Dimensionality and stoichiometry effects on magnetic properties of Fe$_{x}$Co$_{1-x}$ nanostructures on Pt(111) from first principles

We investigate the influence of dimensionality and stoichiometry changes on the behavior of local magnetic moments and exchange coupling parameters of Fe$_{x}$Co$_{1-x}$ nanostructures deposited on the fcc Pt(111) surface. The electronic and magnetic structures of these Fe$_{x}$Co$_{1-x}$/Pt(111) systems are studied using the first-principles RS-LMTO-ASA method in the framework of the DFT. We consider different configurations of linear-shaped or compact-shaped trimers and heptamers, varying the internal positions and the concentration of Fe or Co atoms. The existence of a strictly decreasing nonlinear trend of the average orbital moments with the Fe concentration for the compact clusters is demonstrated, and differs from what was found for higher-dimensional Fe$_{x}$Co$_{1-x}$ systems (monolayer/Pt(111) and bulk). Although all studied linear and compact Fe$_{x}$Co$_{1-x}$ configurations have shown to be substancially ferromagnetic between nearest Fe or Co neighbors, not all revealed a collinear ground state, presenting, in some cases, oscillating exchange parameters for further distances and a non-negligible Dzyaloshinskii-Moriya interaction, induced by the Pt strong spin-orbit coupling.