Rattling and tunneling of off-center local oscillator in clathrate compounds

We have investigated an off-center local oscillator of a guest atom in cage of clathrate compounds R3Pd20Ge6 (R=La, Ce, Pr, Nd) and a filled skutterudite PrOs4Sb12 using ultrasonic measurements. The observation of ultrasonic dispersions in transverse C44 mode of R3Pd20Ge6 and in transverse (C11-C12)/2 mode of PrOs4Sb12 revealed the rattling of the off-center oscillator characterized by a relaxation time with Arrhenius-type temperature dependence. A low-temperature softening of C44 in La3Pd20Ge6 below 3 K down to 20 mK and a softening of (C11-C12)/2 in PrOs4Sb12 above the heavy Fermion superconducting transition indicate the charge fluctuation due to the degenerate off-center oscillators.