Derivation of effective spin-orbit Hamiltonians and spin lifetimes, with application to SrTiO$_3$ heterostructures

A general approach is derived for constructing an effective spin-orbit Hamiltonian for nonmagnetic materials, which is useful for calculating spin-dependent properties near an arbitrary point in momentum space with pseudospin degeneracy. The formalism is verified through comparisons with other approaches for III-V semiconductors, and its general applicability is illustrated by deriving the spin-orbit interaction and predicting spin lifetimes for strained SrTiO$_3$ and a two-dimensional electron gas in SrTiO$_3$ (such as at the LaAlO$_3$/SrTiO$_3$ interface). These results suggest robust spin coherence and spin transport properties in SrTiO$_3$-based materials at room temperature.