  This study examines the magnetic interactions between spatially-variable
manganese and chromium trimers substituted into a graphene superlattice. Using
density functional theory, we calculate the electronic band structure and
magnetic populations for the determination of the electronic and magnetic
properties of the system. To explore the super-exchange coupling between the
transition-metal atoms, we establish the magnetic magnetic ground states
through a comparison of multiple magnetic and spatial configurations. Through
an analysis of the electronic and magnetic properties, we conclude that the
presence of transition-metal atoms can induce a distinct magnetic moment in the
surrounding carbon atoms as well as produce an RKKY-like super-exchange
coupling. It hoped that these simulations can lead to the realization of
spintronic applications in graphene through electronic control of the magnetic
clusters.
