We study origin of Rashba spin-orbit interaction at SrTiO${}_3$ surfaces and LaAlO${}_3$/SrTiO${}_3$ interfaces by considering the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. We show that in a simple tight-binding model involving $3d$ $t_{2g}$ bands of Ti ions, the induced spin-orbit coupling in the $d_{xz}$ and $d_{yz}$ bands is cubic in momentum whereas the spin-orbit interaction in the $d_{xy}$ band has linear momentum dependence. We also find that the spin-orbit interaction in one-dimensional channels at LaAlO${}_3$/SrTiO${}_3$ interfaces is linear in momentum for all bands. We discuss implications of our results for transport experiments on SrTiO${}_3$ surfaces and LaAlO${}_3$/SrTiO${}_3$ interfaces. In particular, we analyze the effect of a given spin-orbit interaction term on magnetotransport of LaAlO${}_3$/SrTiO${}_3$ by calculating weak antilocalization corrections to the conductance and to universal conductance fluctuations.

• Received 10 April 2013

DOI:https://doi.org/10.1103/PhysRevB.87.245121