  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.
