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Two-dimensional multiferroic materials are highly sought after due to theirhuge potential for applications in nanoelectronic and spintronic devices. Here,we predict, based on first-principle calculations, a single phase {\ittriferroic} where three ferroic orders; ferromagnetism, ferroelectricity andferroelasticity, coexist simultaneously in hole doped GdCl$_2$ monolayer (aferromagnetic semiconductor). This is achieved by substituting 1/3rd of theGd$^{2+}$ ions with Eu$^{2+}$ in the hexagonal structure of GdCl$_2$ monolayer.The resulting metallic state undergoes a bond-centered charge ordering drivinga distortion in the hexagonal structure making it semiconducting again and {\itferroelastic}. Further, the lattice distortion accompanied by a breaking of thelattice centrosymmetry renders a non-centrosymmetric charge distribution whichmakes the monolayer {\it ferroelectric}, at the same time. The two ferroicorders, ferroelectricity and ferroelasticity, present in Eu doped GdCl$_2$monolayer are found to be strongly coupled making it a promising candidate fordevice applications. The doped monolayer remains a ferromagnetic semiconductorwith large 4f magnetic moment just like the parent monolayer and possesses aneven higher (out-of-plane) magnetic anisotropy energy (MAE) than its pristinecounterpart as desired for two dimensional magnets to have high transitiontemperature.

Two-dimensional Rare-earth Halide Based Single Phase Triferroic