Spin coupling around a carbon atom vacancy in graphene

We investigate the details of the electronic structure in the neighborhoods of a carbon atom vacancy in graphene by employing magnetization-constrained density-functional theory on periodic slabs, and spin-exact, multireference, second-order perturbation theory on a finite cluster. The picture that emerges is that of two local magnetic moments (one π-like and one σ-like) decoupled from the π band and coupled to each other. We find that the ground state is a triplet with a planar equilibrium geometry where an apical C atom opposes a pentagonal ring. This state lies ∼0.2 eV lower in energy than the open-shell singlet with one spin flipped, which is a bistable system with two equivalent equilibrium lattice configurations (for the apical C atom above or below the lattice plane) and a barrier ∼0.1 eV high separating them. Accordingly, a bare carbon atom vacancy is predicted to be a spin-1 paramagnetic species, but spin-12 paramagnetism can be accommodated if binding to foreign species, ripples, coupling to a substrate, or doping are taken into account.