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 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 .

Magnetic ordering of hyperfine-coupled nuclear and4f-electron moments in the clathrate compoundPr3Pd20Ge6Iwakami1, Namisashi2, Abe3 et al. 2014Phys. Rev. B3010View full textAdd to dashboardCite

“…Therefore, the susceptibility behavior between 30 and 60 mK can be attributed to an abrupt increase in relaxation time from τ 1/ω to τ 1/ω. In ultrasonic measurements of Pr 3 Pd 20 Ge 6 , it was reported that the attenuation coefficient of the C 44 mode increases around 60 mK, and the elastic constant C 44 at 20 mK shows hysteresis during a field change below 0.4 T [22]. These results support the idea that the complicated susceptibility behavior was because of dissipation phenomena caused by the 5 triplet ground state at the 4a site.…”

“…The field dependence of the peak temperature and the negative λ 4a indicate that the AFM ordering of the 5 triplet at the 4a site occurs at T N1 . It is possible that this transition corresponds to that observed by ultrasound measurements at T Q2 [22]. The difference in transition temperatures of these two measurements may be caused by a sample dependence because the R 3 Pd 20 X 6 phase possesses a very narrow homogeneous range [27].…”

“…The Pr-based compound Pr 3 Pd 20 Ge 6 shows quadrupole order of 4f electrons and rattling motions of Pr atoms at the 4a site [22]. The CEF level schemes of Pr 3+ ions at the 4a and 8c sites, as determined by inelastic neutron scattering and magnetization experiments, are 5 (0 K)-3 (5.4 K)-4 (50 K)-1 (113 K) and 3 (0 K)-5 (6 K)-4 (46 K)-1 (111 K), respectively [23,24].…”

“…According to ultrasound measurements of Pr 3 Pd 20 Ge 6 at zero magnetic field [22], the elastic constants (C 11 − C 12 )/2 and C 44 exhibited considerable softening below 10 K and showed minima at T Q1 = 250 mK and T Q2 = 60 mK, respectively. The analysis of elastic constants indicated that the minima at T Q1 and T Q2 were ascribed to the AFQ ordering of the 3 doublet at the 8c site and the FQ ordering of the 5 triplet at the 4a site, respectively.…”

“…The single crystal used in our investigation was from the same batch of high-quality samples, grown by a floating zone method, for which ultrasound measurements were reported [22]. The sample, about 4 × 4 × 6 mm 3 in size, was cooled with a copper nuclear demagnetization refrigerator and a 3 He-4 He dilution refrigerator down to 500 μK.…”