▎ 摘　　要

Carbon (C)-doped hexagonal boron nitride (hBN) has been experimentally reported to be ferromagnetic at room temperature. Substitution by C in hBN has also been reported to form islands of graphene. In this work, we derive a mechanistic understanding of ferromagnetism with graphene islands in hBN from first principles and the mean-field Hubbard model. We find a general property that in bipartite lattices where the sublattices differ in on-site energies, as in hBN, the ordering between local magnetic moments can be substantial and predominantly antiferromagnetic (AFM) if they are embedded in the same sublattice, unless dominated by Mott-like intersublattice spin separation due to strong localization. The dominant AFM order is rooted at spin-resolved spatial separation of lone pairs of nitrogen (N) and back-transferred electrons on boron (B) due to Coulomb repulsion, thus essentially implying a superexchange pathway. Subsequently, we propose a class of ferrimagnetically ordered interpenetrating superlattices of magnetic graphene islands in hBN, which can be chosen to be a ferromagnetic semiconductor or a half-metal, and we retain a net nonzero magnetic moment at room temperature.