Effect of Magnetic Breakdown on the Magnetoconductivity of Cadmium

Abstract

The magnetoconductivity and magnetoresistivity tensors of cadmium have been calculated by the path integral method for magnetic fields in the [Formula: see text] and [Formula: see text] directions. A uniform relaxation time and a modified nearly free electron Fermi surface were used. Magnetic breakdown across the HAL spin–orbit energy gap vitiated Kohler's rule and necessitated separate calculations for different relaxation times. Even with open orbits, cadmium was found to be a 'compensated' metal in that the Hall terms never dominated the conductivity tensor determinant. A single breakdown field was found to be inadequate to describe magnetic breakdown on the sheaf of orbits which touch the HAL plane. A range of breakdown fields was calculated across the sheaf of open orbits. From an explanation of induced torque data, it was found that the ratio of the spin–orbit energy gap in the HAL plane to the Fermi velocity is 1.4 × 10−8 eV s cm−1. The resulting field dependences of the magnetoconductivity and magnetoresistivity tensor components are presented and discussed. The use of the path integral technique when there is magnetic breakdown is also presented.