  We formulate a model for magnetic and superconducting ordering at
LaAlO3/SrTiO3 interfaces containing both localized magnetic moments and
itinerant electrons. Though these both originate in Ti 3d orbitals, the former
may be due to electrons more tightly-bound to the interface while the latter
are extended over several layers. Only the latter contribute significantly to
metallic conduction and superconductivity. In our model, the interplay between
the two types of electrons, which is argued to be ferromagnetic, combined with
strong spin-orbit coupling of the itinerant electrons, leads to magnetic
ordering. Furthermore, we propose a model for interfacial superconductivity,
consisting of random superconducting grains in the bulk STO driven, via
coupling to the interface conduction band, towards long-ranged or
quasi-long-ranged order. Most interestingly, the magnetic order and strong spin
orbit coupling can lead in this manner to unconventional interfacial
superconductivity, yielding a possible realization of Majorana physics.
