Towards atomic resolution EELS of anisotropic materials

Abstract

We present a quantification scheme for the analysis of electron energy-loss spectra of materials with magnetic or crystalline anisotropy. The acquisition of such spectra in a dedicated scanning transmission electron microscope yields nanoscale information, consistent with operating with a coherent electron nanoprobe. A model is presented to analyze the effect of the localized probe on the core-level electron energy-loss spectra of uniaxial materials. The resulting cross-section can be expressed as a linear superposition of a product of (a) a term dependent on the scattering geometry and (b) one involving the overlap of initial and final wave functions. The numerical evaluation of (a) shows that, under certain conditions of convergence and acceptance angle, significant differences in the observed inelastic scattering can be expected. We discuss this in terms of the momentum transfer dependence and the coherent contribution to the electron energy-loss cross-section. The quantification procedure is then applied in two cases. It is firstly used to simulate the experimental variation with probe position of the core level 1s to 2p π ∗ intensity of carbon within a nanotube and good agreement is observed. At the very edge of the nanotube, there is a discrepancy between our theory and the experimental result, which maybe related to the neglect of channeling effects and/or the effect of surface absorbates. In the next case, the two components of the dielectric function in the antiferromagnetic compound Hematite (α-Fe 2O 3) are extracted from two spectra acquired with different convergence angles. From the resulting difference spectrum, the orientation of the Fe magnetic moments is deduced to be perpendicular to the trigonal axis in this crystal, consistent with simulation by atomic multiplet structure model taking into account of the quantification procedure. The success in both cases opens the way for the study of anisotropic electronic structure at high spatial resolution – an example would be the imaging of changes in spin orientation at domain walls.