Highly anisotropic strain dependencies in PrIr$_2$Zn$_{20}$

We report thermal expansion and magnetostriction of the cubic non-Kramers system PrIr$_2$Zn$_{20}$ with a non-magnetic $\varGamma_{3}$ ground state doublet. In previous experiments, antiferroquadrupolar order at \hbox{$T_{\mathrm{Q}}=0.11$\,K} and a Fermi liquid state around $B_{\mathrm{c}}\approx5$\,T for \hbox{$\boldsymbol{B}\parallel[001]$}, indicative of possible ferrohastatic order, were discovered. For magnetic fields \hbox{$\boldsymbol{B}\parallel[001]$}, the low temperature longitudinal and transverse thermal expansion and magnetostriction are highly anisotropic. The resulting volume strain is very small, indicating that the Pr valence remains nearly constant as a function of magnetic field. We conclude that the Fermi liquid state around $B_{\mathrm{c}}$ forms through a very little change in c-f hybridization. This result is in sharp contrast to Ce- and Yb-based Kramers Kondo lattices which show significantly larger volume strains due to the high sensitivity of the Kondo temperature to hydrostatic pressure.