Theory of the Nonlinear Polar Kerr Magneto-Optic Effect in Ferromagnetic Metals

Abstract

A theory of the nonlinear polar Kerr magneto-optic effect in ferromagnetic metals is developed. The material model is based on the classical equation of motion for a free electron with a finite relaxation frequency under the action of a Lorentz force. A second-harmonic current density is found of the form: J2=αE2+βh(H1)E1+ξ(E1V·E1)where α, βh (H1), and ξ are nonlinear conductivity tensors, E1 and H1 are the fundamental electric and magnetic fields, and E2 is the induced second-harmonic electric field. Results of this theory reduce, in the limit of a vanishing ferromagnetic state, to results obtained from the Boltzmann transport equation for conduction electrons subject to a potential barrier at the metal surface. As required, the theory reduces to the linear polar Kerr magneto-optic effect in the absence of second-harmonic generation. The second-harmonic reflection coefficients are derived. To the degree of approximations made, all four coefficients vanish at normal and grazing incidence. They are maximum at intermediate angles of incidence, depending upon the physical properties of the metal.