Theory of the Non-linear Longitudinal Kerr Magneto-optic Effect in Ferromagnetic Metals

Abstract

A theory of the non-linear longitudinal 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 + β h (H 1)E1 + σ (E1∇ · E1), where α, βh (H 1) and σ are non-liner 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 by Jha [1] 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 longitudinal 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 grazing incidence. Unlike the non-linear polar Kerr effect, they do not vanish at normal incidence.