Quantum Structure in the Dielectric Function of Metals and Anomalous Propagation Modes

Semiclassically, the dielectric constant of a free-electron gas in a magnetic field is highly absorptive within the cone $\omega ={\omega }_e\pm v_{F}q$. But quantum mechanically, within this region there are many large "windows" in which the absorptive component ${{\epsilon }_2}^{-}(\omega , q)=0\mathrm{}$. In the first part of this paper we describe these large windows in detail. We then consider propagation within them. We show that in a nonmagnetic material there are other solutions of the dispersion relation in addition to a heliconlike mode. We next consider a ferromagnetic metal, and predict that in nickel a propagating magnon-helicon mode may exist up to microwave frequencies for wave numbers up to $q\simeq {10}^6$ ${\mathrm{cm}}^{-1\mathrm{}}$, which is ${10}^3$ times the $q$ of the Kjeldaas edge. The usual microwave transmisson or reflection experiments are not suited to the observation of these effects, or the related phenomenon of giant quantum oscillations in helicon attenuation which has been previously predicted. To be successful, an experiment must be able to determine both the frequency and the wave number of the absorption process. Perhaps inelastic photon (Raman) scattering could be used for this purpose.