Combined Cumulant and Ligand Field Multiplet Theory approach to X-ray spectra

Theoretical treatments of electronic correlations in open shell systems are notoriously difficult, especially in condensed matter systems. While ligand field multiplet theory (LFMT) has been extremely successful in treating the effects of these correlations in x-ray spectra, the theory is in many cases highly parameterized, and although recent progress has been made [1], the approach is not fully ab initio. In addition, multiplet based methods ignore itinerant states and associated excitations, e.g., plasmon excitations. The cumulant expansion for the one-electron Green's function has been shown to treat these itinerant, quasi-bosonic excitations exceptionally well, producing near quantitative agreement with experimental results.  Here we propose an approximation to combine the cumulant approach with LFMT to treat local and itinerant states in x-ray spectra. The approach is inspired by previous developments which have used DMFT to treat the effects of correlation [2]. The cumulant is calculated with a real-time TDDFT approach, which relates the quasi-bosoni excitation spectrum to the density induced by the sudden appearance of the core-hole. We calculate the XPS of Fe₂O₃ and find good agreement with experiment, both in the peaks related to multiplet splitting, in shake-up satellite peaks, and in the broad background produced by low energy itinerant excitations. The real-time approach allows an analysis of the shake-up excitations in terms of charge oscillations dominated by transfer between ligand states and the minority spin channel of the metal atoms.

[1] M. W. Haverkort, M. Zwierzycki, and O. K. Andersen, Phys. Rev. B 85, 165113 (2012)

[2] M. Casula, A. Rubtsov, and S. Biermann, Phys. Rev. B 85, 035115 (2012)