The valley degrees of freedom of carriers in crystals is useful to process information and perform logic operations, and it is a key factor for valley application to realize the...

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A two-dimensional (2D) material system with both piezoelectric and ferromagnetic (FM) orders, referred to as a 2D piezoelectric ferromagnetism (PFM), may open up unprecedented opportunities for intriguing physics. Inspired by experimentally synthesized Janus monolayer MoSSe from MoS2, in this work, the Janus monolayer CrBr1.5I1.5 with dynamic, mechanical, and thermal stabilities is predicted, which is constructed from synthesized ferromagnetic CrI3 monolayer by replacing the top I atomic layer with Br atoms. Calculated results show that monolayer CrBr1.5I1.5 is an intrinsic FM half semiconductor with valence and conduction bands being fully spin-polarized in the same spin direction. Furthermore, monolayer CrBr1.5I1.5 possesses a sizable magnetic anisotropy energy. By symmetry analysis, it is found that both in-plane and out-of-plane piezoelectric polarizations can be induced by a uniaxial strain in the basal plane. The calculated in-plane d22 value of 0.557 pm/V is small. However, more excitingly, the out-of-plane d31 is as high as 1.138 pm/V, which is obviously higher compared with that of other 2D known materials. The strong out-of-plane piezoelectricity is highly desirable for ultrathin piezoelectric devices. Moreover, strain engineering is used to tune piezoelectricity of monolayer CrBr1.5I1.5. It is found that compressive strain can improve d22 and tensile strain can enhance d31. A FM order to antiferromagnetic order phase transition can be induced by compressive strain, and the critical point is about 0.95 strain. That is to say that 2D piezoelectric antiferromagnetism can be achieved by compressive strain, and the corresponding d22 and d31 are 0.677 and 0.999 pm/V at 0.94 strain, respectively. It is also found that magnetic order has important effects on piezoelectricity of monolayer CrBr1.5I1.5. Finally, similar to CrBr1.5I1.5, the PFM can also be realized in the monolayers CrF1.5I1.5 and CrCl1.5I1.5. Amazingly, their d31 can reach up to 2.578 and 1.804 pm/V for monolayers CrF1.5I1.5 and CrCl1.5I1.5. Our paper proposes a realistic way to achieve PFM with large d31, making these systems very promising for multifunctional semiconductor spintronic applications.

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