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Carbon (C) doped hexagonal boron nitride (hBN) has been experimentallyreported to be ferromagnetic at room temperature. Substitution by C in hBN hasbeen also reported to form islands of graphene. In this work we derive amechanistic understanding of ferromagnetism with graphene islands in hBN fromfirst principles and mean-field Hubbard model. We find a general property, thatin bipartite lattices where the sublattices differ in on-site energies, as inhBN, the ordering between local magnetic moments can be substantial andpredominantly anti-ferromagnetic (AFM) if they are embedded in the samesublattice, unless dominated by Mott like inter-sublattice spin separation dueto strong localization. The dominant AFM order is rooted at spin resolvedspatial separation of lone pairs of nitrogen (N) and back transferred electronson boron (B) due to Coulomb repulsion thus essentially implying asuper-exchange pathway. Subsequently we propose a class of ferri-magneticallyordered inter-penetrating super-lattices of magnetic graphene islands in hBN,which can be chosen to be a ferromagnetic semiconductor or a half-metal, andretain a net non-zero magnetic moment at room temperature.

Hybrid superlattices of graphene and hexagonal boron nitride: A ferromagnetic semiconductor at room temperature