Magnetic phase diagram of graphene nanorings in an electric field

Magnetic properties of graphene nanorings are investigated in the presence of an electric field. Within the formalism of Hubbard model, the graphene nanorings of various geometric configurations are found to exhibit rich phase diagram. For a nanoring system which has degenerate states at the Fermi level, the system is shown to undergo an abrupt phase transition from the antiferromagnetic to a nonmagnetic state in an electric field applied cross its zigzag edges. However, the nanoring is found to always stay in the antiferromagnetic state when the electric field is applied cross its armchair edges. For the other nanoring system with a finite single-particle gap, the magnetic moments of its antiferromagnetic ground state is seen to decrease gradually to zero with the electric field applied cross the zigzag edges. When the electric field is applied cross the armchair edges, the nanoring is shown to undergo several magnetic phase transitions before settling itself in a nonmagnetic ordering.