Intrinsic triferroicity in a two-dimensional lattice

Intrinsic triferroicity is essential and highly sought for novel device applications, such as high-density multistate data storage. So far, the intrinsic has only been discussed in three-dimensional systems. Herein on basis of first principles, we report a two-dimensional lattice. Being exfoliatable from layered bulk, single-layer $\mathrm{Fe}{\mathrm{O}}_{2}\mathrm{H}$ shown to be an intrinsically triferroic semiconductor, presenting antiferromagnetism, ferroelasticity, ferroelectricity simultaneously. Moreover, directional control its ferroelectric polarization achievable by 90 \ifmmode^\circ\else\textdegree\fi{} reversible ferroelastic switching. In addition, identified harbor in-plane piezoelectric effect. The unveiled phenomena mechanism triferroics this system not broaden scientific technological impact but also enable wide range nanodevice applications.