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

Magneto-optical (MO) Kerr effects are widely used for a thin film magnetism study. The optical and MO properties of laver media are desribed through the permitivity 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 (second-order effects) 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 (characteristic) equation is solved including bath the linear and the quadratic terms in the permitivity tensor. The boundary conditions of the electric and magnetic fields at interface are described using 4 x 4 Yeh's matrices. The reflection coefficients from 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 (rotation, ellipticity) are dependent on the crystal axes orientations. The experimental measurements of the quadratic MO effects in reflection from an epitaxial bcc Fe layer are presented.