Damped Alfvén Waves in Bismuth: A Determination of Charge-Carrier Relaxation Times

Abstract

The average charge-carrier relaxation times in single-crystal bismuth at 4.2\ifmmode^\circ\else\textdegree\fi{}K have been measured using a new technique. For Alfv\'en waves propagating in a slab of thickness $d$, the amplitude of Alfv\'en-wave oscillations increases with magnetic field $B$ as $(\frac{V}{c}){e}^{\frac{\ensuremath{-}d}{V\ensuremath{\tau}}}$, where $V$ is the Alfv\'en-wave velocity proportional to $B$. Inasmuch as $V$ can be determined from the standing-wave oscillations, our measurements of the amplitude growth in $B$ provide us with a direct determination of the average relaxation time $\ensuremath{\tau}$. We studied Alfv\'en-wave propagation along the three crystal axes using a resonant-cavity method in magnetic fields up to 11 kG. Strongly anisotropic relaxation times ranging from 0.15 to 0.40 nsec were obtained. The results are in good agreement with McLachlan's determination of the same quantities, but are in poor agreement with Brownell and Hygh's theory of Alfv\'en-wave damping. The experimental methods used here have several advantages over the usual galvanomagnetic and size-effect methods of determining $\ensuremath{\tau}$. In addition, we predicted an interference effect in nonparallel-plate samples analogous to the Newton's-rings effect; this was borne out in our observations.