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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 present results of specific heat measurements on a Ce3Pd20Si6 single crystal and construct the magnetic phase diagram for the three cubic principal directions [100], [110] and [111]. The highly anisotropic phase diagram is discussed and can be qualitatively explained by the Zeeman splitting at the 8c-site. For B ‖ [100], the present study found two different quadrupolar ordered phases, which meet the paramagnetic phase at a tri-critical point and establish the new phase boundaries.

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We have investigated the quadrupole ordering of 4f-electrons and the rattling motion of guest rare-earth ions in the clathrate compound Pr 3 Pd 20 Ge 6 using ultrasonic measurements. The elastic constants ðC 11 À C 12 Þ=2 and C 44 exhibit considerable softening at low temperatures. A minimum of ðC 11 À C 12 Þ=2 at T Q1 ¼ 0:25 K indicates antiferroquadrupole ordering associated with a À 3 doublet of a crystal-field ground state at the 8c site, while a minimum of C 44 at T Q2 ¼ 60 mK indicates the ferroquadrupole ordering of a À 5 triplet of a crystal-field ground state at the 4a site. The antiferroquadrupole phase depending on magnetic field direction shows a highly anisotropic behavior. The fieldinduced ordered phase due to the level crossing of the CEF ground state at the 8c site in magnetic fields along the [001] direction has been found. Furthermore, for the elastic constant C 44 and the attenuation coefficient 44 we found a frequency dependence at two different temperatures of 15 and 25 K, which we describe in terms of the Debye-type dispersion with an Arrhenius-type relaxation time ¼ 0 expðE=k B T Þ for two different activation energies of E L ¼ 102 K and E H ¼ 198 K. These ultrasonic dispersions are caused by the thermally activated rattling motions of guest rare-earth Pr 3þ ions at the 4a site of Pr 3 Pd 20 Ge 6 .