  We present a detailed study of the ground-state magnetic structure of
ultrathin Fe films on the surface of fcc Ir(001). We use the spin-cluster
expansion technique in combination with the relativistic disordered local
moment scheme to obtain parameters of spin models and then determine the
favored magnetic structure of the system by means of a mean field approach and
atomistic spin dynamics simulations. For the case of a single monolayer of Fe
we find that layer relaxations very strongly influence the ground-state spin
configurations, whereas Dzyaloshinskii-Moriya (DM) interactions and biquadratic
couplings also have remarkable effects. To characterize the latter effect we
introduce and analyze spin collinearity maps of the system. While for two
monolayers of Fe we find a single-q spin spiral as ground state due to DM
interactions, for the case of four monolayers the system shows a noncollinear
spin structure with nonzero net magnetization. These findings are consistent
with experimental measurements indicating ferromagnetic order in films of four
monolayers and thicker.
