The valley degree of freedom provides a promising route for functionalizing two-dimensional materials, yet a unified principle for realizing the anomalous valley Hall effect (AVHE) in tetragonal systems under static control has remained elusive. Here, we establish a general symmetry criterion for achieving AVHE in two-dimensional tetragonal magnetic materials through systematic analysis of magnetic layer groups. We demonstrate that finite valley polarization emerges only when type-2/3/4 symmetry operations (constraining Berry curvature and enforcing valley degeneracy) are broken by external fields, while type-1 symmetries are preserved. By screening magnetic layer groups, we identify specific systems in which this condition can be satisfied through perpendicular electric fields and uniaxial strain, and we validate our criterion using first-principles calculations and tight-binding analyses of ${\mathrm{Fe}}_2\mathrm{BeBrP}$ and bilayer ${\mathrm{VS}}_2$. Our results reveal that the symmetry class of a magnetic layer group dictates the minimal control pathway for generating AVHE, thereby providing a unified theoretical framework for spin-valley control and device design in two-dimensional tetragonal magnetic materials.

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• Anomalous Hall effect
• Valleytronics
• 2-dimensional systems
• First-principles calculations
• Tight-binding model