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

Hasan Ali1, Jan Rusz2, Daniel E Bürgler3

  • 1Department 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.

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|December 3, 2023
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Summary

Electron magnetic circular dichroism (EMCD) measurements can be biased by noisy signals, complicating magnetic moment quantification. This study uses bootstrapping to quantify EMCD errors and proposes guidelines to minimize bias in nanoscale magnetic moment estimation.

Keywords:
BootstrappingElectron energy loss spectroscopyElectron magnetic circular dichroismError analysisNoise dependent biasScanningTransmission electron microscopy

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Electron Microscopy

Background:

  • Electron magnetic circular dichroism (EMCD) offers nanoscale, element-specific magnetic moment analysis.
  • Weak EMCD signals and precise quantification requirements pose significant challenges.
  • Accurate magnetic moment estimation is crucial for understanding magnetic materials.

Purpose of the Study:

  • To investigate the impact of signal noise on magnetic moment quantification using EMCD.
  • To develop a method for estimating noise-dependent errors in EMCD measurements.
  • To provide guidelines for minimizing bias in EMCD-based magnetic moment calculations.

Main Methods:

  • Application of bootstrapping, a statistical resampling technique, to experimental EMCD data.
  • Utilizing Monte Carlo simulations to generate error distributions.
  • Analysis of EMCD sum rules applied to body-centered cubic (bcc) iron in a 3-beam orientation.

Main Results:

  • Empirical estimation of noise-dependent error distributions in EMCD sum rule applications.
  • Experimental observation of signal noise preferentially biasing magnetic moment estimations.
  • Validation of bias through Monte Carlo simulations.

Conclusions:

  • Noisy EMCD signals introduce significant bias in magnetic moment quantification.
  • Bootstrapping provides a reliable method for assessing EMCD measurement uncertainties.
  • Guidelines are proposed to improve the accuracy and reliability of nanoscale magnetic moment determination via EMCD.