Elemental Dilution Effect on the Elastic Response of the Non-Kramers Systems $\rm{Y{1-{\it x}}Pr{{\it x}}Ir{2}Zn{20}}$

$\rm{Pr{\it T}_{2}{\it X}_{20}}$ ($T$ = transition metal, $X$ = Al, Zn, and Cd) systems, which crystallize in the cubic $\rm{CeCr_{2}Al_{20}}$-type structure ($Fd\bar{3}m, O^{7}_{h}, {\rm No. 227}$), show exotic phenomena such as quadrupolar Kondo effect and quadrupolar-fluctuation driven superconductivity. These compounds have a non-Kramers doublet crystalline electric field ground state in which the $\Gamma_{3}$-type electric quadrupoles can be active. The title compound $\rm{PrIr_{2}Zn_{20}}$ is one of this series showing antiferroquadrupolar and superconducting transitions occur at $T_{{\rm Q}}$ = 0.11 K and $T_{{\it c}}$ = 0.05 K, respectively. In addition, the Y-dilution effect has also been studied systematically. In particular, on the Y-diluted limit system ${\rm Y_{0.966}Pr_{0.034}Ir_{2}Zn_{20}}$ (Pr-3.4% system), the elastic constant $\left(C_{11}-C_{12}\right)/2$, corresponding to $\Gamma_{3}$-symmetry multipolar response, shows a logarithmic temperature dependence, which corresponds to the theoretical calculation based on the “single-site” quadrupolar Kondo effect.
　In the present study, we measured $\left(C_{11}-C_{12}\right)/2$ of the intermediate Pr concentration system $\rm{Y_{0.63}Pr_{0.37}Ir_{2}Zn_{20}}$ (Pr-37% system) by means of ultrasound between 0.04 K to 120 K to reveal how the single-site quadrupolar Kondo effect is modulated by increasing the Pr concentration from the dilute limit. The Curie-like softening of $\left(C_{11-}C_{12}\right)/2$ above 2 K of the present Pr-37% system can be reproduced by a calculation taking into account the contribution of the electric quadrupole $O_{v}$ and hexadecapole $H_{v}$ assuming the $\Gamma_{3}$ crystalline electric field ground state. Further on cooling below 0.15 K, a temperature dependence proportional to $+\sqrt{T}$ is observed, which rather corresponds to a theoretical calculation using a quadrupolar Kondo ''lattice'' model. In addition, we found a low-energy ultrasonic dispersion in the temperature region 0.15 K $\leq T \leq$ 2 K, which was not observed in the Pr-3.4% system. The low-energy ultrasonic dispersion suggests the presence of a low-energy phonon excitation whose energy scale is close to that of the quadrupolar Kondo effect. A similar low-energy ultrasonic dispersion has also been found in the non-Kramers $\Gamma_{3}$ doublet system ${\rm PrMg_{3}}$, in which a coupling between the low-energy phonons and the non-Kramers doublet has been suggested. Assuming the coupling also exists in the present Pr-37\% system, it can be expected that the phonon excitation and the quadrupolar Kondo effect are related. We discuss the Y-dilution effect on the quantum state at very low temperatures and show a detailed analysis of the low-energy ultrasonic dispersion.