Unconventional Magnetism, Sliding Ferroelectricity, and Magneto-Optical Kerr Effect in Multiferroic Bilayers

Antiferromagnetic (AFM) materials provide a platform to couple altermagnetic (AM) spin-splitting with the magneto-optical Kerr effect (MOKE), offering potential for next-generation quantum technologies. In this work, first-principles calculations, symmetry analysis, and k·p modeling are employed to show that interlayer sliding in AFM multiferroic bilayers enables control of electronic, magnetic, and magneto-optical properties. This study reveals an intriguing dimension-driven AM crossover: the 2D paraelectric (PE) bilayer exhibits spin-degenerate bands protected by the $[C_2\parallel M_c]$ spin-space symmetry, whereas the 3D counterpart manifests AM spin-splitting along k_z ≠ 0 paths. Furthermore, interlayer sliding breaks this $M_c$ symmetry and stabilizes a ferroelectric (FE) state with compensated ferrimagnetism, where the Zeeman-like field is responsible for the nonrelativistic spin-splitting. In the FE phase, spin-orbit coupling (SOC) lifts accidental degeneracies and produces "alternating" spin-polarized bands through the interplay of Zeeman and Rashba effects. Crucially, spin polarization, ferrovalley polarization (ΔE_V), and the Kerr angle (θ_k) can all be reversed by switching either sliding ferroelectricity or the Néel vector. Our findings reveal the rich coupling among electronic, magnetic, and optical orders in sliding multiferroics, illustrating new prospects for ultralow-power spintronic and optoelectronic devices.