Ultrasonic Attenuation in the Normal State of High-Purity Thallium

Abstract

The normal-state electronic attenuation of longitudinal ultrasonic waves (10 to 130 MHz) has been studied in high-purity thallium. The attenuation is in general agreement with the Pippard real-metal theory, but does not agree with the free-electron theory. The attenuation is highly anisotropic, in part because of anisotropies in the electron mean free path, the total curvature of the Fermi surface, and the product of the curvature and the Pippard deformation parameter. The electron mean free path was determined from the acoustic measurements for q \ensuremath{\parallel}[0001], $\mathbf{H}\ensuremath{\parallel}[10\overline{1}0]$ and $\mathbf{q}\ensuremath{\parallel}[\overline{1}2\overline{1}0]$, $\mathbf{H}\ensuremath{\parallel}[10\overline{1}0]$. The results indicate that the anisotropy in the electron mean free path is due to impurity scattering. The phonon scattering contribution was proportional to ${T}^{\ensuremath{-}b}$, where $b=3.6\ifmmode\pm\else\textpm\fi{}0.1$ for both directions, whereas $b=5$ has been reported from electrical resistivity measurements. A frequency-dependent component of the electronic attenuation was observed for q \ensuremath{\parallel}[0001] which could not be explained on the basis of the Pippard theories.