  Two-dimensional (2D) ferromagnetic and ferroelectric materials attract
unprecedented attention due to the spontaneous-symmetry-breaking induced novel
properties and multifarious potential applications. Here we systematically
investigate a large family (148) of 2D MGeX3 (M = metal elements, X =
O/S/Se/Te) by means of the high-throughput first-principles calculations, and
focus on their possible ferroic properties including ferromagnetism,
ferroelectricity, and ferroelasticity. We discover eight stable 2D ferromagnets
including five semiconductors and three half-metals, 21 2D antiferromagnets,
and 11 stable 2D ferroelectric semiconductors including two multiferroic
materials. Particularly, MnGeSe3 and MnGeTe3 are predicted to be
room-temperature 2D ferromagnetic half metals with Tc of 490 and 308 K,
respectively. It is probably for the first time that ferroelectricity is
uncovered in 2D MGeX3 family, which derives from the spontaneous symmetry
breaking induced by unexpected displacements of Ge-Ge atomic pairs, and we also
reveal that the electric polarizations are in proportion to the ratio of
electronegativity of X and M atoms, and IVB group metal elements are highly
favored for 2D ferroelectricity. Magnetic tunnel junction and water-splitting
photocatalyst based on 2D ferroic MGeX3 are proposed as examples of wide
potential applications. The atlas of ferroicity in 2D MGeX3 materials will spur
great interest in experimental studies and would lead to diverse applications.
