Theory of Interedge Superexchange in Zigzag Edge Magnetism

A graphene nanoribbon with zigzag edges has a gapped magnetic ground state with an antiferromagnetic interedge superexchange interaction. We present a theory based on asymptotic properties of the Dirac-model ribbon wave function which predicts W^-2 and W^-1 ribbon-width dependencies for the superexchange interaction strength and the charge gap, respectively. We find that, unlike the case of conventional atomic-scale superexchange, opposite spin orientations on opposite edges of the ribbon are favored by both kinetic and interaction energies.