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We calculate the nonlinear magneto-optical response of free-standing fcc(001), (110) and (111) oriented Fe monolayers. The bandstructures aredetermined from first principles using a full-potential LAPW method with theadditional implementation of spin-orbit coupling. The variation of thespin-orbit coupling strength and the nonlinear magneto-optical spectra uponlayer orientation are investigated. We find characteristic differences whichindicate an enhanced sensitivity of nonlinear magneto-optics to surfaceorientation and variation of the in-plane lattice constants. In particular thecrossover from onedimensional stripe structures to twodimensional films of(111) layers exhibits a clean signature in the nonlinear Kerr-spectra anddemonstrates the versatility of nonlinear magneto-optics as a tool for in situthin-film analysis.Comment: 28 pages, RevTeX, psfig, submitted to PR

Nonlinear magneto-optics of Fe monolayers from first principles: Structural dependence and spin-orbit coupling strength