123Sb-NQR study of unconventional superconductivity in the filled skutterudite heavy-fermion compound PrOs4Sb12 under high pressure up to P = 3.82 GPa

We report $^{123}$Sb nuclear quadrupole resonance (NQR) measurements of the filled skutterudite heavy-fermion superconductor PrOs$_4$Sb$_{12}$ under high pressure. The temperature dependence of NQR frequency and the spin-lattice relaxation rate $1/T_1$ indicate that the crystal-electric-field splitting $\Delta_{\rm CEF}$ between the ground state $\Gamma_1$ singlet and the first excited state $\Gamma_4^{(2)}$ triplet decreases with increasing pressure. Ac-susceptibility measurements indicate that the superconducting transition temperature ($T_{\rm c}$) also decreases with increasing pressure. However, above $P$ $\sim$ 2 GPa, both $\Delta_{\rm CEF}$ and $T_{\rm c}$ do not depend on external pressure up to $P$ = 3.82 GPa. These pressure dependences of $\Delta_{\rm CEF}$ and $T_{\rm c}$ suggest an intimate relationship between quadrupole excitations associated with the $\Gamma_4^{(2)}$ level and unconventional superconductivity in PrOs$_4$Sb$_{12}$. In the superconducting state, 1/$T_1$ below $T_{\rm c}$ = 1.55 and 1.57 K at $P$ = 1.91 and 2.63 GPa shows a power-law temperature variations and are proportional to $T^5$ at temperatures considerably below $T_{\rm c}$. These data can be well fitted by the gap model $\Delta(\theta) = \Delta_0\sin\theta$ with $\Delta_0$ = 3.08 $k_{\rm B}T_{\rm c}$ and 3.04 $k_{\rm B}T_{\rm c}$ for $P$ = 1.91 and 2.63 GPa, respectively. The results indicate there exists point nodes in the gap function.