Kondo Interactions from Band Reconstruction in ${\mathrm{YbInCu}}_4$

We combine resonant inelastic x-ray scattering and model calculations in the Kondo lattice compound ${\mathrm{YbInCu}}_4$, a system characterized by a dramatic increase in Kondo temperature and associated valence fluctuations below a first-order valence transition at $T\simeq 42\mathrm{K}$. The bulk-sensitive, element-specific, and valence-projected charge excitation spectra reveal an unusual quasigap in the Yb-derived state density which drives an instability of the electronic structure and renormalizes the low-energy effective Hamiltonian at the transition. Our results provide long-sought experimental evidence for a link between temperature-driven changes in the low-energy Kondo scale and the higher-energy electronic structure of this system.

Figure 1

Color plot of the $\mathrm{Yb}\text{−}{L}_3$ RIXS plane with the absorption spectrum (solid white line) measured at (a) 70 and (b) 35 K, and (d) calculated for the LT phase using the SIAM and scaled to the experimental intensity. (c) The difference between the spectra measured at 35 and 70 K. The excitation labels ($A$), ($B$), ($C$), ($D$) correspond to the transitions in Fig. 2.

Figure 2

(a) Band diagram showing the occupied and unoccupied Yb $d$ DOS used in the SIAM and the transitions assigned to RIXS peaks. (b) Total energy level scheme for a mixed-valence Yb ion, with radiative transitions in the SIAM and calculated RIXS and XAS spectral functions and their ${\mathrm{Yb}}^{2+}$ and ${\mathrm{Yb}}^{3+}$ components.

Figure 3

Incident energy resolved RIXS profile measured at 35 and 70 K across the 8948.5–8952.5 eV (a) and 8958.5–8962.5 eV (c) incident energy ranges, which, respectively, correspond to the ${\mathrm{Yb}}^{2+}$ and ${\mathrm{Yb}}^{3+}$ components in the LT XAS spectrum. In (a), the filled and open triangles indicate the peak position of ($A$) and ($B$) at 35 and 70 K, respectively. The ${\mathrm{Yb}}^{3+}$ spectra in (c) are intensity scaled by 0.4 for comparison with ${\mathrm{Yb}}^{2+}$ in (a), and for each incident energy the HT spectra are normalized to the area of the LT spectra over the 0.5–5.0 eV range to ease the comparison between the low-energy features. The raw RIXS spectra averaged over these respective incident energy ranges are shown in (b) and (d) along with the corresponding calculated spectra for the LT phase. In (b), the arrows indicate the direction of variations in the RIXS intensity upon cooling from 70 to 35 K.

Figure 4

(a) Schematic illustration of the nonrigid shift of the Yb $5d$ band across the transition. The shift towards lower binding energies is about twice for the shoulder in the unoccupied states around 1.5 eV than for the occupied states, as inferred from the 0.2 eV blueshift of ($A$) and 0.2 eV redshift of ($B$) in the RIXS data. (b) The Fermi level moves out of the quasigap while the Yb $5d$ Fermi DOS [Fig. 2] sharply increases at LT.