Effect of Sample Geometry on Magnetomorphic Oscillations in the Hall Effect in Cadmium at Liquid-Helium Temperatures

Size-effect oscillations in the Hall resistivity have been studied in a monocrystal of highly pure cadmium at liquid-helium temperatures. Samples ranging in thickness from 2.01 to 0.09 mm were prepared from a single monocrystal by successively reducing the thickness using spark planing followed by electropolishing. The probes were not removed during this process to ensure that the samples were representative of a common background of orientation, strain, purity, and surface condition. The magnetic field was applied parallel to the hexagonal axis, and dependence on thickness parallel to this direction was studied in the period, phase, and amplitude of the oscillations. The amplitude was observed to increase as thickness was reduced. The oscillations are not strictly periodic, but the apparent period is proportional to the reciprocal thickness. The phase of the oscillations is determined to be zero, although existing theory predicts a phase of $\frac{\pi }{2}$. It is concluded that the lens-shaped pocket of electrons in the third Brillouin zone is responsible for the oscillations. The radius of curvature of the lens apex in the hexagonal direction is determined to be $k_F=1.37\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. A study of the temperature dependence of the amplitude of the oscillations implies that the mean free path is in the millimeter range at liquid-helium temperatures. A careful search for short-period oscillations observed by other researchers was fruitless. Data from an electropolished sample were compared to those from a spark-planed sample of the same dimensions; the amplitude of the oscillations was found to be twice as large in the spark-planed sample data as in the electropolished sample data. A slight increase in amplitude was effected by abrading an electropolished sample with No. 600 SiC paper. This enhancement in amplitude implies that an appreciable number of electrons scatter specularly at the electropolished surfaces. It is suggested that a very thin distorted layer at the crystal surface may be necessary to observation of the short-period oscillations.