Spin-Orbital texture and magnetic proximity effect of Bi$_2$Se$_3$/EuS heterostructure

A topological insulator Bi$_2$Se$_3$ has gapless Dirac surface states topologically protected by time reversal symmetry with the helical spin texture. The spin texture has a unique orbital dependence and it allows topological insulator hybrid structures to be used for spintronics or spin transfer torque devices. Recently, an interface between a topological insulator Bi$_2$Se$_3$ and a ferromagnetic insulator EuS, has been experimentally realized, which provides an opportunity to study effects of magnetic interface on Dirac surface states of Bi$_2$Se$_3$. In this talk, we present our study of magnetic proximity effects and spin-orbital texture of the topological surface states of Bi$_2$Se$_3$ at the Bi$_2$Se$_3$/EuS interface, by using first-principles calculations and an low-energy effective model [A. T. Lee et al., Phys. Rev. B. 90, 155103 (2014)]. We discuss an energy gap opening due to the out-of-plane magnetic moment induced by the EuS, and a new Dirac cone occurring for thick Bi$_2$Se$_3$ slabs. Furthermore, we show an interesting coupling between the out-of-plane spin moment and the orbitals caused by broken time reversal symmetry.