  We calculate the nonlinear magneto-optical response of free-standing fcc
(001), (110) and (111) oriented Fe monolayers. The bandstructures are
determined from first principles using a full-potential LAPW method with the
additional implementation of spin-orbit coupling. The variation of the
spin-orbit coupling strength and the nonlinear magneto-optical spectra upon
layer orientation are investigated. We find characteristic differences which
indicate an enhanced sensitivity of nonlinear magneto-optics to surface
orientation and variation of the in-plane lattice constants. In particular the
crossover from onedimensional stripe structures to twodimensional films of
(111) layers exhibits a clean signature in the nonlinear Kerr-spectra and
demonstrates the versatility of nonlinear magneto-optics as a tool for in situ
thin-film analysis.
