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

Ferromagnetism and Antiferromagnetism of Correlated Topological Insulator with Flat Band