  The nonlinear magneto-optical Kerr-effect (NOLIMOKE) is determined for
freestanding Fe monolayers with several in-plane structures from first
principles. Based on the theory of nonlinear magneto-optics by H\"ubner and
Bennemann [Phys. Rev. B, {\bf 40}, 5973 (1989)] we calculate the nonlinear
susceptibilities of the monolayers using the ab initio FLAPW-method WIEN95 with
the additional implementation of spin-orbit coupling and the calculation of the
dipole transition matrix elements appropriate for freestanding monolayers. We
present results for the spectral dependence of the nonlinear susceptibility
tensor elements and the resulting intensities and Kerr angles. Special
emphasize is put on the effects of structural changes such as the variation of
the lattice constant and different surface orientations. The influence of
spin-orbit coupling on the tensor elements for different magnetization
directions is presented as well as the azimuthal dependence of the intensities
generated by several low index surfaces, showing the pronounced sensitivity of
second harmonic generation to lateral structural changes as well as magnetic
properties even in the monolayer range.
