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

Abstract

A diluted oxide interface of $\mathrm{LaA}{\mathrm{l}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{n}}_{x}\mathrm{O}/\mathrm{SrTi}{\mathrm{O}}_{3}$ (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 $(0.2\ensuremath{\le}x\ensuremath{\le}0.3)$ 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 ${d}_{xy}$ orbits are populated $(5.3\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}\ensuremath{\le}{n}_{s}\ensuremath{\le}1.0\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2})$. 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.