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Spontaneous persistent currents in magnetically ordered graphene ribbons

We present a new mechanism for dissipationless persistent charge current. Two dimensional topological insulators hold dissipationless spin currents in their edges so that, for a given spin orientation, a net charge current flows which is exactly compensated by the counter-flow of the opposite spin. Here we show that ferromagnetic order in the edge upgrades the spin currents into persistent charge currents, without applied fields. For that matter, we study an interacting graphene zigzag ribbon with spin-orbit coupling. We find three electronic phases with magnetic edges that carry currents reaching 0.4nA, comparable to persistent currents in metallic rings, for the small spin orbit coupling in graphene. One of the phases is a valley half-metal.