Single-site quadrupolar Kondo effect in a diluted non-Kramers doublet system Y$_{1-x}$Pr$_x$Ir$_2$Zn$_{20}$ for $x = 0.028$ viewed from magnetization
A diluted non-Kramers doublet system Y$_{1-x}$Pr$_x$Ir$_2$Zn$_{20}$ is a promising candidate for exhibiting single-site quadrupolar (two-channel) Kondo effect. We have measured temperature-dependent magnetization of a sample for $x$ = 0.028 down to 0.1 K at various constant magnetic fields to extract the characteristic behaviors due to the quadrupolar Kondo effect. The Curie--Weiss fit to the magnetic susceptibility between 50 and 300 K yields a negative paramagnetic Curie temperature of $-$7.0 K, indicative of on-site antiferromagnetic interaction. The magnetization divided by magnetic field, $M(T)/B$, at $B = 0.5$ T is saturated to a constant value below 3 K. On the contrary, in higher magnetic fields of $B$ = 1 and 2 T, $M(T)/B$ exhibits $-$ln$T$ dependence from 1 to 0.1 K, which temperature dependence is consistent with that of the quadrupolar susceptibility detected from ultrasonic measurements. The $-$ln$T$ form of $M(T)/B$ appears to reflect the behavior of quadrupolar susceptibility, through the magnetic-field-induced magnetic moment due to the mixing of the non-Kramers doublet and crystalline-electric-field excited states of Pr$^{3+}$. In $B$ = 4 T, $M(T)/B$ approaches a constant on cooling below 0.3 K, because of the quenching of the quadrupoles in the field-induced singlet ground state.