Ultrasonic Study of rattling in clathrate compounds

1)我们以前在重费米子超导体ProS_4Sb_(？)12&gt；中观察到了声学弥散Si_6n。此外，在4K以下发现了与1/T成正比的弹性软化，温度T_c=1.85K，这归因于笼中Pr离子的偏心隧穿。这些结果支持了PrS_4Sb_&lt；12&gt；2)Ru替代Pr(Os_&lt；1-x&gt；Rux)_4Sb_&lt；12&gt；结果表明，随着Ru掺杂浓度的增加，超声弥散的Si6n逐渐减弱，并在BCS超导体PrRu_4Sb_(？)我们提出偏心隧穿和传导电子之间的耦合将导致ProS_4Sb_(12)&gt；12&gt；中的重费米子态和超导电性。3)我们研究了没有4f电子的LaOS_4Sb_&lt；12&gt；，以研究碎裂和4f电子之间的关联。观察到C&lt；11和Gt；中超声弥散的Si6N，t…更多的HAT意味着在没有4f电子的情况下出现嘎嘎声。4)用三个4f电子测量了nDOS_4Sb_(12)&Gt；的弹性常数。C&lt；11&gt；在40K和15K附近观察到两个明显的超声弥散Si6N。这一结果表明，在笼子中形成了非谐势的多重结构，表现为两个不同的激活能E和特征时间τ_0。5)在低温下，我们观察到C&lt；11&gt；和C&lt；44&gt；与1/T成正比的弹性软化。根据四极极化率的分析，我们确定了4f^3电子态的晶场能级的基态是Γ_4Sb；67&gt；四重态。结果表明，La_3Pd_t；20&gt；Si_6和Ce_3Pd_t；20&gt；Si_6中没有超声弥散，这与我们以前的研究结果相反。7)我们观察到Ce_3Pd；20&gt；Si_6中的(C_&lt；11&gt；-C_&gt；12&gt；)/2和C_&lt；44&gt；在低温下的弹性软化与1/T成正比。我们用四极磁化率得到了晶场能级，分别为8c位的Γ_8 1/4位和4a位的Γ_7二重态。此外，我们还揭示了磁场中反铁-四极有序相的存在。较少

1)We previously observed ultrasonic disperSi_6n due to rattling in heavy-fermion superconductor PrOs_4Sb_<12>. Furthermore, elastic softening proportional to the 1/T was found below 4 K down to T_c=1.85 K, which is attributed to off-center tunneling of Pr ion in a cage. These results support that the strong correlation between rattling/tunneling and heavy-fermion and it's superconductivity in PrOs_4Sb_<12>.2)We have made ultrasonic experiments of the Ru substitutional Pr(Os_<1-x>RuX)_4Sb_<12>. As a result, ultrasonic disperSi_6n becomes weak with more substitution of Ru concentration and completely disappears in BCS superconductor PrRu_4Sb_<12>. We proposed that the coupling between the off-center tunneling and conduction electrons will cause the heavy-fermion state and superconductivity in PrOs_4Sb_<12>.3)We have examined LaOs_4Sb_<12> without 4f-electron in order to investigate the correlation between rattling and 4f electrons. Ultrasonic disperSi_6n in C_<11> was clearly observed, t … More hat means rattling appears without 4f-electron. We conclude that the coupling between off-center mode and surrounding conduction electrons is crucial for the rattling and tunneling.4)We have measured elastic constants of NdOs_4Sb_<12> with three 4f electrons. Two distinct ultrasonic disperSi_6ns around 40 K and 15 K were observed in C_<11>. This result indicates that multiple structure of anharmonic potential is formed in a cage as it were, illustrated by two deferent activation energy E and characteristic time τ_0 of the rattling in NdOs_4Sb_<12>.5)We have observed elastic softening of C_<11> and C_<44> proportional to the 1/T at low temperatures in NdOs_4Sb_<12>. According to the analysis using quadrupolar susceptibility, we confirmed that the ground state of the crystal field levels of 4f^3 electronic state is Γ_<67> quartet in NdOs_4Sb_<12>.6)We have performed ultrasonic measurements of isomorphic compound La_3Pd_<20>Si_6 and Ce_3Pd_<20>Si_6 to study rattling and tunneling. As a result, no ultrasonic dispersions were found in La_3Pd_<20>Si_6 and Ce_3Pd_<20>Si_6 contrary to our previous results of R_3Pd_<20>_Ge6. Here we report that the importance of the conduction bands as well as clathrate structure for the occurrence of rattling and tunneling.7)We have observed elastic softening of (C_<11>-C_<12>)/2 and C_<44> proportional to the 1/T at low temperatures in Ce_3Pd_<20>Si_6. We obtained crystal field levels by use of quadrupolar susceptibility to be a Γ_8 quarter ground at 8c site and a Γ_7 doublet ground at 4a site, respectively. Furthermore, we revealed that the presence of antiferro-quadrupolar ordering phase in magnetic fields. Less