Heavy Fermion Systems Research Articles

Valence Instability and Superconductivity in Heavy Fermion Systems

Many cerium-based heavy fermion (HF) compounds have pressure-temperature phase diagrams in which a superconducting region extends far from a magnetic quantum critical point. In at least two compounds, CeCu2Si2 and CeCu2Ge2, an enhancement of the superconducting transition temperature was found to coincide with an abrupt valence change, with strong circumstantial evidence for pairing mediated by critical valence, or charge transfer, fluctuations. This pairing mechanism, and the valence instability, is a consequence of a f-c Coulomb repulsion term U_fc in the hamiltonian. While some non-superconducting Ce compounds show a clear first order valence instability, analogous to the Ce alpha-gamma transition, we argue that a weakly first order valence transition may be a general feature of Ce-based HF systems, and both magnetic and critical valence fluctuations may be responsible for the superconductivity in these systems.

First-order quantum phase transitions

Quantum phase transitions have been the subject of intense investigations in the last two decades. Among other problems, these phase transitions are relevant in the study of heavy fermion systems, high-temperature superconductors and Bose–Einstein condensates. More recently there is increasing evidence that in many systems which are close to a quantum critical point (QCP) different phases are in competition. In this paper we show that the main effect of this competition is to give rise to inhomogeneous behavior associated with quantum first-order transitions. These effects are described theoretically using an action that takes into account the competition between different order parameters. The method of the effective potential is used to calculate the quantum corrections to the classical functional. These corrections generally change the nature of the QCP and give rise to interesting effects even in the presence of non-critical fluctuations. An unexpected result is the appearance of an inhomogeneous phase with two values of the order parameter separated by a first-order transition. Finally, we discuss the universal behavior of systems with a weak first-order zero temperature transition in particular as the transition point is approached from finite temperatures. The thermodynamic behavior along this line is obtained and shown to present universal features.

Localization of 4 f State in YbRh2Si2 under Magnetic Field and High Pressure: Comparison with CeRh2Si2

We present detailed measurements of the electrical resistivity and microcalorimetry under magnetic field and high pressure which confirm the proximity of YbRh 2 Si 2 to a quantum critical point at ambient pressure. Our data seems to rule out the divergence of the heavy quasiparticle mass at the magnetic field tuned quantum critical point. Further Mössbauer spectroscopy gives evidence that the observed ESR resonance cannot be assigned directly to the trivalent Yb local spin dynamics. We report for the first time on quantum oscillations in YbRh 2 Si 2 . The obtained angular dependence is compared with band-structure calculation. A significant change of the resistivity and specific heat under high pressure and magnetic field is observed. Above 5 GPa ferromagnetic coupling plays the dominant role. The unusual high pressure phase diagram of YbRh 2 Si 2 cannot be explained in term of the Doniach phase diagram. In Yb heavy fermion case, slow valence fluctuations may occur due to an occupation number of the trivalent state which differs notably from unity. The differences between the Ce and Yb heavy fermion systems are discussed. In particular a comparison is made between CeRh 2 Si 2 and YbRh 2 Si 2 . The observed field and pressure variations of the Hall voltage in CeRh 2 Si 2 are not straightforwardly linked to the change in the Fermi surface topology. A tiny change in the 4 f electron occupation number will have a huge effect on the effective mass of different orbits of the complex band structure and thus on the Hall effect in this multiband electronic structure. A similar scenario must be certainly considered for YbRh 2 Si 2 .

Transport properties of Yb 3Si 5 single crystals under high pressure

The electrical resistance of single-crystalline Yb 3Si 5 was measured under high pressure up to 60 GPa generated in an diamond anvil cell with the main aim to search for pressure-induced long-range magnetic ordering. Though no magnetic transitions were found, a clear crossover behavior in the pressure dependence of the characteristic temperature T* was observed. The results are discussed in terms of complex influence of pressure on the Kondo temperature, specific to Yb-based heavy fermion systems.

Electronic structure of [formula omitted] studied by Ce [formula omitted] resonant photoemission

We have performed Ce 4 d – 4 f resonant photoemission (RPE) spectroscopy on the isostructural heavy fermion system CeNiGe 2 - x Si x ( 0 ⩽ x ⩽ 1 ) . With increasing x, the unit volume decreases by about 5% and the ground state originating in Ce 4f character varies from an antiferromagnetic regime (AFM, 0 ⩽ x ⩽ 0.8 ) to a quantum critical point (QCP, x = 1 ). RPE data reveals that the cf-hybridization intensity becomes stronger as the ground state of Ce 4f electron changes from AFM to QCP, which is exclusively caused by the increase of chemical pressure due to the reduction of lattice constant in CeNiGe 2 - x Si x system.

Elastic properties of the ferromagnetic heavy fermion system SmOs4Sb12

Ultrasonic measurements were made on a single crystal of the filled skutterudite compound SmOs4Sb12. A remarkable elastic softening toward low temperature was observed in the elastic constants C11, (C11-C12)/2 and C44 as a function of temperature, followed by a sharp drop which is associated with the onset of ferromagnetic ordering, and then display a monotonic increase below Tc. The present results indicate that the crystalline electric field (CRF) effect would not support straightforward the observed elastic softening toward low temperature. We suggest that this fact is originated from valence instability of the Sm ion at low temperature in SmOs4Sb12. The 4f electronic ground state of the Sm ion and its elastic property are discussed.

Phase transition between the itinerant and the localized antiferromagnetic orders in [formula omitted

We have studied on the shift of the itinerant-electron-type magnetic order (SDW) to localized-electron-type antiferromagnetic order (LAF) in the heavy fermion system Ce ( Ru 0.9 Rh 0.1 ) 2 ( Si 1 - y Ge y ) 2 . The strength of the cf-hybridization in Ce ( Ru 0.9 Rh 0.1 ) 2 Si 2 is reduced by substituting Ge for Si. The electrical resistivity of the y = 0.3 sample shows a sharp downturn anomaly at T N indicating that the magnetic order of this compound is of the LAF. On the other hand, in the samples with y ⩽ 0.2 , the resistivity shows an sharp upturn anomaly at T N supposedly due to the energy gap at the Fermi surface associating with the onset of the SDW. The most remarkable result is that for y = 0.26 the resistivity shows both of the downturn and the upturn anomaly in the same sample, which strongly indicates a first-order phase transition between the LAF order and the SDW order.

Low temperature behavior of the heavy fermion [formula omitted

The compound Ce 3 Co 4 Sn 13 is an extremely heavy cubic heavy fermion system with a low temperature electronic specific heat of order ∼ 4 J / mol K 2 . If the compound is nonmagnetic, it would be one of the heaviest nonmagnetic Ce-based heavy fermions reported to date and therefore would be expected to lie extremely close to a quantum critical point. However, a broad peak of unknown origin is observed at 0.8 K in the specific heat and magnetic susceptibility, suggesting the possibility of antiferromagnetic order. We present neutron diffraction data from polycrystalline samples which do not show any sign of magnetic scattering below 0.8 K. In addition, we present inelastic neutron scattering data from a single crystal sample which is consistent with the 1.2 K energy scale for Kondo spin fluctuations determined from specific heat measurements.

High-field phase diagram of the heavy-fermion metal YbRh2Si2

The tetragonal heavy-fermion (HF) metal YbRh2Si2 (Kondo temperature TK≈ 25 K) exhibits a magnetic field-induced quantum critical point related to the suppression of very weak antiferromagnetic (AF) ordering (TN = 70 mK) at a critical field of Bc = 0.06 T (B⊥ c). To understand the influence of magnetic fields on quantum criticality and the Kondo effect, we study the evolution of various thermodynamic and magnetic properties upon tuning the system by magnetic field. At B > Bc, the AF component of the quantum critical fluctuations becomes suppressed, and FM fluctuations dominate. Their polarization with magnetic field gives rise to a large increase of the magnetization. At B* = 10 T, the Zeeman energy becomes comparable to kBTK, and a steplike decrease of the quasi-particle mass deduced from the specific-heat coefficient indicates the suppression of HF behaviour. The magnetization M(B) shows a pronounced decrease in slope at B* without any signature of metamagnetism. The field dependence of the linear magnetostriction coefficient suggests an increase of the Yb-valency with field, reaching 3+ at high fields. A negative hydrostatic pressure dependence of B* is found, similar to that of the Kondo temperature. We also compare the magnetization behaviour in pulsed fields up to 50 T with that of the isoelectronic HF system YbIr2Si2, which, due to a larger unit-cell volume, has an enhanced TK of about 40 K.

Effect of a nonmagnetic impurity in a nearly antiferromagnetic Fermi liquid: Magnetic correlations and transport phenomena

In nearly antiferromagnetic (AF) metals such as high-Tc superconductors (HTSC's), a single nonmagnetic impurity frequently causes nontrivial widespread change of the electronic states. To elucidate this long-standing issue, we study a Hubbard model with a strong onsite impurity potential based on an improved fluctuation-exchange (FLEX) approximation, which we call the GV^I-FLEX method. This model corresponds to the HTSC with dilute nonmagnetic impurity concentration. We find that (i) both local and staggered susceptibilities are strongly enhanced around the impurity. By this reason, (ii) the quasiparticle lifetime as well as the local density of states (DOS) are strongly suppressed in a wide area around the impurity (like a Swiss cheese hole), which causes the ``huge residual resistivity'' beyond the s-wave unitary scattering limit. We stress that the excess quasiparticle damping rate caused by impurities has strong momentum-dependence due to non-s-wave scatterings induced by many-body effects, so the structure of the ``hot spot/cold spot'' in the host system persists against impurity doping. This result could be examined by the ARPES measurements. In addition, (iii) only a few percent of impurities can causes a ``Kondo-like'' upturn of resistivity ($d\rho/dT<0$) at low temperatures when the system is very close to the AF quantum critical point (QCP). The results (i)-(iii) obtained in the present study, which cannot be derived by the simple FLEX approximation, naturally explains the main impurity effects in HTSC's. We also discuss the impurity effect in heavy fermion systems and organic superconductors.

A quantum multi-critical point in CeCu 6−xAu x

CeCu 6− x Au x is a well-known heavy-fermion system in which the ground state is antiferromagnetically ordered for x>0.1 and temperatures below 1 K. Non-Fermi liquid behaviour occurs around this critical concentration. The parent compound, CeCu 6, exhibits a structural phase transition near 230 K, where it changes from the Pnma orthorhombic room-temperature structure to the P2 1/c monoclinic structure. The monoclinicity increases as temperature falls, with β reaching 91.44° at 10 K. In the work presented here, powder neutron diffraction is used to explore the monoclinicity at 8 K as a function of composition for 0.0< x<0.08, just short of the critical concentration. Extrapolation of the square of the monoclinic strain, ( ac cos β) 2, suggests that the distortion vanishes at x=0.13. A reanalysis of single-crystal diffraction data on the magnetically ordered side of the phase diagram, x>0.1, indicates that long-range order disappears at exactly the same critical concentration. At a minimum, the structural distortion and antiferromagnetism seem to be competing with each other, and this raises the intriguing possibility that lattice degrees of freedom are important in the non-Fermi liquid regime.

Compton scattering studies of 4f ferromagnetism

Ferromagnetism can be studied in Compton scattering experiments, which use high-energy, elliptically polarised synchrotron radiation. The basis of the method and its interpretation in terms of site-specific moments will be explained and illustrated by a series of examples of archetypal compounds. For example, the hexaborides exhibit a wide range of electronic properties. Data will be presented for the heavy Fermion system CeB 6 and the controversial ferromagnet Ca 1− x La x B 6. Undoped CeB 6 exhibits a delocalised spin moment, more characteristic of the 5d than the 4f orbital. Whereas the magnetism in the Ca 1− x La x B 6 system has been suggested to be an extrinsic effect arising from iron contamination, our data indicate that the magnetism is intrinsic and inconsistent with what would be expected for an iron 3d moment. This supports the proposal that this system is, indeed, a weak itinerant ferromagnet. In Ru 2SrGdCu 20 8, we observe a combination of Gd 4f, Gd 5d and Ru 4d moments and the 5d moment appears to flip orientation below the Néel temperature.

Crystalline-Electric-Field Effect on the Resistivity of Ce-based Heavy Fermion Systems

The behavior of the resistivity of Ce-based heavy fermion systems is studied using a 1/$N$-expansion method a la Nagoya, where $N$ is the spin-orbital degeneracy of f-electrons. The 1/$N$-expansion is performed in terms of the auxiliary particles, and a strict requirement of the local constraints is fulfilled for each order of 1/N. The physical quantities can be calculated over the entire temperature range by solving the coupled Dyson equations for the Green functions self-consistently at each temperature. This 1/N-expansion method is known to provide asymptotically exact results for the behavior of physical quantities in both low- and high-energy regions when it is applied to a single orbital periodic Anderson model (PAM). On the basis of a generalized PAM including crystalline-electric-field splitting with a single conduction band, the pressure dependence of the resistivity is calculated by parameterizing the effect of pressure as the variation of the hybridization parameter between the conduction electrons and f-electrons. The main result of the present study is that the double-peak structure of the $T$-dependence of the resistivity is shown to merge into a single-peak structure with increasing pressure.

Electronic structure ofCaCu3Ru4O12studied by x-ray photoemission spectroscopy

We have studied the electronic structure of the $d$-electron heavy-fermion system ${\mathrm{CaCu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ using x-ray photoemission spectroscopy and a cluster model calculation. The $\mathrm{Ru}\phantom{\rule{0.3em}{0ex}}3d$ core level spectrum shows a double-peak structure as commonly observed in metallic Ru oxides. In ${\mathrm{CaCu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$, the well-screened peak has dominating intensity, indicating that the $\mathrm{Ru}\phantom{\rule{0.3em}{0ex}}4d$ electrons in ${\mathrm{CaCu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ are highly itinerant. On the other hand, the $\mathrm{Cu}\phantom{\rule{0.3em}{0ex}}2{p}_{3∕2}$ core level peak is accompanied by a satellite and shows that the valence state of Cu is close to $3{d}^{9}$ $({\mathrm{Cu}}^{2+})$ with localized character. In addition, the main $\mathrm{Cu}\phantom{\rule{0.3em}{0ex}}2{p}_{3∕2}$ peak shows an asymmetric line shape due to the screening effect, suggesting the hybridization effect between the $\mathrm{Cu}\phantom{\rule{0.3em}{0ex}}3d$ and $\mathrm{Ru}\phantom{\rule{0.3em}{0ex}}4d$ orbitals. The present results show that, among the $d$-electron heavy-fermion materials, the electronic structure of ${\mathrm{CaCu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ best resembles that of the $f$-electron Kondo system.

Interplay of Magnetism, Structure and Superconductivity in Heavy‐Fermion Systems CeMIn5 and PuMGa5

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Non-Fermi-liquid behavior inCe(Ru1−xFex)2Ge2: Cause and effect

We present inelastic neutron scattering measurements on the intermetallic compounds Ce(Ru$_{1-x}$Fe$_x$)$_2$Ge$_2$ ($x$=0.65, 0.76 and 0.87). These compounds represent samples in a magnetically ordered phase, at a quantum critical point and in the heavy-fermion phase, respectively. We show that at high temperatures the three compositions have the identical response of a local moment system. However, at low temperatures the spin fluctuations in the critical composition are given by non-Fermi-liquid dynamics, while the spin fluctuations in the heavy fermion system show a simple exponential decay in time. In both compositions, the lifetime of the fluctuations is determined solely by the distance to the quantum critical point. We discuss the implications of these observations regarding the possible origins of non-Fermi-liquid behavior in this system.

Energy Dispersion of4f-Derived Emissions in Photoelectron Spectra of the Heavy-Fermion CompoundYbIr2Si2

Angle-resolved photoemission spectra of the heavy-fermion system YbIr(2)Si(2) are reported that reveal strong momentum (k) dependent splittings of the 4f(13) bulk and surface emissions around the expected intersection points of the 4f final states with valence bands in the Brillouin zone. The obtained dispersion is explained in terms of a simplified periodic Anderson model by a k dependence of the electron hopping matrix element disregarding clearly interpretation in terms of a single-impurity model.

Spin-split masses and a critical behavior of almost localized narrow-band and heavy-fermion systems

The recent discovery of spin-dependent effective masses ( m * = m σ * ) in the de Haas–van Alphen measurements for CePd 2Si 2, CeRu 2Si 2, and CeCoIn 5 confirmed our earlier prediction and provides a good test for the mean-field theory of correlated electrons in narrow-band systems. This effect is particularly strong for almost localized systems near the metamagnetic transition, where the quantum electron liquid splits into two components with m ↑ * < m ↓ * . We overview the phenomenon, which appears naturally for both the Mott–Hubbard and the Anderson–Kondo lattice metallic systems; in the former for non-half-filled cases, whereas in the latter when the valency of either Ce atoms deviates slightly from the integers valence. We also address the question of quantum critical behavior at the localization–delocalization transition in both the systems.

Grand Kadowaki–Woods relation of heavy-fermion systems with degeneracy

Recent experimental and theoretical studies have revealed that the Kadowaki–Woods relation is not valid for heavy-fermion systems with large degeneracy, like intermediate-valence Yb- and Ce-compounds. Instead, we have successfully derived a new universal relation, namely, the grand Kadowaki–Woods relation for general degeneracy. This relation is found to be valid in the whole range of f-electron based systems with various degeneracies.

Heat capacity studies of the [formula omitted] system

The first studies of the effect of neptunium doping on the quadrupolar ordering transitions of UPd 3 have been made using heat capacity measurements. Here we report details of the heat capacities of ( U 1 - x Np x ) Pd 3 with x = 0 , 0.02 , 0.05 and ThPd 3 , a non-magnetic analogue, measured under identical conditions for T = 2 – 300 K . Whilst the heat capacity for x = 0.02 is qualitatively similar to that of pure UPd 3 , the heat capacity for x = 0.05 is significantly different with the transitions suppressed to below 4 K. Measurements on ( U 0.98 Np 0.02 ) Pd 3 in fields up to 9 T show that the transition temperatures increase in field, indicating that a 2% Np doping does not destroy the quadrupolar order. The much increased value of C p / T at T = 2 K in these doped samples either suggests these are heavy-fermion systems or that there are further transitions below T = 2 K .