Quantitative near-atomic-resolution oxidation-state mapping in complex oxide heterostructures by electron energy-loss spectroscopy
We present a theoretical framework for quantitative oxidation state mapping of transition-metal and rare-earth elements from near-atomic-resolution electron energy-loss spectroscopy (EELS) in complex oxide heterostructures. The total inelastic differential cross section of transition-metal L$_{2,3}$ and rare-earth M$_{4,5}$ edges is calculated by combining the relaxed Dirac-Hartree-Fock ionization cross section with ligand-field multiplet theory for the discrete transitions. We apply the approach to two correlated-oxide heterostructures, La$_{0.67}$Sr$_{0.33}$MnO$_3$/LaCr$_{0.2}$Mn$_{0.2}$Fe$_{0.2}$Co$_{0.2}$Ni$_{0.2}$O$_3$/SrTiO$_3$ and NdNiO$_3$/La$_{0.67}$Sr$_{0.33}$MnO$_3$/NdGaO$_3$, which include a wide range of transition-metal and rare-earth elements with overlapping features. The method resolves the oxidation states of Cr, Mn, Fe and Co and identifies the Ni contribution within the LaCr$_{0.2}$Mn$_{0.2}$Fe$_{0.2}$Co$_{0.2}$Ni$_{0.2}$O$_3$ layer at near-atomic resolution. We find predominantly Co$^{2+}$ together with mixed Mn$^{2+}$/Mn$^{3+}$/Mn$^{4+}$ character, indicating site-specific valence redistribution within the layer. We also separate overlapping spectral features, such as La-M$_{4,5}$ and Ni-L$_{2,3}$ edges in the NdNiO$_3$/La$_{0.67}$Sr$_{0.33}$MnO$_3$/NdGaO$_3$ heterostructure, thereby recovering the intrinsic Ni-L$_{2,3}$ excitation spectrum. We find that the effective Ni valence in NdNiO$_3$ deviates from the simple ionic picture. More broadly, this work establishes a generic method for quantitative valence mapping from near-atomic-resolution EELS, applicable to a wide range of experimental conditions for the study of local electronic structure of complex oxides.