Coexisting Ferroelectric, Ferromagnetic, and Ferrovalley Polarizations in Single Quintuple Layer ReAlGe₂X₆ (X = S, Se)

Ferromagnetic semiconductors with coexisting ferroelectric and ferrovalley polarizations are highly desirable for next-generation electronic devices and have rarely been discovered till date. Herein, we employ the first-principles calculations to identify the stable two-dimensional semiconductors ReAlGe2X6 (X = S, Se) to concurrently exhibit ferroelectric (FE), ferromagnetic (FM), and ferrovalley (FV) polarizations. The FE derives from the spontaneous spatial mirror (P) asymmetry induced by a vertical displacement of Ge–Ge dimers. The FM arises from the Re–X–Ge–X–Re supersuperexchange interactions, which enhances the Curie temperature (TC) up to 192 and 180 K for S and Se systems, respectively. Furthermore, due to the strong spin–orbit coupling of d shell of Re atoms, ReAlGe2X6 (X = S, Se) capture a remarkable perpendicular magnetocrystalline anisotropy energy of 4.86 and 3.79 meV, which breaks time-inversion (T) symmetry, and consequently, posse the giant FV polarization of 280 and 260 meV, as well as polarized Berry curvature and circularly light absorption, which notably enables exceptional anomalous valley Hall and circular dichroism effects. The tuning properties of the valley and magnetic states are further characterized by strain.