Effective Operator for $dd$ Transitions in Nonresonant Inelastic X-ray Scattering

TL;DR

This paper develops an effective operator framework for interpreting nonresonant inelastic X-ray scattering ($dd$ transitions), enabling better analysis of local excitations and ground state properties in materials.

Contribution

It introduces a general effective operator approach for $dd$ transitions in nonresonant IXS, linking experimental observables to ground state information.

Findings

Operators explain nodal directions in IXS

Different operators can be probed via momentum dependence

Framework aids in extracting ground state info from IXS

Abstract

Recent experiments by Larson et al. demonstrate the feasibility of measuring local $dd$ excitations using nonresonant inelastic X-ray scattering (IXS). We establish a general framework for the interpretation where the $dd$ transitions created in the scattering process are expressed in effective one-particle operators that follow a simple selection rule. The different operators can be selectively probed by employing their different dependence on the direction and magnitude of the transferred momentum. We use the operators to explain the presence of nodal directions and the nonresonant IXS in specific directions and planes. We demonstrate how nonresonant IXS can be used to extract valuable ground state information for orbiton excitations in manganite.