- Nguyen, KX;
- Jiang, Y;
- Cao, MC;
- Purohit, P;
- Yadav, AK;
- García-Fernández, P;
- Tate, MW;
- Chang, CS;
- Aguado-Puente, P;
- Íñiguez, J;
- Gomez-Ortiz, F;
- Gruner, SM;
- Junquera, J;
- Martin, LW;
- Ramesh, R;
- Muller, DA
Orbital angular momentum (OAM) and torque transfer play central roles in a wide range of magnetic textures and devices including skyrmions and spin-torque electronics. Analogous topological structures are now also being explored in ferroelectrics, including polarization vortex arrays in ferroelectric/dielectric superlattices. Unlike magnetic toroidal order, electric toroidal order does not couple directly to linear external fields. Instead, we find that the presence of an electric toroidal moment in a ferrorotational phase transfers measurable torque and OAM 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 vortexlike phases.