Reversible electric field manipulation of the Dzyaloshinskii-Moriya interactions in transition metal dimers

The anisotropic antisymmetric Dzyaloshinskii-Moriya (DM) interactions between local magnetic moments μᵢ and μⱼ, which can be induced by an external electric field (EF) are investigated in the framework of density functional theory by considering all $3d, 4d$, and $5d$ freestanding transition metal dimers. The possibilities of triggering and reversibly tuning chiral magnetic couplings by electric means are demonstrated. The dependence of the DM-coupling vector Dᵢⱼ on the EF strength E is shown to be approximately linear for |E|≤0.6 V/{}, with only minor third-order corrections. The first- and third-order zero-field electric susceptibility of the DM couplings are determined and analyzed as a function of d-band filling. The correlations between them and the chirality of the spin-orbit energy are displayed. From a microscopic perspective, the EF-induced DM couplings are shown to stem from the permanent electric dipole moments p⁰ that are already present in the field-free dimers whenever their local magnetic moments are not collinear. The symmetry rules governing p⁰ and its chirality are discussed. Finally, the dependence of the EF-induced DM couplings on the degree of noncollinearity of the magnetic order is quantified by varying systematically the angle θ between the local moments. While the electronic calculations show that the changes in the effective Dᵢⱼ can be quite important for arbitrary θ, one also observes that Dᵢⱼ depends weakly on θ and is thus transferable within a limited range of noncollinear magnetic arrangements, provided that they are not too far from the lowest-energy configuration.