Calculation of Helicon Propagation and Gantmakher-Kaner Oscillations in Copper

Abstract

The transmission of electromagnetic fields through thin copper slabs with the magnetic field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}$ and the propagation vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ along the [001] and [111] directions has been investigated numerically and the results compared with experimental results of Wood and Gavenda. The conductivity tensor used in the calculations is derived from a model Fermi surface proposed by Halse. Only the variation of the area $A$ enclosed by the charge carriers and the derivatives of the area with respect to ${k}_{z}$, $\frac{\ensuremath{\partial}A}{\ensuremath{\partial}{k}_{z}}$ are considered. For ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}\ensuremath{\parallel}[001]$, the calculated and experimental values of the helicon edge differ less than 3% for the frequencies studied. The electrons responsible for the helicon edge are associated with a value 9.5 \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ for $|\frac{\ensuremath{\partial}A}{\ensuremath{\partial}{k}_{z}}|$. A discussion of the relative damping effects by the charge carriers is given. For ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}\ensuremath{\parallel}[111]$. Gantmakher-Kaner (GK) oscillations with a period of 590 G are observed in both the calculated and experimental results. The amplitude modulation of the GK oscillations leads to an interpretation in terms of a beating of two separate sets of GK oscillations, one set associated with maximum in $|\frac{\ensuremath{\partial}A}{\ensuremath{\partial}{k}_{z}}|$ and the other set associated with a minimum in $|\frac{\ensuremath{\partial}A}{\ensuremath{\partial}{k}_{z}}|$