Interedge magnetic coupling in transition-metal terminated graphene nanoribbons

The magnetic structures and interedge magnetic couplings of Fe, Co and Ni transition-metal terminated graphene nanoribbons with zigzag (ZGNR) and armchair (AGNR) edges are studied by first-principles calculations. Fe-ZGNR is found to show antiferromagnetic (AF) coupling between two edges, while the interedge coupling of Co-ZGNR is ferromagnetic (FM). For Fe-AGNRs and Co-AGNRs, increasing the interedge distance we follow oscillatory transitions from FM to AF coupling with a period of about 3.7 {\AA}. The damped oscillatory behavior indicates a Ruderman-Kittel-Kasuya-Yosida type interedge magnetic coupling and the oscillation period is determined by the critical spanning vector which connects two inequivalent Dirac points in the graphene Brillouin zone. The two edges in Ni-ZGNR are decoupled independent of the ribbon width and Ni-AGNRs are found to be nonmangetic.