Size Effects and Doppler-Shifted Cyclotron Resonance of Helicons in Copper

Abstract

Gantmakher-Kaner (GK) oscillations and Doppler-shifted cyclotron resonance (DSCR) of helicons have been investigated in very pure copper with the magnetic field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}$ and the propagation vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ along the [101], [001], and [111] directions. The results are compared with a model Fermi surface proposed by Halse. For ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}\ensuremath{\parallel}[101]$, the GK mode is excited by a heavily damped helicon which enhances the effective skin depth for certain values of $q$. Using a period of 314 \ifmmode\pm\else\textpm\fi{} 7 G for the GK oscillations, we assign a value of ${|{m}_{c}{\overline{v}}_{z}|}_{\mathrm{ext}}=(0.648\ifmmode\pm\else\textpm\fi{}0.014)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ g cm ${\mathrm{sec}}^{\ensuremath{-}1}$ to electrons with orbits near the plane $a|{k}_{z}|=2.675$, where $a$ is the lattice constant, ${m}_{c}$ the cyclotron effective mass, and ${\overline{v}}_{z}$ the drift velocity along ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}$. The value of ${|{m}_{c}{\overline{v}}_{z}|}_{\mathrm{ext}}$ calculated from the model Fermi surface is 0.609\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}19}$ g cm ${\mathrm{sec}}^{\ensuremath{-}1}$. Damping of the helicon by open-orbit electrons near the planes $a|{k}_{z}|=4.225\ensuremath{-}4.625$ has also been observed. For ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}\ensuremath{\parallel}[001]$, no GK oscillations were observed; we attribute this to the large-amplitude oscillations in ${v}_{z}$ for electron orbits near the plane $a|{k}_{z}|=1.95$. The helicon edge does not appear to be a measure of ${|{m}_{c}{\overline{v}}_{z}|}_{max}$ since $|{m}_{c}{\overline{v}}_{z}|$ may go to infinity around the necks. For ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}\ensuremath{\parallel}[111]$, GK oscillations with a period of 590 \ifmmode\pm\else\textpm\fi{} 7G were observed. This period yields ${|{m}_{c}{\overline{v}}_{z}|}_{\mathrm{ext}}=(1.26\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ g cm ${\mathrm{sec}}^{\ensuremath{-}1}$ for electron orbits near the plane $a|{k}_{z}|=3.625$, while the value calculated from the model Fermi surface is 1.34\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}19}$ g cm ${\mathrm{sec}}^{\ensuremath{-}1}$. We emphasize that alignment of ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}$ along a crystal axis can be extremely critical, particularly when open-orbit electrons are present.