $k_c$ trajectory for $\mathrm{B}\parallel \left(b \mathrm{axis}\right)$ is discussed. Finally, a nonlinear frequency dependence, and an anisotropic, nonquadratic field dependence of the induced torque are understood to occur through the long mean free path and short skin-depth parameters in gallium at 1.4°K.