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Magnetic interaction with the gapless surface states in topological insulator(TI) has been predicted to give rise to a few exotic quantum phenomena.However, the effective magnetic doping of TI is still challenging inexperiment. Using first-principles calculations, the magnetic doping properties(V, Cr, Mn and Fe) in three strong TIs (Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$ andSb$_{2}$Te$_{3}$) are investigated. We find that for all three TIs thecation-site substitutional doping is most energetically favorable withanion-rich environment as the optimal growth condition. Further our resultsshow that under the nominal doping concentration of 4%, Cr and Fe dopedBi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$, and Cr doped Sb$_{2}$Te$_{3}$ remain asinsulator, while all TIs doped with V, Mn and Fe doped Sb$_{2}$Te$_{3}$ becomemetal. We also show that the magnetic interaction of Cr doped Bi$_{2}$Se$_{3}$tends to be ferromagnetic, while Fe doped Bi$_{2}$Se$_{3}$ is likely to beantiferromagnetic. Finally, we estimate the magnetic coupling and the Curietemperature for the promising ferromagnetic insulator (Cr dopedBi$_{2}$Se$_{3}$) by Monte Carlo simulation. These findings may provideimportant guidance for the magnetism incorporation in TIs experimentally.

Stability, Electronic and Magnetic properties of magnetically doped topological insulators Bi2Se3, Bi2Te3 and Sb2Te3