Deformation-Potential Theory of Magnetoacoustic Attenuation

Using a free-electron deformation-potential (FED) approximation, ${δ}E={{ε}}:D={-}k{·{}}{{ε}}{·{}}{{∂}E}{{∂}k}$, we have calculated the ultrasonic attenuation of a transverse wave propagating along a magnetic field for the two Fermi surfaces ${E}F={(2m)}^{{-}1}{{}}²({{k}_{{⊥}}}²{-}{{k}z}²+{{{k}z}⁴}{2{{k}₀}²})$ and ${E}F=(2{m}^{{-}1}){{}}²[{{k}_{{⊥}}}²(1+{β}{{k}z}²){-}{{k}z}²(1{-}{{{k}z}²}{2{{k}₀}²})]$, where H is in the $z$ direction. For the former Fermi surface, which is free-electron-like in the ${⊥}$ direction, Eckstein's jellium result is obtained; it displays dips in the attenuation when the conductivity tensor has peaks. For the latter, more general Fermi surface, the attenuation differs from the jellium prediction. However, both calculations again predict dips in the attenuation, contrary to the experimental data, which display peaks. In the Appendix we compare the FED with the true deformation potential for a real crystal. We conclude that it is cylindrically symmetric Fermi surfaces, and not errors in the FED approximation, which cause the absence of peaks in the attenuation.