Spectroscopy of strongly correlated systems: Resonant x-ray scattering without energy resolution in the scattered beam

The total emission of photons excited by x rays (90° between incident and detected photons) is measured vs the incident photon energy at the $\mathrm{Ce}{M}_{4,5}$ edges in $\mathrm{Ce}{\mathrm{In}}_3$, $\mathrm{Ce}\mathrm{Sn}{\mathrm{In}}_2$, $\mathrm{Ce}{\mathrm{Al}}_2$, $\mathrm{Ce}{\mathrm{Pd}}_3$, and $\mathrm{Ce}{\mathrm{Rh}}_2$, and at the $\mathrm{Ni}{L}_{2,3}$ edges in NiO. The results show the signature of a second-order process; these experiments must be interpreted as genuine resonant inelastic scattering (though without energy resolution of the emitted photons) and not as absorption spectroscopy measured by the total fluorescence yield. In Ce compounds, information on bulk hybridization can thus be obtained simply and with high sensitivity. The branching ratio between the different scattering channels is also measured. This approach opens innovative perspectives in resonant inelastic x-ray scattering.

Figure 1

(Color online) Panels A–D: TES spectra (measured with a photodiode) with perpendicular incident polarization (black dotted lines) and with parallel incident polarization (red lines and middle line in gray) across the $M_{4,5}$ edges of Ce. The thin black solid lines are the XAS (drain current). Panel E: temperature effects in the $\mathrm{Ce}{\mathrm{In}}_3$ satellite above $M_5$. Panel F: effect of partial substitution of In with Sn in $\mathrm{Ce}{\mathrm{In}}_3$ in the satellite above $M_5$ (perpendicular incident polarization). In panels E and F, the $M_5$ peaks were set equal to 100. The geometry of the experiment is sketched in the inset.

Figure 2

(Color online) Valence IRRS spectra (measured with a multilayer) with perpendicular incident polarization (black dotted lines) and with parallel incident polarization (red and gray lines) across the $M_{4,5}$ edges of Ce.

Figure 3

(Color online) Lower panel: simplified total energy diagram showing the main transitions in absorption and in resonant inelastic x-ray scattering in Ce. Scattering path A in green (light gray) and path B in black. Upper panel: qualitative picture of the TES results (see the text for explanations).

Figure 4

(Color online) IRRS spectra from NiO (pellet of compressed powder). Upper panel: $L_{2,3}$ isotropic valence IRRS spectrum (i.e., summed over the incident and the outgoing polarization). Central panel: IRRS spectra in the $L_2$ region with incident perpendicular (black) and parallel polarization (red and gray); the valence and inner shell spectra are given to the same scale together with the valence linear dichroism (blue). The spectra are identified also by the labels. Lower panel: comparison between $L_2$ theoretical and experimental valence flipping ratio; the experiment is given by the red points, the theory without saturation by the thin black line, and the theory with saturation by the heavy black line.