The electronic structure and magnetic properties of vacancies and voids both in graphene and graphene ribbons were considered. By using a mean-field Hubbard model, the appearance of magnetic textures associated with removing a single atom (vacancy) and multiple adjacent atoms (voids) as well as the magnetic interactions between them were studied. A simple set of rules, based on the Lieb theorem, linked the atomic structure and the spatial arrangement of the defects, to the emerging magnetic order. The total spin S of a given defect depended upon its sub-lattice imbalance, but some defects with S=0 could still have local magnetic moments. The sub-lattice imbalance also governed whether the defects interacted ferromagnetically or antiferromagnetically with one another. The range of these magnetic interactions was studied for some simple cases. It was found that in semiconducting armchair ribbons and 2-dimensional graphene without global sub-lattice imbalance, there was a maximum defect density above which local magnetization disappeared. The electronic properties of semiconducting graphene ribbons with uncoupled local moments were very similar to those of diluted magnetic semiconductors, and exhibited giant Zeeman splitting.

Vacancy-Induced Magnetism in Graphene and Graphene Ribbons. J.J.Palacios, J.Fernández-Rossier, L.Brey: Physical Review B, 2008, 77[19], 195428 (14pp)