Linear and quadratic magneto-optical measurements of the spin reorientation in epitaxial Fe films on MgO

We have undertaken a detailed study by magneto-optical techniques of in-plane magnetization reversal behaviour in epitaxial Fe films grown by MBE on (1 0 0) oriented MgO substrate. We measure M-H loops for both orthogonal in-plane magnetization components M-l (component parallel to the magnetic field) and M-t (component perpendicular to the field) and for various orientations of the magnetic field with respect to the crystalline axis. These measurements show the classical four-fold cubic anisotropy for large Fe film thickness and confirm the appearance of weak uniaxial in-plane anisotropy superimposed for thinner films (t = 20 Angstrom). We have demonstrated the appearance of strong asymmetrical hysteresis loop for p-polarized incident light. We explain this behaviour as the mixing of transverse magnetization contribution to the longitudinal magnetization measurements on the basis of quadratic magneto-optical effects. The calculation of these effects based on eigenmode propagation in anisotropic layered media are developed by including the second-order magneto-optical terms in the permittivity tensor characteristic of a cubic crystal. The second-order reflection coefficients are discussed in the case of the normal incidence of the laser beam and for the magnetic field along the hard axis of the Fe film.