Second harmonic generation spectroscopy in magnetic and multiferroic materials

► Previously unexplored mechanisms of nonlinear spectroscopy are demonstrated. ► Second harmonic generation as a tool for studying electronic and magnetic structures. ► Examples are antiferromagnets Cr2O3, NiO, CuB2O4 and multiferroics YMnO3, TbMn2O5. ► Second harmonic generation spectroscopy of magnetic semiconductors. ► Unique ability of nonlinear spectroscopy for distinguishing antiferromagnetic domains.