Antiferromagnetic order of topological orbital moments in atomic-scale skyrmion lattices

Topological orbital moments can arise in non-coplanar spin structures even in the absence of spin-orbit coupling and a net topological orbital magnetization occurs for the triple-Q state and for isolated skyrmions. For atomic-scale skyrmion lattices, a significant effect can also be expected, however, no studies have been reported yet. Here, we observe via spin-polarized scanning tunneling microscopy a non-coplanar atomic-scale spin structure with a nearly square magnetic unit cell for a pseudomorphic Fe monolayer on three atomic Ir layers on the Re(0001) surface. Employing density functional theory (DFT) calculations we consider different skyrmionic lattices to find the magnetic ground state. By mapping the DFT total energies to an atomistic spin model we demonstrate that these spin textures are stabilized by the interplay of the Dzyaloshinskii-Moriya and four-spin interactions. We evaluate the emerging phenomena of the different non-coplanar magnetic states and find significant local topological orbital moments oriented perpendicular to the surface, which order in an antiferromagnetic fashion.