Localization of magnetic circular dichroic spectra in transmission electron microscopy experiments with atomic plane resolution

Inelastic electron scattering is a consequence of mostly Coulomb interaction between electrons in the sample and electron beam and, as such, it is a nonlocal event. In atomic resolution experiments, it thus opens the following question: How far is the origin of the inelastic scattering signal that is observed when the electron beam is passing nearby an atomic column or plane? We analyze computationally the delocalization of the magnetic signal in electron magnetic circular dichroism (EMCD) experiments in the so-called three-beam orientation, allowing one to image individual atomic planes. We compare the classical EMCD setup using the double-difference procedure (DD-EMCD) to a recently introduced atomic plane resolution EMCD (APR-EMCD) geometry, assuming the same probe size. We observe a strong localization of the EMCD signal to the closest atomic plane, confirming the potential of EMCD to study an evolution of magnetic properties near surfaces or interfaces with atomic plane resolution. The localization of the EMCD signal is remarkably higher than the localization of the nonmagnetic component of the inelastic scattering cross section. We also analyze double-channeling effects and find them particularly strong for the DD-EMCD method, while for APR-EMCD they appear to be minor. The DD-EMCD signal, on the other hand, appears to be more robust with respect to sample thickness than that of the APR-EMCD.