1s2p resonant inelastic X-ray scattering combined dipole and quadrupole analysis method

Abstract

In this study an analysis strategy towards using the resonant inelastic X-ray scattering (RIXS) technique more effectively compared with X-ray absorption spectroscopy (XAS) is presented. In particular, the question of when RIXS brings extra information compared with XAS is addressed. To answer this question the RIXS plane is analysed using two models: (i) an exciton model and (ii) a continuum model. The continuum model describes the dipole pre-edge excitations while the exciton model describes the quadrupole excitations. Applying our approach to the experimental 1s2p RIXS planes of VO and TiO, it is shown that only in the case of quadrupole excitations being present is additional information gained by RIXS compared with XAS. Combining this knowledge with methods to calculate the dipole contribution in XAS measurements gives scientists the opportunity to plan more effective experiments.

1s2p RIXS Calculations for 3d Transition Metal Ions in Octahedral Symmetry

“…The 1s2p RIXS cross-section at the first quadrupole peak shows three peaks in qualitative agreement 14 Journal of Spectroscopy Figure 14. Bagger et al analysed the quadrupole and dipole RIXS separately [1]. We note that the ionic limit as calculated in Figure 14 is likely to be reached by 1s2p RIXS experiments at the K-edge on divalent calcium systems (Ca 2+ ), including octahedral CaO and cubic CaF 2 .…”

“…Because the point group O 3 (resp., O h ) contains the inversion, a parity information should be added for gerade or ungerade to the term, + or − for the atomic (spherical) terms, and g or u for the crystal field terms. The 3d N initial state and the intermediate state 1s 1 3d N + 1 in 1s2p RIXS are gerade (g), and the final state 2p 5 3d N + 1 is, due to the open 2p shell, ungerade. In the following, the parity of the spherical term will be omitted for simplicity.…”

“…In other words, for 1s2p RIXS, the selection rules are the conditions for which the matrix elements f T 2 n and n T 1 i in the Kramers-Heisenberg equation (1) are nonzero. The operators T 1 and T 2 describe the interaction of the photon with matter.…”

“…When spin-orbit coupling (SOC) and crystal field are both to be included, there are in principle two ways to derive the term symbols: (1) by first deriving the branching of the uncoupled atomic terms (with ℒ and S) in O h symmetry and then by deriving the spin-orbital coupling or (2) by first deriving the atomic J quantum number in the ℒ S coupling scheme and then deriving the branching of the J value in the O h point group. Both methods yield identical final results and the identical ground state for a given Hamiltonian (see, e.g., Figure 2).…”

“…The 1s2p RIXS plane related to excitations at the edge can be explained from a convolution of the 1s XAS spectral shape and the 1s2p nonresonant XES spectral shape [1,2].…”