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

The rotation of the plane of polarization and attenuation of a shear sound wave at 4.2°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 $\frac{\nu }{B}$, where $\nu$ is the sound frequency. The period for the attenuation is 0.0201±0.0005 Mc/sec G, whereas the period for the rotation is 0.0402±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 ${\omega }_c\tau$, where ${\omega }_c$ is the cyclotron frequency and $\tau$ the relaxation time; a value of $m_c{\overline{v}}_z=0.381\mathrm{}\pm 0.009\times {10}^{-19\mathrm{}}$ g cm/sec is assigned to electrons with orbits near the plane $k_z=0.45\mathrm{}\times {10}^8$ ${\mathrm{cm}}^{-1\mathrm{}}$, where $m_c$ is the cyclotron effective mass, ${\overline{v}}_z$ is the drift velocity, and $k_z$ is the [001] direction.