Oscillatory Magnetoresistance in Gray Tin

The oscillatory component of magnetoresistance has been measured for single crystals of $n$-type gray tin at liquid-helium temperatures. The period of oscillation is independent of magnetic field direction, confirming an isotropic effective mass and, therefore, a conduction-band edge at the center of the Brillouin zone. Oscillations were also observed in a polycrystalline specimen. Carrier concentrations deduced from the oscillatory period are in reasonably good agreement with values obtained from the Hall coefficient over a range of almost two orders of magnitude in this parameter. An electron effective mass of 0.024 $m_0$ was obtained from the field and temperature dependence of the oscillatory amplitude for samples having carrier concentrations on the order of ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Nonthermal damping of the oscillations is attributed mainly to inhomogeneities in the impurity distribution. The experimental results are compared with theory.