A unified symmetry framework for spin-ferroelectric coupling in altermagnetic multiferroics

Altermagnetic multiferroics, hosting coexisting spin-splitting bands and ferroelectric polarization, offer a promising route to magnetoelectric coupling beyond conventional relativistic spin-orbit mechanism. However, the lack of a unified principle connecting ferroelectric switching symmetry to spin-band topology has impeded rational material design. Here, we establish a universal symmetry-based framework that classifies all possible spin-ferroelectric couplings in altermagnets into three fundamental types: decoupling, pseudo-time-reversal coupling, and asymmetric momentum mapping. This classification stems directly from the relation between ferroelectric switching operators and the spin Laue group, creating a decisive symmetry-to-function paradigm. First-principles calculations on bilayer MnPS₃ confirm the framework, showing that distinct ferroelectric switching paths produce characteristic spin-band reconstructions and discriminable electrical transport signatures. The universality of the framework is further validated in BiFeO₃. Our work provides a predictive design principle for voltage-programmable spintronics, effectively transforming ferroelectric symmetry from a structural descriptor into a dynamic functional control knob for altermagnetic spin states.