Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

Abstract We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal–insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D i =e i (0) E i +χ i (3) | E i | 2 E i . We assume that linear ei(0) and cubic nonlinear χi(3) dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal–insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function χeff(3) can be significantly greater (up to 103 times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity.