The electronic properties of the polar interface between insulating oxides is a subject of great current interest. An exciting new development is the observation of robust magnetism at the interface of two non-magnetic materials LaAlO_3 (LAO) and SrTiO_3 (STO). Here we present a microscopic theory for the formation and interaction of local moments, which depends on essential features of the LAO/STO interface. We show that correlation-induced moments arise due to interfacial splitting of orbital degeneracy. We find that gate-tunable Rashba spin-orbit coupling at the interface influences the exchange interaction mediated by conduction electrons. We predict that the zero-field ground state is a long-wavelength spiral and show that its evolution in an external field accounts semi-quantitatively for torque magnetometry data. Our theory describes qualitative aspects of the scanning SQUID measurements and makes several testable predictions for future experiments.
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