One intriguing finding in graphene is the vacancy-induced magnetism that highlights the interesting interaction between local magnetic moments and conduction electrons. Within density functional theory, the current understanding of the ground state is that a Stoner instability gives rise to ferromagnetism of π-electrons aligned with the localized moment of a σ dangling bond and the induced π magnetic moments vanish at low vacancy concentrations. However, the observed Kondo effect suggests that π-electrons around the vacancy should antiferromagnetically couple to the local moment and should carry nonvanishing moments. Here we propose that a phase possessing both significant out-of-plane displacements and π bands with antiferromagnetic coupling to the localized σ moment is the ground state. With the features we provide, it is possible for spin-resolved scanning tunneling microscopy, scanning tunneling spectroscopy, and angle-resolved photoelectron spectroscopy measurements to verify the proposed phase.
