In this paper we study the possible relation between the electronic and magnetic structure of the TiO2/LaAlO3 interface and the unexpected magnetism found in undoped TiO2 films grown on LaAlO$_3$. We concentrate on the role played by structural relaxation and interfacial oxygen vacancies. LaAlO3 has a layered structure along the (001) direction with alternating LaO and AlO2 planes, with nominal charges of +1 and -1, respectively. As a consequence of that, an oxygen deficient TiO2 film with anatase structure will grow preferently on the AlO2 surface layer. We have therefore performed ab-initio calculations for superlattices with TiO2/AlO2 interfaces with interfacial oxygen vacancies. Our main results are that vacancies lead to a change in the valence state of neighbour Ti atoms but not necessarily to a magnetic solution and that the appearance of magnetism depends also on structural details, such as second neighbor positions. These results are obtained using both the LSDA and LSDA+U approximations.
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