Using ab initio methods based on the density functional theory, we study the magnetic properties of different point defects in graphene. We consider separately, atomic hydrogen, atomic fluorine, and single vacancies. The three defects have completely different magnetic properties. A local spin one-half magnetic moment is well defined at a hydrogen impurity, while single fluorine adatoms do not induce a well-defined magnetic moment unless there is a fluorine concentration of at least of a 0.5%. In this case, the induced magnetic moment is of the order of 0.45 ${\mu }_B$ per defect. This behavior is interpreted as being due to the charge transfer between fluorine and graphene. The case of magnetic moments localized at $\pi$ electrons near vacancies is different from both previous cases; the size of the induced magnetic moment decreases with the dilution of defects and it is compatible with zero in the isolated vacancy. The effect of hole doping on these magnetic behaviors is studied and compared with the available experimental data. In the three cases, hole doping inhibits the formation of $\pi$ states magnetic moments.

• Received 26 September 2014
• Revised 25 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.245420