  Based on first-principles density-functional theory calculations, we present
a comparative study of the elec- tronic structures of ultranarrow zigzag
graphene nanoribbons (ZGNRs) embedded in 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 with a weakly stabilized
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: i.e., 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.
