Magnetoacoustic Effect in Impure Metals

A simple but approximate theory is given for the acoustic attenuation in impure metals or semimetals in a strong magnetic field. In the extreme quantum case the acoustic attenuation is an oscillatory function of the magnetic field. It is shown that the qualitative nature of the oscillation depends on two parameters ${\omega }_q\tau$ and $q_{z}l$, where ${\omega }_q$ is the phonon frequency, $\tau$ the mean collision time, q the phonon wave vector, and $l$ the electron mean free path, and the $z$ axis is chosen as the direction of the field. For ${\omega }_q\tau \gg 1$ the quantum oscillation is gigantic, as pointed out by Gurevich et al. The large absorption occurs when the electrons near the Fermi level drift in phase with the sound. In the intermediate region where ${\omega }_q\tau \lesssim 1$ but $q_{z}l\gg 1$, the oscillation is still giant in the sense that only one quantum level contributes to the absorption, but the oscillation is purely a density-of-states effect. When $q_{z}l\lesssim 1$, all levels contribute to the absorption, and the oscillation is of the de Haas-van Alphen type. The effect of varying the direction of sound propagation relative to the field is also discussed in all three regions.