Figure 1: Basic properties.

(a) Sketch of multiferroic Ge1−xMnxTe with FE displacement of Ge(Mn)-atoms inside the rhombohedrally distorted unit cell along [111] as indicated by the orange arrow. (b) Schematic Rashba-gas band maps of a ferromagnetic semiconductor (FMS) compared with a ferromagnetic Rashba semiconductor (FERS) (c) and a multiferroic Rashba semiconductor (MUFERS) in d, with their dependence on the orientations of the FM (M) and FE (Pe) order (see text). (e) Typical out-of-plane FE phase hysteresis measured by piezo-force-microscopy for FE GeTe and preserved in Ge1−xMnxTe (ref. 8). (f) Out-of-plane FM hysteresis curve of multiferroic Ge0.87Mn0.13Te measured by SQUID. (g,h) Band plots of the two upper occupied RZ-split valence bands as a function of k-vectors around Z-point of Ge1−xMnxTe and corresponding spin-texture switching upon colinear reversal of Mz and Pz.