Ferromagnetic graphene nanoribbons: Edge termination with organic radicals

The intramolecular magnetic exchange coupling of edge terminated zigzag graphene nanoribbon (ZGNR) was studied with density functional theory calculations. In order to examine the applicability of the spin alternation rule and a classification scheme for radicals and couplers on functionalized graphene nanoribbons, we investigated the magnetic behaviors of pristine zigzag graphene nanoribbon with eight zigzag chains (8-ZGNR) and 8-ZGNRs terminated with trimethylenemethane (TMM) and 6-oxoverdazyl (OVER) radicals,that is, TMM-ZGNR-TMM (TZT), OVER-ZGNR-OVER (OZO), and TMM-ZGNR-OVER (TZO). As expected, only ZGNR terminated with different group radicals on each edge (TZO) had a ferromagnetic (high-spin) ground state with an energy gap of 39 meV/supercell (321.57 cm^-1) relative to the low-spin state. This strongly supports the validity of the spin alternation rule and the classification scheme for radicals and couplers on extensively conjugated large graphene nanoribbons. TZT and OZO were found to have an antiferromagnetic (low-spin) ground state with magnetic coupling weaker than that of interedge antiferromagnetic superexchange of pristine 8-ZGNR. Based on the spin distribution pattern on magnetic ground states, GNR prefers to have each edge in antiferromagnetic order, which satisfies Liebâ€s theorem on the Hubbard model and spin alternation rule. All of the terminated ZGNRs exhibited semiconducting properties with an energy gap of 0.06-0.21 eV.