Doppler-shifted Cyclotron Resonance Research Articles

Helicon Propagation in Metals near the Cyclotron Edge

The theory of Doppler-shifted cyclotron resonance with helicon waves is elaborated by calculating the magnetic-field dependence of the surface impedance near the cyclotron absorption (Kjeldaas) edge. It is found that the location of the edge, defined as that field for which the field derivative of the surface reactance is a minimum, deviates significantly from the threshold field defined by the Doppler-shifted frequency criterion. The deviations are large when ${\ensuremath{\omega}}_{c}\ensuremath{\tau}<50$. The theory is compared with the experimental work of Taylor on Na and K. The data agree well with the free-electron model for Na, but there is a large discrepancy (770 G for 10-Mc/sec helicons) in K. The surface impedance is also calculated for a metal with a spin-density-wave ground state, in order to test the hypothesis of such a ground state, previously made to explain other anomalies in K. The edge field derived for a spin-density-wave state appropriate to K is 730 G less than that required by the free-electron model, and agrees with the published data.

Cyclotron Resonance in Cadmium

Extensive observations at 1.5\ifmmode^\circ\else\textdegree\fi{}K and both 23.8 Gc/sec and 74.2 Gc/sec of cyclotron-resonance phenomena in cadmium are reported. One group of experiments is done with the steady applied field parallel to the sample plane (Azbel'-Kaner geometry). A large number of signals are observed, only some of which are sufficiently reliable to identify with cyclotron masses. All the masses are plotted versus the crystallographic orientation of the steady applied field in three of the principal planes. The reliable, well resolved signals are identified and associated tentatively with orbits. Most of these orbits are consistent with the current model of the Fermi surface of cadmium, but some of them require small modifications of it. These orbits are either on the "pillow" or on the large surface associated with holes in the second band. The masses observed with the magnetic field parallel to the sample plane are all too large to identify plausibly with the smaller pieces of the Fermi surface such as the "butterflies" and "cigars". It is suggested that the resonances associated with the charge carriers of smaller mass are lost in the signals from harmonics of those of larger mass. In another group of experiments, data have been obtained with the steady applied field normal to the sample surface. Here signals are obtained at classical cyclotron-resonance fields equal to those observed in the other geometry although the signals are in the anomalous-skin-effect regime and the much larger effects associated with Doppler-shifted cyclotron resonance are at magnetic fields too high to be observed. A theoretical treatment and a discussion of the physics of these effects is given. In this geometry, a cyclotron mass of approximately 0.22 ${m}_{0}$ is also observed. The related orbit is only tentatively identified, but it is definitely thought to involve one of the smaller pieces of the Fermi surface.

Doppler-Shifted Cyclotron Resonance with Helicon Waves

Doppler-Shifted Cyclotron Resonance with Helicon Waves

Doppler-Shifted Cyclotron Resonance with Helicon Waves in Sodium

Doppler-Shifted Cyclotron Resonance with Helicon Waves in Sodium

Doppler-Shifted Cyclotron Resonance and Alfvén Wave Damping in Bismuth

At large magnetic fields the transmission of microwaves through bismuth is essentially undamped and can be regarded as Alfv\'en waves in a solid-state plasma. A large kink has been observed in the 9-Gc/sec microwave absorption of bismuth as a perpendicularly applied magnetic field was varied through 1500 G. These experiments have been performed at 2\ifmmode^\circ\else\textdegree\fi{}K with a field parallel to the binary axis. The kink has been identified as a Doppler-shifted cyclotron resonance whose position is approximately given by the formula $\ensuremath{\omega}={\ensuremath{\omega}}_{c}\ensuremath{-}{v}_{0x}{k}_{A}$ where ${v}_{0x}$ is the maximum Fermi velocity along the field and ${k}_{A}$ is the wave number of the microwaves in the metal. The kink marks the onset of Alfv\'en wave behavior where the surface resistance is proportional to magnetic field. A calculation of the surface resistance using a nonlocal theory applied to a three-carrier model yields a variation with field which shows both the Doppler-shifted peak and the high-field linear region which can be extrapolated back through the origin. The frequency dependence of the peak derived from this calculation has been verified experimentally. By tilting the field slightly away from the perpendicular it was shown that the peak was a Doppler shift in the cyclotron resonance of the holes rather than of the electrons. This experiment provides a very accurate measure of the ratio of the Fermi velocity to the Alfv\'en velocity and, thus, knowing one, the other may be determined. For this reason, the Alfv\'en velocity in the same crystals was independently measured using an interference technique. Oscillations with a constant period in $\frac{1}{H}$ were observed in the reflected power as the applied magnetic field was varied. From the period of oscillation and the thickness of the crystal, the velocity was deduced. The work also provides a graphic measure of the sharpness of the Fermi surface.

Angular dependence of the velocity of sound in semimetals

A wide range of phenomena of the electromagnetic generation of sound in metals in a magnetic field is reviewed. All phenomena of mutual conversion of waves and of sound generation are due to the interaction of conduction electrons with phonons. A wide variety of resonance effects in a magnetic field determines numerous mechanisms for direct sound generation by an external microwave.The basic equations and boundary conditions for the problem of electron-phonon interaction in metals are presented in the quasiclassical approximation. In the low-temperature region under the conditions of the anomalous skin effect the wave conversion is caused, besides by inductive interaction, also by electron-phonon interaction via the deformation potential. The major conversion mechanism of an electromagnetic wave into sound results in various resonance effects in a magnetic field in conditions of strong spatial dispersion. We present an exact solution of the problem for an alkali metal in a magnetic field normal to the surface. We analyze the asymptotic approximations related with the skin-effect anomaly, the coupling of electromagnetic and acoustic waves in metals, and the role of surface scattering. We study the effect of resonance renormalization of electron-phonon interaction in metals with a complex dispersion law, which results in a partial compensation of resonance singularities and appears in Doppler-shifted cyclotron resonances. The doppleron-phonon resonance and its polarization effects are investigated.The electromagnetic generation of sound in metals in a magnetic field parallel to the surface is due to the additional mechanism of selecting “effective” electrons, where resonance effects are observed. We study geometric and cyclotron resonances, and the resonance coupling of a sound wave with a cyclotron wave. The amplitude and phase of the generated sound depend on the character of electron scattering on the metal boundary because in specular scattering a group of surface electrons move in the skin layer and get reflected many times from the separation boundary.The tilt effect in electron-phonon interaction appears during the electromagnetic generation of sound as strong peculiarities of the sound amplitude in terms of the tilting angle of the magnetic field relative to the surface of the metal. It is caused by an abrupt introduction of the mechanism of collisionless resonance interaction of conduction electrons with sound, as the angle between the magnetic field H and the direction of sound wave propagation varies.A new type of sound wave is generated in metals which are placed in a magnetic field under irradiation by a microwave. Besides a conventional wave propagating with sound velocity s0, an improper sound is excited; depending on the magnetic field orientation relative to the metal surface, it propagates with the Fermi electron velocity vF s0 in the case of a perpendicular magnetic field. In a titled magnetic field the improper sound is a standing wave in a semibounded sample, having the form of peaks of the acoustic field, situated at distances multiple of the cyclotron electron diameter. The peak amplitude is (qδ)2 1 times larger than the amplitude of usual sound (q = ω/s0) is the sound wave vector, δ is the thickness of the skin layer). The effect is caused by ballistic transport of energy of an electromagnetic wave from a skin layer to the bulk of the metal by specific electrom groups. The “angular resonance effect” refers to the rapid growth of the improper sound peak amplitude as a function of the tilting angle of the magnetic field relative to the surface.The diamagnetic resonance appears as peculiarities of the electromagnetic signal and improper sound when it passes through a metal plate whose thickness is comparable with the length of the electron mean free path. The resonance lineshape is studied.All the theoretical results are in good agreement with the known experimental data. The conversion of an electromagnetic wave into sound has become widely applicable to various techniques aimed at studying the electro-acoustic properties of metals, and provides the basis of a new method, the “hybrid spectroscopy of metals”.

Damping of the low frequency magnetoplasma resonance by cyclotron absorption in sodium

The observation of Doppler shifted cyclotron resonance absorption of the magnetoplasma resonance in sodium plates is reported. The absorption was excited by a wave the frequency of which was five orders of magnitude less than the cyclotron frequency. The agreement between the observations and theory was investigated. (D.C.W.)

Doppler-Shifted Cyclotron Resonance and Alfvén Wave Damping in Bismuth

Doppler-Shifted Cyclotron Resonance and Alfvén Wave Damping in Bismuth