@article{10902/28086, year = {2022}, month = {4}, url = {https://hdl.handle.net/10902/28086}, abstract = {Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO3/SrTiO3 superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.}, organization = {K.T.K., S.Y.P., and D.R.L acknowledge financial support by National Research Foundation of Korea (Grant No. NRF-2020R1A2C1009597, NRF-2019K1A3A7A09033387, and NRF-2021R1C1C1009494). M.M. and R.R. were supported by the Quantum Materials program from the Office of Basic Energy Sciences, US Department of Energy (DE-AC02-05CH11231). V.A.S., J.W.F., and L.W.M. acknowledge the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC-0012375 for support to study complex-oxide heterostructure with X-ray scattering. L.W.M. and R.R. acknowledge partial support from the Army Research Office under the ETHOS MURI via cooperative agreement W911NF-21-2-0162. J.Í. acknowledges financial support from the Luxembourg National Research Fund through project FNR/C18/MS/12705883/REFOX. M.A.P.G. was supported by the Czech Science Foundation (project no. 19-28594X). Diamond Light Source, UK, is acknowledged for beamtime on beamline I10 under proposal NT24797. Use of the Advanced Light Source, Lawrence Berkeley National Laboratory, was supported by the U.S. Department of Energy (DOE) under contract no. DE-AC02-05CH11231, and use of the Advanced Photon Source was supported by DOE’s Office of Science under contract DE-AC02-06CH11357.}, publisher = {Nature Publishing Group}, publisher = {Nature Communications, 2022, 13, 1769}, title = {Chiral structures of electric polarization vectors quantified by X-ray resonant scattering}, author = {Kim, Kook Tae and McCarter, Margaret R. and Stoica, Vladimir A. and Das, Sujit and Klewe, Christoph and Donoway, Elizabeth P. and Burn, David M. and Shafer, Padraic and Rodolakis, Fanny and Gonçalves, Mauro A. P. and Gómez Ortiz, Fernando and Íñiguez, Jorge and García Fernández, Pablo (físico) and Junquera Quintana, Francisco Javier and Susarla, Sandhya and Lovesey, Stephen W. and Laan, Gerrit van der and Park, Se Young and Martin, Lane W. and Freeland, John W.}, }