Ultrashort Lifetime Expansion for Indirect Resonant Inelastic X-ray Scattering

TL;DR

This paper derives an effective scattering cross section for indirect RIXS that simplifies calculations by integrating out intermediate states, revealing how charge and spin contributions can be tuned via photon energy.

Contribution

It introduces a novel method to simplify RIXS analysis by removing intermediate states, applicable to multi-band systems and varying core-hole potentials.

Findings

Effective cross section expressed as a resonant factor times charge and spin response functions.

Asymptotically exact results for strong and weak core-hole potentials.

Ability to tune charge and spin spectral weights by incident photon energy.

Abstract

In indirect resonant inelastic X-ray scattering (RIXS) an intermediate state is created with a core-hole that has a ultrashort lifetime. The core-hole potential therefore acts as a femtosecond pulse on the valence electrons. We show that this fact can be exploited to integrate out the intermediate states from the expressions for the scattering cross section. By this we obtain an effective scattering cross section that only contains the initial and final scattering states. We derive in detail the effective cross section which turns out to be a resonant scattering factor times a linear combination of the charge response function $S({\bf q},\omega)$ and the dynamic longitudinal spin density correlation function. This result is asymptotically exact for both strong and weak local core-hole potentials and ultrashort lifetimes. The resonant scattering pre-factor is shown to be weakly temperature dependent. We also derive a sum-rule for the total scattering intensity and generalize the results to multi-band systems. One of the remarkable outcomes is that one can change the relative charge and spin contribution to the inelastic spectral weight by varying the incident photon energy.