Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering

Margaret R. McCarter, Kook Tae Kim, Vladimir A. Stoica, Sujit Das, Christoph Klewe, Elizabeth P. Donoway, David M. Burn, Padraic Shafer, Fanny Rodolakis, Mauro A. P. Gonçalves, Fernando Gómez-Ortiz, Jorge Íñiguez, Pablo García-Fernández, Javier Junquera, Stephen W. Lovesey, Gerrit van der Laan, Se Young Park, John W. Freeland, Lane W. Martin, Dong Ryeol Lee, and Ramamoorthy Ramesh

Phys. Rev. Lett. 129, 247601 – Published 5 December 2022

Abstract

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Received 12 November 2021
Revised 8 March 2022
Accepted 23 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.247601

Physics Subject Headings (PhySH)

Ferroelectrics Multilayer thin films Nanostructures

Resonant elastic x-ray scattering X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Margaret R. McCarter ^1,*, Kook Tae Kim^2,*, Vladimir A. Stoica^3,4, Sujit Das ⁵, Christoph Klewe⁶, Elizabeth P. Donoway ¹, David M. Burn ⁷, Padraic Shafer ⁶, Fanny Rodolakis ³, Mauro A. P. Gonçalves ⁸, Fernando Gómez-Ortiz ⁹, Jorge Íñiguez ^10,11, Pablo García-Fernández ⁹, Javier Junquera ⁹, Stephen W. Lovesey ^7,12, Gerrit van der Laan ⁷, Se Young Park ², John W. Freeland ³, Lane W. Martin ^13,14, Dong Ryeol Lee ^2,†, and Ramamoorthy Ramesh ^1,13,14,‡

¹Department of Physics, University of California, Berkeley, California 94720, USA
²Department of Physics, Soongsil University, Seoul 06978, Korea
³Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁴Department of Materials Science and Engineering, Pennsylvania State University, Pennsylvania 16802, USA
⁵Materials Research Centre, Indian Institute of Science, Bangalore 560012, India
⁶Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁷Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
⁸Institute of Physics of the Czech Academy of Sciences, 18221 Prague 8, Czech Republic
⁹Departmento de Ciencias de la Tierra y Física de la Materia Condensada, Universidad de Cantabria, 39005 Santander, Spain
¹⁰Materials Research and Technology Department, Luxembourg Institute of Science and Technology (LIST), 5 avenue des Hauts-Fourneaux, L-4362 Esch/Alzette, Luxemburg
¹¹Department of Physics and Materials Science, University of Luxembourg, Rue du Brill 41, L-4422 Belvaux, Luxembourg
¹²Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom
¹³Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
¹⁴Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA