Signature of enhanced spin-orbit interaction in the magnetoresistance of LaTiO${}_3$/SrTiO${}_3$ interfaces on $\delta$-doping

We present a study of modulation of spin-orbit interaction (SOI) at the interface of LaTiO${}_3$/SrTiO${}_3$ by $\delta$-doping with an iso-structural ferromagnetic perovskite LaCoO${}_3$. The sheet carrier density at the interface decreases exponentially with $\delta$-doping thickness. We have explored that the spin-orbit scattering time (${\tau }_{so}$) can be decreased by nearly 3 orders of magnitude, whereas the inelastic scattering time (${\tau }_i$) remains almost constant with $\delta$-doping thickness. We have also observed that the ${\tau }_i$ varies almost inversely proportional to temperature and ${\tau }_{so}$ remains insensitive to temperature, which suggest that the spin relaxation in these interfaces follows D’yakonov-Perel mechanism. The observed in-plane anisotropic magnetoresistance is attributed to the mixing of the spin up and spin down states of d-band at Fermi level due to SOI.