Large and Reversible Strain-Tunable Valley Polarization in Two-Dimensional Altermagnetic Zr-Based Oxyhalide Monolayers

Altermagnets combine compensated magnetic order with momentum-dependent spin splitting, providing a promising platform for spin-valley control without net magnetization. Here, using first-principles calculations, we identify monolayer Zr₂Cl₂O, Zr₂Br₂O, and Janus Zr₂ClBrO as dynamically stable altermagnetic semiconductors that retain their structural frameworks in 300 K AIMD simulations. The X and Y valleys are dominated by Zr 4d orbitals and carry opposite spin polarizations in the nonrelativistic limit. Uniaxial strain shifts the two valleys in opposite directions, enabling reversible control of both the magnitude and sign of the valley polarization. Under only ±2% uniaxial strains, the valence-band valley splittings reach 192-212 meV in Zr₂Cl₂O and Zr₂Br₂O and 84.4-158.8 meV in Zr₂ClBrO. Moreover, rotating the strain axis by 90◦ reverses the valley ordering. In addition, stronger compression closes the band gap and induces an inversion between opposite-spin bands, while the crossing opens a small gap with SOC. These results establish Zr-based oxyhalide monolayers as promising candidates for mechanically tunable altermagnetic valleytronics.