  We introduce a model to explain the observed ferromagnetism and
superconductivity in LAO/STO oxide interface structures. Due to the polar
catastrophe mechanism, 1/2 charge per unit cell is transferred to the interface
layer. We argue that this charge localizes and orders ferromagnetically via
exchange with the conduction electrons. Ordinarily this ferromagnetism would
destroy superconductivity, but due to strong spin-orbit coupling near the
interface, the magnetism and superconductivity can coexist by forming an
FFLO-type condensate of Cooper pairs at finite momentum, which is surprisingly
robust in the presence of strong disorder.
