Azbel'-Kaner Cyclotron Resonance in Mercury

Abstract

Azbel'-Kaner cyclotron-resonance experiments have been carried out with two very flat mercury crystals at a microwave frequency of 34.28 GHz and a temperature of 1.2 \ifmmode^\circ\else\textdegree\fi{}K. Cyclotron effective masses of ten orbits were measured with an error of less than 2%. Five of the orbits (labeled $\ensuremath{\mu}\ensuremath{\gamma}$, ${\ensuremath{\gamma}}_{2}$, $\ensuremath{\kappa}$, ${\ensuremath{\mu}}_{2}$, and ${\ensuremath{\epsilon}}_{1}$) were observed for the first time by Azbel'-Kaner cyclotron resonance. The cyclotron masses of $\ensuremath{\alpha}$ orbits in the electron lenses were represented by an interpolation scheme which gives the mass for any field direction. This interpolation scheme showed that the second-zone electron lens is tipped 3\ifmmode^\circ\else\textdegree\fi{} out of a (100) plane of the reciprocal lattice toward the [111] direction and that there is a 9% anisotropy of the mass in the (100) plane. A similar interpolation scheme describing the frequencies of de Haas-van Alphen (dHvA) oscillations, which correspond to the $\ensuremath{\beta}$ arms of the first-zone hole surface, is also presented. The oscillations were caused by two effects which could not be separated: quantum oscillations of the microwave surface impedance and dHvA torque. Methods for accurately determining the crystal orientation within the experimental apparatus, using the symmetry of the electron-lens masses and of signal peaks arising from open-orbit induced-torque effects, are presented. Cyclotron resonance with the magnetic field inclined to the sample surface is discussed. Several effects indicate anomalous penetration of the electromagnetic field into the metal.