X-ray Emission Spectroscopy of Cerium Across the $\gamma \mathrm{\text{−}}\alpha$ Volume Collapse Transition

High-pressure x-ray emission measurements are used to provide crucial evidence in the longstanding debate over the nature of the isostructural ($\alpha$, $\gamma$) volume collapse in elemental cerium. Extended local atomic model calculations show that the satellite of the $L\gamma$ emission line offers direct access to the total angular momentum observable $⟨J^2⟩$. This satellite experiences a 30% steplike decrease across the volume collapse, validating the Kondo model in conjunction with previous measurements. Direct comparisons are made with previous predictions by dynamical mean field theory. A general experimental methodology is demonstrated for analogous work on a wide range of strongly correlated $f$-electron systems.

Figure 1

(a) The full Ce $L{\gamma }_1$ emission line as measured experimentally and calculated by the extended atomic model. All theory spectra are shifted by a constant $E_0=175\mathrm{eV}$ and broadened by convolution with a 5 eV Lorentzian form. (b) Comparison of the calculated shoulder intensity of the $L{\gamma }_1$ emission line with the instantaneous (bare) $⟨J^2⟩$ moment. Both decrease with growing hybridization with the shoulder intensity dropping slightly faster than the moment. (c) A close-up of the satellite region revealing the steplike nature of the VC process. The closeup also shows the virtually identical lineshapes for all the pressures below the VC (2.6, 6.0, and 6.3 kbar) and—with a reduced satellite—above the VC (15.2, 22, and 45 kbar). The lines are well fit by a sum of two Lorentzians in the spectral region of interest and the black curve shows the contribution of the main peak in the shoulder region. The calculated spectra with and without hybridization are displayed, showing that this extension outside the atomic limit effectively captures the spectral evolution through the VC.

Figure 2

Comparison of experimental data with DMFT predictions. Left axis: Comparison of the normalized shoulder intensity (data points with error bars) with predictions for the angular quantum number $⟨J^2⟩$ (dashed line), which has been normalized with regard to its atomic value. The predicted $⟨J^2⟩$ changes in the opposite direction than does the data. The thick line through the XES data points is a guide for the eye. Right axis: Number of $4f$ electrons $n_f$. The previous experimental results (large squares) show a drop of 20%, while predicted $n_f$ (solid line) decreases only slightly across the VC. Note that the satellite intensity roughly follows the previous measurement of $n_f$, with the drop in intensity being slightly larger. The modified atomic calculations predict this greater drop in satellite intensity in comparison to $n_f$, just as they do in comparison to $⟨J^2⟩$, as shown in Fig. 1b.