The theoretical understanding of the spin-orbit coupling (SOC) effects at LaAlO${}_3$/SrTiO${}_3$ interfaces and SrTiO${}_3$ surfaces is still in its infancy. We perform first-principles density-functional-theory calculations and derive from these a simple tight-binding Hamiltonian, through a Wannier function projection and group theoretical analysis. We find striking differences to the standard Rashba theory for spin-orbit coupling in semiconductor heterostructures due to multiorbital effects: By far the biggest SOC effect is at the crossing point of the $xy$ and $yz$ (or $zx$) orbitals, and around the $\Gamma$ point a Rashba spin splitting with a cubic dependence on the wave vector $\vec{k}$ is possible.

• Received 4 July 2012

DOI:https://doi.org/10.1103/PhysRevB.87.161102