Charge Spin Ti Ti O Ti O O O O Al Al O O Al Al O FIG. 7: Charge and spin density maps for super-lattice B, near the AlO$_{2}$/TiO$_{2}$ interface with 2 oxygen vacancies. The effect of relaxation is too small to be seen in this scale, but the AlO$_{2}$ plane is buckled. Magnetism is mostly localized at the inter-facial Ti atom, spin isolines in the figure start at 0.01 and are spaced by 0.03. Charge isolines start at 0.1 and are spaced 0.1, The interface is indicated by a dotted horizontal line. 15