Exchange interaction of magnetic impurities in graphene

The indirect exchange interaction between magnetic impurities localized in a graphene plane is considered theoretically, with the influence of intrinsic spin-orbit interaction taken into account. Such an interaction gives rise to an energy gap at the Fermi level, which makes the usual RKKY model not applicable. The results show that the effective indirect exchange interaction is described by a range function which decays exponentially with the distance between magnetic moments. The interaction is also shown to depend on whether the two localized moments belong to the same sublattice or are located in two different sublattices.