Chiral Magnetic Interactions in Small Fe Clusters Triggered by Symmetry-Breaking Adatoms

Abstract

The chirality of the interaction between the local magnetic moments in small transition-metal alloy clusters is investigated in the framework of density-functional theory. The Dzyaloshinskii–Moriya (DM) coupling vectors Dij between the Fe atoms in Fe2X and Fe3X with X = Cu, Pd, Pt, and Ir are derived from independent ground-state energy calculations for different noncollinear orientations of the local magnetic moments. The local-environment dependence of Dij and the resulting relative stability of different chiral magnetic orders are analyzed by contrasting the results for different adatoms X and by systematically varying the distance between the adatom X and the Fe clusters. One observes that the adatoms trigger most significant DM couplings in Fe2X, often in the range of 10–30 meV. Thus, the consequences of breaking the inversion symmetry of the Fe dimer are quantified. Comparison between the symmetric and antisymmetric Fe-Fe couplings shows that the DM couplings are about two orders of magnitude weaker than the isotropic Heisenberg interactions. However, they are in general stronger than the anisotropy of the symmetric couplings. In Fe3X, alloying induces interesting changes in both the direction and strength of the DM couplings, which are the consequence of breaking the reflection symmetry of the Fe trimer and which depend significantly on the adatom-trimer distance. A local analysis of the chirality of the electronic energy shows that the DM interactions are dominated by the spin-orbit coupling at the adatoms and that the contribution of the Fe atoms is small but not negligible.