Engineering Altermagnetism via Layer Shifts and Spin Order in Bilayer MnPS$_3$

Altermagnetic materials combine compensated magnetic order with momentum-dependent spin splitting, offering a fundamentally new route for spintronic functionality beyond conventional ferromagnets and antiferromagnets. While most studies have focused on three-dimensional compounds, the emergence of altermagnetism in few-layer two-dimensional materials remains largely unexplored. Here, we demonstrate that bilayer MnPS$_3$, a prototypical 2D van der Waals magnet, can host stacking-induced altermagnetic phases. Using density-functional theory and spin-Laue symmetry analysis, we show that interlayer spin alignment and lateral displacement act as coupled symmetry control parameters that switch the system between Type II (collinear AFM) and Type III (altermagnetic) phases. Our systematic exploration reveals how specific stacking geometries enable momentum-dependent spin polarization without net magnetization, even in the absence of spin-orbit coupling. These results establish stacking engineering as a powerful, purely structural route for designing tunable altermagnetic states in 2D magnets, opening pathways toward symmetry-driven spintronic and magnetoelectronic devices.