Chiral magnetism of magnetic adatoms generated by Rashba electrons

We investigate long-range chiral magnetic interactions among adatoms mediated by surface states spin-splitted by spin–orbit coupling. Using the Rashba model, the tensor of exchange interactions is extracted wherein a thepseudo-dipolar interaction is found, in addition to the usual isotropic exchange interaction and the Dzyaloshinskii–Moriya interaction. We find that, despite the latter interaction, collinear magnetic states can still be stabilized by the pseudo-dipolar interaction. The interadatom distance controls the strength of these terms, which we exploit to design chiral magnetism in Fe nanostructures deposited on a Au(111) surface. We demonstrate that these magnetic interactions are related to superpositions of the out-of-plane and in-plane components of the skyrmionic magnetic waves induced by the adatoms in the surrounding electron gas. We show that, even if the interatomic distance is large, the size and shape of the nanostructures dramatically impacts on the strength of the magnetic interactions, thereby affecting the magnetic ground state. We also derive an appealing connection between the isotropic exchange interaction and the Dzyaloshinskii–Moriya interaction, which relates the latter to the first-order change of the former with respect to spin–orbit coupling. This implies that the chirality defined by the direction of the Dzyaloshinskii–Moriya vector is driven by the variation of the isotropic exchange interaction due to the spin–orbit interaction.