Quadrupole fluctuation and off-center rattling motion in heavy fermion superconductor PrOs4Sb12

We have made ultrasonic measurements on a filled skutterudite PrOs4Sb12 showing a heavy Fermion superconductivity at TC=1.85K. The elastic constants (C11-C12)/2 and C44 of PrOs4Sb12 exhibit low-temperature softenings below 20K down to TC, indicating a quadrupole fluctuation of Pr3+ ion. A minimum of (C11-C12)/2 in magnetic fields along the [110] direction around 8T shows a level crossing of one of a excited Γ4(2) triplet to a ground state Γ1 singlet. An ultrasonic dispersion in (C11-C12)/2 around 30K suggests a thermally activated off-center rattling of Pr ion in a cage of Sb-icosahedron. The observed relaxation time shows the Arrhenius-type temperature dependence τ=τ0exp(E/kBT) with an attempt time τ0=8.8x10-11s and an activation energy E=168K. The charge fluctuation of the off-center motion and the quadrupole fluctuation of the 4f electron may participate in the formation of the heavy fermion and the superconductivity in PrOs4Sb12