Spin Ordering on the Surface of a Topological Insulator with Magnetic Ions

Abstract

We study the effect of magnetic doping on appearance of ferromagnetic (FM) order on the surface of a three-dimensional topological insulator. Assuming the exchange coupling of the Dirac fermions with the dilute magnetic ions, we find that the system under consideration is unstable with respect to a spontaneous uniform magnetization along the out-of-plane direction. The appearance of the magnetization is accompanied by opening of a gap in the spectrum of surface states. In the framework of a mean-field approach, we analyze the possibility of the FM order on the magnetically doped surface of topological insulator at different temperatures and positions of the chemical potential.