Ferromagnetism in graphene traced to antisymmetric orbital combination of involved electronic states

Based on first principles calculations, we reveal that the origin of ferromagnetism caused by [Formula: see text] electrons in graphene with vacancies can be traced to electrons partially filling [Formula: see text]-antibonding and [Formula: see text]-nonbonding states, which are induced by the vacancies and appear near the Fermi level. Because the spatial wavefunctions of both states are composed of atomic orbitals in an antisymmetric configuration, their spin wavefunctions should be symmetric according to the electron exchange antisymmetric principle, leading to electrons partially filling these states in spin polarization. Since this [Formula: see text] state originates not from interactions between the atoms but from the unpaired [Formula: see text] orbitals due to the removal of [Formula: see text] orbitals on the minority sublattice, the [Formula: see text] state is constrained, distributed on the atoms of the majority sublattice, and decays gradually from the vacancy as  ∼[Formula: see text]. According to these characteristics, we concluded that the [Formula: see text] state plays a critical role in magnetic ordering in graphene with vacancies. If the vacancy concentration in graphene is large enough to cause the decay-length regions to overlap, constraining the [Formula: see text] orbital components as little as possible on the minority sublattice atoms in the overlap regions results in the vacancy-induced [Formula: see text] states being coherent. The coherent process in the overlap region leads to the wavefunctions in all the involved regions antisymmetrized, consequently causing ferromagnetism according to the electron exchange antisymmetric principle. This unusual mechanism concerned with the origin of [Formula: see text]-electron magnetism and magnetic ordering has never before been reported and is distinctly different from conventional mechanisms. Consequently, we can explain how such a weak magnetization with such a high critical temperature can be experimentally observed in proton-irradiated graphene.