  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.
