Sum rule to evaluate the exchange energy in core-level photoemission

Abstract

A sum rule is derived that relates the exchange coupling between core and open valence shell electrons in correlated systems to the main and satellite features of their complex photoemission spectra. The principle focus of our analysis is on the photoionization of the metal $2s$ and $3s$ shells in ionic transition-metal compounds. In spite of charge-transfer and near-degeneracy effects, which may induce a considerable redistribution of the spectral weight among a manifold of configurations, this rule points out that the exchange splitting evaluated with the sum rule is equal to the value obtained with the ground-state exchange integral for the material. Application of the sum rule to ${\mathrm{MnF}}_2$ and NiO shows that the exchange integral given by the sum rule is very close to that calculated for the free ion; this shows the dominant ionic character of these materials. Deviations of the sum rule for ${\mathrm{MnF}}_2$ from the ionic exchange interaction are taken as evidence that satellite structure present in the photoemission spectra may not have been identified.