Long-range exchange interaction between magnetic impurities in graphene

The effective spin exchange 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.