Quantum Effects in Ultrasonic Attenuation in Metals in a Magnetic Field

Abstract

A study is carried out of quantum effects in the dependence of ultrasonic attenuation in metals on the intensity of an applied magnetic field. It is found that the coefficient of absorption of acoustic waves exhibits an oscillatory behavior as a function of the strength of the applied magnetic field. This paper limits its scope to the case in which $\ensuremath{\omega}\ensuremath{\tau}$, the product of the frequency of the sound wave and the relaxation time for the electrons, is much smaller than unity. The oscillations predicted in this work have an amplitude proportional to ${(\frac{\ensuremath{\hbar}{\ensuremath{\omega}}_{0}}{{\ensuremath{\zeta}}_{0}})}^{\frac{3}{2}}$ for propagation at right angles to the magnetic field, and they are negligibly small for propagation in the direction of the magnetic field. The latter result is in contrast with the one described in the preceding paper (for $\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\gg}1$), where giant oscillations of the attenuation can occur.