Polarization vortices in a ferromagnetic metal via twistronics

Advances in moiré engineering have revealed new pathways for manipulating lattice distortions and electronic properties in low-dimensional materials via stacking two crystalline layers with a twist angle between them. Here we demonstrate that twisted bilayer stacking can induce dipolar vortices in metallic SrRuO₃ membranes, despite the presence of free charge. These vortices are correlated with moiré-periodic flexoelectricity induced by shear strain gradients, and their magnitude depends on both the twist angle and proximity to the interface. In addition, below the ferromagnetic Curie temperature of the films, ferromagnetic order coexists-and appears to compete-with the dipolar order, showing opposite twist-angle dependencies of the respective magnitudes of the two multiferroic order parameters. Density functional theory calculations provide insight into the microscopic origin of these observations. These findings extend the scope of topological polarization design beyond dielectric materials and into metals.