  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.
