We investigate the interactions between two identical magnetic impurities substituted into a graphene superlattice. Using a first-principles approach, we calculate the electronic and magnetic properties for transition-metal substituted graphene systems with varying spatial separation. These calculations are compared for three different magnetic impurities, manganese, chromium, and vanadium. We determine the electronic band structure, density of states, and Millikan populations (magnetic moment) for each atom, as well as calculate the exchange parameter between the two magnetic atoms as a function of spatial separation. We find that the presence of magnetic impurities establishes a distinct magnetic moment in the graphene lattice, where the interactions are highly dependent on the spatial and magnetic characteristic between the magnetic atoms and the carbon atoms, which leads to either ferromagnetic or antiferromagnetic behavior. Furthermore, through an analysis of the calculated exchange energies and partial density of states, it is determined that interactions between the magnetic atoms can be classified as an RKKY interaction.
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