Strain engineering serves as an effective approach for tuning diverse properties in quantum materials and electronic devices. One may establish a dual Hall effect based on the systematic response to the uniaxial strain induced symmetry reduction in multifunctional materials. Here, we predict a stable two-dimensional altermagnet monolayer ${\mathrm{Ta}}_2{\mathrm{Te}}_2\mathrm{O}$, which is a direct gap semiconductor. More interestingly, the magnetic anisotropy energy of monolayer ${\mathrm{Ta}}_2{\mathrm{Te}}_2\mathrm{O}$ shows the rare biaxial anisotropy in the xy plane, while exhibiting conventional uniaxial anisotropy in the xz plane. The four-leaf-clover-shaped magnetic anisotropy in the xy plane originates from the fourth-order single-ion interactions. Importantly, uniaxial strain can not only induce ${\mathrm{Ta}}_2{\mathrm{Te}}_2\mathrm{O}$ to transform from a semiconductor to a semimetal, but also effectively tune the direction and magnitude of valley polarization. Therefore, when the magnetization direction changes in the xy plane, the variation laws of valley splitting in the valence and conduction bands are exactly opposite to each other. In addition, uniaxial strain can break inversion symmetry, thereby inducing the anomalous Hall effect and nonlinear Hall effect. Our work demonstrates that two-dimensional altermagnets serve as an ideal platform for multifunctional devices, bridging linear and nonlinear magnetoelectric effects via strain engineering.

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• Density of states
• Electronic structure
• First-principles calculations
• Hall effect
• Magnetic anisotropy
• Magnetic order
• Spin-orbit coupling
• Spintronics
• Valley degrees of freedom
• Valleytronics