Magnetoacoustic Attenuation of Circularly Polarized Ultrasound in Sn, Al, and Sb

Abstract

The attenuation of circularly polarized sound as a function of magnetic field $H$, oriented parallel to the sound propagation direction, was measured for Al, Sn, and Sb at 4.2 and 1.2°K. This direction was chosen to be along the [100] axis in Al, the [001] axis in Sn, and the trigonal axis in Sb. The dispersion was also measured in Al and Sn. Doppler-shifted cyclotron resonance, causing peaks and edges in the attenuation, was observed in the case of Al and Sn. For Al the peaks are periodic in $\frac{1}{H}$ with a period of (1.8±0.04) ×${10}^{-4\mathrm{}}$ ${\mathrm{G}}^{-1\mathrm{}}$. These peaks were found to be caused by holes coming from the second Brillouin zone. In Sn both types of carriers contributed to the peaks. Geometric resonance, causing sinusoidal oscillations in the attenuation periodic in $\frac{1}{H}$, was observed in Sb with a period of (44±2)×${10}^{-4\mathrm{}}$ ${\mathrm{G}}^{-1\mathrm{}}$. This resonance was found to be caused by the hole ellipsoids in Sb. The earlier theories of magnetoacoustic attenuation have been extended to general Fermi surfaces and to include the simultaneous presence of electrons and holes and deformation effects. The relationship between the attenuation and the Fermi surface geometry is discussed for different crystal symmetries and carrier compensations. A comparison between the known Fermi surfaces of Al and Sb and the observed attenuation for these metals is made.