Ultrasonic Attenuation in Oblique Magnetic Fields

The propagation of acoustic waves at oblique angles to a dc magnetic field in a material with an arbitrary closed Fermi surface is studied. In addition to the conventional geometric resonances, absorption edges due to Doppler-shifted cyclotron resonance, and geometric resonances associated with nonextremal orbits on the Fermi surface can occur. A formal theory is developed and applied to two simple models of the ground state of potassium: the free-electron model and the spin-density-wave model. Experimental results on the attenuation of 60-Mc/sec longitudinal acoustic waves in potassium are presented and compared with the predictions of both models. The experimental results appear to favor the free-electron model, but they are not definitive in view of the low value of $\mathrm{ql}$, the product of acoustic wave number and electron mean free path, attained in the experiments. The general features of the attenuation as a function of magnetic field for a fixed oblique angle, which agree well with the detailed theory, are discussed in terms of a simple intuitive picture.