@article{10902/31590, year = {2023}, month = {5}, url = {https://hdl.handle.net/10902/31590}, abstract = {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.}, organization = {Y.J., D.A.M., and ptychography supported by the U.S. Department of Energy, Grant No. DE-SC0002334. Electron microscopy experiments by K.X.N. and equipment supported by the Cornell Center for Materials Research, through the National Science Foundation MRSEC program, Award No. DMR-1719875. Torque transfer theory (M.C.) supported by the Air Force Office of Scientific Research through the 2D Electronics MURI Grant No. FA9550-16-1-0031. Support for the MM-PAD development in S.M.G.'s lab was provided by the U.S. Department of Energy, Grant No. DE-FG02-10ER46693. The adaptation to the STEM was supported by the Kavli Institute at Cornell for Nanoscale Science. J.I. acknowledges support from the Luxembourg National Research Fund under Grant No. C15/MS/10458889 NEWALLS. P.G.F. and J.J. acknowledge financial support from the Spanish Ministry of Science, Innovation and Universities through Grant No. PGC2018-096955-B. R.R. acknowledges support from the Quantum Materials program funded by the U.S. Department of Energy, Office of Science.}, publisher = {American Physical Society}, publisher = {Physical Review B, 2023, 107(20), 205419}, title = {Transferring orbital angular momentum to an electron beam reveals toroidal and chiral order}, author = {Nguyen, K. X. and Jiang, Y. and Cao, M. C. and Purohit, P. and Yadav, A. K. and García Fernández, Pablo (físico) and Tate, M. W. and Chang, C. S. and Aguado Puente, Pablo and Íñiguez, J. and Gómez Ortiz, Fernando and Gruner, S. M. and Junquera Quintana, Francisco Javier and Martin, L. W. and Ramesh, R. and Muller, D. A.}, }