λ/λ$_{0}$ is larger than 0.5, the bands at the Γ point are inverted, and the spin susceptibility starts to increase appreciably around this point. In the following, we apply a tight binding version of the Zener model 20–22 to calculate the possible Curie temperature at the mean field level. Let’s first assume that some magnetic local moments are introduced iso-electronically into the Bi$_{2}$Se$_{3}$ compounds without changing the insulating behavior. We show that ferromagnetic ordering with T$_{c}$ as high as 70K can be achieved via the van-Vleck paramagnetism, without requiring the existence of free carriers as in conventional DMS systems. The total Hamiltonian of our system can be written as with is the single particle Hamiltonian (obtained from first-principles calculations) expressed in the basis of local Wannier functions $^{33}$. Here i and j denote the sites, I only runs over all the unit cells containing magnetic ions and µν are the orbital/spin indices. The coupling strength between the local spin S$_{I}$ and the band spin s$_{µν}$ of band electrons is described by the effective exchange parameter J$_{eff}$ . Performing the mean field approximation and applying the virtual crystal approximation (CPA) to average out the spatial inhomogeneity, Eq.(4) can be written as where M α L = 〈 S α I $_{=0}$〉 , M α e = 〈 s α $_{µν}$c † 0 $_{,µ}$c$_{0}$$_{,ν}$ 〉 are the mean field magnetization for the local moments and band electrons respectively, with and H$_{total}$ = H$_{LDA}$ + ∑ Iµν,α = xyz J$_{eff}$ S α I · s α $_{µν}$c † $_{I,µ}$c$_{I,ν}$ + h.c. (4) H$_{LDA}$ = ∑ ij,µν t µν ij c † $_{i,µ}$c$_{j,ν}$ H$_{MF}$ = H$_{e}$ + H$_{L}$ − xJ$_{eff}$ M α L · M α e (5) H$_{e}$ = H$_{LDA}$ +$^{α}$$^{=}$$^{xyz}$ ∑ iµν J$_{eff}$ M α L · s α $_{µν}$c † $_{i,µ}$c$_{i,ν}$ + h.c. H$_{L}$ = α = xyz ∑ I J$_{eff}$ S α I · M α e 7 III. MEAN FIELD THEORY FOR THE MAGNETIC TOPOLOGICAL INSULA- TORS