Electron energy loss spectroscopy of core-electron excitation in anisotropic systems: Magic angle, magic orientation, and dichroism

A general theory for the detection of the core-level electronic excitation in anisotropic systems using angular integrated electron energy-loss spectroscopy (EELS) has been presented. Magic angle conditions, at which spectra are independent of specimen orientation, are proved to be valid for all anisotropic systems. Discrepancies in the magic angle determination are thoroughly investigated from the theoretical point of view. The magic angle electron energy loss spectroscopy (MAEELS) can be directly interpreted as spherical averaged spectroscopy. From the explicit expression for the EELS cross section for all the anisotropic systems, a magic specimen orientation is also found to exist in certain low symmetry systems, where spectra acquired are also equivalent to the fully orientationally averaged spectra. Our analysis provides a useful guide for the experimental determination of electronic structure information in anisotropic systems, including their dichroic signals.