Prediction of spin, valley, and topological properties in Janus TiGeZ₂X (Z = P, As; X = Br, I) monolayers

We perform systematic first-principles calculations to investigate the structural, electronic, magnetic, and valley-related properties of TiGeZ₂X (Z = As, P; X = Br, I) monolayers. These two-dimensional compounds are dynamically, mechanically, and thermally stable, exhibiting intrinsic ferromagnetism and semiconducting behavior. Electronic structure calculations reveal that Ti-3d orbitals dominate the low-energy states, forming well-defined valleys at K and K'. The interplay of spin-orbit coupling and ferromagnetism breaks time-reversal symmetry, resulting in spontaneous valley polarization without external fields, as reflected by pronounced Berry-curvature localization at the valleys. Moreover, modest strain can drive topological phases across the TiGeZ₂X family, producing protected edge states and quantized Hall conductance. These features, together with the anomalous valley Hall effect (AVHE), highlight TiGeZ₂X monolayers as versatile platforms for valleytronic and spintronic applications.