Cyclotron Wave Propagation in Silver

Azbel'-Kaner cyclotron resonance in metals is accompanied by electromagnetic waves propagating in a direction perpendicular to the magnetic field. Taking into account the anisotropy of the silver Fermi surface, the dispersion relation for these waves is calculated in the limit where the wavelength is much smaller than the orbit diameter of the electrons. Thus it is shown that a number of previously observed oscillations in the surface impedance of a semiinfinite silver specimen arise from points of zero-group velocity on the dispersion relation. Physically, the oscillations reflect a matching of the electron-orbit diameter with an integer number of wavelengths. They may, therefore, be looked upon as geometric resonances in the surface impedance, complementary to the temporal cyclotron resonances. The surface impedance is calculated under the assumption of specular surface scattering. Satisfactory agreement with experiments is obtained by using an independent-particle model for the electron gas and band parameters based on APW calculations. The influence of the Fermi-surface geometry is demonstrated by comparing with calculations for a cylindrical and a spherical Fermi surface. The electric field in the metal is calculated for selected magnetic fields, and the expected result of a transmission experiment is presented. Finally, the absence of Fermi liquid effects in the experiments is briefly discussed.