Intertwined Lattice Deformation and Magnetism in Monovacancy Graphene

Using density functional calculations we have investigated the local spin moment formation and lattice deformation in graphene when an isolated vacancy is created. We predict two competing equilibrium structures: a ground state planar configuration with a saturated local moment of 1.5 $\mu_B$, and a metastable non-planar configuration with a vanishing magnetic moment, at a modest energy expense of ~50 meV. Though non-planarity relieves the lattice of vacancy-induced strain, the planar state is energetically favored due to maximally localized defect states (v$\sigma$, v$\pi$). In the planar configuration, charge transfer from itinerant (Dirac) states weakens the spin-polarization of v$\pi$ yielding a fractional moment, which is aligned parallel to the unpaired v$\sigma$ electron through Hund's coupling. In the non-planar configuration, the absence of orthogonal symmetry allows interaction between v$\sigma$ and local d$\pi$ states, to form a hybridized v$\sigma^\prime$ state. The non-orthogonality also destabilizes the Hund's coupling, and an antiparallel alignment between v$\sigma$ and v$\pi$ lowers the energy. The gradual spin reversal of v$\pi$ with increasing non-planarity opens up the possibility of an intermediate structure with balanced v$\pi$ spin population. If such a structure is realized under external perturbations, diluted vacancy concentration may lead to v$\sigma$ based spin-1/2 paramagnetism.