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

Gantmakher-Kaner (GK) oscillations and Doppler-shifted cyclotron resonance (DSCR) of helicons have been investigated in very pure copper with the magnetic field ${\overrightarrow{\mathrm{B}}}_0$ and the propagation vector $\overrightarrow{\mathrm{q}}$ along the [101], [001], and [111] directions. The results are compared with a model Fermi surface proposed by Halse. For ${\overrightarrow{\mathrm{B}}}_0\parallel \mathrm{}\left[101\right]\mathrm{}$, 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 ± 7 G for the GK oscillations, we assign a value of ${\left|m_c{\overline{v}}_z\right|}_{\mathrm{ext}}=(0.\mathrm{}648\pm 0.014)\times {10}^{-19\mathrm{}}$ g cm ${\sec }^{-1\mathrm{}}$ to electrons with orbits near the plane $a\left|k_z\right|=2.675\mathrm{}$, where $a$ is the lattice constant, $m_c$ the cyclotron effective mass, and ${\overline{v}}_z$ the drift velocity along ${\overrightarrow{\mathrm{B}}}_0$. The value of ${\left|m_c{\overline{v}}_z\right|}_{\mathrm{ext}}$ calculated from the model Fermi surface is 0.609×${10}^{-19\mathrm{}}$ g cm ${\sec }^{-1\mathrm{}}$. Damping of the helicon by open-orbit electrons near the planes $a\left|k_z\right|=4.\mathrm{}225-4.625$ has also been observed. For ${\overrightarrow{\mathrm{B}}}_0\parallel \mathrm{}\left[001\right]\mathrm{}$, no GK oscillations were observed; we attribute this to the large-amplitude oscillations in $v_z$ for electron orbits near the plane $a\left|k_z\right|=1.\mathrm{}95$. The helicon edge does not appear to be a measure of ${\left|m_c{\overline{v}}_z\right|}_{max}$ since $\left|m_c{\overline{v}}_z\right|$ may go to infinity around the necks. For ${\overrightarrow{\mathrm{B}}}_0\parallel \mathrm{}\left[111\right]\mathrm{}$, GK oscillations with a period of 590 ± 7G were observed. This period yields ${\left|m_c{\overline{v}}_z\right|}_{\mathrm{ext}}=(1.\mathrm{}26\pm 0.02)\times {10}^{-19\mathrm{}}$ g cm ${\sec }^{-1\mathrm{}}$ for electron orbits near the plane $a\left|k_z\right|=3.\mathrm{}625$, while the value calculated from the model Fermi surface is 1.34×${10}^{-19\mathrm{}}$ g cm ${\sec }^{-1\mathrm{}}$. We emphasize that alignment of ${\overrightarrow{\mathrm{B}}}_0$ along a crystal axis can be extremely critical, particularly when open-orbit electrons are present.