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Magnetic properties of a single vacancy in graphene is a relevant and stillmuch discussed problem. The experimental results point to a clearly detectablemagnetic defect state at the Fermi energy, while calculations based on densityfunctional theory (DFT) yield widely varying results for the magnetic moment,in the range of $\mu=1.04-2.0$ $\mu_{B}$. We present a multi-tool \textit{abinitio} theoretical study of the same defect, using two simulation protocolsfor a defect in a crystal (cluster and periodic boundary conditions) anddifferent DFT functionals - bare and hybrid DFT, mixing a fraction ofHartree-Fock exchange (XC). Our main conclusions are two-fold: First, we findthat due to the $\pi$-character of the Fermi-energy states of graphene,inclusion of XC is crucial and for a single isolated vacancy we can predict aninteger magnetic moment $\mu=2\mu_{B}$. Second, we find that due to thespecific symmetry of the graphene lattice, periodic arrays of single vacanciesmay provide interesting diffuse spin-spin interactions.

Vacancy in graphene: insight on magnetic properties from theoretical modeling