Helicons and their Effect on the Surface Impedance of Metals

Abstract

The properties of helicons in metals as they are affected by the Doppler-shifted cyclotron-resonance (DSCR) absorption, and the relation of helicons to the surface impedance, are considered in this paper. The onset of DSCR absorption can be caused by electrons either at an elliptic limiting point or on a finite orbit on the Fermi surface. These two cases are called point edge and orbit edge, respectively. The model chosen to illustrate the point edge is the free-electron gas, while the model chosen to illustrate the orbit-edge case is Overhauser's spin-density-wave (SDW) model. The novel feature of this problem is that the conductivity function that governs the propagation of helicons in metals is dependent only on the wave number and not the frequency, in contrast with the usual case of the propagation of electromagnetic waves where the conductivity function depends only on frequency. In the limit where the product of the cyclotron frequency of the electrons and the relaxation time $\tau$ of the electrons becomes infinite, the imaginary part of the conductivity for the orbit-edge case has a delta-function-like singularity at the absorption edge, i.e., at the wave number where the real part of the conductivity becomes nonzero because of DSCR. For the point-edge case, the conductivity is everywhere finite. The singularity in the conductivity function for the orbit-edge case produces a double-valued frequency-wave-number dispersion relation for helicons of all frequencies. In the point-edge case helicons can also have a double-valued dispersion relation, but only for a small frequency range near the maximum. The surface impedance of a metal with a magnetic field normal to the surface is shown to have sharp structure produced by helicons. However, it is found that this sharp structure, such as the peak in the surface resistance, occurs at the frequency where the helicons have zero group velocity, and not at the absorption edge. Detailed numerical calculations of the free-electron and SDW models are given for potassium with various values of ${\omega }_c\tau$. It is found that the available experimental data of surface impedance for potassium are consistent with both of these models, though the agreement is best for the SDW one. To differentiate between these two models requires material with larger values of ${\omega }_c\tau$ than have been used. Available experimental surface-impedance data for sodium show quite good agreement with the free-electron model.