Abstract
We investigate the spin-dependent transport properties of a two-dimensional electron gas formed at oxides' interface in the presence of a magnetic field. We consider several scenarios for the oxides' properties, including oxides with co-linear or spiral magnetic and ferroelectric order. For spiral multiferroic oxides, the magnetoelectric coupling and the topology of the localized magnetic moments introduce additional, electric field controlled spin-orbit coupling that affects the magneto-oscillation of the current. An interplay of this spin-orbit coupling, the exchange field, and of the applied magnetic field results in a quantum, gate-controlled spin and charge Hall conductance.
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