Theoretical study of static magnetic properties for the chiral and reconstructed graphene nanoribbons

Recent theoretical study of the chiral graphene nanoribbons(CGNR) has demonstrated the magnetic ordering of the edge states below a certain chiral angle$^{\mathrm{1}}$. Based on the Hubbard model for the CGNR, we study the static properties of the magnetic edge states such as the intra-edge and inter-edge spin stiffness, which are the two crucial parameters to control the thermodynamics of the effective magnetic hamiltonian. For the systematic study of the anti-ferromagnetic inter-edge spin correlations, we calculate the inter-edge spin stiffness as a function of ribbon width and transverse electric field. We also attempt to calculate the electronic and magnetic properties for the other edge geometries such as a reconstructed edge geometry, which has been experimentally confirmed as an edge shape other than zigzag or armchair nanoribbon$^{\mathrm{2}}$ 1. Oleg V. Yazyev, Rodrigo B. Capaz, and Steven G. Louie, Phys. Rev. B 84, 115406 (2011). 2. Pekka Koskinen, Sami Malola, and Hannu Hakkinen, Phys. Rev. B 80, 073401 (2009).