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

Quantum confinement and interference often generate exotic properties in
nanostructures. One recent highlight is the experimental indication of a
magnetic phase transition in zigzag-edged graphene nanoribbons at the critical
ribbon 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 ribbon
width, the magnetic correlation of the two edges can exhibit an intriguing
oscillatory behavior between antiferromagnetic and ferromagnetic, driven by
acquiring the positive coherence between the two edges to lower the free
energy. The oscillation effect is readily tunable in applied magnetic fields.
These novel properties suggest new experimental manifestation of the edge
magnetic orders in graphene nanoribbons, and enhance the hopes of graphene-like
spintronic nanodevices functioning at room temperature.