  Based on first principles calculations, this study reveals that magnetism in
otherwise non-magnetic materials can originate from the partial occupation of
antibonding states. Since the antibonding wavefunctions are spatially
antisymmetric, the spin wavefunctions should be symmteric according to the
exchange antisymmetric principle of quantum mechanics. We demonstrate that this
phenomenon can be observed in a graphitic carbon nitride material,
$g$-C$_4$N$_3$, which can be experimentally synthesized and seen as a honeycomb
structure with a vacancy. Three dangling bonds of N atoms pointing to the
vacancy site interact with each other to form one bonding and two antibonding
states. As the two antibonding states are near the Fermi level, and electrons
should partially occupy the antibonding states in spin polarization, this leads
to 1~$\mu_B$ magnetic moment.
