Doppler-Shifted Cyclotron Resonance and Alfvén Wave Damping in Bismuth

At large magnetic fields the transmission of microwaves through bismuth is essentially undamped and can be regarded as Alfvén waves in a solid-state plasma. A large kink has been observed in the 9-Gc/sec microwave absorption of bismuth as a perpendicularly applied magnetic field was varied through 1500 G. These experiments have been performed at 2°K with a field parallel to the binary axis. The kink has been identified as a Doppler-shifted cyclotron resonance whose position is approximately given by the formula $\omega ={\omega }_c-v_{0x}{k}_A$ where $v_{0x}$ is the maximum Fermi velocity along the field and $k_A$ is the wave number of the microwaves in the metal. The kink marks the onset of Alfvén wave behavior where the surface resistance is proportional to magnetic field. A calculation of the surface resistance using a nonlocal theory applied to a three-carrier model yields a variation with field which shows both the Doppler-shifted peak and the high-field linear region which can be extrapolated back through the origin. The frequency dependence of the peak derived from this calculation has been verified experimentally. By tilting the field slightly away from the perpendicular it was shown that the peak was a Doppler shift in the cyclotron resonance of the holes rather than of the electrons. This experiment provides a very accurate measure of the ratio of the Fermi velocity to the Alfvén velocity and, thus, knowing one, the other may be determined. For this reason, the Alfvén velocity in the same crystals was independently measured using an interference technique. Oscillations with a constant period in $\frac{1}{H}$ were observed in the reflected power as the applied magnetic field was varied. From the period of oscillation and the thickness of the crystal, the velocity was deduced. The work also provides a graphic measure of the sharpness of the Fermi surface.