We demonstrate in situ 90° electric field-induced uniform magnetization rotation in single domain submicron ferromagnetic islands grown on a ferroelectric single crystal using x-ray photoemission electron microscopy. The experimental findings are well correlated with micromagnetic simulations, showing that the reorientation occurs by the strain-induced magnetoelectric interaction between the ferromagnetic nanostructures and the ferroelectric crystal. Specifically, the ferroelectric domain structure plays a key role in determining the response of the structure to the applied electric field, resulting in three strain-induced regimes of magnetization behavior for the single domain islands.

Macroscopic ferroelectric order in $\alpha$-GeTe with its noncentrosymmetric lattice structure leads to a giant Rashba spin splitting in the bulk bands due to strong spin-orbit interaction. Direct measurements of the bulk band structure using soft x-ray angle-resolved photoemission (ARPES) reveals the three-dimensional electronic structure with spindle torus shape. By combining high-resolution and spin-resolved ARPES as well as photoemission calculations, the bulk electronic structure is disentangled from the two-dimensional surface electronic structure by means of surface capping, which quenches the complex surface electronic structure. This unravels the bulk Rashba-split states in the ferroelectric Rashba $\alpha$-GeTe(111) semiconductor exhibiting a giant spin splitting with Rashba parameter ${\alpha }_R$ around 4.2 eV Å, the highest of so-far known materials.

Entanglement of the spin–orbit and magnetic order in multiferroic materials bears a strong potential for engineering novel electronic and spintronic devices. Here, we explore the electron and spin structure of ferroelectric α-GeTe thin films doped with ferromagnetic Mn impurities to achieve its multiferroic functionality. We use bulk-sensitive soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to follow hybridization of the GeTe valence band with the Mn dopants. We observe a gradual opening of the Zeeman gap in the bulk Rashba bands around the Dirac point with increase of the Mn concentration, indicative of the ferromagnetic order, at persistent Rashba splitting. Furthermore, subtle details regarding the spin–orbit and magnetic order entanglement are deduced from spin-resolved ARPES measurements. We identify antiparallel orientation of the ferroelectric and ferromagnetic polarization, and altering of the Rashba-type spin helicity by magnetic switching. Our experimental results are supported by first-principles calculations of the electron and spin structure.