Intertwined lattice deformation and magnetism in monovacancy graphene

Abstract

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 ${\ensuremath{\mu}}_{B}$ and a metastable nonplanar configuration with a vanishing magnetic moment, at a modest energy expense of 50 meV. Though nonplanarity relieves the lattice of vacancy-induced strain, the planar state is energetically favored due to maximally localized defect states $(v\ensuremath{\sigma}$, $v\ensuremath{\pi})$. In the planar configuration, charge transfer from itinerant (Dirac) states weakens the spin polarization of $v\ensuremath{\pi}$ yielding a fractional moment, which is aligned parallel to the unpaired $v\ensuremath{\sigma}$ electron through Hund's coupling. As a by-product, the Dirac states $(d\ensuremath{\pi})$ of the two sublattices undergo a minor spin polarization and couple antiferromagnetically. In the nonplanar configuration, the absence of orthogonal symmetry allows interaction between $v\ensuremath{\sigma}$ and local $d\ensuremath{\pi}$ states, to form a hybridized $v{\ensuremath{\sigma}}^{\ensuremath{'}}$ state. The nonorthogonality also destabilizes the Hund's coupling, and an antiparallel alignment between $v\ensuremath{\sigma}$ and $v\ensuremath{\pi}$ lowers the energy. The gradual spin reversal of $v\ensuremath{\pi}$ with increasing nonplanarity opens up the possibility of an intermediate structure with a balanced $v\ensuremath{\pi}$ spin population. If such a structure is realized under external perturbations, diluted vacancy concentration may lead to $v\ensuremath{\sigma}$-based spin-$\frac{1}{2}$ paramagnetism. Carrier doping, electron or hole, does not alter the structural stability. However, the doping proportionately changes the occupancy of $v\ensuremath{\pi}$ state and hence the net magnetic moment.