Theory of the Faraday and Kerr Effects in Ferromagnetics

Both the Faraday and (magneto-optic, polar) Kerr effects in ferromagnetics are treated on the basis of the band theory of metals. The spin-orbit interaction gives the electron wave functions such left-right asymmetry that the "magnetic" electrons, under the action of a plane polarized light wave, produce an average current perpendicular to the plane of polarization. The polarizability and conductivity tensors are evaluated. The model is capable of describing the rotation of the plane of polarization of the light and the elliptical polarization resulting from transmission or reflection on the ferromagnetic medium. Order of magnitude estimates of the tensor components, based on plausible assumptions on the nature of the electronic wave functions and the energy bands in ferromagnetics, give values that agree reasonably well with experimental results. The temperature and frequency dependence of these effects as given by the formulas is also in agreement with experiment.