Goldstone-mode phonon dynamics in the pyrochlore Cd2Re2O7

We have measured the polarized Raman scattering spectra of Cd2Re2O7, the first superconducting pyrochlore, as a function of temperature. For temperatures below the cubic-to-tetragonal structural phase transition (SPT) at 200 K, a peak with B1 symmetry develops at zero frequency with divergent intensity. We identify this peak as the first observation of the Goldstone phonon in a crystalline solid. The Goldstone phonon is a collective excitation that exists due to the breaking of the continuous symmetry with the SPT. Its emergence coincides with that of a Raman-active soft mode. The order parameter for both features derives from an unstable doubly degenerate vibration (with Eu symmetry) of the O1 atoms which drives the SPT.     

Superconducting properties of the pyrochlore oxide Cd2Re2O7

We report the superconducting properties of the pyrochlore oxide Cd₂Re₂O₇. The bulk superconducting transition temperature T_c is about 1.0 K, and the upper critical field H_c2 determined by the measurement of specific heat under magnetic fields is 0.29 T. The superconducting coherence length is estimated to be 34 nm. Specific heat data measured on single crystals suggest that the superconducting gap of Cd₂Re₂O₇ is nodeless.     

Metallic "ferroelectricity" in the pyrochlore Cd2Re2O7

A class of materials known as "ferroelectric metals" was discussed theoretically by Anderson and Blount in 1965 [Phys. Rev. Lett. 14, 217 (1965)]], but to date no examples of this class of materials have been reported. Here we present measurements of the elastic moduli of Cd2Re2O7 through the 200 K cubic-to-tetragonal phase transition. A Landau analysis of the moduli reveals that the transition is consistent with Cd2Re2O7 being classified as a ferroelectric metal in the weaker sense described by Anderson and Blount (loss of a center of symmetry). First-principles calculations of the lattice instabilities indicate that the dominant lattice instability corresponds to a twofold degenerate mode with E(u) symmetry and that motions of the O ions forming the O octahedra dominate the energetics of the transition.     

Temperature dependence of the magnetic penetration depth in YBa2Cu3O6.95

We report precision transverse fieldSR measurements of the internal field distribution in the vortex state of crystalline YBa₂Cu₃O_6.95. A novel low background apparatus was used to study a mosaic sample of three high quality single crystals (T_c=93.3K). The observed frequency spectra in magnetic fields of 5kG and 15 kG applied along the c-axis have the characteristic features expected for a regular vortex lattice with some additional broadening. From a preliminary analysis we find that [(0)/(T)]² has a linear temperature coefficient forT<30 K. Such a term is inconsistent with simple s-wave pairing in the superconducting state. These results support recent microwave measurements of(T) on similar crystals in zero applied field but differ significantly from previousSR reports on sintered powders and crystals with lower T_c.This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

Pressure effects on the transition temperature and the magnetic field penetration depth in the pyrochlore superconductor RbOs2O6

Magnetization measurements under hydrostatic pressure up to 8 kbar in the pyrochlore superconductor RbOs2O6 (T(c) approximately or equal 6.3 K at p=0) were carried out. A positive pressure effect on T(c) with dT(c)/dp=0.090(3) K/kbar was observed, whereas no pressure effect on the magnetic penetration depth lambda was detected. The pressure independent ratio 2 Delta(0)/k(B)T(c)=3.72(2) (Delta(0) is the superconducting gap at zero temperature) was found to be close to the BCS value 3.52. Magnetization and muon-spin rotation measurements of lambda(T) indicate that RbOs2O6 is an adiabatic s-wave BCS-type superconductor. The value of lambda extrapolated to zero temperature and ambient pressure was estimated to be 230(30) nm.     

Electronic bandstructures on 5d-transition metal pyrochlore: Cd2Re2O7 and Cd2Os2O7

The electronic bandstructure calculations for Cd₂Re₂O₇ and Cd₂Os₂O₇ are performed by using an FLAPW method based on the local density approximation, where the spin–orbit interactions are taken into account. It is found that the spin–orbit interaction changes significantly Re/Os-5d (t_2g) band dispersion situated near the Fermi level. Cd₂Re₂O₇ is a semi-metal, the Fermi level is located just in the valley, the specific heat coefficient is calculated as 2.7 mJ/K² mol Re and the carrier number is 0.039/cell in each hole and electron. The Re/Os-5d bands hybridize well with the O-p bands so that the Re/Os-5d component significantly appears even in the bottom of the wide O-p bands. Therefore, it is important to consider Re-5d O-p hybridization to investigate the physical properties of these compounds.     

Effective "penetration depth" in the vortex state of a d-wave superconductor

The temperature and the field dependence of the effective magnetic penetration depth (lambdaeff) in the vortex state of a d-wave superconductor, as measured by muon spin rotation (muSR) experiments, is calculated using a nonlocal London model. We show that at temperatures below [EQUATION: SEE TEXT], the linear T dependence of lambda-2eff crosses over to a T3 dependence. This could provide an explanation for the low temperature flattening of the lambda-2eff curve observed in a recent muSR experiment.     

Temperature and magnetic field dependences of the London penetration depth and coherence length in the vortex state of YBa2Cu3O7-\delta

We report TF‐μ⁺SR measurements of the London penetration depth in the high‐T_c superconductor YBa₂Cu₃O_7-\delta as a function of temperature T and magnetic field H. The magnetic field distribution in high quality single crystals of YBa₂Cu₃O_6.95 was fit assuming a triangular vortex lattice with an average in‐plane penetration depth \lambda_ab=1155(3) Å, extrapolated to zero temperature and magnetic field. We find that \lambda_ab(T,H) increases linearly both as a function of magnetic field and temperature in the field range studied. This unusual behaviour is attributed to an unconventional pairing scheme in which there are line nodes in the superconducting energy gap function. Measurements have also been made on a deoxygenated sample, YBa_2Cu_3O_6.60. The lineshapes for YBa₂Cu₃O_6.60 clearly show the high‐field cutoff due to the finite coherence length \xi_ab. A preliminary analysis indicates that \xi_ab(T,H) increases linearly as a function of temperature and decreases with increasing magnetic field.     

Dielectric relaxation and ferroelectricity in Cd2Nb2O7 pyrochlore

The dielectric dispersion of Cd₂Nb₂O₇ pyrochlore in a weak electric field was studied in a broad frequency range (100 Hz to 13 MHz) using the crystal samples slowly cooled (0.5 K/min) in the temperature interval from 300 to 80 K. As the temperature decreased down to T _c=196 K and T _max～190 K, the dielectric permittivity exhibited deviation from the Curie-Weiss law. It is suggested that this behavior is related to the development of a short-range correlation between microscopic polar regions formed at T→T _max ⁺ . The local order parameter q(T) ～ 〈P _i P _j 〉^1/2 was calculated using the permittivity ε′(T) measured at various frequencies. The variation of this parameter is compared to that of the spontaneous polarization P _s (T) determined from the measurements of a pyroelectric current in the external electric field E _dc =0.95 kV/cm. In the frequency range from 100 Hz to 13 MHz, the dispersion of the dielectric response in the temperature region of 180–192 K is characteristic of a relaxator ferroelectric featuring a glasslike behavior. The parameters of this state were determined, including the activation energy of the polarization fluctuations (E _a ≈0.01 eV), the relaxation rate at T → ∞ (f ₀=1.9×10¹² Hz), and the polarization fluctuation freezing temperature (T _f =183 K). In Cd₂Nb₂O₇ pyrochlore, in contrast to the known relaxator ferroelectrics of the PMN type studied previously, this state coexists with the normal ferroelectric state appearing at T _c.     

Phase transitions sequence in pyrochlore Cd2Nb2O7 studied by IR reflectivity

The infrared reflectivity of Cd₂Nb₂O₇ single crystal was studied in the temperature interval of 10-540 K, together with complementary dielectric measurements. A ferroelectric soft mode was revealed above the ferroelectric phase transition at T _c = 196 K coupled with a central-mode type dispersion in the near-millimetre range. This proves the mixed displacive and order-disorder nature of the transition. Below T _c many new modes were detected due to lowering of the symmetry, especially below the previously suggested incommensurate transition at 85 K. Discussion of the possible phase transitions based on symmetry considerations is presented with the conclusion that the ferroelectric transition is proper with the F_1u symmetry of the order parameter, whereas the intermediate ferroelastic transition is improper and triggered by the coupling with the ferroelectric order parameter. Received 17 July 2000     

Absence of long-range magnetic ordering in the pyrochlore compound Er2Sn2O7

The low temperature behaviour of powder Er2Sn2O7 samples has been studied by magnetic susceptibility, heat capacity, and neutron scattering experiments. We report here the absence of magnetic ordering down to 100 mK. Anomalies in the heat capacity can be accounted for through an analysis of the crystal field spectrum observed by inelastic neutron scattering spectroscopy. These new measurements on Er2Sn2O7 suggest a new lower bound for the frustration index of f = |Θ(CW)|/T(N) = 14/0.1 = 140, placing this compound into a highly frustrated regime.     

NMR observation of rattling phonons in the pyrochlore superconductor KOs2O6

We report nuclear magnetic resonance studies on the beta-pyrochlore oxide superconductor KOs2O6. The nuclear relaxation at the K sites is entirely caused by fluctuations of the electric field gradient, which we ascribe to highly anharmonic low frequency oscillation (rattling) of K ions. A phenomenological analysis shows a crossover from overdamped to underdamped behavior of the rattling phonons with decreasing temperature and its sudden sharpening below the superconducting transition temperature T(c). Suppression of the Hebel-Slichter peak in the relaxation rate at the O sites below T(c) also indicates strong electron-phonon coupling.     

Evidence for charged critical behavior in the pyrochlore superconductor RbOs2O6

We analyze magnetic penetration depth (lambda) data of the recently discovered superconducting pyrochlore oxide RbOs(2)O(6). Our results strongly suggest that in RbOs(2)O(6) charged critical fluctuations dominate the temperature dependence of lambda near T(c). This is in contrast with the mean-field behavior observed in conventional superconductors and the uncharged critical behavior found in nearly optimally doped cuprate superconductors. However, this finding agrees with the theoretical predictions for charged criticality and the charged criticality observed in underdoped YBa(2)Cu(3)O(6.59).     

Lifshitz时空s波超导模型的关联长度和穿透深度

在D=d+2维各向异性的Lifshitz黑洞时空背景中, 在探子极限下, 用解析方法研究了临界温度附近引力系统的微扰, 计算出超导的关联长度ξα(1/T_c)(1-(T/T_c)^-1/2, 这与平均场论的结果一致. 进一步, 考虑在该系统中加一个均匀外磁场, 计算出穿透深度λα(T_c-T)^-1/2, 该结果与Ginzburg-Landau理论相符.     

Superconductivity and magnetic fluctuations in Cd(2))Re(2)O(7) via Cd nuclear magnetic resonance and re nuclear quadrupole resonance

We report Cd nuclear magnetic resonance (NMR) and Re nuclear quadrupole resonance (NQR) studies on Cd(2)Re(2)O(7), the first superconductor among pyrochlore oxides (T(c) approximately 1 K). The Re NQR spectrum at zero magnetic field below 100 K rules out any magnetic or charge order. The spin-lattice relaxation rate below T(c) exhibits a pronounced coherence peak and follows the weak-coupling BCS theory with nearly isotropic energy gap. The results of Cd NMR point to a moderate ferromagnetic enhancement at high temperatures followed by a rapid decrease of the density of states below the structural transition temperature of 200 K.