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. We demonstrate these coupling mechanisms using a minimal tight-binding model. First-principles calculations on bilayer MnPS ₃ validate the framework, showing that distinct ferroelectric switching paths produce characteristic spin-band reconstructions and discriminable electrical transport signatures. 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.