Pyrochlore Superconductor Research Articles

Spin-orbit coupling and electron correlation effects on phonon anharmonicity of KOs2O6

Spin-orbit coupling and electron correlation effects from Os 5d electrons on phonon anharmonicity of β−pyrochlore superconductor KOs2O6 are systematically studied by first-principles frozen-phonon calculations. Spin-orbit coupling eliminates double-well potential, weakens imaginary frequency and enhances lattice stability. However, the gotten T2g and A1g asymmetrical modes show that the lattice is still instable. Then, the on-site Coulomb interaction as an important factor is considered, which completes with the spin-orbit coupling and makes greater influence on the anharmonicity. Therefore, KOs2O6 is a strong spin-orbit coupling and electronic correlation superconductor, and the multiple interactions have great effects on the anharmonicity, which may play an important role to the superconductivity of KOs2O6.

Dynamical instability, strong anharmonicity and electron-phonon coupling in KOs2O6: First-principles calculations

First-principles pseudopotential calculations on phonon and electronic properties of β−pyrochlore superconductor KOs2O6 are performed. The imaginary soft-phonon modes with a special double-well potential for the lowest Eu(1) mode and the second lowest T1u(1) mode are reported, which indicates the dynamical instability in KOs2O6. However, the double wells are too small to induce a structural phase transformation in KOs2O6. The strong anharmonicity especially for K T2g(1) phonon mode is got, which is approved to be from the strong electron-phonon coupling that supports the superconductivity in KOs2O6.

Anomalous fermi liquid state in pyrochlore heavy electron superconductor Cd2Re2O7

Cd2Re2O7 is a pyrochlore superconductor with a transition temperature Tc near 2K. We report on the electronic background of Cd2Re2O7 at temperatures above and below Tc as determined from the far-infrared optical properties. In the normal state at low temperatures and frequencies, Cd2Re2O7 behaves as a mass enhanced Fermi liquid. Comparing the coefficients of the quadratic frequency and temperature dependence of the optical- and dc-resistivities leads to the conclusion that Cd2Re2O7 is an anomalous Fermi liquid with contributions to the scattering from elastic processes. In the superconducting state the elastic scattering is found to be somewhat reduced. We also find evidence for a weak pseudogap-like feature which may be due to the hybridization of the localized and itinerant-electron states. The superconducting state magnetic penetration depth extracted from the imaginary part of the optical conductivity is a relatively large value of λ(T=0.5K)≈6200Å.

Dichroism as a probe for parity-breaking phases of spin-orbit coupled metals

Recently, a general formalism was presented for gyrotropic, ferroelectric, and multipolar order in spin-orbit coupled metals induced by spin-spin interactions. Here, I point out that the resulting order parameters are equivalent to expectation values of operators that determine natural circular dichroic signals in optical and x-ray absorption. Some general properties of these operator equivalents and the resulting dichroisms are mentioned, and I list several material examples in this connection, including Weyl semimetals. The particular case of the tensor order in the pyrochlore superconductor Cd2Re2O7 is treated in more detail, including calculations of the x-ray absorption and circular dichroism at the O K edge.

X-ray scattering studies of structural phase transitions in pyrochlore Cd2Nb2O7

Structural phase transitions in pyrochlore Cd2Nb2O7 were studied by means of single crystal x-ray scattering. On cooling below the ferroelastic transition at T1 = 204 K, the cubic Bragg peaks broaden in a manner consistent with weak orthorhombic distortion. The distortion evolves rather smoothly through the ferroelectric transition at T2 = 196 K, which explains the absence of sharp anomalies in the heat capacity and dielectric constant at this transition. At lower temperatures, the anomalous relaxor-like character of this compound is evident as a gradual reduction in the Bragg peak intensities, which continues down to the onset of another transition at T3 = 85 K. The studies of two Bragg peaks that are forbidden within the cubic phase reveal an interesting disparity: while the intensity for one of them increases in a classical mean-field manner below T1, the other shows unconventional behavior that is reminiscent of the pyrochlore superconductor Cd2Re2O7.

Far-IR excitations in Cd2Re2O7 in the normal and superconducting states

Cd2Re2O7 is a pyrochlore superconductor with a transition temperature Tc near 1 K. We report on the far-infrared optical properties of Cd2Re2O7 at temperatures above and below Tc with a particular emphasis on changes in the spectrum below Tc. Seventeen phonon modes are observed in the normal state optical conductivity spectrum of Cd2Re2O7 at low temperatures in good agreement with a factor group analysis. In the superconducting state, a softening (∼1 cm−1) of the phonon modes at 35 and 61 cm−1 occurs and thermal reflectance spectra show the development of two additional strong absorption features, near 9.6 and 19.3 cm−1. The dominant presence of lattice vibrational modes in the optical spectrum suggests that electron–phonon interaction plays an important role in the normal and superconducting state properties of Cd2Re2O7.

Magnetic and charge transport properties of the Na-based Os oxide pyrochlore

The Na-based osmium oxide pyrochlore was synthesized for the first time by an ion-exchange method using KOs 2O 6 as a host. The composition was identified as Na 1.4Os 2O 6·H 2O by electron probe micro-analysis, thermogravimetric analysis, and structural analysis using synchrotron X-ray diffraction. Na 1.4Os 2O 6·H 2O crystallizes in a regular pyrochlore structure with some defects (space group: Fd-3 m, a=10.16851(1) Å). Electrical resistivity, heat capacity, and magnetization measurements clearly showed absence of superconductivity down to 2 K, being in large contrast to what was found for the β-type pyrochlore superconductor AOs 2O 6 ( A=Cs, Rb, and K). The Sommerfeld coefficient is 22 mJ K −2 mol −1, being the smallest among AOs 2O 6. A magnetic anomaly at ∼57 K and associated magneto-resistance (+3.7% at 2 K in 70 kOe) were found.

Scanning Tunneling Spectroscopy in the Superconducting State and Vortex Cores of theβ-PyrochloreKOs2O6

We performed the first scanning tunneling spectroscopy measurements on the pyrochlore superconductor KOs2O6 (T(c)=9.6 K) in both zero magnetic field and the vortex state at several temperatures above 1.95 K. This material presents atomically flat surfaces, yielding spatially homogeneous spectra which reveal fully gapped superconductivity with a gap anisotropy of 30%. Measurements performed at fields of 2 and 6 T display a hexagonal Abrikosov flux line lattice. From the shape of the vortex cores, we extract a coherence length of 31-40 A, in agreement with the value derived from the upper critical field H(c2). We observe a reduction in size of the vortex cores (and hence the coherence length) with increasing field which is consistent with the unexpectedly high and unsaturated upper critical field reported.

NMR Relaxation and Resistivity from Rattling Phonons in Pyrochlore Superconductors

We calculate the temperature dependence of the NMR relaxation rate and electrical resistivity for coupling to a local, strongly anharmonic phonon mode. We argue that the two-phonon Raman process is dominating NMR relaxation. Due to the strong anharmonicity of the phonon an unusual temperature dependence is found having a low temperature peak and becoming constant towards higher temperatures. The electrical resistivity is found to vary like T2 at low temperatures and following a square root T behavior at high temperatures. Both results are in qualitative agreement with recent observations on beta-pyrochlore oxide superconductors.

Interplay of Superconductivity and Rattling Phenomena inβ-PyrochloreKOs2O6Studied by Photoemission Spectroscopy

The electronic structure near the Fermi level (EF) of the beta-pyrochlore superconductor KOs2O6 is studied using laser-excited ultrahigh-resolution photoemission spectroscopy. The superconducting gap clearly opens across the superconducting transition (Tc=9.6 K), with the strong electron-phonon coupling value of 2Delta(0)/k B Tc>or=4.56. A fitting analysis identifies clear anomalies at Tp=7.5 K in the temperature dependencies of the superconducting gap size and the quasiparticle relaxation lifetime. These anomalies and the fine spectral structures arising from phonons suggest that the existence of the rattling behavior of K ions significantly affects the superconductivity in KOs2O6.

Manifestations of fine features of the density of states in the transport properties ofKOs2O6

We performed high-pressure transport measurements on high-quality single crystals of $\mathrm{K}{\mathrm{Os}}_{2}{\mathrm{O}}_{6}$, a $\ensuremath{\beta}$-pyrochlore superconductor. While the resistivity at high temperatures might approach saturation, there is no sign of saturation at low temperatures, down to the superconducting phase. The anomalous resistivity is accompanied by a nonmetallic behavior in the thermoelectric power (TEP) up to temperatures of at least $700\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which also exhibits a broad hump with a maximum at $60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The pressure influences mostly the low-energy electronic excitations. A simple band model based on enhanced density of states in a narrow window around the Fermi energy $({E}_{F})$ explains the main features of this unconventional behavior in the transport coefficients and its evolution under pressure.

Thermal Conductivity of the Pyrochlore SuperconductorKOs2O6: Strong Electron Correlations and Fully Gapped Superconductivity

To elucidate the nature of the superconducting ground state of the geometrically frustrated pyrochlore KOs2O6 (Tc=9.6 K), the thermal conductivity was measured down to low temperatures (approximately Tc/100). We found that the quasiparticle mean free path is strikingly enhanced below a transition at Tp=7.8 K, indicating enormous electron inelastic scattering in the normal state. In magnetic fields, the conduction at T-->0 K is nearly constant up to approximately 0.4Hc2, in contrast with the rapid growth expected for superconductors with an anisotropic gap. This unambiguously indicates a fully gapped superconductivity, in contrast with previous studies. These results highlight that KOs2O6 is unique among superconductors with strong electron correlations.

Large mass enhancement in [formula omitted

Heat capacity measurements on the recently discovered geometrically frustrated β -pyrochlore superconductor RbOs 2 O 6 ( T c = 6.4 K ) yield a Sommerfeld coefficient of 44 mJ / mol f . u . / K 2 . This is about four times larger than the one found in band structure calculations. In order to specify the enhancement due to electron–electron interactions, we have measured the electron–phonon enhancement. By a suitable analysis, an electron–phonon coupling constant λ ep = 1 ± 0.1 is derived from the specific heat jump at T c . This leaves a significant additional λ add = 2.1 ± 0.3 for enhancement due to other mechanisms, possibly related to the triangular lattice. To arrive at these results, an appropriate analysis method for bulk thermodynamic data based on the condensation energy was applied.

NMR studies of [formula omitted]-pyrochlore superconductors with osmium, under hydrostatic pressure

We report pressure effects on the Rb 87 nuclear relaxation rate 1 / T 1 in the osmate superconductor RbOs 2 O 6 . The superconducting transition temperature T c increases from 6.3 K at ambient pressure to 8.2 K at 2 GPa. Although 1 / ( T 1 T ) is slightly enhanced by pressure at low temperatures, the temperature dependence of 1 / ( T 1 T ) hardly changes below T c . Even though T c of RbOs 2 O 6 at 2 GPa reaches a value close to that of KOs 2 O 6 at ambient pressure (9.6 K), they show completely different nuclear relaxation behaviors.

Magnetic penetration depth inRbOs2O6studied by muon spin rotation

Measurements of the magnetic field penetration depth $\ensuremath{\lambda}$ in the pyrochlore superconductor ${\mathrm{RbOs}}_{2}{\mathrm{O}}_{6}$$({T}_{c}\ensuremath{\simeq}6.3\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ were carried out by means of the muon-spin-rotation $(\ensuremath{\mu}\mathrm{SR})$ technique. At low temperatures ${\ensuremath{\lambda}}^{\ensuremath{-}2}(T)$ saturates and becomes constant below $T\ensuremath{\simeq}0.2{T}_{c}$, in agreement with what is expected for weak-coupled $s$-wave BCS superconductors. The value of $\ensuremath{\lambda}$ at $T=0$ was found to be in the range of 250--300 nm. $\ensuremath{\mu}\mathrm{SR}$ and equilibrium magnetization measurements both reveal that at low temperatures $\ensuremath{\lambda}$ is almost (at the level of 10%) independent of the applied magnetic field. This result suggests that the superconducting energy gap in ${\mathrm{RbOs}}_{2}{\mathrm{O}}_{6}$ is isotropic.

Order-disorder-order phase transitions in the pyrochlore superconductorCd2Re2O7

The structural phase transitions of the pyrochlore superconductor Cd2Re2O7 are investigated by Raman light scattering. The cubic to tetragonal transition at 200 K is characterized by the appearance of a broad mode originating from oxygen ion motion in agreement with recent theoretical predictions [I. A. Sergienko , Phys. Rev. Lett. 92, 065501 (2004)]. The appearance of well-defined low-frequency modes at the 120-K transition indicates that it is driven by ordering of the Cd ions within the channel voids of the distorted pyrochlore.

Intrinsic thermodynamic properties of the pyrochlore superconductorRbOs2O6extracted by condensation energy analysis

We develop a general procedure for the analysis of bulk thermodynamic data of a superconductor for samples containing a metallic non-superconducting second phase. The method is based on the condensation energy and it allows the extraction of the intrinsic properties of a superconductor even for non-ideal samples. Applying this procedure to the recently discovered geometrically frustrated beta-pyrochlore superconductor RbOs2O6 (Tc = 6.4 K) yields a Sommerfeld coefficient as high as 79 mu J/g/K^2 (44 mJ/mol_f.u./K^2). RbOs2O6 is inferred to be a strong type-II superconductor (kappa(Tc) = 23) in the intermediate-coupling regime similar to niobium (lambda_ep \approx 1). From the upper critical field mu_0 H_c2 \approx 6 T at 0 K, we estimate a Ginzburg-Landau coherence length xi \approx 74 AA. The condensation energy is 860 mu J/g (483 mJ/mol_f.u.) resulting in 1/(8 pi) (gamma_1 Tc^2)/DeltaU_1 \approx 0.15, a value well in the range of conventional phonon-mediated superconductors. The superconducting electronic specific heat indicates conventional s-wave pairing. The experimental Sommerfeld coefficient of 44 mJ/mol_f.u./K^2 is about 4 times larger than the one found in band structure calculations. Together with the electron-phonon coupling constant lambda_ep \approx 1 this leaves an additional lambda_add \approx 2.4 for enhancement due to other mechanisms.

Possible Anisotropic Order Parameter in Pyrochlore Superconductor KOs2O6 Probed by Muon Spin Rotation

Magnetic penetration depth ($\lambda$) in a pyrochlore superconductor KOs$_2$O$_6$ was studied by means of muon spin rotation (\msr). The temperature dependence of transverse spin relaxation rate, which is proportional to $\lambda ^{-2}$, exhibits a considerable deviation from that expected for the empirical two-fluid model ($\propto T^4$), rather obeying a $T^2$-tendency. Furthermore, $\lambda$ apparently increases with increasing applied field, suggesting the presence of nonlinear and nonlocal effects. These findings strongly suggest that the superconducting order parameter in KOs$_2$O$_6$ is anisotropic.

Pressure Effects on the Transition Temperature and the Magnetic Field Penetration Depth in the Pyrochlore SuperconductorRbOs2O6

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.

Superconductivity in the geometrically frustrated pyrochloreRbOs2O6

We report the basic thermodynamic properties of the new geometrically frustrated beta-pyrochlore bulk superconductor RbOs2O6 with a critical temperature Tc = 6.4 K. Specific heat measurements are performed in magnetic fields up to 12 T. The electronic density of states at the Fermi level in the normal state results in gamma = (33.7 \pm 0.2) mJ/mol_f.u./K^2. In the superconducting state, the specific heat follows conventional BCS-type behavior down to 1 K, i.e. over three orders of magnitude in specific heat data. The upper critical field slope at Tc is 1.2 T/K, corresponding to a Maki-parameter alpha = 0.64 \pm 0.1. From the upper critical field mu0 Hc2 \approx 6 T at 0 K, we estimate a Ginzburg-Landau coherence length xi \approx 7.4 nm. RbOs2O6 is the second reported metallic AB2O6 type pyrochlore compound after KOs2O6, and one of only three pyrochlore superconductors in addition to Cd2Re2O7 and KOs2O6.