Magnetic Counting Rule of Radical Carbon Edge Nano Graphene

In order to explain room-temperature ferromagnetism of graphite-like materials, this paper offers a new magnetic counting rule of radical carbon zigzag edge nano graphene. Multiple spin state analysis based on a density function theory shows that the highest spin state is most stable. Energy difference with next spin state overcomes kT=2000K suggesting a room-temperature ferromagnetism. Local spin density at a radical carbon shows twice a large up-spin cloud which comes from two orbital with tetrahedral configuration occupied by up-up spins. This leads a new magnetic counting rule to give a localized spin Sz=+2/2 to one radical carbon site, whereas Sz= -1/2 to the nearest carbon site. Applied to five model molecules, we could confirm this magnetic counting rule. In addition, we enhanced such concept to oxygen substituted zigzag edge occupied by four electrons.