Quadrupolar effect and rattling motion in the heavy-fermion superconductorPrOs4Sb12

Abstract

The elastic properties of a filled skutterudite PrOs 4 Sb 12 with a heavy fermion superconductivity at T C ϭ1.85 K have been investigated. The elastic softening of (C 11 ϪC 12 )/2 and C 44 with lowering temperature down to T C indicates that the quadrupolar fluctuation due to the CEF state plays a role for the Cooper paring in superconducting phase of PrOs 4 Sb 12 . A Debye-type dispersion in the elastic constants around 30 K revealed a thermally activated ⌫ 23 rattling due to the off-center Pr-atom motion obeying ϭ 0 exp(E/k B T) with an attempt time 0 ϭ8.8ϫ10 Ϫ11 s and an activation energy Eϭ168 K. It is remarkable that the charge fluctuation of the off-center motion with ⌫ 23 symmetry may mix with the quadrupolar fluctuation and enhance the elastic softening of (C 11 ϪC 12 )/2 just above T C .The rare-earth cubic compounds based on Pr 3ϩ ions have received much attention because various unusual properties are expected at low temperatures. The system with a non-ϪJ y 2 favors a quadrupole ordering. We refer the ⌫ 3 ground state systems as a metallic compound PrPb 3 showing the antiferro-quadrupole ordering at T Q ϭ0.4 K 1 and a semiconductor PrPtBi undergoing ferroquadrupole ordering at T Q ϭ1.2 K. 2 PrSb is known as a singlet ground state system. 3 The elastic constant (C 11 ϪC 12 )/2 is responsible for the quadrupolar susceptibility of O 2 0 and O 2 2 with ⌫ 3 symmetry, while C 44 is for the susceptibility of O yz ϭJ y J z ϩJ z J y , O zx ϭJ z J x ϩJ x J z , O xy ϭJ x J y ϩJ y J x with ⌫ 5 symmetry. The softening of (C 11 ϪC 12 )/2 and C 44 is useful proof to clarify the quadrupolar effects of Pr-based compounds.Recently, Bauer et al. have found a new-type of the heavy-fermion superconductor in a filled skutterudite PrOs 4 Sb 12 with space group T h 5 (Im3). 4 The heavy fermion state with a large specific heat coefficient ␥ϭ750 mJ/mol K 2 of PrOs 4 Sb 12 exhibits the superconducting transition at T C ϭ1.85 K associated with a large jump ⌬C/T C ϳ500 mJ/mol K 2 . A sign of the double transition in the specific heat has been found. 5 The thermal transport measurement in fields suggests the two distinct superconducting phases in PrOs 4 Sb 12 . 6 The nuclear spin relaxation rate 1/T 1 of Sb indicates unconventional superconductivity possessing neither a coherence peak nor a T 3 -power law. 7 The muon spin relaxation in PrOs 4 Sb 12 yields a penetration depth indicating a new type of energy gap. 8 The odd-parity Cooper pairing mediated by the quadrupole fluctuation is argued as unconventional heavy-fermion superconductivity in PrOs 4 Sb 12 . 9 Because the magnetic susceptibility is rather silent to distinguish non-magnetic ⌫ 23 doublet from ⌫ 1 singlet, it has not been settled whether the CEF ground state of PrOs 4 Sb 12 is ⌫ 23 doublet or ⌫ 1 singlet. 4,10 The measurement of (C 11 ϪC 12 )/2 and C 44 responsible for the quadrupolar sus-ceptibility in PrOs 4 Sb 12 is a central issue to clarify the CEF state and the interplay of the quadrupolar fluctuation to the superconductivity in PrOs 4 Sb 12 .

Simultaneous Measurements of Elastic Constant and Resistivity near the Tc of Non-BCS-Type Superconductor PrOs4Sb12

“…We obtained an activation energy of E = 221 K and attempt time τ 0 = 29 ns from the Arrhenius plot ( Fig. 1 (b)), which is consistent with the previous report by Goto et al [15]. We conclude that the bulk quality of the specimen used in the present study is good enough consistent with previous reports.…”

“…UD is seen at around 40 K for the frequency range between 30 MHz and 250 MHz, which is consistent with the previous reports [15,18]. Thus far, UD has been understood phenomenologically as a Debye-type dispersion formula,…”

“…In this case, several ultrasonic modes, e.g., longitudinal C 11 and transverse C 44 , could be mixed together due to the reflection of the waves from the sides of the specimen. Indeed, it is reported that large softening was observed in C 44 [15]. Thus, the softening of C 11 in the 30 MHz data may be caused by an accidentally mixed C 44 mode.…”

“…By means of ultrasonic measurements, rattling can also be observed as a frequency dependent elastic anomaly and an increase in ultrasonic attenuation, which are collectively called ultrasonic dispersion (UD) [14,15]. UD has been found even in non-4f systems such as LaOs 4 Sb 12 and La 3 Pd 20 Ge 6 [16,17].…”

“…The origin of the softening in these non-4f systems is considered to be a quantum tunneling state of the guest ion. It is reported that the elastic constant (C 11 -C 12 )/2 of PrOs 4 Sb 12 shows UD at around 30 K and exhibits a softening from 20 K to 2K and a leveling off just below T c [15]. The features of the softening and the leveling off cannot be explained only by CEF effect, thus, the presence of a quantum tunneling state of the guest ion has been considered.…”