The Magic Angle "Mystery" in Electron Energy Loss Spectroscopy: Relativistic and Dielectric Corrections

TL;DR

This paper investigates the relativistic and dielectric corrections affecting the magic angle in electron energy loss spectroscopy, revealing additional higher-order and macroscopic effects that influence the interpretation of spectra for heavy elements.

Contribution

It introduces a new correction term of order (Zα)^2 and discusses how macroscopic electrodynamic effects can alter the magic angle's sample-independence.

Findings

Additional (Zα)^2 correction significant for heavy elements

Macroscopic effects can break the magic angle's sample-independence

Relativistic effects can be explained by refined matrix element treatment

Abstract

Recently it has been demonstrated that a careful treatment of both longitudinal and transverse matrix elements in electron energy loss spectra can explain the mystery of relativistic effects on the {\it magic angle}. Here we show that there is an additional correction of order $(Z\alpha)^2$ where $Z$ is the atomic number and $\alpha$ the fine structure constant, which is not necessarily small for heavy elements. Moreover, we suggest that macroscopic electrodynamic effects can give further corrections which can break the sample-independence of the magic angle.