The magnetism in graphene due to single-atom defects is examined by using spin-polarized density functional theory. The magnetic moment per defect due to substitutional atoms and vacancy defects is dependent on the density of defects, while that due to adatom defects is independent of the density of defects. It reduces to zero with decrease in the density of substitutional atoms. However, it increases with decrease in density of vacancies. The graphene sheet with B adatoms is nonmagnetic, but with C and N adatoms it is magnetic. The adatom defects distort the graphene sheet near the defect perpendicular to the sheet. The distortion in graphene due to C and N adatoms is significant, while the distortion due to B adatoms is very small. The vacancy and substitutional atom (B, N) defects in graphene are planar in the sense that there is in-plane displacement of C atoms near the vacancy and substitutional defects. Upon relaxation the displacement of C atoms and the formation of pentagons near the vacancy site due to Jahn-Teller distortion depends upon the density and packing geometry of vacancies.
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