Transferring Orbital Angular Momentum to an Electron Beam Reveals Toroidal and Chiral Order.

Orbital angular momentum and torque transfer play central roles in a wide range of magnetic textures and devices including skyrmions and spin-torque electronics(1-4). Analogous topological structures are now also being explored in ferroelectrics, including polarization vortex arrays in ferroelectric/dielectric superlattices(5). Unlike magnetic toroidal order, electric toroidal order does not couple directly to linear external fields. To develop a mechanism that can control switching in polarization vortices, we utilize a high-energy electron beam and show that transverse currents are generated by polar order in the ballistic limit. We find that the presence of an electric toroidal moment in a ferro-rotational phase transfers a measurable torque and orbital angular momentum to the electron beam. Furthermore, we find that the complex polarization patterns, observed in these heterostructures, are microscopically chiral with a non-trivial axial component of the polarization. This chirality opens the door for the coupling of ferroelectric and optical properties.