Ferromagnetism in nitrogen-doped graphene

Inducing a robust long-range magnetic order in diamagnetic graphene remains a challenge. While nitrogen-doped graphene is reported to be a promising candidate, the corresponding exchange mechanism endures unclear and is essential to tune further and manipulate magnetism. Within the first-principles calculations, we systematically investigate the local moment formation and the concurrent interaction between various defect complexes. The importance of adatom diffusion on the differential defect abundance is discussed. The individual nitrogen complexes that contribute toward itinerant and a local magnetic moment are identified. The magnetic interaction between the complexes is found to depend on the concentration, complex type, sublattice, distance, and orientation. We propose that the direct exchange mechanism between the delocalized magnetic moment originating from the itinerant $\pi$-electron at the prevalent graphitic complexes to be responsible for the observed ferromagnetism. We show that B co-doping further improves ferromagnetism. Present results will assist in the microscopic understanding of the current experimental results and motivate experiments to produce robust magnetism following the proposed synthesis strategy.