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Signature of enhanced spin-orbit interaction in the magnetoresistance of LaTiO$_3$/SrTiO$_3$ interfaces on $δ$-doping

We present a study of modulation of spin-orbit interaction (SOI) at the interface of LaTiO$_3$/SrTiO$_3$ by $δ$-doping with an iso-structural ferromagnetic perovskite LaCoO$_3$. The sheet carrier density at the interface decreases exponentially with $δ$-doping thickness. We have explored that the spin-orbit scattering time ($τ_{so}$) can be decreased by nearly 3 orders of magnitude, whereas the inelastic scattering time ($τ_{i}$) remains almost constant with $δ$-doping thickness. We have also observed that the $τ_{i}$ varies almost inversely proportional to temperature and $τ_{so}$ 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.