We theoretically investigate the possibility of establishing ferromagnetism in the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ via magnetic doping of $3d$ transition metal elements. The formation energies, charge states, band structures, and magnetic properties of doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ are studied using first-principles calculations within density functional theory. Our results show that Bi substitutional sites are energetically more favorable than interstitial sites for single impurities. Detailed electronic structure analysis reveals that Cr and Fe doped materials are still insulating in the bulk but the intrinsic band gap of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is substantially reduced due to the strong hybridization between the $d$ states of the dopants and the $p$ states of the neighboring Se atoms. The calculated magnetic coupling suggests that Cr doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is possible to be both ferromagnetic and insulating, while Fe doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ tends to be weakly antiferromagnetic.

• Received 3 May 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.266405