Manuel Bibes1
CNRS/Thales1
Two-dimensional electron gases (2DEG) based on SrTiO<sub>3</sub> (STO) display fascinating properties such as low-temperature superconductivity and Rashba spin-orbit coupling allowing to interconvert spin and charge currents through the Edelstein effect. We have introduced ferroelectricity in these 2DEGs in order to achieve a non-volatile electrical control of their properties. Practically, we replaced STO by Ca-substituted STO (Ca-STO) which is ferroelectric up to about 30 K and generated 2DEGs either by sputtering a thin Al film or growing perovskite overlayers by pulsed laser deposition. We will present spin-charge and charge-spin conversion measurements and their control by the ferroelectric state. We will also show how magnetism can be introduced in the system and use x-ray absorption spectroscopy and magnetotransport to demonstrate the coexistence of ferroelectricity and magnetism with metallicity. Our data evidence the non-volatile control of polar displacements, magnetization and anomalous Hall effect upon switching the polarization direction, indicating a magnetoelectric coupling. Our results provide new opportunities in quantum matter arising from the interplay between ferroelectricity, ferromagnetism, metallicity, and Rashba spin-orbit coupling in low dimensions.