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Based on first-principles density-functional theory calculations, we presenta comparative study of the elec- tronic structures of ultranarrow zigzaggraphene nanoribbons (ZGNRs) embedded in hexagonal boron nitride (BN) sheet andfully hydrogenated graphene (graphane) as a function of their width N (thenumber of zigzag C chains composing the ZGNRs). We find that ZGNRs/BN have thenonmagnetic ground state except at N = 5 and 6 with a weakly stabilizedhalf-semimetallic state, whereas ZGNRs/graphane with N >= 2 exhibit a strongantiferromagnetic coupling between ferromagnetically ordered edge states oneach edge. It is revealed that the disparate magnetic properties of the twoclasses of ZGNRs are attributed to the contrasting interedge superexchangeinteractions arising from different interface structures: i.e., the asymmetricinterface structure of ZGNRs/BN gives a relatively short-range and weaksuperexchange interaction between the two inequivalent edge states, while thesymmetric interface structure of ZGNRs/graphane gives a long-range, stronginteredge superexchange interaction.

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