Attenuation and Rotation of Plane-Polarized Ultrasound in Copper in a Longitudinal Magnetic Field

Abstract

The rotation of the plane of polarization and attenuation of a shear sound wave at 4.2\ifmmode^\circ\else\textdegree\fi{}K have been measured for the propagation vector q parallel to the magnetic field B in the [001] direction in copper. Frequencies from 30 to 110 Mc/sec were used. Both the attenuation and rotation are periodic in $\frac{\ensuremath{\nu}}{B}$, where $\ensuremath{\nu}$ is the sound frequency. The period for the attenuation is 0.0201\ifmmode\pm\else\textpm\fi{}0.0005 Mc/sec G, whereas the period for the rotation is 0.0402\ifmmode\pm\else\textpm\fi{}0.001 Mc/sec G. A. theory is presented which describes this effect. The oscillations in the attenuation are of the type predicted by Kaner, Peschanskii, and Privorotskii, with a peak in the attenuation preceding an absorption edge. An absorption edge is observed at about one-fourth the magnetic field value expected for the free-electron case. The results are interpreted in terms of the Fermi surface of copper as put forth by Roaf. A method is suggested for determining ${\ensuremath{\omega}}_{c}\ensuremath{\tau}$, where ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency and $\ensuremath{\tau}$ the relaxation time; a value of ${m}_{c}{\overline{v}}_{z}=0.381\ifmmode\pm\else\textpm\fi{}0.009\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ g cm/sec is assigned to electrons with orbits near the plane ${k}_{z}=0.45\ifmmode\times\else\texttimes\fi{}{10}^{8}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, where ${m}_{c}$ is the cyclotron effective mass, ${\overline{v}}_{z}$ is the drift velocity, and ${k}_{z}$ is the [001] direction.