In-plane magnetization investigation in Fe films using magneto-optical effects in reflection

The magneto-optical effects in reflection are often used for the investigation of the in-plane magnetization behavior in thin ferromagnetic films. The methods of the magneto-optical hysteresis loop measurements are presented for both magnetization components parallel and perpendicular to the external magnetic field. The influence of the longitudinal and the transverse magnetization on the reflection coefficients including the second order magneto-optical effects is presented. The formulas for the reflection coefficients and the magneto-optical angles are brought for the interface between an isotropic medium and a cubic magnetic crystal with the in-plane magnetization. The Yeh's 4 by 4 matrix formalism, based on eigen modes propagation in the anisotropic magneto- optical medium, is used for the calculation. The theory is introduced for the epitaxial Fe film evaporated on MgO substrate for the field along a magnetically hard axis. The second order effect of the transverse magnetization component suprposes on the linear longitudinal Kerr effect. This undesirable second order effect can be attenuated by choosing the optimal magneto-optical quantity and the measurement geometry. On the other hand the normal incidence geometry is optimal for investigation of the second order magneto-optical effects, because the linear longitudinal and transverse Kerr effects disappear. The pure second order hysteresis loops are measured in this geometry. There is the reflection analogy of the Voigt or the Cotton-Mouton geometry.