Ferromagnetism and Antiferromagnetism of Correlated Topological Insulator with Flat Band

In this paper, based on the mean field approach and random-phase-approximation, we study the magnetic properties of the spinful Haldane model on honeycomb lattice of topological flat band with on-site repulsive Coulomb interaction. We find that the antiferromagnetic (AF) order is more stable than ferromagnetic (FM) order at (or near) half-filling; while away from half-filling the phase diagram becomes complex: At large doping, FM order is more stable than AF order due to the flatness of band structure. In particular, we find that at quarter filling case, the system becomes a Q=1$ topological insulator which is induced by the FM order.