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

Abstract

The local magnetism induced by vacancies in the presence of the spin–orbit interaction is investigated based on the half-filled Kane–Mele–Hubbard model on the honeycomb lattice. Using a self-consistent mean-field theory, we find that the spin–orbit 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–orbit coupling tends to suppress the counter-polarized ferrimagnetic order on the upper and lower edges, because of the open of the spin–orbit 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–orbit coupling. • Spin–orbit coupling (SOC) localizes a vacancy-induced magnetism on honeycomb lattice. • SOC suppresses counter-polarized magnetism on both inner edges around vacancy chain. • Zero mode protects magnetism around vacancy chain with odd number of sites from SOC.