Probing magnetic-field-induced multipolar ordering through field-angle-resolved magnetostriction and thermal expansion in PrIr${}_2$Zn${}_{20}$

We performed field-angle-resolved magnetostriction and thermal-expansion measurements on PrIr${}_2$Zn${}_{20}$, a cubic non-Kramers compound exhibiting antiferroquadrupolar order below $T_{\mathrm{Q}}=0.125$ K. Thermal expansion exhibits two qualitatively different anomalies under magnetic fields applied along the $[001]$ direction, providing experimental support for the existence of an intermediate A phase previously reported. Furthermore, comparison between the experimental results and theoretical modeling indicates a strong anisotropic coupling of the $O_{20}$ quadrupolar moment, which plays a key role in stabilizing the A phase. These findings demonstrate that multipolar states in non-Kramers systems can be effectively tuned by magnetic-field orientation, providing insights into the anisotropic nature of quadrupolar interactions.