Harmonic Series of Cyclotronlike Resonances in Bismuth

Abstract

which go beyond Landau-Ginzburg theory and which do not have this restriction show that the change in the character of the phase transition from second to first order with decreasing temperature occurs as long as K <0,4. Here K is the ratio XQ{T)/i{T), When /c> 0.7 the phase transition is always second order. When 0.4</c < 0.7 the transition starts out second order becoming first order as the temperature is lowered and the magnetic field increased. At very low temperatures the transition reverts to being second order, ^^It should be noted that this problem is then formally like that of a ferroelectric in an electric field. It is well known that coexistence surfaces exist for ferroelectric s in finite electric fields when the coefficient of the quartic term in the free energy is negative.Cyclotronlike resonances have been observed in the far-infrared transmission spectra of centimeter-thick single crystals of bismuth.The past decade or so has seen considerable interest in the propagation of radio and microwave frequencies through metals. We have successfully extended the range of useful frequencies into the far infrared and have seen a harmonic series of cyclotronlike resonances not previously observed in any metal.To place this work in perspective, it would be well to review briefly the scope of previous work in this field. Both helicon waves^ and Alfven waves^ have been studied in metals, and both rely upon the application of a large magnetic field to drive the cyclotron frequencies of the charge carriers above the frequencies to be transmitted. For an isotropic metal in an axial magnetic field, the two normal modes are circularly polarized in opposite senses. One of these modes has its electric vector rotating in the same direction as the electrons are orbiting, and this helicon mode propagates with relatively little attenuation for a)T»l and for frequencies below the cyclotron frequency a?^ (here, r is the relaxation time). The other mode is nonpropagating at these frequencies. In practice, the frequency range of helicon propagation is further restricted to frequencies well below co^, since electrons at the Fermi surface move with velocities approaching the speed of light in the metal and the cyclotron resonance is strongly Doppler broadened. The onset of Doppler-shifted cyclotron resonance is typically at radio frequencies.Alfven waves propagate through metals which 1041

Magnetic-field-induced far-infrared transmission in bismuth

“…However, the two band model does not take into account the influence of other bands, and they can cause the Fermi 47 surface to be slightly non-ellipsoidal. After transformation, the hole Fermi surface is then a slightly distorted sphere and the cyclotron motion is no longer simple harmonic in character.…”