Indirect exchange interaction between magnetic adatoms in graphene

We present a theoretical study of indirect exchange interaction between magnetic adatoms in graphene. The coupling between the adatoms to a graphene sheet is described in the framework of a tunneling Hamiltonian. We account for the possibility of this coupling being of resonant character if a bound state of the adatom effectively interacts with the continuum of 2D delocalized states in graphene. In this case the indirect exchange between the adatoms mediated by the 2D carriers appears to be substantially enhanced compared to the results known from Ruderman-Kittel-Kasuya-Yosida (RKKY) theory. Moreover, unlike the results of RKKY calculations in the case of resonant exchange, the magnetic coupling between the adatoms sitting over different graphene sublattices does not cancel each other. Thus, for a random distribution of the magnetic adatoms over a graphene surface, a nonzero magnetic interaction is expected. We also suggest the idea of controlling the magnetism by driving the tunnel coupling in and out of resonance by a gate voltage.