Ferroelectric and Room-Temperature Ferromagnetic Semiconductors in the 2D M I M II Ge 2 X 6 Family: First-Principles and Machine Learning Investigations.

Inspired by experimentally discovering ferromagnetism and ferroelectricity in two-dimensional (2D) CrGeTe ₃ and CuInP ₂ S ₆ with similar geometric structures, respectively, we systematically investigated ferroic properties in a large family of 2D M _I M _II Ge ₂ X ₆ (M _I and M _II = metal elements, X = S/Se/Te) by combining high-throughput first-principles calculations and the machine learning method. We identified 12 stable 2D multiferroics containing simultaneously ferromagnetic (FM) and ferroelectric (FE) properties and 35 2D ferromagnets without FE polarization. Particularly, the predicted FM Curie temperatures ( T _C ) of eight 2D FM+FE semiconductors are close to or above room temperature. The ferroelectricity originates from the spontaneous geometric symmetry breaking induced by the unexpected shift of Ge-Ge atomic pairs and the emergence of Ge lone pair electrons, which also strengthens the p - d orbital hybridization between X atoms and metal atoms, leading to enhanced super-super-exchange interactions and raising the FM T _C . Our findings not only enrich the family of 2D ferroic materials and present room-temperature FM semiconductors but also disclose the mechanism of the emerging ferroelectricity and enhanced ferromagnetism, which sheds light on the realization of high temperature multiferroics as well as FM semiconductors.