Comparison of resonant inelastic x-ray scattering spectra and dielectric loss functions in copper oxides

We report empirical comparisons of $\text{Cu}K$-edge indirect resonant inelastic x-ray scattering (RIXS) spectra, taken at the Brillouin-zone center, with optical dielectric loss functions measured in a number of copper oxides. The RIXS data are obtained for ${\text{Bi}}_2{\text{CuO}}_4$, ${\text{CuGeO}}_3$, ${\text{Sr}}_2{\text{Cu}}_3{\text{O}}_4{\text{Cl}}_2$, ${\text{La}}_2{\text{CuO}}_4$, and ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$, and analyzed by considering both incident and scattered-photon resonances. An incident-energy-independent response function is then extracted. The dielectric loss functions, measured with spectroscopic ellipsometry, agree well with this RIXS response, especially in ${\text{Bi}}_2{\text{CuO}}_4$ and ${\text{CuGeO}}_3$.

Figure 1

(Color online) (a) The $K$-edge RIXS spectra taken with four incident photon energies as a function of the scattered-photon energy $\left({\omega }_s\right)$ for ${\text{CuGeO}}_3$. Note that the inelastic intensity follows an envelope function (solid line), indicating the scattered-photon resonance. (b) The total fluorescence yield obtained near the $\text{Cu}K$-edge for ${\text{CuGeO}}_3$. Two resonance energies, ${\omega }_{\text{XAS}}$ and ${\omega }_{\text{res}}$, are noted. Similar plots for ${\text{La}}_2{\text{CuO}}_4$ are shown in (c) and (d). The RIXS data for ${\text{La}}_2{\text{CuO}}_4$ are taken from Ref. 13.

Figure 2

(Color online) Comparison of $S\left(\omega \right)$ with the measured $\text{Im}\left[-1/\epsilon \left(\omega \right)\right]$ for various cuprates. Different symbols are used to denote RIXS spectra obtained with different incident energies. These incident photon energies (in eV) are (a) 8997.5 (◼), 8998.5 (○), 8999.5 (△); (b) 8988 (◼), 8990 (○), 8992 (△), 8994 (◻); (c) 8992 (◼), 8993 (○), 8994 (△); (d) 8991 (◼), 8992 (○), 8993 (△), 8994 (◻); and (e) 8993 (◼), 8994 (○), 8995 (△). The EELS data for ${\text{CuGeO}}_3$, ${\text{La}}_2{\text{CuO}}_4$, and ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$ are taken from Refs. 29, 30, 31, respectively. Although there is no EELS spectrum for ${\text{Sr}}_2{\text{Cu}}_3{\text{O}}_4{\text{Cl}}_2$ available in the literature, that of ${\text{Ba}}_2{\text{Cu}}_3{\text{O}}_4{\text{Cl}}_2$ is shown (Ref. 32).

Figure 3

(Color online) The function $S\left(\omega \right)$ extracted from high-resolution RIXS data and compared with $\text{Im}\left[-1/\epsilon \left(\omega \right)\right]$ for (a) ${\text{La}}_2{\text{CuO}}_4$ and (b) ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$.