Topological Character and Magnetism of the Dirac State in Mn-DopedBi2Te3

First-principles and model calculations show that the Dirac surface state of the topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ survives upon moderate Mn doping of the surface layers but can lose its topological character as a function of magnetization direction. The dispersion depends considerably on the direction of the Mn magnetization: for perpendicular magnetization, a gap of 16 meV opens up at the Dirac point; for in-plane magnetization, a tiny gap can be opened or closed in dependence on the magnetization azimuth. The ground state is ferromagnetic, with a critical temperature of 12 K. The results provide a path towards a magnetic control of the topological character of the Dirac surface state and its consequences to spin-dependent transport properties.