Enhancement of spin polarization induced by Coulomb on-site repulsion between localized pz electrons in graphene embedded with line defects.

Abstract

It is well known that the effect of Coulomb on-site repulsion can significantly alter the physical properties of the systems that contain localized d and/or f electrons. However, little attention has been paid to the Coulomb on-site repulsion between localized p electrons. In this study, we demonstrated that Coulomb on-site repulsion between localized pz electrons also plays an important role in graphene embedded with line defects. It is shown that the magnetism of the system largely depends on the choice of the effective Coulomb on-site parameter Ueff. Ueff at the edges of the defect enhances the exchange splitting, which increases the magnetic moment and stabilizes a ferromagnetic state of the system. In contrast, Ueff at the center of the defect weakens the spin polarization of the system. The behavior of the magnetism is explained with the Stoner criterion and the charge accumulation at the edges of the defect. Based on the linear response approach, we estimate reasonable values of Ueff to be 2.55 eV (2.3 eV) at the center (edges) of the defects. More importantly, using a DFT+U+J method, we find that exchange interactions between localized p electrons also play an important role in the spin polarization of the system. These results imply that Coulomb on-site repulsion is necessary to describe the strong interaction between localized pz electrons of carbon related materials.