A two-dimensional (2D) material with piezoelectricity, topological and ferromagnetic (FM) orders, namely 2D piezoelectric quantum anomalous hall insulator (PQAHI), may open new opportunities to realize novel physics and applications. Here, by first-principles calculations, a family of 2D Janus monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) with dynamic, mechanical and thermal stabilities is predict to be room-temperature PQAHI. At the absence of spin-orbit coupling (SOC), monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) is a half Dirac semimetal state. When the SOC is included, these monolayers become quantum anomalous hall (QAH) states with sizable gaps (more than two hundred meV) and two chiral edge modes (Chern number C=2). It is also found that monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) possesses robust QAH states against biaxial strain. By symmetry analysis, it is found that only out-of-plane piezoelectric response can be induced by a uniaxial strain in the basal plane. The calculated out-of-plane $d_{31}$ of $mathrm{Fe_2ICl}$ ($mathrm{Fe_2IBr}$) is 0.467 pm/V (0.384 pm/V), which is higher than or comparable with ones of other 2D known materials. Meanwhile, using Monte Carlo (MC) simulations, the Curie temperature $T_C$ is estimated to be 429/403 K for monolayer $mathrm{Fe_2ICl}$/$mathrm{Fe_2IBr}$ at FM ground state, which is above room temperature. Finally, the interplay of electronic correlations with nontrivial band topology is studied to confirm the robustness of QAH state. The combination of piezoelectricity, topological and FM orders makes monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) become a potential platform for multi-functional spintronic applications with large gap and high $T_C$. Our works provide possibility to use the piezotronic effect to control QAH effects, and can stimulate further experimental works.
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