First-principles prediction of intrinsic ferrovalley properties in Janus rare-earth PrXY (X ≠ Y = Cl, Br, I) monolayers

valleys, the Berry curvature values are opposite to each other, resulting in the anomalous valley Hall effect. In addition, applying moderate biaxial strain can further enhance their magnetic anisotropy energy and valley polarization. These findings do not only emphasize the importance of strain in regulating spin and valley characteristics, but also provide new possibilities for the application of ferromagnetic semiconducting materials in spintronic and valleytronic devices.