Faraday Effect in Solids

Abstract

Expressions for the weak-field Faraday effect in cubic materials are presented for the cases of transmission and reflection. These expressions contain the elements of the complex conductivity tensor. General quantum-mechanical expressions for the diagonal and off-diagonal elements of the frequency-dependent conductivity tensor are computed for arbitrary external magnetic fields and in the zero-wave-vector limit with the aid of dispersion relations. Sum rules for the conductivity tensor elements are also derived. The high-frequency limits of the conductivity elements are shown to reduce to the free-electron-gas results. A simple physical interpretation of the effect of the magnetic field on the conductivity tensor is given and this shows that two effects could contribute to the Faraday effect. These are the Zeeman splittings of the energy levels and the changes of the matrix elements. A calculation of the Faraday effect in the effective-mass approximation is performed. Special attention is given to the contribution of the spin-orbit interaction to first order and it is shown that for practically all nonferromagnetic metals this can be an appreciable effect on the interband part. The spin-orbit effect should be observed as a rapid variation in a comparatively small frequency range. The intraband part is not affected by spin-orbit effects to first order.