FIG. 1: The calculated spin susceptibility and Curie temperature for Bi$_{2}$Se$_{3}$ . (a) The Van-Vleck type spin susceptibility of Bi$_{2}$Se$_{3}$ bulk as a function of spin-orbital-coupling (SOC) strength. λ$_{0}$ is the real SOC strength, and it is uniformly scaled to simulate various SOC strength λ . When λ/λ$_{0}$ is larger than 0.5, the energy bands at Γ are inverted, and Bi$_{2}$Se$_{3}$ becomes strong topological insulator. (b) The spontaneous magnetization M as a function of temperature for Cr-doped ( S$_{z}$ =3/2) Bi$_{2}$Se$_{3}$ bulk as well as thin films with thickness of 3, 4 and 5 quintuple layers (QL). 15  0  0.25  0.5  0.75  1  1.25  1.5  1.75  0  0.25  0.5  0.75  1  1.25  (10 -9  m 3 /mol) / 0 (a)  0  0.5  1  1.5  2  2.5  3  0  20  40  60  80 M ( B ) Temperature (K) (b) QL QL bulk