Ferromagnetism in nitrogen-doped graphene

Inducing a robust long-range magnetic order in diamagnetic graphene remains a\nchallenge. While nitrogen-doped graphene is reported to be a promising\ncandidate, the corresponding exchange mechanism endures unclear and is\nessential to tune further and manipulate magnetism. Within the first-principles\ncalculations, we systematically investigate the local moment formation and the\nconcurrent interaction between various defect complexes. The importance of\nadatom diffusion on the differential defect abundance is discussed. The\nindividual nitrogen complexes that contribute toward itinerant and a local\nmagnetic moment are identified. The magnetic interaction between the complexes\nis found to depend on the concentration, complex type, sublattice, distance,\nand orientation. We propose that the direct exchange mechanism between the\ndelocalized magnetic moment originating from the itinerant $\\pi$-electron at\nthe prevalent graphitic complexes to be responsible for the observed\nferromagnetism. We show that B co-doping further improves ferromagnetism.\nPresent results will assist in the microscopic understanding of the current\nexperimental results and motivate experiments to produce robust magnetism\nfollowing the proposed synthesis strategy.\n