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The electronic structure of SrTiO3 and SrHfO3 (001) surfaces with oxygenvacancies is studied by means of first-principles calculations. We reveal howoxygen vacancies within the first atomic layer of the SrTiO3 surface (i) inducea large antiferrodistortive motion of the oxygen octahedra at the surface, (ii)drive localized magnetic moments on the Ti-3d orbitals close to the vacanciesand (iii) form a two-dimensional electron gas localized within the firstlayers. The analysis of the spin-texture of this system exhibits a splitting ofthe energy bands according to the Zeeman interaction, lowering of the Ti-3dxylevel in comparison with dxz and dyz and also an in-plane precession of thespins. No Rashba-like splitting for the ground state neither for ab-initiomolecular dynamics trajectory at 400K is recognized as suggested recently by A.F. Santander-Syro et al. [1]. Instead, a sizeable Rashba-like splitting isobserved when the Ti atom is replaced by a heavier Hf atom with a much largerspin-orbit interaction. However, we observe the disappearance of the magnetismand the surface two dimensional electron gas when full structural optimizationof the SrHfO3 surface is performed. Our results uncover the sensitive interplayof spin-orbit coupling, atomic relaxations and magnetism when tuning theseSr-based perovskites.

Spin-texture induced by oxygen vacancies in Strontium perovskites (001) surfaces: A theoretical comparison between SrTiO3 and SrHfO3