obvious in Fig. 8: the partial density of states of orbital d$_{xz}$ of the inter-facial Ti overlaps almost completely with that corresponding to orbital d$_{z}$ 2 of the subsurface Ti. In case B, the Al atom that is in the same position as the Ti subsurface atom, destroys this hybridization. It is the geometric difference in second neighbor positions which drives the system to a magnetic solution. 

Another way of looking at this is by plotting the charge density, in an energy range close to the Fermi energy. This is shown in Fig. 9, and as expected it is quite different for both structures. 

Fig. 10 shows that the non-magnetic total density of states at the Fermi level is larger in case B than in case A, in agreement with the presence of magnetism. 

The study of this extreme example, with such a large number of inter-facial defects, shows that oxygen vacancies and consequently the presence of Ti 3 $^{+}$, are a necessary but not sufficient condition to obtain magnetic solutions. This result may be related to the difficulty of producing reproducible experimental results. 

## Acknowledgements 

We acknowledge support by CONICET under grant PIP 112-200801-38, ANPCyT under grant PICT-06-157 and a CNRS-CONICET International Scientific Co operation Project (PICS). 

