Symmetry-locked six-state control of altermagnetism via sliding ferroelectricity

Altermagnetic multiferroics offer a promising route to low-power spintronics by enabling spin splitting without net magnetization, extending beyond conventional spin-orbit coupling. However, achieving deterministic electric control has remained elusive. Here, a six-state platform for high-dimensional magnetoelectric coupling in altermagnets is established by exploiting the nondegenerate transition paths of sliding ferroelectrics as a symmetry-engineering knob, thereby transcending the conventional binary (up/down) paradigm of sliding ferroelectricity. First-principles calculations on bilayer manganese phosphorus trisulfide reveal a spin-polarization symmetry-locking mechanism. Polarization switching along the three nondegenerate paths not only reverses the spin splitting but also rotates its spin-splitting texture in 120° increments, yielding six nonvolatile, electrically addressable altermagnetic states. Furthermore, direct correspondence is established between the spin-splitting texture and the nonlinear Hall response, providing unique electrical fingerprints for each state. This work establishes a paradigm for electric field-driven reconstruction of momentum-space spin geometry, providing a versatile platform for controlling quantum phenomena in altermagnetic spintronics.