Interlayer sliding direction as a symmetry selector in altermagnetic bilayer Fe2WS4: Switchable anomalous Hall and anomalous valley Hall effects

Altermagnets combine compensated collinear magnetic order with momentum-dependent spin splitting, offering a promising platform for coupling spin and valley degrees of freedom with ferroelectricity and Berry-curvature driven transport in the absence of net magnetization. However, achieving nonvolatile and selective control of these intertwined degrees of freedom remains a key challenge. Here, using first-principles calculations, we show that the direction of interlayer sliding serves as a symmetry selective control parameter in altermagnetic bilayer Fe2WS4. Diagonal sliding breaks inversion symmetry and produces two sliding ferroelectric states with opposite out-of-plane polarizations. Reversal of the ferroelectric polarization switches the momentum-dependent spin texture and reverses the anomalous Hall conductivity, revealing strong magnetoelectric coupling and enabling a ferroelectrically switchable anomalous Hall effect. In contrast, axial sliding preserves inversion symmetry but breaks the crystalline symmetry relating the X and Y valleys, leading to reversible valley polarization and a switchable anomalous valley Hall effect. These results establish the direction of interlayer sliding as a nonvolatile symmetry selector for controlling ferroelectricity, spin texture, valley polarization, and Hall transport responses in two-dimensional altermagnetic bilayers.