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 .

Elastic constant measurements on iron pnictide Ba(Fe 0:9 Co 0:1 ) 2 As 2 with an optimal superconducting transition temperature of T SC ¼ 23 K have been performed by the ultrasonic pulse echo method. The shear elastic constant of C 66 associated with elastic strain " xy reveals considerable softening of 21% below 300 K down to T SC and becomes increasing in the superconducting phase below T SC , while other shear elastic constants of ðC 11 À C 12 Þ=2 and C 44 show no sign of softening below 80 K down to 4.2 K. The electric quadrupole O v 0 existing in the degenerate d y 0 z and d zx 0 bands participates in the superconductivity of the present iron pnictide system. KEYWORDS: layered iron pnictide, superconductor, Ba(Fe 0:9 Co 0:1 ) 2 As 2 , elastic softeningThe discovery of the superconductor LaFeAs(O 1Àx F x ) with a high transition temperature of T SC ¼ 26 K by Hosono's group triggered thousands of research works pursuing FeAs-based superconductors with various chemical composites and different structures.1) Five crystal structures with a common iron-based layer structure are now known.2)The high transition temperatures of up to 55 K and high critical magnetic fields beyond 50 T have already been realized.3,4) Among these FeAs-based crystals, the tetragonal compound of Ba(Fe 1Àx Co x ) 2 As 2 , in particular, has received much attention, because large single crystals are available for the investigation of physical properties depending on crystal anisotropy. 5)The end-material BaFe 2 As 2 exhibits a simultaneous transition of structural transition from a tetragonal TrCr 2 Si 2 -type structure of space group D orbitals by Co 2þ with 3d 7 orbitals in Ba(Fe 1Àx Co x ) 2 As 2 reduces both the structural transition temperature of T s and the antiferromagnetic one of T N .8) The superconductivity emerges in the systems above x ¼ 0:03 at the temperatures of T SC below the structural point T s and the antiferromagnetic one T N . The quantum critical point, x QCP , where both structural and antiferromagnetic phases die out, exists in the proximity of x ¼ 0:07. The optimum superconducting temperatures of T SC ¼ 23 K are achieved with x ¼ 0:10, which is a slightly excess of the quantum critical concentration x QCP . The superconductivity vanishes in the highly doped region of x ¼ 0:17.The Fermi surfaces of iron pnictides arise from Fe-3d orbitals and have three hole bands at a À-point and two electron bands at an X-point. These bands consist primarily of d y 0 z and d zx 0 with À 5 under tetragonal symmetry and d x 02 Ày 02 with À 3 .9) The increasing of the Fermi level upon electron doping due to the substitution of Fe with Co reduces the three sheets of hole bands around the À point in the endmaterial BaFe 2 As 2 to two sheets of hole bands in the present Ba(Fe 0:9 Co 0:1 ) 2 As 2 . We adopt the electric quadrupole associated with the degenerate d y 0 z and d zx 0 orbital states to describe elastic properties of the compound Ba(Fe 1Àx Co x ) 2 -As 2 . It is noted that the coordinates x 0 and y 0 of the quadrupole are ori...

No abstract

No abstract