Hall Effect, Magnetoresistance, and Size Effects in Copper

Abstract

Measurements of the Hall coefficient of several annealed polycrystalline Cu strips of resistivity ratio $\frac{\ensuremath{\rho}(273\ifmmode^\circ\else\textdegree\fi{}\mathrm{K})}{\ensuremath{\rho}(4.2\ifmmode^\circ\else\textdegree\fi{}\mathrm{K})}\ensuremath{\sim}450$ and thicknesses ranging from 0.05 to 1.6 mm have revealed the existence of a marked size effect at low temperatures. The effect is orders of magnitude greater than that to be expected on the basis of free-electron theory. It is suggested that earlier low-temperature data on the Hall effect of thin high-purity samples are subject to uncertainties arising from such effects. Size effects were also evident in the transverse magnetoresistance. At high fields, a tendency toward saturation in the transverse magnetoresistance was observed for thick samples. The temperature dependence of the Hall coefficient has also been studied.