▎ 摘　　要

Density Functional Theory study on graphene ribbons with various shapes and sizes shows that as ribbon increases in length and width, its orbital energy gap decreases and prefers a higher spin state. Such a transition occurs when the energy gap between the highest doubly occupied and the lowest unoccupied molecular orbitals of the ground state is about 1.13 eV. Our results suggest that high-spin states are stable, and graphene ribbons have ferromagnetic properties. The results are consistent with recent observations where bulk graphene possesses both ferromagnetic and antiferromagnetic properties as in phase-separated systems. The open-shell singlet state was suggested previously for the antiferromagnetic property of graphene ribbons. Published by Elsevier B.V.