Crystal-field tuning of valley-related multiple Hall effects in ferromagnetic monolayers

Valley-related Hall effects in two-dimensional (2D) materials provide a versatile platform for uncovering novel quantum phenomena and enabling low-dissipation device applications. However, realizing multiple Hall phases within a single material system presents a significant challenge, as the anomalous valley Hall effect typically requires wide-bandgap semiconductors, whereas the quantum anomalous valley Hall (QAVH) effect necessitates narrow-gap topologies. Here, based on low energy k·p model analysis and crystal field theory, we elucidate the origin of the multiple Hall effects by demonstrating that strain tunes the energy splitting between d_xy/d_x²-y² and d_z² orbitals in magnetic hexagonal lattices, thereby driving transitions between distinct valley-related multiple Hall effects. Guided by this general mechanism, we identify ferromagnetic hexagonal ScX (X = S, Se, Te) and TiY (Y = N, P, As) monolayers as ideal candidate systems where this complex phase evolution is realizable under minute biaxial tensile strains (<1.2%). Specifically, these materials exhibit a sequential topological phase transition following the trajectory of ferrovalley (FV) → half-valley metal (HVM) → QAVH → HVM → FV, where the QAVH phase features a nonzero Chern number and chiral spin-valley locking. Our work establishes a unified mechanism for valley-dependent Hall effects and positions the ScX and TiY families as promising platforms for strain-engineered, low-dissipation valleytronics.