  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 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 do not
cancel each other. Thus, for a random distribution of the magnetic adatoms over
graphene surface a non-zero magnetic interaction is expected. We also suggest
an idea of controlling the magnetism by driving the tunnel coupling in and out
of resonance by a gate voltage.
