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

TL;DR

This paper presents a theoretical analysis of how an in-plane magnetic exchange field affects the band structure and spin density distribution in thin films of noble metals and topological insulators, revealing surface coupling effects.

Contribution

The study develops a minimal relativistic $ extbf{k}oldsymbol{ullet} extbf{p}$ model for coupled surface states in thin films, highlighting the impact of exchange fields on spin and spectral properties.

Findings

Exchange field causes spectrum distortions similar to Rashba/Dirac states.

Coupling leads to loss of state counterparts at certain energies.

Spin-density redistribution favors large-angle surface-to-surface electron scattering.

Abstract

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 $\mathbf{k}\cdot\mathbf{p}$ 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 $\bar{\Gamma}$ 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 Sb$_2$Te$_3$ 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.