Indirect coupling between localized magnetic moments in triangular graphene nanoflakes

The indirect, charge-carrier mediated coupling between localized magnetic moments is studied for graphene nanoflakes of triangular shape and zigzag 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 over 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.