Sb-NQR probe for multipole degree of freedom in the first Pr-based heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$

We report $^{121,123}$Sb nuclear quadrupole resonance (NQR) measurements in the filled-skutterudite superconductor PrOs$_4$Sb$_{12}$ in the temperature range of 0.05-30 K. The electric field gradients (EFG), $V_{zz}$ and $V_{xx}-V_{yy}$, at the Sb site exhibit unusual temperature dependence below 30 K. To explain these features, we discuss the coupling between the Sb nuclear quadrupole moment and Pr $4f^2$-derived multipole moments. The observed $T$ dependence of EFG is well explained by the CEF quasi-quartet consisted of $Γ_1$ singlet and $Γ_4^{(2)}$ triplet states in the cubic point group $T_h$. These results, in turn, are indicative of the importance of the coupling between the $^{121,123}$Sb quadrupole moments and the hexadecapole moment caused by the quasi-quartet.