Kondo resonance in PrTi${}_2$Al${}_{20}$: Photoemission spectroscopy and single-impurity Anderson model calculations

The Kondo resonance at the Fermi level is well established for the electronic structure of Ce (4$f^1$ electron) and Yb (4$f^1$ hole) -based systems. In this work, we report complementary experimental and theoretical studies on the Kondo resonance in the Pr-based 4$f^2$ system, PrTi${}_2$Al${}_{20}$. Using Pr 3$d$-4$f$ resonant photoemission spectroscopy and single-impurity Anderson model (SIAM) calculations including the full multiplets of Pr ions, we show that a 4$f^2$ system can also give rise to a Kondo resonance at the Fermi level. The Kondo resonance peak is experimentally observed through a final-state multiplet-dependent resonance and is reproduced with properly tuned hybridization strength in SIAM calculations.

Figure 1

Pr 3$d$-4$f$ XAS spectra of PrTi${}_2$Al${}_{20}$ and Pr metal in comparison with those calculated by the SIAM with the hybridization strength $V=0.55$ eV and the atomic multiplet model for the Pr${}^{3+}$ ion. The labels $A$–$J$ indicate the selected photon energies at which the resonant PES spectra in Figs. 2 and 3 are measured.

Figure 2

Pr 3$d$-4$f$ resonant PES spectra of PrTi${}_2$Al${}_{20}$ (a) and Pr metal (b) measured at the incident energies labeled on XAS spectra in Fig. 1. The solid and dashed gray lines indicate the main peak position of the $f^1$ final state and the lower-$E_{\mathrm{B}}$ shoulder, respectively.

Figure 3

High-resolution Pr 3$d$-4$f$ resonant PES spectra measured at the incident energies $C$, $F$, and $G$ labeled on XAS spectra in Fig. 1 for PrTi${}_2$Al${}_{20}$ (a) and Pr metal (b), along with the corresponding spectral DOS obtained by dividing the resolution-convoluted FDD function. The shaded area shows the region of $E_{\mathrm{B}}<-5k_{\mathrm{B}}T$.

Figure 4

The SIAM simulations for Pr ($f^2$) systems. (a) Calculated Pr 4$f$ PES spectra as a function of $V$. (b) PES and BIS spectra. (c) The $V$ dependence of the distribution of 4$f$ weights (left axis) and the 4$f$ electron count $n_f$ (right axis).