Symmetry analysis of the nonlinear optical response: Second harmonic generation at surfaces of antiferromagnets

Using symmetry arguments we show how optical second harmonic generation (SHG) can be used to detect antiferromagnetism at surfaces and in thin films. Based on the group theoretical analysis of the nonlinear electric susceptibility we propose a new nonlinear magneto-optical effect, which allows even in the presence of unit-cell doubling for the unambiguous discrimination of antiferromagnetic surface spin configurations from ferromagnetic or paramagnetic ones. As an example for this effect we discuss the polarization dependence of SHG from the fee (001) surface of NiO in some detail.