Nonlinear magneto-optical phenomena related to the process of second harmonic generation in anisotropic films of different classes of symmetry are discussed. In the electric-dipole approximation two kinds of nonlinearity of crystallographic and magnetic origin may coexist in noncentrosymmetric crystals. The interference between the corresponding nonlinear optical waves results in novel magneto-optical effects, such as a transversal effect linear in magnetization at normal incidence and a circular magnetic asymmetry with no equivalence between light helicity and magnetization direction change. Epitaxial films of magnetic garnets grown on substrates with different crystallographic orientations were taken as a model anisotropic system for experimental studies. The unambiguous separation of the crystallographic and magnetic contributions to the second harmonic generation is demonstrated with the help of rotational anisotropy experiments. A theoretical model for the nonlinear light propagation in noncentrosymmetric magnetic films is developed. Calculations based on this model are found to be in good agreement with the experimental results.
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