Quadrupole Ordering and Rattling Motion of Clathrate Compound Pr3Pd20Ge6

Abstract

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 ( C 11 - C 12 )/2 and C 44 exhibit considerable softening at low temperatures. A minimum of ( C 11 - C 12 )/2 at T Q1 = 0.25 K indicates antiferroquadrupole ordering associated with a Γ 3 doublet of a crystal-field ground state at the 8c site, while a minimum of C 44 at T Q2 = 60 mK indicates the ferroquadrupole ordering of a Γ 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 field-induced 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 α 44 we found a frequency dependence at two different temperatures of 15 and 25 K, which ...