Vacancy-Induced Magnetic Structures in Graphene Sheet

The observations of magnetic signals in doped fullerenes and other carbon-based systems have initiated numerous studies on the origin of magnetism in these materials. Recently carbon-adatoms or vacancies in graphene and carbon nanotubes are suggested to be an origin of the defect-related magnetism in carbon-based systems.\footnote{P.O. Lehtinen, A. S. Foster, Y. Ma, A.V. Krasheninnikov, and R.M. Nieminen1, Phys. Rev. Lett. {\bf 93}, 187202 (2004)} To investigate the vacnacy-induced structures and magnetic properties of graphene sheet, we carried out first-principles density-functional calculations on the graphene sheet with various vacancy configurations. From the results, it is found that there exist stable ferromagnetic ground states at several different vacancy configurations, and the minimal size and shape of the ``ferromagnetic hole'' is determined. Among the configurations considered in this work, a triangular shaped structure is found to be energetically favored.