  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 neither for ab-initio
molecular dynamics trajectory at 400K is recognized as suggested recently by A.
F. Santander-Syro et al. [1]. Instead, a sizeable 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.
