Gate-tunable Rashba spin-orbit coupling and spin polarization at diluted oxide interfaces

A diluted oxide interface of LaAl_1-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 splitting of the 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 densities. These findings have not yet been observed in LAO/STO interfaces. A fully back-gate-tunable spin-polarized two-dimensional electron liquid is observed at the interface with $x=0.3$ where only dxy orbits are populated $(5.3×{}{10}¹²{{0.16em}{0ex}}c{m}^{{-}2}{≤}{n}ₛ{≤}1.0×{}{10}¹³{{0.16em}{0ex}}c{m}^{{-}2})$. The present results shed light on unexplored territory in SOC at STO-based oxide heterostructures and make LAMO/STO an intriguing platform for spin-related phenomena in $3d$ electron systems.