Layer-locked multiple valley Hall effects in tetragonal altermagnetic/ferromagnetic monolayers M2SiCX2 (M=transition metal; X=S, Se)

Exploring valley physics in materials with nonhexagonal crystal structures is a promising avenue for advancing two-dimensional valleytronics. The valley-related Hall effect enables precise electron control by manipulating the valley degree of freedom. Here, we explore the operability of layer-locked multiple valley Hall effects (VHEs) realized in tetragonal altermagnetic/ferromagnetic monolayers ${M}_{2}\mathrm{SiC}{X}_{2}$ (M is a transition metal atom; $X=\mathrm{S}, \mathrm{Se}$). Using tetragonal monolayers ${\mathrm{Cr}}_{2}\mathrm{SiC}{X}_{2}$ as examples, we examine their collinear altermagnetic trivial state and collinear ferromagnetic nontrivial state through first-principles calculations. The net layer-locked VHE and anomalous dual VHE arise from valley-layer coupling, nonzero Berry curvature, and spin splitting. Additionally, the net layer-locked anomalous VHE can also be realized and switched by applying a vertical external electric field or uniaxial strain. Our results provide a platform for layer-locked multiple VHEs and highlight the potential of these materials in low-power-consumption spin valleytronic devices.