Pressure Dependence of the Hall Constant of the Alkali Metals

Abstract

The pressure dependence of the Hall constant of the five alkali metals has been measured to 15 000 kg/${\mathrm{cm}}^2$ at room temperature. The purpose of the measurements was to investigate the effect of lattice constant on the warping of the Fermi surface. The Hall constant $R$ is written as $\frac{1}{\mathrm{Nec}{n}^{*}}$, where $N$ is the number of carriers/cc and $n^{*}$ expresses the deviation from the free electron value of the Hall constant. In all the alkalis except cesium, $n^{*}$ decreases monotonically with increasing pressure; the decreases range from 5% in 15 000 kg/${\mathrm{cm}}^2$ for lithium to 8% in 15 000 kg/${\mathrm{cm}}^2$ for rubidium. In the case of cesium, $n^{*}$ passes through a minimum at 5000 kg/${\mathrm{cm}}^2$ and rises to a value of 1.2 at 15 000 kg/${\mathrm{cm}}^2$. The change of $n^{*}$ between room and liquid nitrogen temperatures was measured and is less than 3% for all the alkalis except lithium. In lithium, $n^{*}$ decreases about 25% between room and liquid nitrogen temperature. The sign of the pressure dependence of $n^{*}$, as well as its magnitude, can be reconciled with recent band structure calculations by Ham only if highly anisotropic scattering times are considered. The pressure results are explained in a semiquantitative manner using a scattering time, $\tau$, that varies by a factor of 3 over the Fermi surface. Consideration of the factors determining the scattering time indicates the both umklapp processes and the large elastic anisotropy of the alkalis contribute to the anisotropy of $\tau$. A crude calculation shows that the present results can be explained by the effects of umklapp processes alone.