Spin texture induced by oxygen vacancies in strontium perovskite (001) surfaces: A theoretical comparison between SrTiO3 and SrHfO3

The electronic structure of SrTiO3 and SrHfO3 (001) surfaces with oxygen vacancies is studied by means of
first-principles calculations. We reveal how oxygen vacancies within the first atomic layer of the SrTiO3 surface
(i) induce a large antiferrodistortive motion of the oxygen octahedra at the surface, (ii) drive localized magnetic
moments on the Ti 3d orbitals close to the vacancies, and (iii) form a two-dimensional electron gas localized
within the first layers. The analysis of the spin texture of this system exhibits a splitting of the energy bands
according to the Zeeman interaction, lowering of the Ti 3dxy level in comparison with dxz and dyz, and also
an in-plane precession of the spins. No Rashba-like splitting for the ground state or for the ab initio molecular
dynamics trajectory at 400 K is recognized as suggested recently by A. F. Santander-Syro et al. [Nat. Mater. 13,
1085 (2014)]. Instead, a sizable Rashba-like splitting is observed when the Ti atom is replaced by a heavier Hf
atom with a much larger spin-orbit interaction. However, we observe the disappearance of the magnetism and the surface two-dimensional electron gas when full structural optimization of the SrHfO3 surface is performed. Our results uncover the sensitive interplay of spin-orbit coupling, atomic relaxations, and magnetism when tuning these Sr-based perovskites.