Filled-skutterudite Superconductor Research Articles

Decoupling of Rattling Mode and Superconductivity in Filled-Skutterudite BaxIr4Sb12

Abstract The rattling mode, an anharmonic vibrational phonon, is widely recognized as a critical factor in the emergence of superconductivity in caged materials. Here, we present a counterexample in a filled-skutterudite superconductor Ba x Ir4Sb12 (x = 0.8, 0.9, 1.0), synthesized via a high-pressure route. Transport measurements down to liquid 3He temperatures reveal a transition temperature (T c) of 1.2 K and an upper critical field (H c2) of 1.3 T. Unlike other superconductors with caged structures, the Ba x Ir4 X 12 (X = P, As, Sb) family exhibits a monotonic decreasing T c with the enhancement of the rattling mode, as indicated by fitting the Bloch–Grüneisen formula. Theoretical analysis suggests that electron doping from Ba transforms the direct bandgap IrSb3 into a metal, with the Fermi surface dominated by the hybridization of Ir 5d and Sb 5p orbitals. Our findings of decoupled rattling modes and superconductivity distinguish the Ba x Ir4Sb12 family from other caged superconductors, warranting further exploration into the underlying mechanism.

Pressure Tuning of Superconductivity of LaPt4Ge12 and PrPt4Ge12 Single Crystals.

We carried out electrical resistivity and X-ray diffraction (XRD) studies on the filled skutterudite superconductors LaPtGe and PrPtGe under hydrostatic pressure. The superconducting transition temperature is linearly suppressed upon increasing pressure, though the effect of pressure on is rather weak. From the analysis of the XRD data, we obtain bulk moduli of GPa and GPa for LaPtGe and PrPtGe, respectively. The knowledge of the bulk modulus allows us to compare the dependence of on the unit-cell volume from our pressure study directly with that found in the substitution series LaPrPtGe. We find that application of hydrostatic pressure can be characterized mainly as a volume effect in LaPtGe and PrPtGe, while substitution of Pr for La in LaPrPtGe yields features going beyond a simple picture.

Symmetry of Order Parameters in Multiband Superconductors LaRu_{4}As_{12} and PrOs_{4}Sb_{12} Probed by Local Magnetization Measurements.

The temperature dependencies of the lower critical field H_{c1}(T) of several filled-skutterudite superconductors were investigated by local magnetization measurements. While LaOs_{4}As_{12} and PrRu_{4}As_{12} exhibit the H_{c1}(T) dependencies consistent with the single-band BCS prediction, for LaRu_{4}As_{12} (the superconducting temperature T_{c}=10.4 K) with a similar three-dimensional Fermi surface, we observe a sudden increase in H_{c1}(T) deep in a superconducting state below about 0.32T_{c}. Remarkably, a rapid rise of H_{c1}(T) at approximately the same reduced temperature 0.27T_{c} is also found for the heavy-fermion compound PrOs_{4}Sb_{12} (T_{c}≃1.78 K), in fair accord with the earlier macroscopic study. We attribute the unusual H_{c1}(T) dependencies of LaRu_{4}As_{12} and PrOs_{4}Sb_{12} to a kink structure in their superfluid densities due to different contributions from two nearly decoupled bands. Whereas LaRu_{4}As_{12} is established as a two-band isotropic s-wave superconductor, nonsaturating behavior of H_{c1}(T) is observed for PrOs_{4}Sb_{12}, indicative of an anisotropic structure of a smaller gap. For this superconductor with broken time-reversal symmetry, our findings suggest a superconducting state with multiple symmetries of the order parameters.

Suppression of ferromagnetic spin fluctuations in the filled skutterudite superconductor SrOs4As12 revealed by As75 NMR-NQR measurements

Motivated by the recent observation of ferromagnetic spin correlations in the filled skutterudite SrFe$_4$As$_{12}$ [Ding et al., Phys. Rev. B 98, 155149 (2018)], we have carried out $^{75}$As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements to investigate the role of magnetic fluctuations in a newly discovered isostructural superconductor SrOs$_4$As$_{12}$ with a superconducting transition temperature of $T_{\rm c}$ $\sim$ 4.8 K. Knight shift $K$ determined by the NQR spectrum under a small magnetic field ($\le$ 0.5 T) is nearly independent of temperature, consistent with the temperature dependence of the magnetic susceptibility. The nuclear spin-lattice relaxation rate divided by temperature, 1/$T_1T$, is nearly independent of temperature above $\sim$ 50 K and increases slightly with decreasing temperature below the temperature. The temperature dependence is reasonably explained by a simple model where a flat band structure with a small ledge near the Fermi energy is assumed. By comparing the present NMR data with those in SrFe$_4$As$_{12}$, we found that the values of $|K|$ and $1/T_1T$ in SrOs$_4$As$_{12}$ are smaller than those in SrFe$_4$As$_{12}$, indicating no obvious ferromagnetic spin correlations in SrOs$_4$As$_{12}$. From the temperature dependence of 1/$T_1$ in the superconducting state, an $s$-wave superconductivity is realized.

Broken time-reversal symmetry in superconductingPr1−xCexPt4Ge12

We report results of zero-field muon spin relaxation experiments on the filled-skutterudite superconductors~Pr$_{1-x}$Ce$_{x}$Pt$_4$Ge$_{12}$, $x = 0$, 0.07, 0.1, and 0.2, to investigate the effect of Ce doping on broken time-reversal symmetry (TRS) in the superconducting state. In these alloys broken TRS is signaled by the onset of a spontaneous static local magnetic field~$B_s$ below the superconducting transition temperature. We find that $B_s$ decreases linearly with $x$ and $\to 0$ at $x \approx 0.4$, close to the concentration above which superconductivity is no longer observed. The (Pr,Ce)Pt$_4$Ge$_{12}$ and isostructural (Pr,La)Os$_4$Sb$_{12}$ alloy series both exhibit superconductivity with broken TRS, and in both the decrease of $B_s$ is proportional to the decrease of Pr concentration. This suggests that Pr-Pr intersite interactions are responsible for the broken TRS\@. The two alloy series differ in that the La-doped alloys are superconducting for all La concentrations, suggesting that in (Pr,Ce)Pt$_4$Ge$_{12}$ pair-breaking by Ce doping suppresses superconductivity. For all $x$ the dynamic muon spin relaxation rate decreases somewhat in the superconducting state. This may be due to Korringa relaxation by conduction electrons, which is reduced by the opening of the superconducting energy gap.

Pressure Dependence of the Superconducting Transition Temperature of Filled Skutterudites LaT4P12 (T = Fe, Ru)

The filled skutterudite intermetallic compounds with the general formula LnT4X12 (Ln = Lanthanide, T = transition metal, X = pnictogen) have attracted much attention for exhibiting novel physical phenomena, such as superconductivity,1) heavy fermion behavior,2) metal–insulator transition,3) magnetic ordering,4) and their prospect in thermoelectric applications.5) Among the various physical properties, at least 19 filled skutterudites have been reported to be superconductors with the superconducting transition temperature Tc up to 17K. Most of these have been classified as Bardeen– Cooper–Schrieffer (BCS) ones. In BCS superconductivity Tc generally decreases under pressure predominantly due to a stiffness of the lattice with increasing pressure.6) This general rule is followed for most filled skutterudite superconductors in the series of LnT4X12, except for T = Fe.7) In a previous high-pressure study7) in the LaM4P12 (M = Fe, Ru, Os) up to 1.8GPa, it has been found that the Tc of LaFe4P12 increases at a rate of 0.72K/GPa, and those of LaRu4P12 and LaOs4P12 decrease at rates 10.16 and 10.095K/GPa, respectively. The distinct pressure dependence of Tc has been interpreted in terms of two competing contributions: a depression of Tc due to a compression of the filled skutterudite sublattice, and an enhancement of Tc due to a compression of La and its immediate environment. However, their interpretation is based only on the features of the filled skutterudite structure. Although the model gives a feasible explanation for the unique positive pressure coefficient dTc=dP of LaFe4P12, La atoms are inside (FeP6)4 cages and well separated, which makes the model less convincing. Actually, electronic structure calculations8) on LaFe4P12 have implied that its superconductivity is primarily associated with the electrons of its phosphorus sublattice, which form a strong covalentbonded P4 ring and dominate the density of states at the Fermi energy NðEFÞ. Very recently, high pressure studies in the RT4P12 (R = La, Y, T = Fe, Ru) up to 8GPa have been performed,9,10) and found that the dTc=dP’s for LaFe4P12 and YFe4P12 show positive and those for LaRu4P12 and YRu4P12 exhibit negative. Cheng et al.9) have revealed from a closer inspection of the characteristics of crystal and electronic structures in the series RT4P12 that the pressure effect on Tc of the filled skutterudite should have little to do with that of the corresponding R metals. The observed dTc=dP > 0 of YFe4P12 was further confirmed by the band-structure calculations that show an enhancement of both NðEFÞ and the Hopfield parameter11) (©) under pressure at least up to 8GPa. On the other hand, a dTc=dP < 0 for YRu4P12 was also explained by similar calculations. In this note, we present theoretical results of the pressure dependence of Tc for LaT4P12 (T = Fe, Ru) by performing band-structure calculations. Electronic structure calculations are carried out using a full-potential linearized augmented plane wave method (FLAPW) with the local density approximation (LDA) for the exchange correlation potential. For the LDA, the formula proposed by Gunnarsson and Lundqvist is used.12) Calculations are performed at ambient pressure (denoted as 0GPa) and 8GPa. Experimental crystal structure including lattice constants and internal parameters is assumed throughout the calculation.10,13,14) The parameters of the atomic positions at 0GPa are used for 8GPa. The sampling points are uniformly distributed in the irreducible Brillouin Zone, 225 k-points for potential convergence, and 3025 k-points for the final band structures. The used LAPW basis functions are 5425 at the ¥ point. The present calculations for LaT4P12 (T = Fe, Ru) are in good agreement with previous reports15,16) at 0GPa. We evaluate the pressure dependence of Tc using McMillan’s strong-coupling equation17) as well as the case of YT4P12 (T = Fe, Ru).9) By taking the derivative with respect to volume of the equation, we can obtain the relation:

Pressure dependence of the superconducting transition temperature of the filled skutterudite YFe4P12

We have studied the pressure dependence of the superconducting transition temperature T-c of the filled skutterudite YFe4P12 under various quasihydrostatic pressures up to 8 GPa. DC magnetization measurements up to 1.2 GPa in a piston-cylinder cell yields a linear increase of T-c with a positive coefficient dT(c)/dP = 1 K/GPa. Resistivity measurements up to 8 GPa in a cubic anvil apparatus show that Tc increases to 9.3 K at 8 GPa, but the slope decreases gradually with increasing pressure. Besides the previously reported LaFe4P12, YFe4P12 becomes the second filled skutterudite superconductor that exhibits a positive pressure coefficient dT(c)/dP in a broad pressure range. The observed large dT(c)/dP > 0 of YFe4P12 can be rationalized by our band-structure calculations that show an enhancement of density of states at Fermi energy and the Hopfield parameter under pressure at least up to 8 GPa. On the other hand, similar calculations predict a dT(c)/dP < 0 for YRu4P12.

Multiband superconductivity in PrPt4Ge12single crystals

We report measurements of the London penetration depth $\ensuremath{\Delta}\ensuremath{\lambda}(T)$ and the electronic specific heat ${C}_{e}(T)$ on high-quality single crystals of the filled skutterudite superconductor PrPt${}_{4}$Ge${}_{12}$ (${T}_{c}\ensuremath{\simeq}$ 8 K). Both quantities show a weak temperature dependence at $T\ensuremath{\ll}{T}_{c}$, following $\ensuremath{\Delta}\ensuremath{\lambda}\ensuremath{\sim}{T}^{n}$ ($n=3.2\ifmmode\pm\else\textpm\fi{}0.1$) and ${C}_{e}/T\ensuremath{\sim}{T}^{2.8}$. Such temperature dependences deviate from both conventional $s$-wave-type and nodal superconductivity. A detailed analysis indicates that the superfluid density ${\ensuremath{\rho}}_{s}(T)$, derived from the penetration depth, as well as the electronic specific heat can be consistently described in terms of a two-gap model, providing strong evidence of multiband superconductivity for PrPt${}_{4}$Ge${}_{12}$.

Dependence of the superconducting transition temperature of the filled skutterudite compound PrPt4Ge12 on hydrostatic pressure

The temperature-dependent ac susceptibility of the filled skutterudite superconductor PrPt4Ge12 has been measured under hydrostatic He-gas pressure to 0.58GPa. The superconducting transition temperature Tc decreases linearly with pressure P from 7.91K at ambient pressure to 7.83K at 0.58GPa, giving the rate dTc/dP=−0.19±0.03K/GPa. Evidence is presented that suggests that the value of Tc in this compound is slightly reduced due to magnetic pair-breaking effects from the Pr3+ cations.

Comparative photoemission studies on the superconducting gap of the filled skutterudite superconductors LaPt4Ge12and PrPt4Ge12

We performed a comparative study of the superconducting gap in the new filled skutterudite superconductors LaPt4Ge12 and PrPt4Ge12 using high-resolution photoemission spectroscopy. We succeeded in observing spectral changes across Tc that reflect the opening of the superconducting gap in both compounds and also in observing a noticeable difference in their respective superconducting spectral shapes near the Fermi level, pointing toward a more complex superconducting gap structure in PrPt4Ge12. In addition, we found that the two-gap model is more suitable for describing the superconducting-state spectrum of PrPt4Ge12 than the single-isotropic-gap and single-anisotropic-gap models, which suggests an explanation that multiband effects may possibly induce the anomalous superconducting properties of PrPt4Ge12.

Electronic Structure of the Novel Filled Skutterudite PrPt4Ge12Superconductor

We have performed soft x-ray photoemission spectroscopy (SXPES) and resonant photoemission spectroscopy (RPES) of the filled skutterudite superconductor PrPt 4 Ge 12 in order to study the electronic structure of valence band and the character of Pr 4f. SXPES of PrPt 4 Ge 12 measured with 1200 eV photon energy, where spectral contribution of Pr 4f is negligible, was found nearly identical with that of LaPt 4 Ge 12 , indicating similarity of Pt–Ge derived electronic states of the two compounds. Good correspondence with band calculations allows us to ascribe the dominant Ge 4p character of the density of states at the Fermi level (E F ). Pr 3d → 4f RPES shows that, although Pr 4f electrons in PrPt 4 Ge 12 are not as strongly hybridized with conduction electrons near E F as in PrFe4P12, there are finite Pr 4f contribution to the states near E F in PrPt 4 Ge 12 . These PES results give the information of fundamental electronic structure for understanding the physical properties of the novel filled skutterudite superconductor PrPt 4 Ge 12 .

Crossing of the crystalline-electric-field and rattling-phonon excitation energies in the filled skutterudite superconductor Pr(Os1−xRux)4Sb12

By specific heat measurements on Pr(Os1−xRux)4Sb12, we have studied the x-dependences of the 4f-electron crystalline-electric-field first excitation energy and the rattling energy of the Pr ion. The former increases monotonically from ~ 10 K to ~ 85 K, while the latter of ~ 45 K does not change much resulting in a crossing of the two energy levels at x ≊ 0.6. The reported minimum in the superconducting transition temperature Tc at x ≊ 0.6 could be associated with the level crossing.

Superconducting state of filled-skutterudite RPt4Ge12 (R = La, Pr): 73Ge-NQR studies

We report 73Ge-NQR studies on filled-skutterudite superconductors LaPt4Ge12 and PrPt4Ge12 under zero external field. In PrPt4Ge12, the measurement of the nuclear spin-lattice relaxation rate 1/T1 has revealed a distinct coherence peak just below Tc followed by an exponential decrease well below Tc, evidencing that PrPt4Ge12 is an s-wave superconductor with the isotropic gap in a weak-coupling regime. In LaPt4Ge12, the 1/T1 exhibits the exponential decrease well below Tc, suggesting the isotropic s-wave superconductivity. Even though 73Ge-NQR-1/T1 in LaPt4Ge12 has been measured under zero field, its coherence peak was absent, which contrasts with the result in Pr-compound. This may point to a possible anisotropy in the Fermi surface and/or some damping effect of quasiparticles in association with electron–phonon interactions.

Superfluid Density and Energy Gap Function of SuperconductingPrPt4Ge12

The filled skutterudite superconductor PrPt4Ge12 was studied in muon-spin rotation (muSR), specific heat, and electrical resistivity experiments. The continuous increase of the superfluid density with decreasing temperature and the dependence of the magnetic penetration depth lambda on the magnetic field obtained by means of muSR, as well as the observation of a T3 dependence of the electronic specific heat indicate the presence of pointlike nodes in the superconducting energy gap. The gap and the specific heat are found to be well described by two models with point nodes, similar to results obtained for the unconventional heavy fermion skutterudite superconductor PrOs4Sb12.

Electronic band structure, specific heat, andP195tNMR studies of the filled skutterudite superconductorThPt4Ge12

Specific-heat measurements and $^{195}\text{P}\text{t}$ NMR studies have been carried out for actinoid-bearing filled skutterudite superconductor ${\text{ThPt}}_{4}{\text{Ge}}_{12}$ with ${T}_{c}=4.62\text{ }\text{K}$. The lattice contribution to the total specific heat has been analyzed in terms of combination of the Einstein and Debye theories. The data show that ${\text{ThPt}}_{4}{\text{Ge}}_{12}$ has one optical and two acoustic vibrational modes. The numbers of such modes and the magnitudes of the vibration frequencies suggest that the two acoustic modes can be attributed to the Pt and Ge atoms forming two different cages in the cubic bcc skutterudite structure, while the optical mode can be associated with weakly bonded Th atoms occupying a center of these cages. The $^{195}\text{P}\text{t}$ Knight shift and spin-lattice relaxation rates in ${\text{ThPt}}_{4}{\text{Ge}}_{12}$ can be understood in terms of conventional Fermi-liquid picture. Distinct anisotropy in these quantities presumably arises from $d(p)$-orbital components. The experimental data have been confronted with the electronic band structure of ${\text{ThPt}}_{4}{\text{Ge}}_{12}$ calculated by ab initio full-potential relativistic local-orbital method within the local-density approximation. Enhanced value of the mass enhancement coefficient points to considerable electron-phonon interaction and some electron-electron correlations. The Fermi surface of metallic ${\text{ThPt}}_{4}{\text{Ge}}_{12}$ consists of nonspherical hole and electron sheets.

Two-band conduction in superconductingThPt4Ge12

The filled-skutterudite superconductor ${\text{ThPt}}_{4}{\text{Ge}}_{12}$ was studied in the normal state by means of thermoelectric power, magnetoresistance, and Hall-coefficient measurements. The results indicate that this compound exhibits a two-band conductivity with strongly temperature-dependent carrier concentrations and mobilities. At low temperatures, the charge transport is dominated by the contribution due to slowly moving electrons. The experimental findings were corroborated by the results of electronic band-structure calculations performed by the relativistic full-potential local-orbital method.

75As-NQR Studies of Filled-Skutterudites PrRu4As12and LaRu4As12

We report 75 As nuclear quadrupole resonance (NQR) measurements of the filled skutterudite superconductors LaRu 4 As 12 and PrRu 4 As 12 . The temperature dependence of 75 As-NQR line and the nuclear spin–lattice relaxation rate 1/ T 1 show that the Pr 3+ has a crystal electric field (CEF) singlet ground state with a separate first excited state. In the superconducting state of PrRu 4 As 12 and LaRu 4 As 12 , 1/ T 1 has a coherence peak just below the transition temperature and decreases exponentially at low temperatures. This behavior shows that the s-wave superconductivity occurs in both compounds.

75As-NQR Studies of Superconducting Filled Skutterudites PrRu4As12 and LaRu4As12

We report 75 As nuclear quadrupole resonance (NQR) measurements of the filled skutterudite superconductors LaRu 4 As 12 and PrRu 4 As 12 . The temperature dependence of the 75 As-NQR line and the nuclear spin–lattice relaxation rate 1/ T 1 show that Pr 3+ has a crystal electric field (CEF) singlet ground state with a separate first excited state. In the superconducting states of PrRu 4 As 12 and LaRu 4 As 12 , 1/ T 1 has a coherence peak just below the transition temperature and decreases exponentially at low temperatures. This behavior shows that the s-wave superconductivity occurs in both compounds.

Superconducting Gap of Filled Skutterudite Superconductor LaRu4P12 Studied by Sub-meV Resolution Photoemission Spectroscopy

We study the superconducting gap of the filled skutterudite superconductor LaRu 4 P 12 (transition temperature T c =7.2 K) using a newly developed sub-meV resolution photoemission spectrometer with a vacuum-UV laser as a light source. The result at 4.8 K shows the opening of a superconducting gap, whose spectral shape is well explained with an isotropic s-wave Dynes function using a gap size of 1.3 meV. This corresponds to the reduced gap 2Δ(0)/ k B T c of 4.2. The temperature dependence of the superconducting gap shows fairly good agreement with the conventional BCS theory. The present results are consistent with those of a moderately strong-coupling and isotropic s-wave superconductor.

高圧下極低温におけるＰｒＯｓ４Ｓｂ１２の磁化測定

We present here a setup for the dc magnetization measurements at high pressures and low temperatures using a Faraday-type capacitive magnetometer with a miniature BeCu piston-cylinder pressure cell, which allows us to pressurize sample up to 1.5 GPa at low temperatures. The magnetic force is measured capacitively by monitoring the displacement of parallel plate capacitor. The magnetometer can be used at temperatures down to 0.06 K and in high magnetic fields up to 15 T. The magnetometer with the pressure cell has a good sensitivity for magnetic moments of 10-4emu. Its application to the filled skutterudite superconductor PrOs4Sb12 is presented.