Rigorous results for Auger-electron and appearance-potential line shapes in energy bands with orbital degeneracy.

Abstract

A theory for Auger-electron spectroscopy (AES) and appearance-potential spectroscopy (APS) is presented for interacting electrons in degenerate energy bands described in the framework of a generalized multiband model. The model is aimed at electron systems (3d transition metals, 4f rare earths, . . .), the physical properties of which are strongly influenced by correlation effects. Both types of spectroscopy are based on the same two-particle spectral density. It is shown that, independently of the theoretical model applied, integrated AE and AP intensities are determined by the density-density correlation function 〈n${\mathrm{^}}_{\mathit{i}}$n${\mathrm{^}}_{\mathit{i}}$〉, where n${\mathrm{^}}_{\mathit{i}}$= ${\mathit{tsum}}_{\mathit{m}}$ ${\mathit{n}}_{\mathit{i}\mathit{m}\mathrm{\ensuremath{\sigma}}}$ is the total occupation number operator (m is the band index). In the case of spin-resolved AES and APS, which are relevant to the study of magnetic materials, the integrated intensities obey the correlation function 〈m${\mathrm{^}}_{\mathit{i}}$n${\mathrm{^}}_{\mathit{i}}$〉, where m${\mathrm{^}}_{\mathit{i}}$= ${\mathit{tsum}}_{\mathit{m}}$ (${\mathit{n}}_{\mathit{i}\mathit{m}\mathrm{\ensuremath{\uparrow}}}$-${\mathit{n}}_{\mathit{i}\mathit{m}\mathrm{\ensuremath{\downarrow}}}$) is the spin polarization operator. The two-particle spectral density is rigorously calculated within the multiband model for the two limiting cases of empty and fully occupied energy bands, allowing an exact calculation of the direct correlations between the two excited electrons (holes). For not too weak Coulomb interactions, the AE (AP) spectrum consists of a broad, rather unimportant ``band part'' and several satellites. The latter refer to situations where the two excited particles propagate as tightly bound pairs through the lattice. Both intraband and interband satellites are observed. As soon as they are split off from the ``band part,'' they take away almost the full spectral weight. The simple self-convolution model for the two-particle spectral density proves to be inappropriate for treating strongly-correlated-electron systems.