  We study the magnetic properties in the vicinity of a single carbon defect in
a monolayer of graphene. We include the unbound $\sigma$ orbital and the
vacancy induced bound $\pi$ state in an effective two-orbital single impurity
model. The local magnetic moments are stabilized by the Coulomb interaction as
well as a significant ferromagnetic Hund's rule coupling between the orbitals
predicted by a density functional theory calculation. A hybridization between
the orbitals and the Dirac fermions is generated by the curvature of the
graphene sheet in the vicinity of the vacancy. We present results for the local
spectral function calculated using Wilson's numerical renormalization group
approach for a realistic graphene band structure and find three different
regimes depending on the filling, the controlling chemical potential, and the
hybridization strength. These different regions are characterized by different
magnetic properties. The calculated spectral functions qualitatively agree with
recent scanning tunneling spectra on graphene vacancies.
