  The indirect, charge-carrier mediated coupling between localized magnetic
moments is studied for graphene nanoflakes of triangular shape and zig-zag
edge. The characteristic feature of such nanoflakes is the presence of a shell
of zero-energy states in the electronic spectrum. The tight-binding Hamiltonian
supplemented with a Hubbard term is used for electronic structure calculations.
The indirect RKKY (Ruderman-Kittel-Kasuya-Yosida) coupling energy is derived
from the total electronic energy of the system in a non-perturbative way. The
attention is focused on the on-site and plaquette impurities situated along the
edge. The charge doping is also taken into account. It is found that the
zero-energy states may give rise to a coupling mechanism which is describable
by a first-order perturbation calculus and can yield robust indirect coupling
of both ferro- and antiferromagnetic character, which dominates ovet the usual
RKKY mechanism. The numerical results obtained emphasize the importance of the
Hubbard term and the effect of the charge doping on the coupling.
