Effects of the spin-orbital coupling on the vacancy-induced magnetism on the honeycomb lattice

The local magnetism induced by vacancies in the presence of the spin-orbital interaction is investigated based on the half-filled Kane-Mele-Hubbard model on the honeycomb lattice. Using the self-consistent mean-field theory, we find that the spin-orbital coupling will enhance the localization of the spin moments near a single vacancy. We further study the magnetic structures along the zigzag edges formed by a chain of vacancies. We find that the spin-orbital coupling tends to suppress the counter-polarized ferrimagnetic order on the upper and lower edges, because of the open of the spin-orbital gap. As a result, in the case of the balance number of sublattices, it will suppress completely this kind of ferrimagnetic order. But, for the imbalance case, a ferrimagnetic order along both edges exists because additional zero modes will not be affected by the spin-orbital coupling.