Intermediate valence in Yb compounds probed by 4$f$ photoemission and resonant inelastic x-ray scattering

Experimental data from $4f$ photoemission and resonant inelastic x-ray scattering experiments on the intermediate valent compound YbRh${}_2$Si${}_2$ have been compared with results of theoretical simulations. It was found that the high-energy excitations inherent to these techniques affect the spectral intensities related to different $4f$ configurations differently. Although the final states in $4f$ photoemission and x-ray absorption or resonant inelastic x-ray scattering are rather unalike, a comparable influence was found for both cases. Higher occupied $4f$ shells seem to be energetically favored in the excited states and appear overemphasized in the spectrum as compared to the ground state. For a quantitative Yb valence determination from x-ray spectroscopies, diagrams are suggested that seem to be applicable also for other intermediate valent Yb compounds.

Figure 1

(a) Experimental $4f$ photoemission spectra from an intermediate valent Yb and an intermediate valent Ce compound (gray shaded area) compared with predictions made by (b) the ground-state picture, i.e., neglecting final-state effects [Eq. (2)], (c) taking into account final-state effects [Eq. (4)] with zero VB width, and (d) a more realistic model with a finite VB width. The used model parameters were ${\epsilon }_f=-0.05$ eV, $\Delta =0.3$ eV for Yb, ${\epsilon }_f=-1.5$ eV, $\Delta =1$ eV for Ce, and $U_{ff}=$7 eV.

Figure 2

Energy scheme of the excitation and the decay processes in the RIXS experiment.

Figure 3

(a) $4f$ photoemission spectra simulated within the SIAM for three different hybridization strengths $\Delta$. (b) Dependence of the relative intensity of the 2$+$ ($4f^{14}\to 4f^{13}$) component on the Yb valence in the ground state. The dotted line shows the prediction made by the GSP [Eq. (3)], and the filled circles show the results of our simulations. They are well described by a cubical polynomial [red dashed line, Eq. (8)].

Figure 4

(a) Evolution of the calculated spectral intensity along the CXE cut with increasing $\Delta$. (b) Relative intensity of the 2$+$ resonance line in the CEE and the CXE scans as a function of Yb valence in the ground state. The open circles show the results of our simulations, and the dotted lines the prediction made by the GSP.

Figure 5

(a) Zoom-in into a part of the 3$+$ multiplet for a series of spectra, taken with increasing photon energy, revealing considerable lineshape variations. (b) Intensity changes with photon energy of the 3$+$ multiplets assigned to subsurface and deeper (bulk) Yb layers. (c) Relative contribution of the subsurface Yb layer to the overall $4f$ photoemission with increasing photon energy.

Figure 6

Subsurface and bulk parts of the $4f$ plus VB photoemission from YbRh${}_2$Si${}_2$ as obtained by comparison between low- and high-photon-energy data.

Figure 7

(a) TFY-XAS and RIXS spectra in CEE mode of YbRh${}_2$Si${}_2$ at $T=10$ K. (b) Intensity map of the Yb $L{\alpha }_1$ fluorescence yield as a function of excitation and transferred energy. Broadening of the resonances in $x$ and $y$ is given by the lifetimes of the $2p$ and $3d$ core holes, respectively. The CEE and CXE cuts through the maximum of the 2$+$ resonance are indicated by the lines of white and red (gray) circles, respectively. (c) Emission intensity along the CXE cut indicated in (b). (d) Given by the $2p$ lifetime broadening and the excitation energy separation of the 2$+$ and 3$+$ resonances, the latter is reduced to 13$\%$ intensity in the CXE scan as compared to its intensity in the 3$+$ maximum.

Figure 8

Experimental RIXS data for YbRh${}_2$Si${}_2$ at $T=10$ K and results of SIAM simulations for hybridization strength $\Delta =0.26$ eV. The CEE and CXE cuts are shown as blue and red lines running across and horizontal, respectively.