Strain-induced quantum anomalous valley Hall phase in Janus FeClBr monolayer: effective model and crystal-field mechanism.

Achieving the coexistence of valley polarization and nontrivial band topology is a central challenge in two-dimensional valleytronics. Here, we combine first-principles calculations, an effective k∙p model, and crystal-field analysis to develop a unified physical picture of biaxial-strain-driven topological phase transitions in the Janus ferrovalley monolayer FeClBr. First-principles calculations reveal a complete phase-transition sequence. A strain-dependent two-band k∙p model yields the condition for topological nontriviality-opposite signs of the renormalized band gaps at the two valleys-reproducing the full five-stage sequence within a minimal framework. Crystal-field analysis further identifies the microscopic origin: strain, through symmetry-selective modulation, drives orbital inversion, while spin-orbit coupling (SOC) imparts valley-dependent effective-gap shifts that cause the inversions to occur at different critical strains, opening a topologically nontrivial window between them. Our work establishes a complete causal chain from strain to topology and offers general design guidelines for engineering topological valley-polarized states in related two-dimensional magnetic materials.