Theoretical description of near edge EELS and XAS spectra

Abstract

2014 In this communication I want to briefly describe the contents of the talk I presented at the lake Tahoe EELS conference. Since most of what I talked about has or will appear in print in another form, I will restrict myself to very brief descriptions of in my view relevant basic ideas and supply a list of references in which more details can be found. First of all it is important to recognize the similarities and différences between high energy electron energy loss spectroscopy (EELS) and X-ray absorption spectroscopy (XAS). If we neglect the exchange terms in EELS the differential cross-section for energy loss is given by [1] dÇ2dE (7reao)2q2 1 ~(q,03C9)] where e(g, w) is the dielectric function and q is the scattering vector of the incident high energy electrons. We will be dealing with core level spectroscopy and the near edge structure for which Re é(q, '-'J),-v 1 and IM ~(q,03C9)«1 and d 2 0 3 C 3 d 0 3 A 9 d E c 1 -iq·r|i > 12b (hw -Ef + Ei) -1 f 1 q -r 1 i >126 (hW -Ef + Ei) which describes transitions from an initial state Wi to a final state 03A8f which now involve the exci-tation of a core electron to the valence band. For high incident energies and small q the result is similar to that of optical absorption (XAS) 7(XAS) ~ | fie. r|i > |203B4 (hw -Ef + Ei) where the scattering vector q in EELS plays the role of the polarization vector of the light E in XAS. The différences lie primarily in the different characteristics of an electron and a photon beam. a) EELS incident energy can be chosen and at high energy is less surface sensitive than XAS b) Iql can be varied in EELS changing selection scales from dipole to quadrupole and allowing Article available at AS # 0 transitions via the exchange terms. c) An electron source can be easily focused to a very small region (atomic resolution) d) XAS causes less radiation damage in general and can be applied to bulk crystals whereas EELS is limited to thin films e) Photons can be circularly polarized which is interesting for magnetic circular dichroism. We will limit ourselves to dipole selection rules keeping in mind the possibilities of looking at dipole forbidden transitions with EELS. The dipole selection rules are AL = ±1, OS = 0 or AJ = ±1, 0 where AL, 0394S and AJ are the orbital, spin and total angular momenta changes between initial and final states. This means that the choice of the core electron state determines