Gap and spin texture engineering of Dirac topological states at the Cr-Bi$_2$Se$_3$ interface

The presence of an exchange field in topological insulators reveals novel spin related phenomena derived from the combination of topology and magnetism. In the present work we show the controlled occurrence of either metallic or gapped topological Dirac states at the interface between ultrathin Cr films and the Bi$_2$Se$_3$ surface. The opening and closing of the gap at the Dirac point is caused by the spin reorientation transitions arising in the Cr films. We find that atom thin layers of Cr adhered to Bi$_2$Se$_3$ surfaces present a magnetic ground state with ferromagnetic planes coupled antiferromagnetically. As the thickness of the Cr film increases stepwise from one to three atomic layers, the direction of the magnetization changes twice from out-of-plane to in-plane and to out-of-plane again. The out of plane magnetization drives the gap opening and the topological surface states acquire a circular meron spin structure. Therefore, the Cr spin reorientation leads to the metal/insulator transition in the Bi$_2$Se$_3$ surface and to the correlated modification of the surface state spin texture. Consequently, the thickness of the Cr film provides an effective and controllable mechanism to modify the metallic or gapped nature, as well as the spin texture of the topological Dirac states.