Contrasting interedge superexchange interactions of graphene nanoribbons embedded in h-BN and graphane

Based on first-principles density-functional theory calculations, we present a comparative study of the electronic structures of ultranarrow zigzag graphene nanoribbons (ZGNRs) embedded in a hexagonal boron nitride (BN) sheet and fully hydrogenated graphene (graphane) as a function of their width N (the number of zigzag C chains composing the ZGNRs). We find that ZGNRs/BN have the nonmagnetic ground state except at N = 5 and 6 that weakly stabilize as a half-semimetallic state, whereas ZGNRs/graphane with N >= 2 exhibit a strong antiferromagnetic coupling between ferromagnetically ordered edge states on each edge. It is revealed that the disparate magnetic properties of the two classes of ZGNRs are attributed to the contrasting interedge superexchange interactions arising from different interface structures: that is, the asymmetric interface structure of ZGNRs/BN gives a relatively short-range and weak superexchange interaction between the two inequivalent edge states, while the symmetric interface structure of ZGNRs/graphane gives a long-range, strong interedge superexchange interaction.