Inner edge magnetisms in carbon honeycombs

We show by comprehensive ab initio calculations that sp² carbon honeycombs recently synthesised by Krainyukova et al. [Phys. Rev. Lett. 116, 055501 (2016)] exhibit antiferromagnetism, not only at the inner edge of the zigzag ribbon component but also at the chain of sp² carbon that joins three zigzag ribbons. The π antiferromagnetism at the joint chain has spin orientations that alternatively change along the axis and stems from a super-exchange mechanism. Along with the spin-polarization, the joint chain conduction channel opens an energy gap. The spin-polarization of the zigzag edge due to the magnetic instability of the localized edge states is less stable in energy. Through hole doping, the zigzag edge antiferromagnetism is enhanced and stabilized as the magnetic ground state, along with the re-opening of the joint chain conduction channel. When the carbon honeycombs are reconstructed into sp³-sp² hybrid honeycombs, the π states of the joint are diminished, but the zigzag edge magnetism is preserved. Our results propose carbon honeycombs as novel magnetic carbon with competing polarization configurations.