the spatially homogeneous phase, the total free energy of the system can thus be written as, where χ$_{L/e}$ is the spin susceptibility of the local moments/electrons, M$_{L/e}$ denotes the mag- netization for the local moment and electron sub-system and J$_{ex}$ is the magnetic exchange coupling between the local moments and electrons. The onset of the ferromagnetic phase can be determined when the minimization procedure of the above free energy gives a non-zero magnetization without the external magnetic field H , which leads to J 2 ex − χ − 1 L χ − 1 e > 0, or equivalently χ$_{L}$ > 1 J 2 ex χ $_{e}$. In the dilute limit, we can neglect the direct coupling among the local moments, and then the spin susceptibility of the local moment sub-system takes the Curie-Weiss form, χ$_{L}$ = xµ 2 $_{J}$/ (3 k$_{B}$T ), where x is the concentration of the magnetic ions and µ$_{J}$ is the magnetic moment of a single magnetic ion. Therefore, in order to have non-zero FM transition temperature, the above criterion requires a sizable spin susceptibility of the electron sub-system χ$_{e}$ . In most of the DMS systems, e.g. (Ga$_{1}$$_{−}$$_{x}$Mn$_{x}$)As, the electronic spin susceptibility is negligible for the insulator phase and finite carrier concentration is re- quired to conduct the magnetic coupling among local moments. As we shall discuss below, unlike the situation in GaAs, sizable spin susceptibility even exists through the Van Vleck paramagnetism for the insulator Bi$_{2}$Se$_{3}$, providing a new mechanism for ordering the doped magnetic ions. The non-zero paramagnetic spin susceptibility for a band insulator has been known as the Van-Vleck paramagnetism 31 for a long time. For temperature much less than the band gap, the spin susceptibility for a band insulator can be obtained by the second order perturbation on the ground state, which can be written as, where µ$_{0}$ is the vacuum permeability and µ$_{B}$ is the Bohr magneton. It is then quite obvious that the van-Vleck paramagnetism is caused by the mixing of the conduction and valence bands induced by the spin operator in the presence of SOC. Such a mechanism is absent in the GaAs system, because the gap in GaAs is between mostly s and p bands and the matrix element of ˆ S$_{z}$ is nearly zero between conduction and valence bands. In the case of Bi$_{2}$Se$_{3}$ family, the situation is completely different: both the conduction and valence bands are formed by the bonding and anti-bonding p orbitals and the energy gap is opened by the F$_{total}$ = 1 2 χ − 1 L M 2 L + 1 2 χ − 1 e M 2 e − J$_{ex}$M$_{L}$M$_{e}$ − ( M$_{L}$ + M$_{e}$ ) H χ zz e = ∑ E nk <µ ; E mk >µ 4 µ$_{0}$µ 2 B 〈 nk | ˆ S$_{z}$ | mk 〉 〈 mk | ˆ S$_{z}$ | nk 〉 E$_{mk}$ − E$_{nk}$ . (1) 5