Spatial aspects of spin polarization of structurally split surface states in thin films with magnetic exchange and spin-orbit interaction

A theoretical study is presented of the effect of an in-plane magnetic exchange field on the band structure of centrosymmetric films of noble metals and topological insulators. Based on an ab initio relativistic k·p theory, a minimal effective model is developed that describes two coupled copies of a Rashba or Dirac electronic system residing at the opposite surfaces of the film. The coupling leads to a structural gap at Γ and causes an exotic redistribution of the spin density in the film when the exchange field is introduced. We apply the model to a nineteen-layer Au(111) film and to a five-quintuple-layer Sb2Te3 film. We demonstrate that at each film surface the exchange field induces spectrum distortions similar to those known for Rashba or Dirac surface states with an important difference due to the coupling: At some energies, one branch of the state loses its counterpart with the oppositely directed group velocity. This suggests that a large-angle electron scattering between the film surfaces through the interior of the film is dominant or even the only possible for such energies. The spin-density redistribution accompanying the loss of the counterpart favors this scattering channel.