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The Edelstein effect provides the purely electrical generation and control ofa homogeneous magnetization in primarily nonmagnetic materials with brokeninversion symmetry. Usually, only the spin density response to an externalelectric field is discussed. Here, we report on the electrically inducedmagnetization containing spin as well as orbital contributions in thetopological oxide two-dimensional electron gas at the interface betweenSrTiO$_3$ and AlO. We find that in this particular system the orbital Edelsteineffect exceeds the spin Edelstein effect by more than one order of magnitude.The main reason are orbital moments of different magnitude in theRashba-like-split band pairs.

Spin and orbital Edelstein effect in an oxide two-dimensional electron gas: theory and application to AlO$_x$/SrTiO$_{3}$