Theory of Ultrasonic Cyclotron Resonance in Metals at Low Temperatures

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Abstract
The extent to which measurement of the propagation characteristics of circularly polarized acoustic shear waves as a function of a magnetic field applied parallel to the direction of propagation can reveal information about the band structure of metals is investigated theoretically. The interaction between the electrons and sound waves is treated classically and is viewed as taking place via an internal electric field and by scattering modified by the sound wave. The treatment is based on the combined solution of Boltzmann's and Maxwell's equations for a free-electron model. A simple physical picture involving cyclotron resonance is developed by means of which the treatment is extended to more general band models. The most striking results are obtained in case the mean free path is larger than the wavelength. Under these conditions, it is found that subject to certain restrictions, (1) absorption edges exist, the measurement of which can be related to the curvature of the Fermi-surface; (2) the shape of the Fermi-surface may be determinable from the shape of attenuation and dispersion curves within the absorption region; and (3) the cyclotron frequency may be measured. The results (2) and (3) may be dependent upon the simplifying assumption regarding the electron sound wave interaction.