Anisotropy of the quadratic magneto-optical effects in a cubic crystal

Abstract

Magneto-optical (MO) Kerr effects are widely used for a thin film magnetism study. The otpical and MO properties of layer media are described through the permittivity tensor. A cubic crystal is optically isotropic and the linear MO effects are independent on the rotation of the crystal axes. On the contrary the MO effects quadratic in the magnetization are anisotropic in a medium with a cubic symmetry as well. In the paper, the anisotropy of the quadratic MO effects is discussed in the case when the magnetization lies in the plane of the layer. This configuration especially at a normal incidence is very suitable for the quadratic MO effects observations. The eigenmode equation is solved including both the linear and the quadratic terms in the permittivity tensor. The boundary conditions of the electric and magnetic fields at interface are described using 4 X 4 Yeh's matrices. The reflection coefficients form an interface between isotropic and MO media are derived including the quadratic MO terms. The quadratic MO effects observed through the conversion reflection coefficients and through the MO angles are dependent on the crystal axes orientations. The experimental measurements of the quadratic MO effects in reflection form an epitaxial bcc Fe layer are presented.