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

Intertwined Lattice Deformation and Magnetism in Monovacancy Graphene