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.