Magic Angle Electron Energy Loss Spectroscopy (MAEELS) of core electron excitation in anisotropic systems

A general theory for the core-level electron excitation of anisotropic systems using angular integrated electron energy-loss spectroscopy has been derived. We show that it is possible to define a magic angle condition at which the specimen orientation has no effect on the electron energy-loss spectra. We have not only resolved the existing discrepancy between different studies of the magic angle condition, but also extended its applicability to all anisotropic systems. We have demonstrated that magic angle electron energy loss spectroscopy is equivalent to the orientation averaged EELS, although the specimen remains stationary. Our analysis provides the theoretical framework for the comparison between theoretical calculation and experimental measurement of core-level electron excitation spectra in anisotropic systems. In addition to MAEELS, we have also discovered a magic orientation condition which will also give rise to orientationally averaged spectra. It's relation with the magic angle X-ray absorption spectroscopy and magic angle spinning nuclear magnetic resonance is demonstrated.