Stability, electronic, and magnetic properties of the magnetically doped topological insulatorsBi2Se3, Bi2Te3, and Sb2Te3

Magnetic interaction with the gapless surface states in a 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 in the experiment. Using first-principles calculations, the magnetic doping properties (V, Cr, Mn, and Fe) in three strong TIs (Bi${}_{2}$Se${}_{3}$, Bi${}_{2}$Te${}_{3}$, and Sb${}_{2}$Te${}_{3}$) are investigated. We find that for all three TIs the cation-site substitutional doping is most energetically favorable with the anion-rich environment as the optimal growth condition. Further, our results show that under the nominal doping concentration of 4%, Cr- and Fe-doped Bi${}_{2}$Se${}_{3}$, Bi${}_{2}$Te${}_{3}$, and Cr-doped Sb${}_{2}$Te${}_{3}$ remain as insulators, while all the V- and Mn-doped TIs, and Fe-doped Sb${}_{2}$Te${}_{3}$ become metal. 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 be antiferromagnetic. Finally, we estimate the magnetic coupling and the Curie temperature for the promising ferromagnetic insulator (Cr-doped Bi${}_{2}$Se${}_{3}$) by Monte Carlo simulation. These findings may provide important guidance for the magnetism incorporation in TIs experimentally.