Ferromagnetism and superconductivity are, in most cases, adverse. However, recent experiments reveal that they coexist at interfaces of LaAlO${}_3$ and SrTiO${}_3$. We analyze the magnetic state within density functional theory and provide evidence that magnetism is not an intrinsic property of the two-dimensional electron liquid at the interface. We demonstrate that the robust ferromagnetic state is induced by the oxygen vacancies in SrTiO${}_3$ or in the LaAlO${}_3$ layer. This allows for the notion that areas with increased density of oxygen vacancies produce ferromagnetic puddles and account for the previous observation of a superparamagnetic behavior in the superconducting state.

• Received 28 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.020407