Spin-polarized density functional theory has been used to study the properties of vacancies in a graphene sheet and in single-walled carbon nanotubes (SWNTs). For graphene, we find that the vacancies are magnetic and the symmetry of the sheet is broken by the distortion of an atom next to the vacancy site. We also studied vacancies in four armchair SWNTs from (3,3) to (6,6) and six zigzag SWNTs from (5,0) to (10,0). Our calculations demonstrate that vacancies can change the electronic structure of SWNTs, converting some metallic nanotubes to semiconductors and vice versa. Metallic nanotubes with vacancies exhibit ferro- or ferrimagnetism, whereas some semiconducting nanotubes with vacancies show an antiferromagnetic order. The magnetic properties depend on chiralities of the tubes, the configuration of the vacancy and the concentration of the vacancies.
Ma, Y., Lehtinen, P. O., Foster, A. S., & Nieminen, R. M. (2004). Magnetic properties of vacancies in graphene and single-walled carbon nanotubes. New Journal of Physics, 6, 1-15. . https://doi.org/10.1088/1367-2630/6/1/068