Kondo scaling of $4f$-electron states and the Kondo singlet breakdown in heavy fermions

TL;DR

This study uses bulk-sensitive RIXS spectroscopy combined with SIAM calculations to quantitatively verify Kondo scaling and the breakdown of the Kondo singlet in 4f-electron systems like CeSi$_2$, revealing temperature-dependent spectral weight changes.

Contribution

It demonstrates the effectiveness of RIXS as a bulk probe for Kondo physics, providing a quantitative method to determine the Kondo temperature and observe singlet breakdown.

Findings

RIXS spectra show a decrease in $f^0$ occupancy with increasing temperature.

Spectral weight shifts in $f^n$ states match SIAM calculations.

Results reveal Kondo singlet breakdown and magnetic state occupation at higher temperatures.

Abstract

The low-energy spin- and charge-sensitive thermodynamic properties of a broad range of strongly correlated 4f-electron systems follow Kondo scaling, with a characteristic Kondo temperature, $T_K$. While the theory is known for thermodynamic properties and high-energy spectroscopies of Kondo materials, the surface sensitivity of electron spectroscopy limits the extent to which Kondo scaling can be quantitatively verified. In this study, bulk-sensitive photon-in photon-out temperature-dependent resonant inelastic X-ray scattering (RIXS), in combination with single-impurity Anderson model (SIAM) calculations, is used to provide quantitative evidence of low- and high-energy Kondo scaling in CeSi$_2$. RIXS Ce M$_5$-edge spectra show a clear decrease in the occupancy of the $f^0$ state as temperature increases accompanied by an increase of the spectral weight of the $f^1\underline L^1$ state, in good agreement with the SIAM calculations. The results demonstrate the breakdown of the Kondo singlet state, coupled with thermal occupation of the low-lying first-excited magnetic states. The RIXS data reveal a temperature evolution of the $f^n$ spectral weights, which is in stark contrast to that extracted from photoemission and inverse photoemission spectroscopies. This study provides an accurate spectroscopic method to determine the Kondo energy $k_B$$T_K$ that is consistent with thermodynamic measurements, and highlights soft X-ray RIXS as a quantitative bulk probe of low- and high-energy-scale hybridization effects in strongly correlated materials.