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We extend our previous study of the polarization dependence of the nonlinearoptical response to the case of magnetic surfaces and buried magneticinterfaces. We calculate for the longitudinal and polar configuration thenonlinear magneto-optical Kerr rotation angle. In particular, we show whichtensor elements of the susceptibilities are involved in the enhancement of theKerr rotation in nonlinear optics for different configurations and wedemonstrate by a detailed analysis how the direction of the magnetization andthus the easy axis at surfaces and buried interfaces can be determined from thepolarization dependence of the nonlinear magneto-optical response, since thenonlinear Kerr rotation is sensitive to the electromagnetic field componentsinstead of merely the intensities. We also prove from the microscopic treatmentof spin-orbit coupling that there is an intrinsic phase difference of90$^{\circ }$ between tensor elements which are even or odd under magnetizationreversal in contrast to linear magneto-optics. Finally, we compare our resultswith several experiments on Co/Cu films and on Co/Au and Fe/Cr multilayers. Weconclude that the nonlinear magneto-optical Kerr-effect determines uniquely themagnetic structure and in particular the magnetic easy axis in films and atmultilayer interfaces.Comment: 23 pages Revtex, preprintstyle, 2 uuencoded figure

physical review. b, condensed matter

Electronic theory for the nonlinear magneto-optical response of transition metals at surfaces and interfaces: Dependence of the Kerr rotation on the polarization and magnetic easy axis