Magnetic properties on Chern insulator of checkerboard lattice with topological flat band

By means of the mean-field method and the random phase approximation, we study the magnetic properties of the correlated Chern insulator on a checkerboard lattice with topological flat band. The antiferromagnetic (AF) order is found to be more stable than the ferromagnetic (FM) order at half filling. While at quarter filling, the system becomes a FM-Chern insulator induced by the FM order. The phase diagram is more complex for other fillings. FM order is more stable than AF order for small doping due to the flatness of band structure, while FM and AF orders compete at large doping.