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.
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