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Magnetization of a single crystalline Ce 3 Pd 20 Si 6 was measured at low temperatures down to 90 mK in fields up to 11 T for the three principal directions [100], [110], and [111]. For all directions, two transitions were observed in the temperature variation of the magnetization MðTÞ at 0.2 T; a broad peak at 0.28 K associated with a phase-III transition, and an upward bending at $0:5 K due to a phase-II ordering from the paramagnetic state (phase-I). The latter critical temperature T I{II is found to be strongly enhanced in magnetic fields B, depending on the field direction, and T I{II ðBÞ becomes highly anisotropic. These results suggest that phase-II is an antiferroquadrupole state originated from a À 8 ground state. By contrast, no appreciable anisotropy is found in the phase-III state. At 90 mK, phase-III collapses by applying a field of $0:63 T for all directions. Above this field, the magnetization curve MðBÞ becomes strongly anisotropic. The magnetization value per Ce in the phase-I region at 90 mK is apparently smaller than the À 8 moment, indicating that either 8c or 4a site has a À 7 ground state.

We have performed ultrasonic experiments on clathrate compounds ROs4Sb12 and R3Pd20Ge6 to explore rattling and tunneling of a guest rattler's motion. We have found frequency dependence of the elastic constants and ultrasonic attenuations, which is called as ultrasonic dispersion, due to thermally activated rattling. At low temperatures, Curie-type elastic softening obeying 1/T with antiferro-type intersite interaction, which corresponds to quantum tunneling, appears and continues even to the lowest 20 mK in LaOs4Sb12 and La3Pd20Ge6. The understanding of the local charge fluctuation, rattling and tunneling, being coupled to conduction electrons in metals is a basic issue in the aspect of electron-phonon interaction in strongly correlated phenomena such as heavy fermion state, superconductivity and multi-channel Kondo screening effect.

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Electric quadrupole effects in a Pr-based clathrate compound Pr3Pd20Si6 have been investigated by ultrasonic measurements. Elastic constants of (C11 − C12)/2 and C44 in Pr3Pd20Si6 show curie-type softenings with decreasing temperature below 20 K, which are described in terms of quadrupole effects of 4f-electron for the ground state either Γ3 doublet or Γ5 triplet. H -T phase diagram of Pr3Pd20Si6 under the magnetic fields along [110] is obtained from elastic anomalies in (C11 − C12)/2 mode. KEYWORDS: ultrasound, clathrate, quadrupole susceptibilityThe ternary intermetallic compounds R 3 Pd 20 X 6 ( R = rare-earth ions, X = Si, Ge ) crystallize in a cubic Cr 23 C 6 -type structure with two crystallographic inequivalent R sites of 4a and 8c. The R ion on the 4a site, with cubic O h symmetry, is located inside a cage consisting of twelve Pd ( 48h ) ions and six X ( 24e ) ions. On the other hand, R-ion on the 8c site, with cubic T d symmetry, is located inside a cage consisting of sixteen Pd ( 32f and 48h ) ions. In the clathrate compounds R 3 Pd 20 X 6 , the germanium-based R 3 Pd 20 Ge 6 ( R = Ce, Pr, Nd ) show anomalous phenomena associated with the 4f states. For instance, elastic constants of C 11 , (C 11 − C 12 )/2 and C 44 in Ce 3 Pd 20 Ge 6 with a Γ 8 ground state show a curie-type softenings. The huge softening about 50% in the transverse (C 11 − C 12 )/2 mode in particular indicates a O 0 2 -type ferro-quadrupole ordering at T Q = 1.25 K.1 Furthermore, the C 44 shows a frequency dependence and ultrasonic attenuation at around 10-30 K, which is due to a thermally activated off-center rattling of R ion in the 4a site. Since no ultrasonic dispersion has been found in C 11 and (C 11 − C 12 )/2, the rattling motion in Ce 3 Pd 20 Ge 6 accompanies a charge fluctuation with Γ 5 symmetry. 1On the other hand, Ce 3 Pd 20 Si 6 shows a heavy fermion behavior and is one of a heaviest Kondo compounds with the Sommerfeld-value of γ = 8 J/mol·K 2 . Magnetic entropy estimated from specific heat data suggests that the ground state is Γ 8 quartet for crystalline electric field (CEF) levels. Magnetic susceptibilities in Ce 3 Pd 20 Si 6 shows anomaly at around 150 mK, which relates to a heavy fermion state associated with Γ 8 quartet with multipole degrees of freedom.2 Moreover, elastic softenings of Ce 3 Pd 20 Si 6 stop around 180 mK. This result implies the appearance of a long range ordering or a Kondo singlet state under low fields at low temperatures in Ce 3 Pd 20 Si 6 . In addition, no ultrasonic dispersion in Ce 3 Pd 20 Si 6 was observed, which indicates absence of rattling. 3A Pr-based clathrate compound Pr 3 Pd 20 Si 6 has been studied by specific heat, electrical resistivity, and magnetic susceptibility. The magnetic susceptibility of Pr 3 Pd 20 Si 6 shows a kink around 50 mK. Based on a specific heat experiment on Pr 3 Pd 20 Si 6 , CEF ground states of Pr ion with Γ 3 doublet at 4a site, and Γ 5 triplet at 8c site is proposed.4 Recent neutron scattering experiments, however, proposed that the CEF ground state for 8c...