Magnetic Field Dependence of Ultrasonic Attenuation in Metals at Low Temperatures

A theory of the effect of a constant magnetic field on the behavior of ultrasonic attenuation in normal metals at low temperatures of the order of liquid helium temperatures is given. The ideas are of the same kind as those suggested by Pippard to account for the attenuation in the absence of an external field. The different geometries are specified by the directions of three vectors, the wave vector q of the acoustic wave, the direction of polarization ${\mathbf{u}}_0$, and the external magnetic field ${\mathbf{H}}_0$. The analysis shows that, for a transverse wave polarized in the direction of ${\mathbf{H}}_0$ (i.e., ${\mathbf{u}}_0$ and ${\mathbf{H}}_0$ are parallel and both are perpendicular to q) the attenuation decreases as ${\left|{\mathbf{H}}_0\right|}^{-2\mathrm{}}$ for large fields. When ${\mathbf{u}}_0$ and ${\mathbf{H}}_0$ are perpendicular and q is perpendicular to both, the attenuation increases as ${\left|{\mathbf{H}}_0\right|}^2$ for large|${\mathbf{H}}_0$|. For a wave such that ${\mathbf{u}}_0$ and q are parallel and ${\mathbf{H}}_0$ is perpendicular to q, the attenuation increases asymptotically to a constant value as ${|\mathbf{H}}_0$| increases. The maxima and minima obtained experimentally by Morse and co-workers cannot be explained on this model. An absorption similar to that occurring in cyclotron resonance absorption is obtained in the attenuation of transverse waves (${\mathbf{u}}_0$ perpendicular to q) when ${\mathbf{H}}_0$ is parallel to q.