Longitudinal Magnetoacoustic Effect in Aluminum

The experimental data on the longitudinal magnetoacoustic effect in aluminum are interpreted in detail in terms of the known Fermi surface and Fermi velocity. Both attenuation and dispersion of circularly polarized transverse waves and of longitudinal waves are considered. The "Doppler-shifted cyclotron resonance" peaks are discussed, and it is shown why they occur for transverse waves at considerably lower magnetic fields H than one might naively expect. The conductivity $\sigma$ is calculated from the shape of the Fermi surface and the variation of electron velocity over it. The relaxation time $\tau$ was determined from the measured residual resistance ratio, and the data could be fitted without invoking anisotropy of $\tau$. The theory for the attenuation involves terms which we have expressed as an effective number $Z^{*}$ of electrons. Existing theory suggests $Z^{*}=2.5\mathrm{}$, whereas we find a valve $Z^{*}=-0.91\mathrm{}$ is needed to fit the data. The $Z^{*}$ arises from the part of the conduction-electron density which follows the motion of the ions adiabatically because of "band-structure effects." The treatment of these effects appears, therefore, to be seriously incomplete in the existing theories.