It is shown that $f$-electron multipole is naturally defined as spin-charge one-electron density operator in the second-quantized form with the use of tensor operator on the analogy of multipole expansion of electromagnetic potential from charge distribution in electromagnetism. Due to this definition of multipole, it is possible to determine multipole state from a microscopic viewpoint on the basis of the standard linear response theory for multipole susceptibility. In order to discuss multipole properties of filled skutterudites, we analyze a seven-orbital impurity Anderson model by employing a numerical renormalization group method. We show our results on possible multipole states of filled skutterudite compounds.
We discuss multipole properties of filled skutterudites containing heavy lanthanide Ln from a microscopic viewpoint on the basis of a seven-orbital Anderson model. For Ln=Gd, in contrast to naive expectation, quadrupole moments remain in addition to main dipole ones. For Ln=Ho, we find an exotic state governed by octupole moment. For Ln=Tb and Tm, no significant multipole moments appear at low temperatures, while for Ln=Dy, Er, and Yb, dipole and higher-order multipoles are dominant. We briefly discuss possible relevance of these multipole states with actual materials.
We discuss low-temperature multipole states of Nd-based filled skutterudites by analyzing a multiorbital Anderson model with the use of a numerical renormalization group method. In order to determine the multipole state, we take a procedure to maximize the multipole susceptibility matrix. Then, it is found that the dominant multipole state is characterized by the mixture of 4u magnetic and 5u octupole moments. The secondary state is specified by 2u octupole. When we further take into account the coupling between $f$ electrons in degenerate $Γ_{67}^{-}$ ($e_{\rm u}$) orbitals and dynamical Jahn…
In order to clarify exotic multipole properties of filled skutterudites, we evaluate multipole susceptibility for $n$=1$\sim$5, where $n$ is the local $f$-electron number, on the basis of a multiorbital Anderson model constructed using the $j$-$j$ coupling scheme. For $n$=1, magnetic fluctuations dominate over low-temperature electronic properties, while for $n$=2 and 4, electronic states are dominated by both magnetic and quadrupole fluctuations. For $n$=3 and 5, octupole fluctuations are found to be significant, depending on the crystalline electric field potential. We discuss possible relev…
In order to clarify magnetic properties of filled skutterudites, we analyze the Anderson model including seven $f$ orbitals hybridized with an $a_{\rm u}$ conduction band using a numerical technique. For $n$=2 corresponding to Pr-based filled skutterudites, where $n$ is the local $f$-electron number, even if the ground state is a singlet, there remain significant magnetic fluctuations from a triplet state with a small excitation energy. This result can be understood by the fact that $f$-electron states are clearly distinguished as itinerant and localized ones in the filled skutterudite structu…
A simple tight-binding model is constructed for the description of the electronic structure of some Ce-based filled skutterudite compounds showing an energy gap or pseudogap behavior. Assuming band-diagonal electron interactions on this tight-binding model, the optical conductivity spectrum is calculated by applying the second-order self-consistent perturbation theory to treat the electron correlation. The correlation effect is found to be of great importance on the description of the temperature dependence of the optical conductivity. The rapid disappearance of an optical gap with increasing …
Anomalous metal-insulator transition observed in filled skutterudite CeOs$_4$Sb$_{12}$ is investigated by constructing the effective tight-binding model with the Coulomb repulsion between f electrons. By using the mean field approximation, magnetic susceptibilities are calculated and the phase diagram is obtained. When the band structure has a semimetallic character with small electron and hole pockets at $Γ$ and H points, a spin density wave transition with the ordering vector $\mathbf{Q}=(1,0,0)$ occurs due to the nesting property of the Fermi surfaces. Magnetic field enhances this phase in …
The phonon dynamics of filled skutterudite CeRu4Sb12 have been studied at room temperature by inelastic neutron scattering. Optical phonons associated with a large vibration of Ce atoms are observed at a relatively low energy of E = 6 meV, and show anticrossing behavior with acoustic phonons. We propose that the origin of the low lattice thermal conductivity in filled skutterudites can be attributed to intensive Umklapp scattering originating from low-lying optical phonons. By an analysis based on a Born-von Karman force model, the longitudinal force constants of the nearest Ce-Sb and Ce-Ru pa…
Electrical resistivity $ρ$, specific heat C, and magnetic susceptibility $χ$ measurements made on the filled skutterudite CeRu_4As_{12} reveal non-Fermi liquid (NFL) T - dependences at low T, i.e., $ρ$(T) $\sim$ T^{1.4} and weak power law or logarithmic divergences in C(T)/T and $χ$(T). Measurements also show that the T - dependence of the thermoelectric power S(T) deviates from that seen in other Ce systems. The NFL behavior appears to be associated with fluctuations of the Ce valence between 3^+ and 4^+ rather than a typical Kondo lattice scenario that would be appropriate for an integral Ce…
The filled-skutterudite compound CeRu$_4$Sb$_{12}$ shows a pseudo-gap structure in the optical conductivity spectra similar to the Kondo insulators, but metallic behavior below 80 K. The resistivity shows a large peak at 80 K, and the Seebeck coefficient is positive and also shows a large peak at nearly the same temperature. In order to explain all these features, a simplified tight-binding model, which captures the essential features of the band calculation, is proposed. Using this model and introducing the correlation effect within the framework of the dynamical mean field approximation and …
Rare-earth metal filled skutterudites RPt4Ge12 with R=La-Nd, and Eu exhibit a variety of different ground states, e.g., conventional and unconventional superconductivity in LaPt4Ge12 and PrPt4Ge12, respectively, and intermediate valence behavior in CePt4Ge12. In this work we investigate the magnetic state of NdPt4Ge12 and EuPt4Ge12 by specific heat, dc-susceptibility and magnetization. NdPt4Ge12 shows two magnetic phase transitions at T_N1=0.67 K and T_N2=0.58 K, while EuPt4Ge12 displays a complex magnetic phase diagram below the magnetic ordering temperature of 1.78 K. The specific heat indic…
In order to gain a deep insight into $f$-electron properties of filled skutterudite compounds from a microscopic viewpoint, we investigate the multiorbital Anderson model including Coulomb interactions, spin-orbit coupling, and crystalline electric field effect. For each case of $n$=1$\sim$13, where $n$ is the number of $f$ electrons per rare-earth ion, the model is analyzed by using the numerical renormalization group (NRG) method to evaluate magnetic susceptibility and entropy of $f$ electron. In order to make further step to construct a simplified model which can be treated even in a period…
Magnetization, specific heat, and electrical resistivity measurements were made on single crystals of the filled skutterudite compound PrOs$_{4}$As$_{12}$. Specific heat measurements indicate an electronic specific heat coefficient $γ$ $\sim 50-200$ mJ/mol K$^{2}$ at temperatures 10 K $\leq T \leq 18$ K, and $\sim 1$ J/mol K$^{2}$ for $T \leq 1.6$ K. Magnetization, specific heat, and electrical resistivity measurements reveal the presence of two, or possibly three, ordered phases at temperatures below $\sim 2.3$ K and in fields below $\sim 3$ T. The low temperature phase displays antiferromagn…
Rare 4f^2-based heavy-fermion behaviors have been revealed recently in Pr-based filled skutterudites PrFe4P12 and PrOs4Sb12. Recent studies on the thermal properties on both compounds are reported, putting emphasis on the field-induced ordered phase found in PrOs4Sb12.
Characteristics of hybridization and multipole orders of $4f$-electrons in Pr skutterudites are explained in terms of a pseudo-quartet composed of crystalline electric field (CEF) singlet and the triplet. It is shown that the contrasting behaviors observed in PrFe$_4$P$_{12}$ and PrOs$_4$Sb$_{12}$ are ascribed to the difference in triplet wave functions and the CEF splittings.Since a macroscopic degeneracy remains even in the ordered phase with the $Γ_3$-type antiferro-quadrupole (AFQ) order,a model with strong AFQ fluctuation and static monopole/hexadecapole order is proposed for PrFe$_4$P$_{…
We report experimental results of nuclear magnetic resonance (NMR) at the La site and nuclear quadrupole resonance (NQR) at the Sb site in the filled skutterudite LaOs$_4$Sb$_{12}$. We found that the nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ at the La site exhibits a different temperature dependence from that at the Sb site. Although $1/T_1T$ at the Sb site is explained by the Korringa mechanism, $1/T_1T$ at the La site exhibits a broad maximum around 50 K, showing the presence of an additional contribution at the La site. The additional low-lying excitations observe…
X-ray diffraction, electrical resistivity, magnetization, specific heat, and thermoelectric power measurements are presented for single crystals of the new filled skutterudite compound {\CeOsAs}, which reveal phenomena that are associated with f - electron - conduction electron hybridization. Valence fluctuations or Kondo behavior dominates the physics down to $T$ $\sim$ 135 K. The correlated electron behavior is manifested at low temperatures as a hybridization gap insulating state. The small energy gap $Δ$$_1$/k$_B$ $\sim$ 73 K, taken from fits to electrical resistivity data, correlates with…
Specific heat and transport measurements have revealed an unconventional heavy-fermion (HF) state in SmOs4Sb12 single crystals. The electronic specific-heat coefficient (gamma=0.82 J/K^2mol) and the coefficient (A) of the quadratic temperature dependence of electrical resistivity are largely enhanced, although the ratio A/gamma^2 is reduced from the Kadowaki-Woods ratio of HF materials. Both gamma and A do not show any significant decrease in applied field in contrast with Ce-based HF compounds, suggesting an unconventional origin of the heavy quasiparticles. A weak ferromagnetic ordering sets…
We report the de Haas-van Alphen (dHvA) experiment on the filled skutterudite PrFe$_4$P$_{12}$ exhibiting apparent Kondo-like behaviors in the transport and thermal properties. We have found enormously enhanced cyclotron effective mass $m^{\rm \ast}_{\rm c}=81 m_{\rm 0}$ in the high field phase (HFP), which indicates that PrFe$_4$P$_{12}$ is the first Pr-compound in which really heavy mass has been unambiguously confirmed. Also in the low field non-magnetic ordered phase (LOP), we observed the dHvA branch with $m^{\rm \ast}_{\rm c}=10 m_{0}$ that is quite heavy taking into account its small Fe…
Motivated by current research efforts towards exploring the interplay between magnetism and superconductivity in multiband electronic systems, we have investigated the effects of Eu substitution through thermodynamic measurements on the superconducting filled skutterudite alloys Pr$_{1-x}$Eu$_x$Pt$_4$Ge$_{12}$. An increase in Eu concentration leads to a suppression of the superconducting transition temperature consistent with an increase of magnetic entropy due to Eu local moments. While the low-temperature heat capacity anomaly is present over the whole doping range, we find that in alloys wi…
We report evidence for a close relation between the thermal activation of the rattling motion of the filler guest atoms, and inhomogeneous spin dynamics of the Eu2+ spins. The spin dynamics is probed directly by means of Eu2+ electron spin resonance (ESR), performed in both X-band (9.4 GHz) and Q-band (34 GHz) frequencies in the temperature interval 4.2 < T < 300 K. A comparative study with ESR measurements on the Beta-Eu8Ga16Ge30 clathrate compound is presented. Our results point to a correlation between the rattling motion and the spin dynamics which may be relevant for the general understan…
A detailed study of the spin dynamics of the S-state ions Gd3+ and Eu2+ in the filled skutterudites La1-xRxPt4Ge12 (R= Gd, Eu) is reported. The spin dynamics is investigated directly by means of Gd3+ and Eu2+ electron spin resonance (ESR), performed at X-band (~ 9.4 GHz) and Q-band (~ 34 GHz) frequencies in the temperature intervals 8<T<300 K and 1.5<T<300 K respectively. The ESR parameters provide direct evidence for the vibrational behavior of the Gd3+ ions but not for the Eu2+ ions. These results are interpreted in the light of recent discussions about the spin relaxation in cage systems. I…
Theoretical account is given of 4f-electron dynamics and multipole orders in Pr skutterudites with particular attention to (i) mechanism of the crystalline electric field (CEF) splitting leading to a pseudo-quartet ground state;(ii) Kondo effect due to exchange interactions involving the pseudo-quartet;(iii) multipole orders in the lattice of the pseudo-quartet in magnetic field.Competition between the point-charge interaction andhybridization between 4f and conduction electrons is identified as the key for controlling the CEF splitting. It is found that one of two pseudo-spins forming the pse…
Studies of superconductivity in multiband correlated electronic systems has become one of the central topics in condensed matter/materials physics. In this paper, we present the results of thermodynamic measurements on the superconducting filled skutterudite system Pr$_{1-x}$Ce$_x$Pt$_4$Ge$_{12}$ ($ 0 \leq x \leq 0.2$) to investigate how substitution of Ce at Pr sites affects superconductivity. We find that an increase in Ce concentration leads to a suppression of the superconducting transition temperature from $T_{c}\sim 7.9$ K for $x=0$ to $T_c\sim 0.6$ K for $x=0.14$. Our analysis of the sp…
We report on a novel phase transition at $T$ = 0.9 K in the Ce-based filled-skutterudite compound CeOs$_{4}$Sb$_{12}$ via measurements of the nuclear-spin lattice relaxation rate $1/T_{1}$ and nuclear quadrupole resonance (NQR) spectrum of Sb nuclei. The temperature ($T$) dependence of $1/T_1$ behaves as if approaching closely an antiferromagnetic (AFM) quantum critical point (QCP), following the relation $1/T_{1}\propto T/(T-T_{\rm N})^{1/2}$ with $T_{\rm N} = 0.06$ K in the range of $T=1.3-25$ K. The onset of either the spin-density-wave (SDW) or charge-density-wave (CDW) order at $T_{\rm 0}…
Specific heat and magnetization measurements have been performed on high-quality single crystals of filled-skutterudite PrFe_4P_{12} in order to study the high-field heavy-fermion state (HFS) and low-field ordered state (ODS). From a broad hump observed in C/T vs T in HFS for magnetic fields applied along the <100> direction, the Kondo temperature of ~ 9 K and the existence of ferromagnetic Pr-Pr interactions are deduced. The {141}-Pr nuclear Schottky contribution, which works as a highly-sensitive on-site probe for the Pr magnetic moment, sets an upper bound for the ordered moment as ~ 0.03 μ…
Filled-skutterudite heavy fermion (HF) compounds host rich ground states depending on the f electron configurations. CeOs4Sb12 (COS) with Ce 4f1, and PrOs4Sb12 (POS) with Pr 4f2 configurations show distinct properties of Kondo insulating and HF superconductivity, respectivity. We unveiled the underlying microscopic origin by angle-resolved photoemission spectroscopy studies. Their eV-scale band structure matches well, representing the common characters of conduction electrons in ROs4Sb12 systems (R = rare earth). However, f electrons interact differently with conduction electrons in them. Stro…
The filled skutterudite compound \PrOsSb{} has been found to exhibit superconductivity with a critical temperature $T_\mathrm{c} = 1.85$ K that develops out of a heavy Fermi liquid with an effective mass $m^{*} \approx 50 m_\mathrm{e}$. The current experimental situation regarding the heavy fermion state, the superconducting state, and a high field, low temperature phase that is apparently associated with magnetic or quadrupolar order in \PrOsSb{} is briefly reviewed herein.
The 31P-NMR (nuclear magnetic resonance) and muSR (muon spin relaxation) measurements on the filled skutterudite system SmFe4P12 have been carried out. The temperature T dependence of the 31P-NMR spectra indicates the existence of the crystalline electric field effect splitting of the Sm3+$ (J = 5/2) multiplet into a ground state and an excited state of about 70 K. The spin-lattice relaxation rate 1/T1 shows the typical behavior of the Kondo system, i.e., 1/T1 is nearly T independent above 30 K, and varies in proportion to T (the Korringa behavior, 1/T1 \propto T) between 7.5 K and 30 K. The T…
Infrared reflectance spectroscopy measurements were made on four members of the MFe_4P_12 family of filled skutterudites, with M=La, Th, Ce and U. In progressing from M=La to U the system undergoes a metal-insulator transition. It is shown that, although the filling atom induces such dramatic changes in the transport properties of the system, it has only a small effect on lattice dynamics. We discuss this property of the compounds in the context of their possible thermoelectric applications.
$^{75}$As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements have been carried out to investigate the magnetic and electronic properties of the filled skutterudite metallic compound SrFe$_4$As$_{12}$. The temperature dependence of Knight shift $K$ determined by the NQR spectrum under a small magnetic field ($\le$ 0.5 T) shows the similar temperature dependence of the magnetic susceptibility $χ$ which exhibits a broad maximum at $T^\ast$ $\sim$ 50 K. The nuclear spin-lattice relaxation rate divided by temperature, 1/$T_1T$, increases with decreasing temperature…
New germanium-platinum compounds with the filled-skutterudite crystal structure were synthesized. The structure and composition were investigated by X-ray diffraction and microprobe analysis. Magnetic susceptibility, specific heat, and electrical resistivity measurements evidence superconductivity in LaPt4Ge12 and PrPt4Ge12 below 8.3K. The parameters of the normal and superconducting states were established. Strong coupling and a crystal electric field singlet groundstate is found for the Pr compound. Electronic structure calculations show a large density of states at the Fermi level. Similar …
We report on systematic study of superconducting characteristics and Pr crystalline-electric-field (CEF) levels of filled-skutterudite \pra ($T_{\rm c}$ = 2.33 K). The temperature dependences of the upper critical field $H_{\rm c2}$ and the Ginzburg-Landau (Maki) parameter $κ_2$ suggest an s-wave clean-limit superconductivity. The electronic specific heat coefficient $γ\sim 95$ mJ/K$^2$mol, being $\sim 1.5$ times larger than that for \lra, indicates $4f$-originating quasiparticle mass enhancement. Magnetic susceptibility $χ(T)$ indicates that the CEF ground state is a $Γ_1$ singlet and a $Γ_4^…
The filled-skutterudite compound CePt4Ge12 is situated close to the border between intermediate-valence of Ce and heavy-fermion behavior. Substitution of Ge by Sb drives the system into a strongly correlated and ultimately upon further increasing the Sb concentration into an antiferromagnetically ordered state. Our experiments evidence a delicate interplay of emerging Kondo physics and the formation of a local 4f moment. An extended non-Fermi-liquid region, which can be understood in the framework of a Kondo-disorder model, is observed. Band-structure calculations support the conclusion that t…
The interplay of superconductivity and magnetism is a subject of ongoing interest, stimulated most recently by the discovery of Fe-based superconductivity and the recognition that spin-fluctuations near a magnetic quantum critical point may provide an explanation for the superconductivity and the order parameter. Here we investigate magnetism in the Na filled Fe-based skutterudites using first principles calculations. NaFe4Sb12 is a known ferromagnet near a quantum critical point. We find a ferromagnetic metallic state for this compound driven by a Stoner type instability, consistent with prio…
It is shown that quadrupole susceptibility can be detected in Gd compounds contrary to our textbook knowledge that Gd$^{3+}$ ion induces pure spin moment due to the Hund's rules in an $LS$ coupling scheme. The ground-state multiplet of Gd$^{3+}$ is always characterized by $J$=7/2, where $J$ denotes total angular momentum, but in a $j$-$j$ coupling scheme, one $f$ electron in $j$=7/2 octet carries quadrupole moment, while other six electrons fully occupy $j$=5/2 sextet, where $j$ denotes one-electron total angular momentum. For realistic values of Coulomb interaction and spin-orbit coupling, th…
We report the de Haas-van Alphen (dHvA) effect and magnetoresistance in the filled-skutterudite superconductor LaRu4P12, which is a reference material of PrRu4P12 that exhibits a metal-insulator (M-I) transition at T_MI~60 K. The observed dHvA branches for the main Fermi surface (FS) are well explained by the band-structure calculation, using the full potential linearized augmented-plane-wave method with the local-density approximation, suggesting a nesting instability with q =(1,0,0) in the main multiply connected FS as expected also in PrRu4P12. Observed cyclotron effective masses of (2.6-11…
Experiments on rare-earth filled skutterudites demonstrate an intriguing array of thermodynamic, transport and superconducting properties, and bring to fore theoretical challenges posed by f-electron systems. First principle calculations based density functional theory and its extensions for strongly correlated systems such as the Hubbard U correction, provide valuable information about electronic structure that can be used to understand experiments. We present a comprehensive study of the electronic structure and Fermi surface of a series of rare earth filled skutterudites, RPt4Ge12 (where R …
Electron Spin Resonance (ESR) measurements performed on the filled skutterudite system Ce1-x$YbxFe4P12 (x< 0.003) unequivocally reveal the coexistence of two Yb3+ resonances, associated with sites of considerably different occupations and temperature behaviors. Detailed analysis of the ESR data suggests a scenario where the fraction of oversized (Fe2P3)4 cages that host Yb ions are filled with a low occupation of on-center Yb3+ sites and a highly occupied T-dependent distribution of off-center Yb3+ sites. Analysis of the 171Yb3+ (I=1/2) isotope hyperfine splittings reveal that these two sites …
The spin polarization of ferromagnetic alkali-metal iron antimonides KFe4Sb12 and NaFe4Sb12 is studied by point-contact Andreev reflection using superconducting Nb and Pb tips. From these measurements an intrinsic transport spin polarization Pt of 67% and 60% for the K and Na compound, respectively, is inferred which establishes these materials as a new class of highly spin polarized ferromagnets. The results are in accord with band structure calculations within the local spin density approximation (LSDA) that predict nearly 100% spin polarization in the density of states. We discuss the impac…
MHz conductivity, torque magnetometer and magnetization measurements are reported on single crystals of CeOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$ using temperatures down to 0.5~K and magnetic fields of up to 60~tesla. The field-orientation dependence of the de Haas-van Alphen and Shubnikov-de Haas oscillations is deduced by rotating the samples about the $[010]$ and $[0\bar{1}1]$ directions. The results indicate that NdOs$_4$Sb$_{12}$ has a similar Fermi surface topology to that of the unusual superconductor PrOs$_4$Sb$_{12}$, but with significantly smaller effective masses, supporting the impor…
Thermal conductivity measurements were performed on single crystal samples of the superconducting filled skutterudite compounds PrOs$_4$Sb$_{12}$ and PrRu$_4$Sb$_{12}$ both as a function of temperature and magnetic field applied perpendicular to the heat current. In zero magnetic field, the low temperature electronic thermal conductivity of PrRu$_4$Sb$_{12}$ is vanishingly small, consistent with a fully-gapped Fermi surface. For PrOs$_4$Sb$_{12}$, however, we find clear evidence for residual electronic conduction as the temperature tends to zero Kelvin which is consistent with the presence of …
We have performed $^{139}$La,$^{31}$P-NMR studies on a filled skutterudite superconductor LaFe$_{4}$P$_{12}$ with a critical temperature $T_c=4.1$ K. In the normal state, the presence of antiferromagnetic (AFM) fluctuations at finite wave vectors is suggested from the relation between the nuclear spin-lattice relaxation rate $1/T_1$ and the Knight shift. In the superconducting (SC) state, the distinct coherence peak was observed just below $T_c$, and is easily suppressed by the applied field. An exponential decrease of $1/T_1$ was observed, suggestive of the isotropic superconducting gap with …
In the unconventional f-electron-associated charge order phase of filled skutterudite PrRu4P12, the low-temperature behaviors of the triplet crystalline-electric-field ground state of Pr ions have been studied by specific heat and magnetization measurements using high quality single crystals. Specific heat shows an anomalous Schottky-type peak structure at 0.30 K in zero field in spite of the absence of any symmetry breaking. Magnetization curve at 0.06 K shows a remarkable rounding below 1 T. It has been revealed that these anomalies provide compelling evidence for the formation of a lattice …
Superconductivity, magnetic order, and quadrupolar order have been investigated in the filled skutterudite system Pr$_{1-x}$Nd$_{x}$Os$_4$Sb$_{12}$ as a function of composition $x$ in magnetic fields up to 9 tesla and at temperatures between 50 mK and 10 K. Electrical resistivity measurements indicate that the high field ordered phase (HFOP), which has been identified with antiferroquadruoplar order, persists to $x$ $\sim$ 0.5. The superconducting critical temperature $T_c$ of PrOs$_4$Sb$_{12}$ is depressed linearly with Nd concentration to $x$ $\sim$ 0.55, whereas the Curie temperature $T_{FM…
We report $^{123}$Sb nuclear quadrupole resonance (NQR) measurements of the filled skutterudite heavy-fermion superconductor PrOs$_4$Sb$_{12}$ under high pressures of 1.91 and 2.34 GPa. The temperature dependence of NQR frequency and the spin-lattice relaxation rate $1/T_1$ indicate that the crystal-electric-field splitting $Δ_{\rm CEF}$ between the ground state $Γ_1$ singlet and the first excited state $Γ_4^{(2)}$ triplet decreases with increasing pressure. The 1/$T_1$ below $T_c$ = 1.55 K at $P$ = 1.91 GPa shows a power-law temperature variation and is proportional to $T^5$ at temperatures c…
The filled skutterudite compound \PrOsSb{} exhibits superconductivity below a critical temperature $T_\mathrm{c} = 1.85$ K that develops out of a nonmagnetic heavy Fermi liquid with an effective mass $m^{*} \approx 50 m_\mathrm{e}$, where $m_\mathrm{e}$ is the free electron mass. Analysis of magnetic susceptibility, specific heat, electrical resistivity and inelastic neutron scattering measurements within the context of a cubic crystalline electric field yields a Pr$^{3+}$ energy level scheme that consists of a $Γ_{3}$ nonmagnetic doublet ground state that carries an electric quadrupole moment…
The optical conductivity [$σ(ω)$] spectra of alkaline-earth-filled skutterudites with the chemical formula $A^{2+}M_{4}$Sb$_{12}$ ($A$ = Sr, Ba, $M$ = Fe, Ru, Os) and a reference material La$^{3+}$Fe$_{4}$Sb$_{12}$ were obtained and compared with the corresponding band structure calculations and with calculated $σ(ω)$ spectra to investigate their electronic structures. At high temperatures, the energy of the plasma edge decreased with the increasing valence of the guest atoms $A$ in the Fe$_{4}$Sb$_{12}$ cage indicating hole-type conduction. A narrow peak with a pseudogap of 25 meV was observe…
We study the influence of inelastic rare-earth impurity scattering on electron-phonon mediated superconductivity and mass renormalization in (La$_{1-x}$Pr$_{x}$)Os$_{4}$Sb$_{12}$ compounds. Solving the strong coupling Eliashberg equations we find that the dominant quadrupolar component of the inelastic scattering on Pr impurities yields an enhancement of the superconducting transition temperature T$_c$ in LaOs$_{4}$Sb$_{12}$ and increases monotonically as a function of Pr concentration. The calculated results are in good agreement with the experimentally observed T$_c (x)$ dependence. Our anal…
Comprehensive magnetic-field-orientation dependent studies of the susceptibility and de Haas-van Alphen effect have been carried out on single crystals of the filled skutterudites PrOs$_4$As$_{12}$ and LaOs$_4$As$_{12}$ using magnetic fields of up to 40~T. Several peaks are observed in the low-field susceptibility of PrOs$_4$As$_{12}$, corresponding to cascades of metamagnetic transitions separating the low-field antiferromagnetic and high-field paramagnetic metal (PMM) phases. The de Haas-van Alphen experiments show that the Fermi-surface topologies of PrOs$_4$As$_{12}$ in its PMM phase and L…
Muon spin rotation ($μ$SR) and inelastic X-ray scattering (IXS) were used to investigate the superconducting properties of the filled-skutterudite compound LaRu$_{4}$As$_{12}$. A two-gap isotropic ($s+s$)-wave model can explain the temperature dependence of the superfluid density. Zero field $μ$SR measurements confirm that the time-reversal symmetry does not break upon entering the superconducting state. The measurements of lattice dynamics at 2, 20 and 300 K revealed temperature dependencies of the phonon modes that do not follow strictly a hardening of phonon frequencies upon cooling as expe…
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, …
X-ray powder diffraction, magnetic susceptibility $χ(T)$, and electrical resistivity $ρ(T)$ measurements were made on single crystals of the filled skutterudite series Pr(Os$_{1-x}$Ru$_x$)$_4$Sb$_{12}$. One end of the series ($x = 0$) is a heavy fermion superconductor with a superconducting critical temperature $T_{c} = 1.85$ K, while the other end ($x = 1$) is a conventional superconductor with $T_{c} \approx 1$ K. The lattice constant $a$ decreases approximately linearly with increasing Ru concentration $x$. As Ru (Os) is substituted for Os (Ru), $T_{c}$ decreases nearly linearly with substi…
We report $^{123}$Sb nuclear quadrupole resonance (NQR) measurements of the filled skutterudite heavy-fermion superconductor PrOs$_4$Sb$_{12}$ under high pressure. The temperature dependence of NQR frequency and the spin-lattice relaxation rate $1/T_1$ indicate that the crystal-electric-field splitting $Δ_{\rm CEF}$ between the ground state $Γ_1$ singlet and the first excited state $Γ_4^{(2)}$ triplet decreases with increasing pressure. Ac-susceptibility measurements indicate that the superconducting transition temperature ($T_{\rm c}$) also decreases with increasing pressure. However, above $…
A thorough characterization of many samples of the filled skutterudite compound PrOs4Sb12 is provided. We find that the double superconducting transition in the specific heat Tc1~1.89K and Tc2~1.72K tends to appear in samples with a large residual resistivity ratio, large specific heat jump at the superconducting transition and with the highest absolute value of the specific heat above Tc1. However, we present evidence which casts doubt on the intrinsic nature of the double superconducting transition. The ratio of the two specific heat jumps ΔC(Tc1)/ΔC(Tc2) shows a wide range of values on crys…
We report the electronic and superconducting properties in the Pr-based filled-skutterudite superconductor PrRu$_4$Sb$_{12}$ with $T_c = 1.3$ K via the measurements of nuclear-quadrupole-resonance (NQR) frequency $ν_Q$ and nuclear-spin-lattice-relaxation time $T_1$ of Sb nuclei. The temperature dependence of $ν_Q$ has revealed the energy scheme of Pr$^{3+}$ crystal electric field (CEF) that is consistent with an energy separation $Δ_{CEF}\sim 70$K between the ground state and the first-excited state. In the normal state, the Korringa relation of $(1/T_1T)_{Pr}$=const. is valid, with [$(1/T_{1}…
In this work we report electron spin resonance (ESR) measurements in the semiconducting Ce1-xGdxFe4P12 (x ~ 0.001) filled skutterudite compounds. Investigation of the temperature (T) dependence of the ESR spectra and relaxation process suggests, that in the T-interval of 140-160 K, the onset of a "weak" metal-insulator (M-I) transition takes place due to the increasing density of thermally activated carriers across the semiconducting gap of ~ 1500 K. In addition, the observed low-T fine and hyperfine structures start to collapse at ~ 140 K and is completely absent for > 160 K. We claim that th…
The physical origin of frequency dependence in elastic constants, which are often found in an ultrasound propagation in filled skutterudites and clathrate compounds, is investigated theoretically. This dependence arises from a coupling between the acoustic phonon and some optical phonons, which strongly interact with electrons. Using a self-consistent ladder approximation together with a pseudofermion mapping of the phonon to the single site Holstein Anderson model, a soft mode of the optical phonon at zero frequency is shown to emerge. The temperature dependence of the spectral weight of this…
In order to clarify possible multipole states of Sm-based filled skutterudite compounds, we investigate multipole susceptibility of a multiorbital Anderson model dynamically coupled with Jahn-Teller phonons by using a numerical renormalization group method. Here we take a procedure to maximize the multipole susceptibility matrix to determine the multipole state. When the electron-phonon coupling term is simply ignored, it is found that the dominant multipole state is characterized by 2u octupole for the $Γ_{67}^-$ quartet ground state, while the low-temperature phase is governed by magnetic fl…
The superconducting pairing state of LaPt$_{4}$Ge$_{12}$ is studied by measuring the magnetic penetration depth $λ(T,B)$ and the superfluid density $ρ_s(T)$ using a tunnel-diode-oscillator (TDO)-based method and by transverse field muon-spin rotation ($μ$SR) spectroscopy. $λ(T)$ follows an exponential-type temperature dependence at $T\ll T_{c}$, but its zero-temperature value $λ(0)$ increases linearly with magnetic field. Detailed analyses demonstrate that both $λ(T)$ and the corresponding $ρ_{s}(T)$, measured in the Meissner state by the TDO method are well described by a two-gap $γ$ model wi…
