Magnetic Field Dependence of the Size Effect in the Transport Coefficients of a Cadmium Single Crystal at Liquid-Helium Temperatures

Abstract

Magnetomorphic oscillations periodic in the magnetic field have been observed in transverse magnetic fields in the transport coefficients of a cadmium single crystal at liquid-helium temperatures. The experimental coefficients in which magnetomorphic oscillations have been observed are: the transverse magneto-resistivity ${\ensuremath{\rho}}_{11}$, the Hall resistivity ${\ensuremath{\rho}}_{21}$, the transverse thermal magnetoresistivity ${\ensuremath{\gamma}}_{11}$, the Righi-Leduc resistivity ${\ensuremath{\gamma}}_{21}$, the adiabatic thermoelectric coefficient ${{\ensuremath{\epsilon}}_{11}}^{\ensuremath{'}}$, and the adiabatic Nernst-Ettinghausen coefficient ${{\ensuremath{\epsilon}}_{21}}^{\ensuremath{'}}$. These oscillations have an average period of about 565 G for a sample thickness 1.02 mm and are believed to originate with the lens-shaped Fermi surface in the third Brillouin zone of cadmium. The theory of magnetomorphic oscillation for the case of free electrons is found to agree for the most part with the experimental results, except in the case of the oscillations in the quantity ${{\ensuremath{\epsilon}}_{11}}^{\ensuremath{'}\ensuremath{'}}$ (thermoelectric coefficient), which have been found to be of an order of magnitude 20 times larger than predicted by the free-electron theory. The extension of the theory to the case of nonspherical Fermi surfaces, and to the case of lens-shaped Fermi surfaces in particular, fails to account for the anomaly in this coefficient. In addition to the oscillations of period 565 G, another set of oscillations of period 132 G was detected in the Hall effect. It is suggested that these short-period oscillations may be associated with the hole arms in the second Brillouin zone and are probably due to the truncation of the arm when it splits into its three branches.