Electronic and magnetic properties of the interface LaAlO$_3$/TiO$_2$-anatase from density functional theory

Ab initio calculations using the local spin density approximation and also including the Hubbard $U$ have been performed for three low energy configurations of the interface between LaAlO$_3$ and TiO$_2$-anatase. Two types of interfaces have been considered: LaO/TiO$_2$ and AlO$_2$/TiO, the latter with Ti-termination and therefore a missing oxygen. A slab-geometry calculation was carried out and all the atoms were allowed to relax in the direction normal to the interface. In all the cases considered, the interfacial Ti atom acquires a local magnetic moment and its formal valence is less than +4. When there are oxygen vacancies, this valence decreases abruptly inside the anatase slab while in the LaO/TiO$_2$ interface the changes are more gradual.