Magnetic Breakdown of Open Orbits in Cadmium

Open orbits in cadmium have been investigated in magnetic fields up to 30.5 kOe by an induced-torque method. An analysis of the method is presented. Torque produced by a magnetic field rotating at constant speed is caused by induced, open-orbit current when the magnetic field is perpendicular to the open orbit. The amplitude of the induced torque is related to the open-orbit conductivity. The field dependence of the induced-torque amplitude of the open orbit in cadmium has been examined for field directions in the (0001) plane. The torque amplitude tends to saturate at high fields for all directions of observation. This is attributed to magnetic breakdown between the first and second bands through the spin-orbit-induced energy gap at the AHL plane of the Brillouin zone. The magnetic breakdown occurs at low fields and reduces the open-orbit conductivity to a negligible amount at 30 kOe. The analysis is carried out using a linear-chain model to represent the first- and second-band hole surfaces and the theoretical results of Falicov and Sievert. For the [$10\overline{1}0$] field direction, two breakdown probabilities are indicated, corresponding to breakdown through the energy gaps along $\mathrm{HL}$ and $\mathrm{HA}$ of the Brillouin zone, with an upper breakdown field of approximately 10 kOe. For all field directions in the (0001) plane, the breakdown occurs over a similar range of magnetic field.