Noise-dependent bias in quantitative STEM-EMCD experiments revealed by bootstrapping

Hasan Ali; Jan Rusz; Daniel E Bürgler; Roman Adam; Claus M Schneider; Cheuk-Wai Tai; Thomas Thersleff

doi:10.1016/j.ultramic.2023.113891

Noise-dependent bias in quantitative STEM-EMCD experiments revealed by bootstrapping

Ultramicroscopy. 2024 Mar:257:113891. doi: 10.1016/j.ultramic.2023.113891. Epub 2023 Nov 24.

Authors

Hasan Ali¹, Jan Rusz², Daniel E Bürgler³, Roman Adam³, Claus M Schneider³, Cheuk-Wai Tai⁴, Thomas Thersleff⁴

Affiliations

¹ Department of Materials Science and Engineering, Uppsala University, Box 534, Uppsala 751 21, Sweden; Department of Materials and Environmental Chemistry, Stockholm University, Stockholm 106 91, Sweden; Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany. Electronic address: ali.hasan@angstrom.uu.se.
² Department of Physics and Astronomy, Uppsala University, Box 516, Uppsala 751 20, Sweden.
³ Peter Grünberg Institut, Forschungszentrum Jülich GmbH, Jülich D-52425, Germany.
⁴ Department of Materials and Environmental Chemistry, Stockholm University, Stockholm 106 91, Sweden.

PMID: 38043363
DOI: 10.1016/j.ultramic.2023.113891

Abstract

Electron magnetic circular dichroism (EMCD) is a powerful technique for estimating element-specific magnetic moments of materials on nanoscale with the potential to reach atomic resolution in transmission electron microscopes. However, the fundamentally weak EMCD signal strength complicates quantification of magnetic moments, as this requires very high precision, especially in the denominator of the sum rules. Here, we employ a statistical resampling technique known as bootstrapping to an experimental EMCD dataset to produce an empirical estimate of the noise-dependent error distribution resulting from application of EMCD sum rules to bcc iron in a 3-beam orientation. We observe clear experimental evidence that noisy EMCD signals preferentially bias the estimation of magnetic moments, further supporting this with error distributions produced by Monte-Carlo simulations. Finally, we propose guidelines for the recognition and minimization of this bias in the estimation of magnetic moments.

Keywords: Bootstrapping; Electron energy loss spectroscopy; Electron magnetic circular dichroism; Error analysis; Noise dependent bias; Scanning; Transmission electron microscopy.