Transferring orbital angular momentum to an electron beam reveals toroidal and chiral order

• Published in: Physical review. B 2023-05, Vol.107 (20), Article 205419
• Main Authors: Nguyen, K. X., Jiang, Y., Cao, M. C., Purohit, P., Yadav, A. K., García-Fernández, P., Tate, M. W., Chang, C. S., Aguado-Puente, P., Íñiguez, J., Gomez-Ortiz, F., Gruner, S. M., Junquera, J., Martin, L. W., Ramesh, R., Muller, D. A.
• Format: Article
• Language: English
• Subjects: Angular momentum; Chirality; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Electric polarization; Electron diffraction; Electron microscopy; Ferroelectricity; Ferroelectrics; Scanning transmission electron microscopy
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.107.205419

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.