Multiferroic nematic d-wave altermagnetism driven by orbital-order on the honeycomb lattice

Altermagnets provide promising platforms for unconventional magnetism, whose controllability would enable a whole new generation of spintronic devices. While a variety of bulk altermagnets have been discovered, altermagnetism in two-dimensional van der Waals materials has remained elusive. Here we demonstrate that the strained honeycomb monolayer VCl$_{3}$ is an orbital-order-driven ferroelectric altermagnet, exhibiting a significant and switchable spin-splitting. By using low-energy Hamiltonian and first-principles methods in combination with symmetry analysis, we reveal a unique anti-ferro-orbital-antiferromagnetic phase characterized by a 2D nematic $d$-wave altermagnetic spin splitting, tightly coupled with an orbital-ordered induced ferroelectric polarization. Finally, through symmetry mode analysis, we investigate how structural distortions favor the intricate interplay between orbital, altermagnetic, and ferroelectric degrees of freedom. Our study identifies VCl$_3$ as a prototypical 2D orbital-order-driven multiferroic altermagnet on the honeycomb lattice, establishing a van der Waals monolayer featuring altermagnetic ferroelectricity.