Two-dimensional (2D) multiferroic materials with controllable magnetism have promising prospects in miniaturized quantum device applications, such as high-density data storage and spintronic devices. Here, using first-principles calculations, we propose a coexistence of antiferromagnetism and ferroelasticity in multiferroic $MnF_{4}$ monolayer. The $MnF_{4}$ monolayer is found to be an intrinsic wide-gap semiconductor with large spin polarization ~3 $mu_{B}$/Mn, in which the antiferromagnetic order originates from the cooperation and competition of the direct exchange and super exchange. $MnF_{4}$ monolayer is also characterized by strongly uniaxial magnetic anisotropic behavior, that can be manipulated by the reversible ferroelastic strain and carrier doping. Remarkably, the carrier doping not only leads to an antiferromagnetic to ferromagnetic phase transformation, bult also could switch the easy magnetization axis between the in-plane and out-of-plane directions. In addition, the Neel temperature was evaluated to be about 140 K from the Monte Carlo simulations based on the Heisenberg model. The combination of antiferromagnetic and ferroelastic properties in $MnF_{4}$ monolayer provides a promising platform for studying the magnetoelastic effects, and brings about new concepts for next-generation nonvolatile memory and multi-stage storage.
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