The data we used in this report is obtained from a RIXS experiment on La1.675Eu0.2Sr0.125CuO4. The data have been pre-processed: (1) The spectra are fitted using a 4-gaussian-1-background model, and the elastic signal has been subtracted. (2) intensities are normalized to dd excitations. (3) spectra are shifted so that the elastic peak is located at zero energy loss.
The post-processed RIXS intensities from 0 to 100 meV consists of three components: (1) charge order excitations contribution around 20 meV and disperses up; (2) an acoustic phonon (bond-buckling) mode at around 50 meV; (3) another acoustic phonon (bond-stretching) mode at around 70-90 meV. There could be other unknown contributions of course, but to simplify the analysis, we can assume the charge excitations and the phonon signals dominate
where $T$ is the temperature, $q$ is the momentum transfer, and $\omega$ is the energy loss. Judging from the data, the charge excitations dominates at around H = 0.24 r.l.u., while at H = 0.15 r.l.u. it starts to fade away. Due to the nature of RIXS, the intensity is usually not characterized by the susceptibility. But for now the suceptibility could probably be an approximation.
If we study the temperature dependence of the phonon siganl, we know that it barely depends on the temperature. In RIXS process, the intensity of the phonon is proportional to the Bose factor $(1 - e^{-E/T})$, where in our case $E \geq 50$ meV (about 500 K). In this case, the Bose factor changes by less than $1\%$ going from 21K to 155K, which is effectively negligible. Therefore, we can assume that the temperature dependence only comes from the charge excitations.
A possible pitfall due to data analysis: We subtracted the elastic signal in the preprocess, but this subtraction is not perfect, leading to under or over subtraction. Therefore, the at low energy (lower than the resolution, roughly 20 meV), should be dealt with carefully.
In this report, we use the intensity at 155 K as a benchmark, subtract the intensity at other temperatures from it, and study the intensity difference.
Because phonon intensity varies only marginally between 21 K and 155 K in this energy range, the subtraction largely cancels the phonon background, so the residual signal is expected to highlight mainly the temperature-dependent charge-excitation contribution.
