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 ferro-or paramagnetic ones. As an example for this effect we discuss the polarization dependence of SHG from the fcc (001) surface of NiO in some detail. 78.20.Ls, 75.30.Pd, 75.50.Ee,

Using group theory we classify the nonlinear magneto-optical response at low-index surfaces of fcc antiferromagnets, such as NiO. Structures consisting of one atomic layer are discussed in detail. We find that optical second harmonic generation is sensitive to surface antiferromagnetism in many cases. We discuss the influence of a second type of magnetic atoms, and also of a possible oxygen sublattice distortion on the output signal. Finally, our symmetry analysis yields the possibility of antiferromagnetic surface domain imaging even in the presence of magnetic unit-cell doubling. 78.20.Ls, 75.30.Pd, 75.50.Ee,