Symmetry Analysis of the Nonlinear Optical Response: New Magneto-Optical   Effect in Second Harmonic Generation
  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 discri- mination of antiferromagnetic 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. 
A. Daehn, W. Huebner, and K. H. Bennemann