Fig. 3: Spin structure and topological orbital moments of atomic-scale spin lattices.

a multi-Q state, b double-skyrmionic lattice (d-SkX), and c single-skyrmionic lattice (s-SkX). The multi-Q state is constructed from a superposition of spin spirals with q vectors corresponding to the magnetic unit cell obtained in experiment (see text for details). The d-SkX lattice has been obtained from the multi-Q state by flipping two spins in the antiskyrmionic substructure to optimize the DMI energy. For the s-SkX lattice the antiskyrmionic substructures in the multi-Q state have been replaced by skyrmionic substructures to reduce the size of the magnetic unit cell. The dashed black (purple) box marks the magnetic unit cell of the multi-Q and d-SkX (s-SkX). The color of the hexagons display the topological orbital moment (TOM) for each atom calculated by DFT (see color bar at bottom). Red (blue) color denotes upwards (downwards) pointing TOM with respect to the surface normal. For the ease of discussion in the text, the centers of atomic-scale substructures of the spin lattices are denoted by letters: skyrmionic (S), antiskyrmionic (A), and pseudo-skyrmionic (p-S) which are also shown by the sketches in (d)–(f).