Diluted oxide interface of LaAl1-xMnxO/SrTiO3 (LAMO/STO) provides a new way of tuning the ground states of the interface between the two band insulators of LAO and STO from metallic/superconducting to highly insulating. Increasing the Mn doping level (x) leads to a delicate control of the carrier density as well as a raise in the electron mobility and spin polarization. Herein, we demonstrate a tunable Rashba spin-orbit coupling (SOC) and spin polarization of LAMO/STO (0.2 <= x <= 0.3) by applying a back gate. The presence of SOC causes the splitting of energy band into two branches by a spin splitting energy. The maximum spin splitting energy depends on the Mn doping and decreases with the increasing Mn content and then vanishes at x = 0.3. The carrier density dependence of the spin splitting energy for different compositions shows a dome-shaped behavior with a maximum at different normalized carrier density. These findings have not yet been observed in LAO/STO interfaces. A fully back-gate-tunable spin-polarized 2DEL is observed at the interface with x = 0.3 where only dxy orbits are populated (5.3E12 cm-2 <= ns <= 1.0E13 cm-2). The present results shed light on unexplored territory in SOC at STO-base oxide heterostructures and make LAMO/STO an intriguing platform for spin-related phenomena in 3d-electron systems.
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