Size-Dependent Oscillatory Magnetoresistance Effect in Gallium

Abstract

The nonmonotonic part of the magnetoresistance has been measured in five single crystals of gallium at 1.2\ifmmode^\circ\else\textdegree\fi{}K in the range 0 to 16 kOe using the audio-frequency field-modulation technique. The transverse coefficients were found to oscillate directly with the magnetic field with nondecreasing amplitude in the high-field region defined by ${\ensuremath{\omega}}_{c}\ensuremath{\tau}\ensuremath{\gg}1$. A large number of periods have been resolved by Fourier analysis of the data in the $\mathrm{ab}$ and $\mathrm{ac}$ planes, and a study has been made of the orientation and size dependence of the oscillation frequencies. Formulas are presented for the oscillatory frequencies and amplitudes giving their dependence on magnetic field strength and orientation, Fermi-surface parameters, and sample size. Theory suggests that the high-field amplitude growth may be correlated with the form of the conductivity tensor for a compensated metal and the diffusivity of the sample surface seen by electrons having extremal values of ${m}^{*}〈{v}_{z}〉$. Nearly-free-electron-model calculations show that electrons from the seventh and eighth band surfaces in gallium have these properties. Evidence for magnetic breakdown across the (100) face of the Brillouin zone is presented.