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We study the emergence of spontaneous skyrmion lattices in an Fe monolayer infcc 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 proposedbased on experiments is energetically unfavorable with respect to a hexagonalmulti-Q state with nearly collinear magnetic moments. By mapping our DFTcalculations to an atomistic spin model we demonstrate that the interplay ofpair-wise exchange, higher-order exchange, and Dzyaloshinskii-Moriyainteraction is decisive for the symmetry and collinearity of the obtained spinlattice.

Spontaneous square vs. hexagonal nanoscale skyrmion lattices in Fe/Ir(111)