The nonchalant magnetic ordering of vacancies in graphene

Magnetic properties of graphene monolayer with mono-, di-, and tri-vacancies are studied using spin polarized density functional theory. Detailed analysis of the projected density of the state shows that the magnetic moment associated with single vacancy is due to the combination of pz π-bonding orbital and partially delocalized sp or sp2 hybridized orbitals. A study on 6 × 6 and 9 × 9 supercell reveals the delocalized nature is size independent. The very small energy difference between ferro, anti-ferro and non magnetic states in di- and tri- vacancies predict the nonchalant magnetic ordering for vacancies. Our computational results explain the experimental observations in a recent publication by Nair et al. (2013), that the magnetic response of graphene is paramagnetic, and the single vacancy has a magnetic moment contributed by both itinerant pz orbitals and localized dangling bond. Magnetic moment associated with triple vacancy configuration is 1 μB. This moment is purely localized moment with no role played by pz orbitals in contrast to the magnetic moment associated with single vacancy. The hydrogen passivation of tri-vacancy reveals that the conductivity in the tri-vacancy can be varied from a p type to intrinsic semiconductor type.