Antiferroquadrupolar ordering and magnetic-field-induced phase transition in the cage compound PrRh2Zn20

Abstract

To investigate the origin of a phase transition at ${T}_{\mathrm{Q}}=0.06$ K simultaneously occurring with a superconducting transition in a cage compound PrRh${}_{2}$Zn${}_{20}$, we carried out ultrasonic measurements on a single-crystalline sample. The transverse modulus (${C}_{11}\ensuremath{-}{C}_{12}$)/2 is intimately coupled to the non-Kramers ground doublet ${\ensuremath{\Gamma}}_{3}$, and elastic softening is observed at low temperatures. Below ${T}_{\mathrm{Q}}$, the softening stops, suggesting the disappearance of quadrupole degrees of freedom. We clarified the negative quadrupole-quadrupole coupling constant and reentrant behavior of ${T}_{\mathrm{Q}}(H)$ in a magnetic field $H$. These results reveal that the phase transition at ${T}_{\mathrm{Q}}$ is antiferroquadrupolar ordering. The anisotropic magnetic field-temperature phase diagram is determined for $H\ensuremath{\parallel}[100]$, [110], and [111]. A magnetic-field-induced phase transition is newly found at high fields in all three field directions. We also observed ultrasonic dispersion at around 50 K owing to the rattling motion of Zn atoms at the 16$c$ site, and pointed out the strong electron-phonon coupling in PrRh${}_{2}$Zn${}_{20}$.