Long-range exchange interaction between magnetic impurities in graphene

The effective spin exchange RKKY coupling between impurities (adatoms) on graphene mediated by conduction electrons is studied as a function of the strength of the potential part of the on-site energy $U$ of the electron-adatom interaction. With increasing $U$, the exchange coupling becomes long range, determined largely by the impurity levels with energies close to the Dirac points. When adatoms reside on opposite sublattices, their exchange coupling, normally antiferromagnetic, becomes ferromagnetic and resonantly enhanced at a specific distance where an impurity level crosses the Dirac point.