Fractional Quantum Multiferroics from Coupling of Fractional Quantum Ferroelectricity and Altermagnetism

Multiferroics, which combine ferroelectric and magnetic order, offer a transformative platform for next-generation electronic devices. However, the intrinsic competition between the mechanisms driving ferroelectricity and magnetism in single-phase materials severely limits their performance, typically resulting in weak magnetoelectric coupling at room temperature. Here, we propose a solution to this long-standing challenge through the novel concept of fractional quantum multiferroics (FQMF), where strong magnetoelectric coupling is naturally realized by coupling fractional quantum ferroelectricity (FQFE) with altermagnetism (AM). Symmetry analysis shows that reversing the FQFE polarization necessarily inverts the AM spin splitting under parity-time ($\mathcal{PT}$) or time-reversal ($\mathcal{T}\tau$) operations. A minimal tight-binding model reproduces this effect, demonstrating electrically driven spin control without rotating the N\'eel vector. First-principles calculations further identify a broad family of candidate materials in two and three dimensions including bulk MnTe, Cr$_2$S$_3$, Mn$_4$Bi$_3$NO$_{15}$ and two-dimensional AB$_2$ bilayers such as MnX$_2$ (X=Cl, Br, I), CoCl$_2$, CoBr$_2$, and FeI$_2$. Notably, MnTe exhibits a high N\'eel temperature ($\sim$300 K) and a large electrically switchable spin splitting ($\sim$0.8 eV), demonstrating room-temperature magnetoelectric performance that surpasses that of conventional multiferroics. To further showcase the technological potential, we propose an electric-field-controlled FQMF tunnel junction based on MnTe that achieves tunneling magnetoresistance exceeding 300\%. This work establishes FQMF as a distinct and promising route to achieving room-temperature strong magnetoelectric coupling, opening a new avenue for voltage-controlled spintronics.