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. Unlike magnetic toroidal order, electric toroidal order, found in analogous topological structures in ferroelectrics, do not couple directly to linear external fields. Instead, we show that the presence of an electric toroidal moment in a ferro-rotational phase transfers a measurable torque and orbital angular momentum to a localized electron beam in the ballistic limit. We record these torque transfers from a high-energy electron beam using a momentum-resolved detector. This approach provides a high-sensitivity method to detect polarization fields and their more complex order parameters and topologies. In addition to toroidal order, we also demonstrate high-precision measurements of vorticity and chirality for polar vortex-like phases¹.<br/><br/>[1] K.X. Nguyen et. al, Phys. Rev. B <b>107</b>, 205419.