First-principles study of a monolayer of single-molecule magnets Mn$_{12}$ on a gold surface

Over the past decade, single-molecule magnets have drawn considerable attention due to observed magnetic quantum tunneling and interference and a possibility of using them in devices. There have been significant experimental efforts to build and characterize thin films or monolayers of single-molecule magnets on surfaces or single-molecule magnets bridged between electrodes. In parallel, theoretical models have been proposed to understand the properties of single-molecule magnets coupled to a metal substrate. However, there do not exist atomic-scale simulations on this complex system. We simulate, within density-functional theory, prototype Mn$_{12}$ molecules adsorbed via a thiol group onto a gold surface. We investigate how strongly a Mn$_{12}$ molecule is coupled to the metal surface and how much charge and spin moments are transferred between a Mn$_{12}$ molecule monolayer and the metal surface. In particular, we compare the electronic and magnetic properties of the Mn$_{12}$ monolayer on a gold surface with those of an isolated Mn$_{12}$ in the presence of spin-orbit interaction. Our results may shed light into tailoring of the magnetic properties of nanomagnets as a result of electronic transfer from a proximal metallic surface.