A discussion is given of experiments on the transmission of cyclotron waves through a thin single-crystalline sample of silver at a frequency of 44.86 GHz. From the data information is obtained on the oscillatory dispersion relation for the extraordinary wave, i.e. turning points, slope, and width of the branches of the dispersion relation.



[Russian Text Ignored]

Cyclotron Waves in Silver – Interference Effects

The surface impedance for a metal placed in a magnetic field parallel to the sample surface is calculated for the three cases: a circular cylindrical Fermi surface and ERF perpendicular to B; a spherical Fermi surface and ERF perpendicular to B and ERF//B, respectively. The surface impedance is expressed in an exact form in terms of the roots of the dispersion relation for cyclotron waves of the type relevant to the field configuration considered. An approximate evaluation of the surface impedance and the field distribution in the metal is briefly considered and it is shown that the surface impedance may be written in terms of an average phase velocity for cyclotron waves.

https://iopscience.iop.org/article/10.1088/0305-4608/7/10/012/pdf

Exact expressions for the surface impedance of a metal in a magnetic field

A recently developed formalism (see ibid., vol.7, no.10, p.2109 (1977)) is applied to the calculation of the surface impedance of a metal in a magnetic field for two configurations: (i) a cylindrical Fermi surface and ERF perpendicular to B, and (ii) a spherical Fermi surface and ERF//B. In the former case, especially, the surface impedance anomalies observed above the fundamental Azbel-Kaner resonance are calculated, whereas in the latter case the fundamental Azbel-Kaner resonance is considered. The calculations aim at illustrating the convergence properties of formal expressions presented earlier, and, in case (i), at elucidating the physical nature of the surface impedance anomalies. In this connection a general condition for the occurrence of such anomalies is presented and a possible use for determination of Fermi surface dimensions is suggested.

Surface impedance of a metal in a magnetic field and cyclotron waves: Numerical calculations

A recently developed formalism is applied to the evaluation of the surface impedance for a metal in a magnetic field. A spherical Fermi surface is assumed for the metal and the field configuration considered is the Azbel-Kaner geometry. The formalism makes use of the dispersion relation for extraordinary cyclotron waves in an essential way and the authors therefore give a detailed treatment of this dispersion relation for a finite value of omega tau and for frequencies of the order of 25-50 GHz. The fundamental cyclotron resonance and the surface impedance anomalies, occurring above the fundamental resonance, observed experimentally in potassium by Dunifer and co-workers are calculated. The correlation between the surface impedance and the dispersion relation for the cyclotron waves is pointed out and the significance of the polarisation properties of the waves is emphasised.

Cyclotron resonance line shape and cyclotron waves for a spherical Fermi surface

Experimental evidence for the existence of absorption edges for cyclotron waves propagating in metals, here silver, is given. The edges occur close to the ‘turning points’ of the infinite-ωτ dispersion curve for (extraordinary) cyclotron waves. The experimental results are compared with numerical calculations based on a finite value of ωτ and on Halse's Fermi surface of silver. A physical mechanism accounting for the observations is presented.



Es werden experimentelle Hinweise fur die Existenz von Absorptionskanten fur Zyklotronwellen in Metallen, hier Silber, mitgeteilt. Die Kanten treten in der Nahe der „Umkehrpunkte” der Dispersionskurve fur (auserordentliche) Zyklotronwellen fur unendliches ωτ auf. Die experimentellen Ergebnisse werden mit numerischen Rechnungen auf der Grundlage eines endlichen Wertes fur ωτ und der Fermiflache von Silber nach Halse verglichen. Ein fur die Beobachtungen verantwortlicher physikalischer Mechanismus wird diskutiert.

Absorption edges for cyclotron wave propagation in silver

Azbel'-Kaner cyclotron resonance in metals is accompanied by electromagnetic waves propagating in a direction perpendicular to the magnetic field. Taking into account the anisotropy of the silver Fermi surface, the dispersion relation for these waves is calculated in the limit where the wavelength is much smaller than the orbit diameter of the electrons. Thus it is shown that a number of previously observed oscillations in the surface impedance of a semiinfinite silver specimen arise from points of zero-group velocity on the dispersion relation. Physically, the oscillations reflect a matching of the electron-orbit diameter with an integer number of wavelengths. They may, therefore, be looked upon as geometric resonances in the surface impedance, complementary to the temporal cyclotron resonances. The surface impedance is calculated under the assumption of specular surface scattering. Satisfactory agreement with experiments is obtained by using an independent-particle model for the electron gas and band parameters based on APW calculations. The influence of the Fermi-surface geometry is demonstrated by comparing with calculations for a cylindrical and a spherical Fermi surface. The electric field in the metal is calculated for selected magnetic fields, and the expected result of a transmission experiment is presented. Finally, the absence of Fermi liquid effects in the experiments is briefly discussed.

J. O. Henningsen

Papers

Cyclotron wave propagation in silver