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Summary form only given. The second-harmonic generation (SHG) is suggested as a nonlinear optical readout of magnetic and ferroelectric thin-film-based memories. This nonlinear optical readout is based on the magnetization-induced SHG (MSHG) and dc-electric-field-induced SHG (EFISH) phenomena. The transversal nonlinear magneto-optical Kerr effect (NOMOKE), which is the MSHG intensity changes, is systematically studied in a variety of magnetic materials.