We have derived an expression of the Dzyaloshinskii–Moriya interaction (DMI), where all the three components of the DMI vector can be calculated independently, for a general, non-collinear magnetic configuration. The formalism is implemented in a real space—linear muffin-tin orbital—atomic sphere approximation (RS-LMTO-ASA) method. We have chosen the Cr triangular trimer on Au(111) and Mn triangular trimers on Ag(111) and Au(111) surfaces as numerical examples. The results show that the DMI (module and direction) is drastically different between collinear and non-collinear states. Based on the relation between the spin and charge currents flowing in the system and their coupling to the non-collinear magnetic configuration of the triangular trimer, we demonstrate that the DMI interaction can be significant, even in the absence of spin-orbit coupling. This is shown to emanate from the non-collinear magnetic structure, that can induce significant spin and charge currents even with spin-orbit coupling is ignored.

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We present an approach to control the magnetic structure of adatoms adsorbed on a substrate having a high magnetic susceptibility. Using finite Ni-Pt and Fe-Pt nanowires and nanostructures on Pt(111) surfaces, our ab initio results show that it is possible to tune the exchange interaction and magnetic configuration of magnetic adatoms (Fe or Ni) by introducing different numbers of Pt atoms to link them, or by including edge effects. The exchange interaction between Ni (or Fe) adatoms on Pt(111) can be considerably increased by introducing Pt chains to link them. The magnetic ordering can be regulated allowing for ferromagnetic or antiferromagnetic configurations. Noncollinear magnetic alignments can also be stabilized by changing the number of Pt-mediated atoms. An Fe-Pt triangularly-shaped nanostructure adsorbed on Pt(111) shows the most complex magnetic structure of the systems considered here: a spin-spiral type of magnetic order that changes its propagation direction at the triangle vertices.

The magnetic properties of FexCo1-x nanochains on Pt(1 1 1) were studied using the first-principles real-space linear muffin-tin orbital-atomic sphere approximation (RS-LMTO-ASA) method within the density functional theory. The relative amounts of Fe and Co atoms in a chosen nanochain were varied and several possible arrangements of the atomic species were taken into account. The results of the exchange interaction demonstrates ferromagnetic coupling for the nanowires. Our calculations of Fe and Co average magnetic moments reveal a large enhancement of both spin and orbital moments compared to Fe-Co films deposited on a Pt(1 1 1) surface. The trend for the orbital moments with respect to stoichiometry differs from all previous higher-dimensional Fe-Co alloys on Pt(1 1 1) studies.