Long-range exchange interaction between magnetic impurities in graphene

The effective spin exchange RKKY coupling between magnetic Anderson impurities in graphene is studied as a function of the strength of the onsite potential U. In weak-U limit, the energy levels of impurities lie far from the Dirac points and the electron-mediated interaction can be treated perturbatively. With increasing U, the energy levels of impurities move closer to the Dirac points and the effective interaction becomes long-range. When the impurities reside on the same sublattice, the non-perturbative interaction is antiferromagnetic, in contrast to the weak impurity limit where adatoms are coupled ferromagnetically. When the impurities reside on different sublattices, the exchange coupling, normally antiferromagnetic, becomes ferromagnetic and resonantly enhanced at a specific distance where an impurity level crosses the Dirac point.