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 spintexture 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.

Magnetic antiperovskites, holding chiral noncollinear antiferromagnetic ordering, have shown remarkable properties that cover from negative thermal expansion to anomalous Hall effect. Nevertheless, details on the electronic structure related to the...

In this work, we study the effects of an external magnetic field on the charge and current density in finite monolayer graphene, i.e., with zig-zag and armchair edges. We use the tight-binding model to include the effects of the magnetic field and the effect of the edges. By using the transmission probability and analyzing the local density of states (charge density) ob- tained from Green’s function method, we find an energy region where the wave functions are more localized in the edges and, consequently, the current flow across the borders. On the other hand, for energies close to Landau levels, the charge and current density are localized on the bulk of the system.

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