  The complex oxide heterostructures such as LaAlO3/SrTiO3 (LAO/STO) interface
are paradigmatic platforms to explore emerging multi-degrees of freedom
coupling and the associated exotic phenomena. In this study, we reveal the
effects of multiorbital and magnetic ordering on Rashba spin-orbit coupling
(SOC) at the LAO/STO (001) interface. Based on first-principles calculations,
we show that the Rashba spin splitting near the conduction band edge can be
tuned substantially by the interfacial insulator-metal transition due to the
multiorbital effect of the lowest t_2g bands. We further unravel a competition
between Rashba SOC and intrinsic magnetism, in which the Rashba SOC induced
spin polarization is suppressed by the interfacial magnetic ordering. These
results deepen our understanding of intricate electronic and magnetic
reconstruction at the perovskite oxide interfaces and shed light on the
engineering of oxide heterostructures for all-oxides-based spintronic devices.
