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Nature of the field-induced charge-ordered phase (phase II) of $\mathrm{Sm}{\mathrm{Ru}}_{4}{\mathrm{P}}_{12}$ has been investigated by resonant x-ray diffraction (RXD) and polarized neutron diffraction (PND), focusing on the relationship between the atomic displacements and the antiferromagnetic (AFM) moments of Sm. From the analysis of the interference between the nonresonant Thomson scattering and the resonant magnetic scattering, combined with the spectral function obtained from x-ray magnetic circular dichroism, it is shown that the AFM moment of Sm prefers to be parallel to the field (${\mathbit{m}}_{\text{AF}}\ensuremath{\parallel}\mathbit{H}$), giving rise to large and small moment sites around which the ${\mathrm{P}}_{12}$ and Ru cage contract and expand, respectively. This is associated with the formation of the staggered ordering of the ${\mathrm{\ensuremath{\Gamma}}}_{7}$-like and ${\mathrm{\ensuremath{\Gamma}}}_{8}$-like crystal-field states, providing a strong piece of evidence for the charge order. PND was also performed to obtain complementary and unambiguous conclusion. In addition, isotropic and continuous nature of phase II is demonstrated by the field-direction invariance of the interference spectrum in RXD. Crucial role of the $p\ensuremath{-}f$ hybridization is shown by resonant soft x-ray diffraction at the P $K$ edge ($1s\ensuremath{\leftrightarrow}3p$), where we detected a resonance due to the spin polarized $3p$ orbitals reflecting the AFM order of Sm.

Through a high-precision soft x-ray magnetic circular dichroism (XMCD) study of the intermediate-valence compound $\mathrm{Sm}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$, we show our successful approach of revealing unprecedented details of Kondo screening below a characteristic temperature of ${T}_{0}\ensuremath{\sim}20$ K in the paramagnetic phase. The multiplet XMCD structure at the Sm ${M}_{5}$ edge sensitive to the $4f$ configuration enabled us to observe a clear difference between the temperature evolution above and below ${T}_{0}$ with one- and two-component behavior, respectively. Our findings are in strong contrast to the conventional Kondo crossover that coincides with the valence transition, but are qualitatively accounted for by theoretical XMCD predictions combined with the two-fluid phenomenology recently proposed. This work contributes to the large context of Kondo physics that is closely related to quantum criticality in heavy fermion systems.

The anisotropic changes in the electronic structure of a metal-to-insulator transition (MIT) material, RuAs, with two-step phase transition are reported by using polarized optical conductivity [$\sigma(\omega)$] spectra, angle-integrated photoelectron (PE) spectra, and band calculations based on local density approximation (LDA). Both the PE and $\sigma(\omega)$ spectra not only in the high-temperature (HT) phase but also in the low-temperature (LT) phase as well as the energy gap formation owing to the MIT were almost consistent with those derived from the LDA band calculations, so the fundamental electronic structure in the HT and LT phases can be explained without electron correlations. However, the electronic structure in the middle phase between the HT and LT phases has not been clarified. The polarized $\sigma(\omega)$ spectra revealed not only the anisotropic energy gap formation but also the anisotropic gap-opening temperature, i.e., the energy gap along the $c$ axis in the HT phase starts to open near the higher transition temperature, but that along the $b$ axis opens below the lower transition temperature. The finding suggests that the two-step MIT originates from the anisotropic energy gap formation., Comment: 7 pages, 7 figures

We report $^{75}\mathrm{As}$-NMR results for CrAs under pressure, which shows superconductivity adjoining a helimagnetically ordered state. We successfully evaluated the Knight shift from the spectrum, which is strongly affected by the quadrupole interaction. The Knight shift shows the remarkable feature that the uniform spin susceptibility increases toward low temperatures in the paramagnetic state. This is in sharp contrast to CrAs at ambient pressure, and also to cuprates and Fe pnictides, where antiferromagnetic correlations are dominant. Superconductivity emerges in CrAs under unique magnetic correlations, which probably originate in the three-dimensional zigzag structure of its nonsymmorphic symmetry.

Structural properties of SmRu$_4$P$_{12}$ in the anomalous magnetic ordered phase between $T^*\sim 14 $ K and $T_{\text{N}}=16.5$ K in magnetic fields has been studied by x-ray diffraction. Atomic displacements of Ru and P, reflecting the field-induced charge order of the $p$ electrons, have been deduced by analyzing the intensities of the forbidden Bragg peaks, assuming a cubic space group $Pm\bar{3}$. Also, by utilizing high-resolution x-ray diffraction experiment, we observed a splitting of fundamental Bragg peaks, clarifying that the unit cell in the magnetic ordered phase is rhombohedral elongated along the $[1\, 1\, 1]$ axis. Responses of the rhombohedral domains to the magnetic field, which reflects the direction of the magnetic moment, is studied in detail.

We have performed $^{31}\mathrm{P}$-NMR measurements on single-crystalline CeRuPO under pressure in order to understand the variation in magnetic character against pressure. The nuclear magnetic resonance (NMR) spectra for $\text{H}\ensuremath{\perp}c$ and $\text{H}\ensuremath{\parallel}c$ at 2.15 GPa split below the ordered temperature, which is microscopic evidence of the change in the magnetic ground state from the ferromagnetic state at ambient pressure to the antiferromagnetic (AFM) state under pressure. The analysis of NMR spectra suggests that the magnetic structure in the AFM state is the stripe-type AFM state with the AFM moment ${m}_{\mathrm{AFM}}\ensuremath{\perp}c$ axis, and it changes with a magnetic field perpendicular to the $c\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{axis}$. In addition, the dimensionality of magnetic correlations in the spin and $k$ space is estimated. We reveal that three-dimensional magnetic correlations in CeRuPO are robust against pressure, which is quite different from the suppression of the magnetic correlations along the $c\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{axis}$ by Fe substitution in $\text{Ce}({\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x})\text{PO}$.

This work was supported by Grants-in-Aid for Scientific Research (No. 21204456, No. 21102515, and No. 2430087) from JSPS and MEXT, and by a Basic Science Research Grant from the Sumitomo Foundation.

We have investigated the resistivity $(\ensuremath{\rho}),$ thermoelectric power (TEP), and Hall coefficient ${(R}_{H})$ on high-quality single crystals of $R{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}.$ TEP in ${\mathrm{CeFe}}_{4}{\mathrm{P}}_{12}$ is extremely large $(\ensuremath{\sim}0.5$ mV/K at 290 K) with a peak of $\ensuremath{\sim}0.75$ mV/K at around 65 K. The Hall mobility also shows a peak at $\ensuremath{\sim}65$ K, suggesting carriers with heavy masses developed at lower temperatures related to the f-hybridized band. Both Pr and Nd systems exhibit an apparent increase of $\ensuremath{\rho}$ with decreasing temperature far above their magnetic transition temperatures. In the same temperature ranges, TEP exhibits unusually large absolute values of $\ensuremath{-}50 \ensuremath{\mu}\mathrm{V}/\mathrm{K}$ for ${\mathrm{PrFe}}_{4}{\mathrm{P}}_{12}$ and $\ensuremath{-}15 \ensuremath{\mu}\mathrm{V}/\mathrm{K}$ for ${\mathrm{NdFe}}_{4}{\mathrm{P}}_{12},$ respectively. For ${\mathrm{PrFe}}_{4}{\mathrm{P}}_{12},$ such anomalous transport properties suggest an unusual ground state, possibly related to the quadrupolar Kondo effect.

Magnetoresistance (MR), Hall resistivity, and thermoelectric power in UCoAl, which exhibits a metamagnetic transition (MT) at low temperatures, have been investigated. Across MT, the MR shows a steplike decrease and increase for the transverse and longitudinal geometries, respectively. The temperature dependence of MR indicates that the magnetic scattering due to the spin fluctuations largely contributes to the electrical resistivity around 17 K. The Hall coefficient and the thermoelectric power show drastic changes associated with MT. Both in the low- and high-field states, the extraordinary Hall effect dominates in the temperature dependence of Hall coefficient. The temperature dependence of thermoelectric power can be qualitatively explained by an extended $s\ensuremath{-}d$ model considering the $5f$ band structure.

Magnetization, heat capacity, electrical resistivity, thermoelectric power, and Hall effect have been investigated on single-crystalline ${\mathrm{Ce}}_{2}{\mathrm{PdSi}}_{3}.$ This compound is shown to order antiferromagnetically below N\'eel temperature ${(T}_{N})\ensuremath{\sim}3\mathrm{K}.$ The Sommerfeld coefficient far below ${T}_{N}$ is found to be about $110{\mathrm{m}\mathrm{J}/\mathrm{K}}^{2}\mathrm{mol}\mathrm{Ce},$ which indicates the heavy-fermion character of this compound. The transport and magnetic properties exhibit large anisotropy with an interplay between crystalline-electric-field (CEF) and Kondo effects. The sign of thermoelectric power is opposite for different directions at high temperatures and the ordinary Hall coefficient is anisotropic with opposite sign for different geometries, indicating the anisotropic Fermi surface. The CEF analysis from the temperature dependence of magnetic susceptibility suggests that the ground state is $|\ifmmode\pm\else\textpm\fi{}\frac{1}{2}〉.$ The first and the second excited CEF doublet levels are found to be located at about 30 and 130 K, respectively. The Kondo temperature is estimated to be the same order as ${T}_{N},$ indicating the presence of a delicate competition between the Kondo effect and magnetic order.

We have measured the thermal conductivity $\ensuremath{\lambda}(T)$ on tetragonal ${\mathrm{CeAuAl}}_{3}$ single crystals along both the a and c axes between 0.4 and 40 K. For comparison, the same measurement has been made on a polycrystalline sample of ${\mathrm{LaAuAl}}_{3}.$ The thermal conductivity of the Ce compound is lower than for the La compound and only weakly anisotropic. No distinct anomalies in $\ensuremath{\lambda}(T)$ of ${\mathrm{CeAuAl}}_{3}$ are observed at the antiferromagnetic transition and, far below the N\'eel temperature, the Wiedemann-Franz law is almost fulfilled. For both compounds a maximum in $\ensuremath{\lambda}/T,$ owing to the phonon contribution, has been observed in the vicinity of 10 K. The data are interpreted by considering phonon scattering processes involving the localized $4f$ electron states on the Ce ions.

We have simultaneously measured the field dependence of transverse voltages at two pairs of transverse probes along with the magnetoresistance to detect the motion of ferromagnetic domain walls in a thin NiFe wire. We observed sharp steplike changes of the transverse voltage correlated with the jumps in magnetoresistance, which have been reported previously in thin ferromagnetic wires. The field dependence is explained in terms of the rotation of local magnetization near the transverse probes. This fact suggests that such a local magnetization rotation might contribute to some of the negative domain-wall resistivity reported in recent papers.

Electrical resistivity (\ensuremath{\rho}), magnetoresistance (MR), magnetization, thermopower, and Hall-effect measurements on the single-crystal ${\mathrm{Gd}}_{2}{\mathrm{PdSi}}_{3},$ crystallizing in an ${\mathrm{AlB}}_{2}$-derived hexagonal structure, are reported. The well-defined minimum in \ensuremath{\rho} at a temperature above N\'eel temperature ${(T}_{N}=21\mathrm{K})$ and large negative MR below $\ensuremath{\sim}{3T}_{N},$ reported earlier for the polycrystals, are reproducible even in single crystals. Such features are generally uncharacteristic of Gd alloys. In addition, we also found interesting features in other data, e.g., two-step first-order-like metamagnetic transitions for the magnetic field along [0001] direction. The alloy exhibits anisotropy in all these properties, though Gd is an $S$-state ion.

We find extraordinary superconducting characteristics in the low-temperature specific heat of high quality ${\mathrm{CeCo}}_{2}$ single crystals, suggesting that the superconducting gap is highly anisotropic. The electronic specific-heat jump at the superconducting transition temperature (${\mathrm{T}}_{\mathrm{c}}$ =1.5 K) is \ensuremath{\Delta}${\mathrm{C}}_{\mathrm{e}}$ /\ensuremath{\gamma}${\mathrm{T}}_{\mathrm{c}}$ =0.85, which is reduced compared to the BCS value of 1.43. At low temperatures (0.13/${\mathrm{T}}_{\mathrm{c}}$ \ensuremath{\ll}1), ${\mathrm{C}}_{\mathrm{e}}$ varies approximately as ${\mathrm{T}}^{2}$ , indicating a possibility of lines of nodes in the gap. A possible correlation of the gap anisotropy with the ferromagnetic spin fluctuation is discussed.

We have fabricated Ce/Ta multilayers under ultrahigh vacuum to investigate the magnetic state of Ce in thin layers. The magnetization, electrical resistivity, and Hall effect have been measured for Ce layer thicknesses between 5 and 100 \AA{}. Results of x-ray analysis indicate that Ce atoms crystallize as bulk Ce for ${\mathit{d}}_{\mathrm{Ce}}$=100 \AA{}, and are amorphous for ${\mathit{d}}_{\mathrm{Ce}}$\ensuremath{\leqslant}15 \AA{}. For ${\mathit{d}}_{\mathrm{Ce}}$=100 \AA{}, the Ce \ensuremath{\gamma}-\ensuremath{\alpha} transition observed in the resistivity and reduced magnetization at 2 K suggest the stabilization of \ensuremath{\alpha}-phase Ce at low temperatures. For ${\mathit{d}}_{\mathrm{Ce}}$\ensuremath{\leqslant}15 \AA{}, in contrast, the magnetic susceptibility and extraordinary Hall effect indicate the existence of magnetic Ce down to 1 K. We speculate that the transition to the nonmagnetic state of Ce at low temperatures for ${\mathit{d}}_{\mathrm{Ce}}$\ensuremath{\leqslant}15 \AA{} is prevented by the amorphous structure. \textcopyright{} 1996 The American Physical Society.

Zero-field muon spin relaxation experiments have been carried out in the Pr(Os${}_{1\ensuremath{-}x}$Ru${}_{x}$)${}_{4}$Sb${}_{12}$ and Pr${}_{1\ensuremath{-}y}$La${}_{y}$Os${}_{4}$Sb${}_{12}$ alloy systems to investigate broken time-reversal symmetry (TRS) in the superconducting state, signaled by the onset of a spontaneous static local magnetic field ${B}_{s}$. In both alloy series ${B}_{s}$ initially decreases linearly with solute concentration. Ru doping is considerably more efficient than La doping, with a $~$50% faster initial decrease. The data suggest that broken TRS is suppressed for Ru concentration $x\ensuremath{\gtrsim}0.6$ but persists for essentially all La concentrations. Our data support a crystal-field excitonic Cooper pairing mechanism for TRS-breaking superconductivity.

The superconducting gap structure of LaFePO $({T}_{c}=7.4\text{ }\text{K})$ is studied by thermal conductivity $(\ensuremath{\kappa})$ at low temperatures in fields $H$ parallel and perpendicular to the $c$ axis. A clear two-step field dependence of $\ensuremath{\kappa}(H)$ with a characteristic field ${H}_{s}(\ensuremath{\sim}350\text{ }\text{Oe})$ much lower than the upper critical field ${H}_{c2}$ is observed. In spite of the large anisotropy of ${H}_{c2}$, $\ensuremath{\kappa}(H)$ in both $H$ directions is nearly identical below ${H}_{s}$. Above ${H}_{s}$, $\ensuremath{\kappa}(H)$ grows gradually with $H$ with a convex curvature, followed by a steep increase with strong upward curvature near ${H}_{c2}$. These results indicate multigap superconductivity with active two-dimensional (2D) and passive three-dimensional bands having contrasting gap values. Together with the recent penetration depth results, we suggest that the 2D bands consist of nodal and nodeless ones, consistent with extended $s$-wave symmetry.

Crystal-field excitation spectra of $\text{Pr}\text{ }4f$ electron state in the filled skutterudite ${\text{PrOs}}_{4}{\text{P}}_{12}$ measured by inelastic neutron scattering experiment evolve distinctly with temperature variation. The spectral widths of excitations from the ground-state singlet to the two triplets and their temperature dependences are well reproduced by the theory based on the exchange coupling between $4f$ and conduction electrons. The shift of level energies by around 1 meV below 60 K indicates modification of crystal-field potential with variation of thermal population of $4f$ electron crystal-field states. The spectral evolution is consistent with the specific heat data that deviates from the calculated one for the well-localized $4f$ electron. The result supports the effect of $p\text{\ensuremath{-}}f$ hybridization between $\text{Pr}\text{ }4f$ and $\text{P}\text{ }p$ states in ${\text{PrOs}}_{4}{\text{P}}_{12}$.

We have investigated the Fermi-surface (FS) properties in the Pr-based filled skutterudite ${\text{PrOs}}_{4}{\text{P}}_{12}$ and its reference compound ${\text{LaOs}}_{4}{\text{P}}_{12}$ by means of de Haas--van Alphen experiments and the band-structure calculations. The topology of FS in ${\text{PrOs}}_{4}{\text{P}}_{12}$ is close to that in the reference compound ${\text{LaOs}}_{4}{\text{P}}_{12}$, indicating a localized nature of $4f$ electrons in ${\text{PrOs}}_{4}{\text{P}}_{12}$. Whereas the localized nature of $4f$ electrons, we have confirmed a highly enhanced cyclotron effective mass of up to $18{m}_{0}$ in ${\text{PrOs}}_{4}{\text{P}}_{12}$, which is enhanced about 3.8 times compared to that in ${\text{LaOs}}_{4}{\text{P}}_{12}$. No nesting property with $q=(1,0,0)$ in the FS of ${\text{PrOs}}_{4}{\text{P}}_{12}$ has been confirmed in contrast to good nesting properties in ${\text{PrFe}}_{4}{\text{P}}_{12}$ and ${\text{PrRu}}_{4}{\text{P}}_{12}$ which exhibit unusual ordered states at low temperatures. A role of both the $4f$ electron's contributions and the FS nesting property for unusual phase transitions are discussed.

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 $\Delta_{\rm CEF}$ between the ground state $\Gamma_1$ singlet and the first excited state $\Gamma_4^{(2)}$ triplet decreases with increasing pressure. Ac-susceptibility measurements indicate that the superconducting transition temperature ($T_{\rm c}$) also decreases with increasing pressure. However, above $P$ $\sim$ 2 GPa, both $\Delta_{\rm CEF}$ and $T_{\rm c}$ do not depend on external pressure up to $P$ = 3.82 GPa. These pressure dependences of $\Delta_{\rm CEF}$ and $T_{\rm c}$ suggest an intimate relationship between quadrupole excitations associated with the $\Gamma_4^{(2)}$ level and unconventional superconductivity in PrOs$_4$Sb$_{12}$. In the superconducting state, 1/$T_1$ below $T_{\rm c}$ = 1.55 and 1.57 K at $P$ = 1.91 and 2.63 GPa shows a power-law temperature variations and are proportional to $T^5$ at temperatures considerably below $T_{\rm c}$. These data can be well fitted by the gap model $\Delta(\theta) = \Delta_0\sin\theta$ with $\Delta_0$ = 3.08 $k_{\rm B}T_{\rm c}$ and 3.04 $k_{\rm B}T_{\rm c}$ for $P$ = 1.91 and 2.63 GPa, respectively. The results indicate there exists point nodes in the gap function.

Through the characterization of many samples of the filled skutterudite compound PrOs4Sb12, we found that even though the double superconducting transition in the specific heat (Tc1 ~1.89 K and Tc2 ~ 1.72 K) appears in samples of good quality, there are various pieces of evidence that cast doubt on its intrinsic nature. First, three samples exhibit a single sharp transition of ~15 mK width at Tc~1.7 K. The quality of the samples exhibiting a single transition is clearly better; the width of the transition is smallest and the normalized specific heat jump ((C-Cnormal)/Cnormal)Tc is larger than the sum of the two specific heat jumps when a double transition exists. Second, the ratio of the two specific heat jumps Delta C(Tc1)/Delta C(Tc2) exhibits a wide variation with samples not only among different batches but also even within a batch. Finally, this ratio was strongly reduced by polishing a sample down to ~100 µm, which points to bulk inhomogeneities as an origin of the spurious transition. Our x-ray diffraction analysis points to Pr-vacancy problem in the samples, but it does not show that they are the origin of the double transition. We provide the superconducting phase diagram under magnetic field of a sample exhibiting a single transition and fit the curve Hc2(T) with a two-band model taking into account the appropriate values for the gap as deduced from thermal conductivity measurements.

We have investigated the exotic metal-insulator (M-I) transition in $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{P}}_{12}$ by using hard-x-ray and soft-x-ray photoemission spectroscopies. The significantly large hybridization strength between conduction and $\mathrm{Pr}\phantom{\rule{0.2em}{0ex}}4f$ electrons $(c\text{\ensuremath{-}}f)$ is found not to change much between the metal and insulating phases. These results suggest that the M-I transition does not noticeably affect the $c\text{\ensuremath{-}}f$ hybridization nature and $\mathrm{P}\phantom{\rule{0.2em}{0ex}}3p--\mathrm{Pr}\phantom{\rule{0.2em}{0ex}}4f$ mixed states are highly stable.

Semiconducting skutterudite $\mathrm{Ce}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ is investigated by synchrotron x-ray photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). $\mathrm{Ce}\phantom{\rule{0.2em}{0ex}}3d$ core-level PES and $3d\text{\ensuremath{-}}4f$ XAS, in combination with single-impurity Anderson model (SIAM) calculations, confirm features due to ${f}^{0}$, ${f}^{1}$, and ${f}^{2}$ configurations. The $\mathrm{Ce}\phantom{\rule{0.2em}{0ex}}3d\text{\ensuremath{-}}4f$ resonant-PES spectra provide the $\mathrm{Ce}\phantom{\rule{0.2em}{0ex}}4f$ density of states (DOS), which indicates the absence of a Kondo resonance at the Fermi level, but can still be explained by SIAM with a small gap in non-$f$ DOS. While $\mathrm{Ce}\phantom{\rule{0.2em}{0ex}}4f$ partial DOS from band structure calculations is consistent with the main $\mathrm{Ce}\phantom{\rule{0.2em}{0ex}}4f$ DOS, the importance of SIAM for core-level PES and XAS spectra quantifies the mixed valence for semiconducting $\mathrm{Ce}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$, derived from strong hybridization between non-$f$ conduction and $\mathrm{Ce}\phantom{\rule{0.2em}{0ex}}4f$ DOS.

We present measurements of the local tunneling density of states in the low temperature ordered state of $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$. The temperature dependencies of the Fermi level density of states and of the integrated density of states at low bias voltages show anomalies at $T\ensuremath{\simeq}6.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the onset of multipolar ordering as detected by specific heat and other macroscopic measurements. In the ordered phase, we find a local density of states with a V-shape form, indicating a partial gap opening over the Fermi surface. The size of the gap according to the tunneling spectra is about $2\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$.

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 $\mathrm{La}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$. We found that the nuclear spin-lattice relaxation rate divided by temperature $1∕{T}_{1}T$ at the La site exhibits a different temperature dependence from that at the Sb site. Although $1∕{T}_{1}T$ at the Sb site is explained by the Korringa mechanism, $1∕{T}_{1}T$ at the La site exhibits a broad maximum around $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, showing the presence of an additional contribution at the La site. The additional low-lying excitations observed at the La site can be understood with the relaxation from anharmonic phonons due to the rattling motion of the La atoms.

S. Imada,1 H. Higashimichi,1 A. Yamasaki,2 M. Yano,1 T. Muro,3 A. Sekiyama,1 S. Suga,1 H. Sugawara,4 D. Kikuchi,5 and H. Sato5 1Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan 2Department of Physics, Faculty of Science and Engineering, Konan University, Kobe 658-8501, Japan 3Spring-8/JASRI, Sayo 579-5198, Japan 4Faculty of the Integrated Arts and Sciences, The University of Tokushima, Minami-jyousanjima-machi 1-1, Tokushima 770-8502, Japan 5Graduate School of Science, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan Received 1 June 2007; revised manuscript received 3 September 2007; published 24 October 2007

Zero- and longitudinal-field muon spin relaxation experiments have been carried out in the alloy series $\mathrm{Pr}{({\mathrm{Os}}_{1\ensuremath{-}x}{\mathrm{Ru}}_{x})}_{4}{\mathrm{Sb}}_{12}$ and ${\mathrm{Pr}}_{1\ensuremath{-}y}{\mathrm{La}}_{y}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$ to elucidate the anomalous dynamic muon spin relaxation observed in these materials. The damping rate $\ensuremath{\Lambda}$ associated with this relaxation varies with temperature, applied magnetic field, and dopant concentrations $x$ and $y$ in a manner consistent with the ``hyperfine enhancement'' of $^{141}\mathrm{Pr}$ nuclear spins first discussed by Bleaney [Physica (Utrecht) 69, 317 (1973)]. This mechanism arises from Van Vleck-like admixture of magnetic ${\mathrm{Pr}}^{3+}$ crystalline-electric-field-split excited states into the nonmagnetic singlet ground state by the nuclear hyperfine coupling, thereby increasing the strengths of spin-spin interactions between $^{141}\mathrm{Pr}$ and muon spins and within the $^{141}\mathrm{Pr}$ spin system. We find qualitative agreement with this scenario and conclude that electronic spin fluctuations are not directly involved in the dynamic muon spin relaxation.

We have investigated the elastic properties of the Ce-based filled skutterudite antimonides CeRu$_{4}$Sb$_{12}$ and CeOs$_{4}$Sb$_{12}$ by means of ultrasonic measurements. CeRu$_{4}$Sb$_{12}$ shows a slight increase around 130 K in the temperature dependence of the elastic constants $C$$_{11}$, ($C$$_{11}$-$C$$_{12}$)/2 and $C$$_{44}$. No apparent softening toward low temperature due to a quadrupolar response of the 4$f$-electronic ground state of the Ce ion was observed at low temperatures. In contrast CeOs$_{4}$Sb$_{12}$ shows a pronounced elastic softening toward low temperature in the longitudinal $C$$_{11}$ as a function of temperature ($T$) below about 15 K, while a slight elastic softening was observed in the transverse $C$$_{44}$ below about 1.5 K. Furthermore, CeOs$_{4}$Sb$_{12}$ shows a steep decrease around a phase transition temperature of 0.9 K in both $C$$_{11}$ and$ C$$_{44}$. The elastic softening observed in $C$$_{11}$ below about 15 K cannot be explained reasonably only by the crystalline electric field effect. It is most likely to be responsible for the coupling between the elastic strain and the quasiparticle band with a small energy gap in the vicinity of Fermi level. The elastic properties and the 4$f$ ground state of Ce ions in CeRu$_{4}$Sb$_{12}$ and CeOs$_{4}$Sb$_{12}$ are discussed from the viewpoint of the crystalline electric field effect and the band structure in the vicinity of Fermi level.

We report a muon spin rotation study in single-crystalline samples of the heavy fermion superconductor $\mathrm{Pr}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$. The muon Knight shift is independent of temperature passing through ${T}_{c}$ down to $20\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ at 3 and $17\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$, indicating that the local spin susceptibility does not decrease in the superconducting state. This result is evidence that spin-triplet superconductivity is realized in $\mathrm{Pr}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$.

Magnetic excitations of the filled skutterudite $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{P}}_{12}$ exhibiting a metal-insulator (M-I) transition at ${T}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{I}}=63\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ were studied by inelastic neutron scattering experiment. The spectra at temperatures much lower than ${T}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{I}}$ are described as well-defined crystal-field excitations. With approaching ${T}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{I}}$, the excitation peaks broaden and shift considerably together with the temperature variation of the carrier number and the atomic displacement in the transition. The $4f$ electron states evolve from the well-localized state in the insulator phase to the strongly hybridized itinerant state by $p\text{\ensuremath{-}}f$ mixing near ${T}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{I}}$. The hybridization is responsible for the M-I transition of $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{P}}_{12}$.

We report the de Haas--van Alphen (dHvA) effect and magnetoresistance in the filled-skutterudite superconductor ${\mathrm{LaRu}}_{4}{\mathrm{P}}_{12}$, which is a reference material of ${\mathrm{PrRu}}_{4}{\mathrm{P}}_{12}$ that exhibits a metal-insulator (M-I) transition at ${T}_{\mathrm{MI}}\ensuremath{\simeq}60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. 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 $\mathbf{q}=(1,0,0)$ in the main multiply connected FS as expected also in ${\mathrm{PrRu}}_{4}{\mathrm{P}}_{12}$. Observed cyclotron effective masses of $(2.6\ensuremath{-}11.8){m}_{0}$, which are roughly twice the calculated masses, indicate the large mass enhancement even in the La-skutterudites. Comparing the FS between ${\mathrm{LaRu}}_{4}{\mathrm{P}}_{12}$ and ${\mathrm{PrRu}}_{4}{\mathrm{P}}_{12}$, an essential role of $c\text{\ensuremath{-}}f$ hybridization cooperating with the FS nesting in driving the M-I transition in ${\mathrm{PrRu}}_{4}{\mathrm{P}}_{12}$ is clarified.

We have measured both magnetoresistance and Hall effect in $\mathrm{Ce}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$ to clarify the large resistivity state ascribed to the Kondo insulating one and the origin of the phase transition near $0.9\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ reported in the specific-heat measurement. We found unusual temperature $(T)$ dependence both in the electrical resistivity $\ensuremath{\rho}\ensuremath{\sim}{T}^{\ensuremath{-}1∕2}$ and the Hall coefficient ${R}_{H}\ensuremath{\sim}{T}^{\ensuremath{-}1}$ over the wide temperature range of about two orders of magnitude below $\ensuremath{\sim}30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which can be explained as a combined effect of the temperature dependences of carrier density and carrier scattering by spin fluctuation. An anomaly related with the phase transition has been clearly observed in the transport properties, from which the $H\text{\ensuremath{-}}T$ phase diagram is determined up to $14\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. Taking into account the small entropy change, the phase transition is most probably the spin density wave one. Both the electrical resistivity and Hall resistivity at $0.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is largely suppressed about an order of magnitude by magnetic fields above $\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, suggesting a drastic change of electronic structure and a suppression of spin fluctuations under magnetic fields.

We have studied the electrical resistivity of the filled skutterudite compound $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ under high pressure. The antiferroquadrupolar ordering temperature ${T}_{Q}$ decreases monotonically with increasing pressure up to $2.4\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Above $2.4\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, we have found that a metal-insulator $(M\text{\ensuremath{-}}I)$ transition appears. The insulating state is easily suppressed by a magnetic field. The observed Kondo effect and a field-induced heavy-fermion state at high pressure suggest that the quadrupolar interactions survive in the insulating region. The quadrupolar interactions might play an essential role in the $M\text{\ensuremath{-}}I$ transition. $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ is an unusual compound in that it shows a pressure-induced transition from a metal to an insulator.

$^{31}\mathrm{P}$-NMR studies have been carried out to investigate magnetic properties in the Pr-based filled skutterudite compound $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$. This compound shows an unusual phase transition at ${T}_{A}\ensuremath{\sim}6.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is now regarded as antiferroquadrupole (AFQ) ordering from neutron-diffraction experiments. Splitting of the P-NMR spectrum due to the appearance of two P sites with different hyperfine fields was observed below ${T}_{A}$. From the field dependence, the splitting seems to disappear in zero magnetic field, indicating that the different hyperfine fields are not due to magnetic order, but to the appearance of two inequivalent P sites below ${T}_{A}$. This is ascribed to the distortion of the P cage surrounding a Pr ion below ${T}_{A}$, which is associated with the Pr orbital ordering. The nuclear spin-lattice relaxation rate $(1∕{T}_{1})$ shows the typical behavior of Kondo systems, where onset of local-moment screening due to the coupling between conduction and localized $\mathrm{Pr}\text{\ensuremath{-}}4f$ electrons is observed below $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Far above a critical field ${H}_{A}\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$, the Korringa behavior ${T}_{1}T=\mathrm{const}$ is observed below $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in $100\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$. The Korringa value below $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is one order of magnitude larger than that in $\mathrm{La}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$, which has no $4f$ electrons. Our NMR experiment shows that the heavy-fermion state is realized far above ${H}_{A}$ in $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$. The magnetic fluctuations in $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ are discussed from a comparison with typical heavy-fermion compounds. In magnetic fields below ${H}_{A}$, $1∕{T}_{1}$ shows a sharp decrease below ${T}_{A}$, however, in smaller magnetic fields less than $10\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$, $1∕{T}_{1}$ stays constant far below ${T}_{A}$ with a relatively large value. The temperature and field dependence of $1∕{T}_{1}$ reveals the presence of low-energy spin fluctuations in the low-temperature and low-field region. These unusual magnetic fluctuations are considered to originate from the magnetic dynamics of Pr-nuclear spins since the fluctuating magnetic field $\ensuremath{\sim}1.4\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ and frequency $\ensuremath{\sim}3.5\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ are so small. The nuclear ordering temperature is estimated to be $\ensuremath{\sim}0.08\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ using the nuclear exchange fluctuations derived from the observed $1∕{T}_{1}$ of P. We show that $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ is a quite unique compound in which nuclear magnetism can be detected by P NMR thanks to the nonmagnetic ground state of the $\mathrm{Pr}\text{\ensuremath{-}}4f$ moments.

Pr $4f$ electronic states in Pr-based filled skutterudites $\text{Pr}{T}_{4}{X}_{12}$ ($T=\text{Fe}$ and Ru; $X=\mathrm{P}$ and Sb) have been studied by high-resolution bulk-sensitive Pr $3d\ensuremath{\rightarrow}4f$ resonance photoemission. A very strong spectral intensity is observed just below the Fermi level in the heavy-fermion system ${\text{PrFe}}_{4}{\mathrm{P}}_{12}$. The increase of its intensity at lower temperatures is observed. We speculate that this is the Kondo resonance of Pr, the origin of which is attributed to the strong hybridization between the Pr $4f$ and the conduction electrons.

We present new measurements of the specific heat of the heavy fermion superconductor ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}$, on a sample which exhibits two sharp distinct anomalies at ${T}_{c1}=1.89\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and ${T}_{c2}=1.72\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. They are used to draw a precise magnetic field-temperature superconducting phase diagram of ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}$ down to $350\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. We discuss the superconducting phase diagram of ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}$ and its possible relation with an unconventional superconducting order parameter. We give a detailed analysis of ${H}_{c2}(T)$, which shows the paramagnetic limitation (a support for even parity pairing) and multiband effects.

The elastic properties of a filled skutterudite ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}$ with a heavy fermion superconductivity at ${T}_{\mathrm{C}}=1.85\mathrm{K}$ have been investigated. The elastic softening of ${(C}_{11}\ensuremath{-}{C}_{12})/2$ and ${C}_{44}$ with lowering temperature down to ${T}_{\mathrm{C}}$ indicates that the quadrupolar fluctuation due to the CEF state plays a role for the Cooper paring in superconducting phase of ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}.$ A Debye-type dispersion in the elastic constants around 30 K revealed a thermally activated ${\ensuremath{\Gamma}}_{23}$ rattling due to the off-center Pr-atom motion obeying $\ensuremath{\tau}={\ensuremath{\tau}}_{0}\mathrm{exp}{(E/k}_{\mathrm{B}}T)$ with an attempt time ${\ensuremath{\tau}}_{0}=8.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\mathrm{s}$ and an activation energy $E=168\mathrm{K}.$ It is remarkable that the charge fluctuation of the off-center motion with ${\ensuremath{\Gamma}}_{23}$ symmetry may mix with the quadrupolar fluctuation and enhance the elastic softening of ${(C}_{11}\ensuremath{-}{C}_{12})/2$ just above ${T}_{\mathrm{C}}.$

We report measurements of the magnetic penetration depth $\lambda$ in single crystals of PrRu$_{4}$Sb$_{12}$ down to 0.1 K. Both $\lambda$ and superfluid density $\rho_{s}$ exhibit an exponential behavior for $T$ $

We have performed ultrasonic measurements of the filled skutterudite compound ${\mathrm{NdFe}}_{4}{\mathrm{P}}_{12}$ to investigate the elastic properties and $4f$ ground state of Nd ions split by the crystalline electric-field (CEF) effect. A pronounced elastic softening towards low temperatures was observed in the temperature dependence of the elastic constants ${C}_{11},$ ${(C}_{11}\ensuremath{-}{C}_{12})/2,$ and ${C}_{44}.$ From the present results the CEF ground state of Nd ions and their low-temperature behavior are discussed in connection with the CEF ground state being degenerate with a quadrupolar moment.

We report the electronic and superconducting properties in the Pr-based filled-skutterudite superconductor PrRu 4 Sb 1 2 with T c =1.3 K via the measurements of nuclear-quadrupole-resonance frequency ν Q and nuclear-spin-lattice-relaxation time T 1 of Sb nuclei. The temperature dependence of v Q has revealed the energy scheme of Pr 3 + crystal electric field that is consistent with an energy separation Δ C E F ∼70 K between the ground state and the first-excited state. In the normal state, the Korringa relation of (1/T 1 T) P r =const is valid, with [( 1/T 1 T) p r /(1/T 1 T) L a ] 1 / 2 ∼1.44, where (1/T 1 T) L a is for LaRu 4 Sb 1 2 . These results are understood in terms of a conventional Fermi-liquid picture in which the Pr-4f 2 state derives neither magnetic nor quadrupolar degrees of freedom at low temperatures. In the superconducting state, 1/T 1 shows a distinct coherence peak just below T c , followed by an exponential decrease with a value of 2Δ/k B T c =3.1. These results demonstrate that PrRu 4 Sb 1 2 is a typical weak-coupling s-wave superconductor, in strong contrast with the heavy-fermion superconductor PrOs 4 Sb 1 2 that is in an unconventional strong coupling regime. The present study on PrRu 4 Sb 1 2 highlights that the Pr-4f 2 -derived nonmagnetic doublet plays a key role in the unconventional electronic and superconducting properties in PrOs 4 Sb 1 2 .

We have investigated the de Haas-van Alphen effect in the Pr-based heavy fermion superconductor PrOs$_4$Sb$_{12}$.The topology of Fermi surface is close to the reference compound LaOs$_4$Sb$_{12}$ and well explained by the band structure calculation based on the FLAPW-LDA+U method, where the 4{\it f} electrons are localized. We have confirmed a highly enhanced cyclotron effective mass 2.4$\sim7.6m_{\rm 0}$ which is apparently large compared to the usual Pr-based compounds.

We report the de Haas--van Alphen (dHvA) experiment on the filled skutterudite ${\mathrm{PrFe}}_{4}{\mathrm{P}}_{12}$ exhibiting apparent Kondo-like behaviors in the transport and thermal properties. We have found enormously enhanced cyclotron effective mass ${m}_{\mathrm{c}}^{*}=81{m}_{0}$ in the high field phase, which indicates that ${\mathrm{PrFe}}_{4}{\mathrm{P}}_{12}$ is the first Pr compound in which really heavy mass has been unambiguously confirmed. Also in the low field nonmagnetic ordered phase (LOP), we observed the dHvA branch with ${m}_{\mathrm{c}}^{*}=10{m}_{0}$ that is quite heavy taking into account its small Fermi surface volume (0.15% of the Brillouin zone size). The insensitivity of mass in LOP against the magnetic field suggests that the quadrupolar interaction plays a main role both in the mass renormalization and the LOP formation.

The effect of uniaxial pressure ${(P}_{u})$ on the magnetic susceptibility $(\ensuremath{\chi}),$ magnetization $(M),$ and magnetoresistance (MR) of the heavy-fermion metamagnet ${\mathrm{CeRu}}_{2}{\mathrm{Si}}_{2}$ has been investigated. For the magnetic field along the tetragonal c axis, it is found that characteristic physical quantities, i.e., the temperature of the susceptibility maximum ${(T}_{\mathrm{max}}),$ the paramagnetic Weiss temperature $({\ensuremath{\Theta}}_{p}),$ $1/\ensuremath{\chi}$ at 2 K, and the magnetic field of the metamagnetic anomaly ${(H}_{M}),$ scale approximately linearly with ${P}_{u},$ indicating that all the quantities are related to the same energy scale, probably of the Kondo temperature. The increase (decrease) of the quantities for ${P}_{u}\ensuremath{\Vert}c$ axis ${(P}_{u}\ensuremath{\Vert}a$ axis) can be attributed to a decrease (increase) in the nearest Ce-Ru distance. Consistently in MR and $\ensuremath{\chi},$ we observed a sign that the anisotropic nature of the hybridization, which is believed to play an important role in the metamagnetic anomaly, can be controlled by applying the uniaxial pressure.