  We study the emergence of spontaneous skyrmion lattices in an Fe monolayer in
fcc and hcp stacking on the Ir(111) surface using density functional theory
(DFT). For fcc-Fe/Ir(111) we find the well-known square nanoskyrmion lattice.
However, for hcp-Fe/Ir(111) the hexagonal skyrmion lattice previously proposed
based on experiments is energetically unfavorable with respect to a hexagonal
multi-Q state with nearly collinear magnetic moments. By mapping our DFT
calculations to an atomistic spin model we demonstrate that the interplay of
pair-wise exchange, higher-order exchange, and Dzyaloshinskii-Moriya
interaction is decisive for the symmetry and collinearity of the obtained spin
lattice.
