Non-Kramers doublet ground state in a quaternary cubic compound PrRu₂In₂Zn₁₈ investigated by ultrasonic measurements

We performed ultrasonic measurements on a quaternary cubic compound PrRu$_{2}$In$_{2}$Zn$_{18}$ to explore the ground state properties derived from non-Kramers $\Gamma_{3}$ doublet of Pr$^{3+}$. PrRu$_{2}$In$_{2}$Zn$_{18}$ is a quaternary derivative of the ternary compound PrRu$_{2}$Zn$_{20}$ that exhibits a structural phase transition at $T_{\rm S}$ = 138 K. In PrRu$_{2}$In$_{2}$Zn$_{18}$ the Zn atoms at the 16c site in PrRu$_{2}$Zn$_{20}$ are selectively replaced by In atoms. A monotonic increase was observed in the temperature dependence of elastic constants $C_{\mathrm{L}} = (C_{11}+2C_{12}+4C_{44})/3$ and $C_{\mathrm{T}} = (C_{11}-C_{12}+C_{44})/3$ in the temperature range around $T_{\rm S}$ to which an elastic softening was observed in $(C_{11}-C_{12})/2$ for PrRu$_2$Zn$_{20}$. The disappearance of the softening indicates that the structural transition in PrRu$_2$Zn$_{20}$ is suppressed by the substitution of Zn ions by In ones with a larger ionic radius. Alternatively, the $C_{\mathrm{T}}$ of PrRu$_{2}$In$_{2}$Zn$_{18}$ exhibits a precursor Curie-type elastic softening toward low temperatures being responsible for the non-Kramers $\Gamma_{3}$ ground state. We discuss the ground state and the evolution of the elastic properties of the different single-crystal samples of PrRu$_{2}$In$_{2}$Zn$_{18}$ grown under different conditions.