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Quantum confinement and interference often generate exotic properties innanostructures. One recent highlight is the experimental indication of amagnetic phase transition in zigzag-edged graphene nanoribbons at the criticalribbon width of about 7 nm [G. Z. Magda et al., Nature \textbf{514}, 608(2014)]. Here we show theoretically that with further increase in the ribbonwidth, the magnetic correlation of the two edges can exhibit an intriguingoscillatory behavior between antiferromagnetic and ferromagnetic, driven byacquiring the positive coherence between the two edges to lower the freeenergy. The oscillation effect is readily tunable in applied magnetic fields.These novel properties suggest new experimental manifestation of the edgemagnetic orders in graphene nanoribbons, and enhance the hopes of graphene-likespintronic nanodevices functioning at room temperature.

Width-tuned magnetic order oscillation on zigzag edges of honeycomb nanoribbons