Chiral magnetism of magnetic adatoms generated by Rashba electrons

TL;DR

This paper explores how surface state spin-orbit coupling induces chiral magnetic interactions among adatoms, revealing new interaction components and their dependence on distance and structure, with implications for designing chiral nanostructures.

Contribution

It introduces a detailed analysis of exchange interactions mediated by Rashba surface states, including pseudo-dipolar terms, and links the Dzyaloshinskii-Moriya interaction to changes in isotropic exchange due to spin-orbit coupling.

Findings

Pseudo-dipolar interaction coexists with isotropic and Dzyaloshinskii-Moriya interactions.

Inter-adatom distance influences the strength of magnetic interactions.

Magnetic ground states are affected by nanostructure size and shape.

Abstract

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 pseudo-dipolar interaction is found besides 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 inter-adatom distance controls the strength of these terms, which we exploit to design chiral magnetism in Fe nanostructures deposited on 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 inter-atomic 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 the 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.