Azbel-Kaner Cyclotron Resonance Research Articles

On the anomalous skin-effect in magnetized bounded plasmas

An analytical theory of the RF-field distribution in a warm homogeneous magnetized plasma slab or plasma cylinder, with electron reflecting boundaries, is developed. Simple solutions of the Boltzmann equation coupled to the Maxwell equations are found, in case the effective penetration depth of the RF-field excited at the boundary of the plasma cylinder is small compared to the cylinder radius. These solutions satisfactorily describe experimental results obtained for cylindrical Ar-plasmas in an axial magnetic field. A possibility of the existence of the Azbel-kaner cyclotron-resonance in this model is discussed.

DHvA effect study of the effective cyclotron masses of the central and noncentral zeta orbits in lead

Cyclotron effective masses of two extremal orbits on the third zone electron arm in lead have been studied for the symmetry direction (110) using the de Haas-van Alphen effect. The temperature dependence of the amplitudes of both the node and antinode for the well known 42.5 cycle beat pattern has been analysed to evaluate each of the two individual cyclotron effective masses, i.e. mc* and mn* of the gamma c and gamma n oscillations, respectively. Here gamma c and gamma n denote the dHvA oscillations arising from the larger and smaller extremal orbits on the electron arm, respectively. The cyclotron effective mass ratios thus determined are mc*/m0=0.539+or-0.006 and mn*/m0=0.571+or-0.007, where m0 is the rest mass of the free electron. These mass ratios are favourably compared with the ones recently determined by Onuki et al. (1977) using the Azbel-Kaner cyclotron resonance technique.

Tipping Effects on the Line-Shapes in Azbel-Kaner Cyclotron Resonance in Metals with Non-Ellipsoidal Fermi Surfaces

In a small tip angle region the line shapes in cyclotron resonance in metals with nonellipsoidal Fermi surface are studied. The electrical conductivities are calculated without using the method of steepest decent. It is shown that the behaviours of the central orbit and of the limiting point orbit resonance are quite different from each other on tipping of the static magnetic field from the surface of metal. The line shapes due to the limiting point orbit resonance are strongly modified by tipping and those due to the central orbit resonance are scarcely modified. The results are consistent with that expected from the Doppler shift theory.

Fermi-Liquid Effects in Cyclotron-Phase-Resonance Transmission through Alkali Metals at 116 GHz

Cyclotron phase resonance (CPR) is observed at 116 GHz in sodium and potassium. The CPR signal shows effects due to electron correlations, including notches in the transmission amplitude, an asymmetry, and possibly a shift in resonance field from the Azbel-Kaner cyclotron-resonance (AKCR) value. A simple model describing these effects appears to indicate that CPR is a $k=0$ resonance in the conductivity, i.e., a uniform resonance whose shift from AKCR should give the Fermi-liquid parameter ${A}_{1}$. Values found for ${A}_{1}$, however, disagree with previous estimates.

Cyclotron Resonance in Nickel

Azbel-Kaner cyclotron resonance was studied at 277 GHz and 1.5 \ifmmode^\circ\else\textdegree\fi{}K in a (100)-plane single-crystal specimen of Ni. Resonances from both the neck and belly of the Cu-like majority-spin $s\ensuremath{-}p$-band Fermi surface were seen. The neck yielded $\frac{{m}^{*}}{{m}_{0}}=0.35\ifmmode\pm\else\textpm\fi{}0.014$ when $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ was along $〈011〉$. Beat structure in the subharmonic resonances suggested that belly orbits on both the majority-and minority-spin $s\ensuremath{-}p$-band Fermi surfaces were observed for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ within 28\ifmmode^\circ\else\textdegree\fi{} of $〈001〉$. As $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ was rotated away from $〈001〉$ the heavier mass increased smoothly from $\frac{{m}^{*}}{{m}_{0}}=5.09 \mathrm{to} 5.9$ while the lighter mass increased from 4.33 to 4.86. Only one of the three pairs of symmetry-related minority-spin $d$-band hole pockets were seen. The pockets having their greatest dimension along $〈001〉$ yielded an effective mass which increased from $\frac{{m}^{*}}{{m}_{0}}=0.75\ifmmode\pm\else\textpm\fi{}0.03$ at $〈001〉$ to ${m}^{*}{m}_{0}=1.11$ when $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ was 34\ifmmode^\circ\else\textdegree\fi{} from $〈001〉$.

Acoustic Geometric and Acoustic Cyclotron Resonances in Gallium

Acoustic geometric and acoustic cyclotron resonances in high-purity single crystals of gallium were investigated at 1.3 \ifmmode^\circ\else\textdegree\fi{}K and in the normal geometry where the magnetic field is perpendicular to the wave vector of the ultrasonic waves. These waves, polarized longitudinally and of frequencies in the range 60-400 MHz, were propagated along the three principal crystallographic axes $a$, $b$, and $c$ of gallium. The extremal dimensions of the Fermi surface in the ${k}_{a}{k}_{b}$, ${k}_{b}{k}_{c}$, and ${k}_{c}{k}_{a}$ planes, obtained by measuring the periodicity $\ensuremath{\Delta}(\frac{1}{H})$, of the geometric-resonance oscillations, are compared with the predictions of the augmented-planewave and pseudopotential models. The results are in good agreement with the values given by the pseudopotential model. A map of effective masses in the $\mathrm{ab}$, $\mathrm{bc}$, and $\mathrm{ca}$ planes, obtained from acoustic-cyclotron-resonance experiments, is given. These data are compared to those of Moore, who used the Azbel'-Kaner cyclotron resonance (AKCR). Some branches of effective masses were found which have not been observed by AKCR and, reciprocally, many resonances observed by AKCR were not observed in the present work.

Influence of mass spread on the line shape of Azbel-Kaner cyclotron resonance

When the Azbel-Kaner equation is taken for the line shape of a cyclotron resonance signal and the Fermi surface is taken to be a sphere with a nonconstant M, a splitting of the cyclotron resonance line into a main line with a Chambers shape and a 'satellite line that lies outside the region where Chambers' formula is valid is found. The satellite line problem provides the explanation for some previously uninterpreted resonances in zinc and cadmium.

Exact Solution of the Integral Equations for the Anomalous Skin Effect and Cyclotron Resonance in Metals

The exact solution of several boundary-value problems which arise in the theory of the surface impedance of metals at high frequencies is given. The problems are the anomalous skin effect for arbitrary boundary conditions, and Azbel-Kaner cyclotron resonance for diffuse surface scattering. In both cases, spherical Fermi surfaces are assumed.

Tipping effects in Azbel-Kaner cyclotron resonance

Calculations of Azbel-Kaner line shapes when the magnetic field is tipped out of the surface have been carried out in a number of cases for both the free electron model and an arbitrary Fermi surface with mass spread. For small angles of tip the results substantiate the Doppler shift theory advanced by Koch, Stradling & Kip and provide a consistent explanation of the observed peak shifts or splitting in all cases. Arguments are presented that at larger tip angles the overall absorption will decrease with increasing field, and the original resonance may become inverted, owing to the removal of non-stationary electrons from the skin depth. At large tip angles (5° or so) inverted and doubled resonances observed with parallel polarization are shown to arise from ‘field splashes’ set up by drifting electrons from the limiting points, regardless of the nature of the Fermi surface. Apparently normal resonances observed at very large tip angles are shown to arise from so-called ‘cylinder sections’ where d A /dk 2 H = 0 and v D = 0, A and v D being the area of the orbit in k space and the drift velocity respectively.

Exact Solution of the Integral Equations for the Anomalous Skin Effect and Cyclotron Resonance in Metals

The exact solution of several boundary-value problems which arise in the theory of the surface impedance of metals at high frequencies is given. The problems are the anomalous skin effect for arbitrary boundary conditions, and Azbel-Kaner cyclotron resonance for diffuse surface scattering. In both cases, spherical Fermi surfaces are assumed.

Cyclotron Resonance in Zinc

Azbel-Kaner cyclotron resonance has been studied at 24 Gc/sec and 2\ifmmode^\circ\else\textdegree\fi{}K in the ($10\overline{1}0$), ($11\overline{2}0$), and (0001) planes of zinc. Twelve distinct mass series have been identified and their mass values determined as a function of the orientation of the magnetic field in the sample surface. All of the observed signals are felt to arise from carriers in orbits on either the lens-shaped electron surface in the third band or the hole surface in the second band. One of the mass series is assigned to a limiting-point resonance associated with the electrons on the spherical caps of the lens.

Cyclotron resonance transmission in metals

The cyclotron resonance transmission coefficient of electromagnetic radiation through a metal slab is calculated. Use is being made of the Pippard-Heine method of treating Azbel-Kaner Cyclotron resonance. An explicit dependence on the shape of the Fermi surface is obtained.

Shubnikov-de Haas Effect and Cyclotron Resonance in a Dilute Bi-Sb Alloy

Magnetoresistance oscillations (Shubnikov-de Haas effect) and Azbel-Kaner cyclotron resonance were studied in a dilute Bi-Sb alloy (Sb concentration of 0.96 wt.%) at 4.2\ifmmode^\circ\else\textdegree\fi{}K for various orientations of the magnetic field. It was found that the electron masses, and the extremal cross-sectional areas of the electron Fermi surface, decrease to approximately 80 and 62%, respectively, of the corresponding values in pure Bi. The observed changes in cyclotron masses and Shubnikov-de Haas frequencies in the alloys are consistent with the nonparabolic model and the assumption of rigid motion of the conduction band, and the valence band just beneath it, with respect to the hole band. Effective masses at the bottom of the conduction band were calculated. The electron Fermi energy and concentration in the alloy were determined. The band overlap deduced from this result is in agreement with other work.

Cyclotron resonance in lead at 36000 mc/sec

Abstract Azbel–Kaner cyclotron resonance has been studied in lead at 36 kMc/sec and 1.5°k. The results were found to be consistent with the work of Khaikin and Mina at 9 kMc/sec and have been interpreted on Gold's model of the Fermi surface of lead. It has also been shown that the open orbit data deduced from magneto-resistance and magneto-acoustic measurements can be explained by Gold's model.