One particle excitation spectrum of the Kondo-lattice

The renormalized time ordered perturbation approach for the (impurity -) Anderson model with respect to hybridization is combined with a random walk treatment of coherent scattering in order to calculate the one particle excitation spectrum of an Anderson lattice in the Kondo regime. It is found that the Kondo resonance at the Fermi-level splits into two narrow peaks. With decreasing temperature a gap develops in between these peaks due to coherence effects. These results furnish a more rigorous basis for phenomenological theories explaining experimental data in Kondo lattice systems like CeCu₂Si₂.     

Quasiparticle band structure of CeCu2Si2 and CeAl3

The band structure for the ground state is obtained for CeCu₂Si₂ and CeAl₃ within the local-density approximation (LDA). Subsequently, the quasiparticle band structure is calculated on the basis of the Kondo Lattice Ansatz (KLA) for the Cerium 4f state using the LDA potential parameters for all other electrons. The KLA requires the specification of both the symmetry of the scattering channel, which is taken from the crystal-field (CF) ground state, and the energy dependence of the scattering phase shift, for which a Kondo resonance is assumed. Different results are obtained for two choices of the CF ground-state parameters for CeCu₂Si₂. Based on our results the low temperature specific heat is discussed.     

ESR of Gd-impurities in the heavy fermion compounds CeCu2Si2 and CeAl3

The heavy fermion systems CeCu₂Si₂ and CeAl₃ are characterized by a huge quasiparticle density of states responsible for the large electronic specific heat. The observation of a Gd³⁺ electron spin resonance (ESR) in single crystals CeCu₂Si₂ and in polycrystalline CeAl₃ clearly demonstrates the local character of these quasiparticles. Nevertheless, the Gd-spin relaxation shows remarkable anomalies with respect to the isostructural compounds LaCu₂Si₂ and LaAl₃: Probably via RKKY coupling, Ce 4f-spin fluctuations give rise to an enhanced Gd-spin relaxation resulting in an unusual non-linear thermal broadening around the Kondo temperature. From this we obtain information about the temperature dependence of the Ce 4f-spin correlation time.     

Calorimetric investigation under high pressure of the heavy fermion superconductor CeCu2Si2

The heavy fermion compound CeCu₂Si₂ is commonly regarded as a Kondo lattice system. Though it has been shown that the heavy mass quasiparticles participate in its superconductivity below ～ 0.7 K, a detailed understanding of the interdependence of the superconducting and the Kondo lattice parameters is still to be developed. The application of pressure is one useful approach to study this problem. In this paper we present results of specific heat measurements between 0.3 K and 2 K under pressures up to 5.9 kbar. While in our sample T_c hardly changes, the normal state specific heat, which is exclusively of electronic origin in the present temperature range, is rapidly decreased in a monotonous way, qualitatively corresponding to the expected rise of the Kondo temperature with pressure. In contrast to this behaviour, a strong nonlinear change of the jump Δc(T_c) passing through a maximum near 3 kbar is observed. We suggest that this reflects changes of the Kondo lattice coherence structure in the quasiparticle density of states near E_F.     

Fermi-liquid instability at magnetic–nonmagnetic quantum phase transitions

In metals with strong electronic correlations such as heavy-fermion systems or itinerant-electron magnets it is possible to change from a magnetically ordered to a nonmagnetic groundstate by variation of an external parameter such as composition or pressure. In principle a transition between these groundstates can occur at zero temperature. In case of a continuous transition quantum fluctuations take the role of thermal fluctuations in finite-temperature transitions. The abundance of low-lying magnetic excitations leads in the vicinity of the quantum critical point to unusual behavior of thermodynamic and transport properties at low temperatures T not envisioned by the classical Fermi-liquid behavior that is observed even in strongly correlated electron systems away from the quantum phase transition. We discuss in detail a few examples of this ‘non-Fermi-liquid behavior', viz., CeCu_6−xAu_x, Ce_1−xLa_xRu₂Si₂, Ce₇Ni₃, CeCu₂Si₂ and CeCu₂Ge₂, CePd₂Si₂, and UCu_1−xPd_x. In CeCu_6−xAu_x the very unusual low-T behavior of the linear specific-heat coefficient C/T−ln(T/T₀) and of the resistivity ΔρT can be attributed to quasi-two-dimensional fluctuations as determined from inelastic neutron scattering. The systems CeCu₂Ge₂ and CePd₂Si₂ are particuarly interesting since here the magnetic order which is suppressed under hydrostatic pressure gives way to superconductivity, suggesting that spin fluctuations mediate the formation of Cooper pairs at least in the latter system.     

On the ground state of the Kondo lattice system CeCu6

Magnetization measurements have been performed on a single crystal of CeCu₆ along the three main crystallographic directions between 1.5 and 300 K. The results are interpreted in terms of a crystal field calculation slightly modified by a spin fluctuation contribution of Kondo origin. Anisotropic magnetic properties of the Kondo lattice are discussed.     

Are heavy-fermion metals Fermi liquids?

We present the results of specific-heat and resistivity measurements as a function of temperature, magnetic field and hydrostatic pressure on the Kondo lattice CeNi₂Ge₂, the heavy-fermion superconductors CeCu₂Si₂ and UBe₁₃ as well as the low-carrier-density system Yb₄As₃. “Non-Fermi-liquid” effects in the low-temperature normalstate properties of the three former systems are consistent with the existence of a “nearby” quantum critical point, presumably of antiferromagnetic type. Yb₄As₃, though showing the outward appearance of a Landau-type heavy-fermion metal, behaves very differently, i.e. as an extreme two-fluid system.     

Magnetism and Superconductivity inCeCu2(Si1−xGex)2 Probed by Cu NQR

We report Cu-NQR results on Ge-doped heavy-fermion superconductor CeCu₂(Si_1–x Ge _x )₂ (0<x0.2) and undoped Ce_0.99Cu_2.02Si₂. The main effect of the Ge doping is considered to be a negative pressure, since the strength of hybridization decreases by the Ge doping. With increasing x, the dynamical characteristics of the magnetic order at x=0 change to more static ones which suggests a localized regime above x0.25. From the derived T–x phase diagram, it is suggested that the magnetic and the superconducting phases are almost degenerate in undoped CeCu₂Si₂. An exotic interplay between the magnetism characterized by the slow fluctuations and the superconductivity is implied in the region of small x.     

Concentrated Kondo systems

This review considers the experimental and theoretical studies of concentrated Kondo systems (CKS), Kondo lattices, substitutional solid solutions and their transition from Kondo impurity to Kondo lattice, and ‘intermediate valence compounds’ which are, in fact, high T _K CKS (T _K is the Kondo temperature). The anomalous low temperature properties of CKS are related to the formation of the narrow (～k _B T _K) high-amplitude Abrikosov-Suhl resonance E _R in the vicinity of the Fermi level E _F. This resonance is situated exactly at E _F in low T _K CKS with T _K < Δ_CF and near E _F in high T _K CKS with T _K > Δ_CF (Δ_CF is the crystal field splitting). In low T _K ‘j=1/2’ CKS the condition E _R=E _F leads to an increase of the density of states at E _F, which is large enough to induce heavy fermion superconductivity in CeCu₂Si₂, UBe₁₃. We demonstrate that the transition from low T _K (E _R=E _F) to high T _K CKS (E _R≠E _F) might be what was formerly considered as a ‘Kondo-lattice-intermediate valence state’ transition. It appears that in many cases the essentially non-integer valence state of the rare-earth elements in metallic compounds is thermodynamically unstable with respect to a transition to an almost integer valence state, because it realizes the maximum gain in free energy from the Kondo condensation.     

Temperature and pressure dependence of lattice parameters of the XCu2Si2 compounds (X=Ce,Eu, Yb,La, Gd,Lu, Ca,Th)

The RECU₂Si₂(RE=Rare Earth) series shows pronounced anomalies of the lattice parameters. In those stable valent compounds with 4f orbital angular momentumL0 thec/a ratio shows an anomalous temperature dependence due to crystal field effects. The compounds with unstable valence (RE=Ce, Eu, Yb) show less or no such effects but on the other hand show anomalies of the volume which are temperature dependent. Using these volume anomalies of the unstable valent systems and the measured bulk moduli of the reference compounds we have extracted the valence as function of temperature.Between 4K and 300K the valences of CeCu₂Si₂ and YbCu₂Si₂ change by only a few percent towards 3, while it changes for EuCu₂Si₂ by ca. 20% towards 2. A critical discussion of these valences will be given.     

Crystallographic investigations and comparison of superconducting and nonsuperconducting CeCu2Si2

Two samples of CeCu _x Si₂ withx=1.8 (non superconducting) andx=2.2 (superconducting) have been investigated by neutron powder diffraction. Both samples were characterized crystallographically and then their impurity content and lattice site occupation were determined. Anisotropic thermal vibrations of the Cu and Si atoms is detected at low temperatures. A relationship between the structural parameterz (defining the distance Ce to Si) and the occurance of superconductivity is suggested.     

Synchrotron X-ray diffraction and absorption studies of CeM2X2 (M=Cu, Ni and X=Si, Ge) at high pressure

The equations of state of CeCu₂Si₂ and CeCu₂Ge₂ to about 60 GPa, as well as that of CeNi₂Ge₂ to 22 GPa and the valence state of Ce in CeCu₂Ge₂ to 20 GPa have been studied at room temperature in a diamond-anvil cell using synchrotron radiation sources. In each compound, the ambient-pressure phase (tetragonal ThCr₂Si₂-type structure) persisted to the highest pressure studied. The unit cell volumes of CeNi₂Ge₂ at ∼5 GPa and CeCu₂Ge₂ at ∼7 GPa, respectively, approached that of CeCu₂Si₂ taken at ambient pressure. From the equation-of-state data, the bulk modulus was derived to be 112.0±5.1 GPa for CeCu₂Si₂, 125.6±4.3 GPa for CeCu₂Ge₂, and 178.4±14.3 GPa for CeNi₂Ge₂. The valence state of Ce in CeCu₂Ge₂ remained trivalent throughout the pressure range investigated.     

Electron spin resonance investigation of the Heavy-Fermion compound CeCu2(Si1−x Ge x )2

The Kondo-lattice system CeCu₂(Si_1?x Ge _x )₂ exhibits an alloying induced transition from a coherent Fermi-liquid (x=0) with strongly enhanced effective masses to an antiferromagnetically ordered heavy-fermion system (x=1). This transition is studied by Gd³⁺ ESR in oriented powder samples. The temperature dependence of the ESR line width follows a characteristic pattern which allows one to distinguish between the different ground states. The results obtained in polycrystalline CeCu₂Si₂ are in good agreement with the measurements performed in single crystals. Finally we compare our results with⁶³Cu-NMR data obtained from CeCu₂Si₂ and CeCu₂Ge₂.     

Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu2Si2 versus YbRh2Si2

In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu₂Si₂, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu₂Si₂. In YbRh₂Si₂, superconductivity appears to be suppressed at T???10?mK by AF order (T_N?=?70?mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at T_A slightly above 2?mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at T_c?=?2?mK. Like the pressure – induced QCP in CeRhIn₅, the magnetic field – induced one in YbRh₂Si₂ is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher T_cs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.     

Superconductivity in heavy fermion systems

The heavy fermion state in the f-electron systems is due to competition between the RKKY interaction and the Kondo effect. The typical compound is CeCu₆. To understand the electronic state, we studied the Fermi surface properties via the de Haas–van Alphen (dHvA) experiment and energy band calculation for CeSn₃,CeRu₂Si₂,UPt₃, and nowadays, transuranium compounds. Pressure is also an important technique to control the electronic state. The Néel temperature T_N decreases with increasing pressure P and becomes zero at the critical pressure for . The typical compound is an antiferromagnet CeRhIn₅, which we studied from the dHvA experiment under pressure. A change of the 4f-electronic state from localized to itinerant is realized at , revealing the first-order phase transition, together with a divergent tendency of the cyclotron mass at P_c. It is stressed that appearance of superconductivity in CeRhIn₅ is closely related to the heavy fermion state. It is also noted that the parity-mixed novel superconducting state might be realized in a pressure-induced superconductor CeIrSi₃ without inversion symmetry in the crystal structure.     

Superconductivity in CeCu2Si2

Resistivity measurements of CeCu₂Si₂ are carried out under pressures p up to 12 kbars. Unlike polycrystalline samples, no traces of superconductivity have been observed in CeCu₂Si₂ at ambient pressure. When pressure is applied, CeCu₂Si₂ monocrystals become superconducting with anomalously large ratio H_c2(0)/T_c (0) = 34 K0e/K and with the derivative dH_c2/dT(T=T_c) = 140 K0e/K     

Coexistence model of anisotropic electron hole pairing and unconventional superconductivity in Heavy Fermion compounds

Various Heavy Fermion compounds exhibit unconventional superconductivity together with another electronic instability like a spin density wave or possibly a more general type of anisotropic electron-hole pairing, e.g. a spin nematic state. The coexistence behaviour of these order parameters is studied within a simple weak coupling model. It is found that depeding on the symmetry of the order parameters coexistence or phase expulsion may occur. Whereas the former case is possibly realized for theU-based superconductors, CeCu₂Si₂ may be an example of the second case as observed and discussed in the context of elastic constant anomalies.     

CeCu2Si2和UBe13的超导理论(Ⅰ) ——模型,Tc及序参量

本文从周期性的Anderson晶格模型出发,考虑到局域电子与局域晶格形变的作用,对CeCu₂Si₂和UBe₁₃的重费密子超导现象进行了理论研究。通过计算,得到了合理的超导转变温度T_c;给出了描述同位素效应大小的参数α<1/2,甚至等于零(在BCS理论中α=1/2),说明现在的理论给出的同位素效应比BCS理论小,甚至可以不存在同位素效应,这与重费密子超导的实验相符合;此外还给出了序参量随温度及态密度变化的关系曲线,由此可 关键词：     

Kondo lattice behaviour in CePt2(Si1−xSnx)2 alloys

Measurements of electrical resistivity are presented for polycrystalline alloys in the CePt₂(Si_1−xSn_x)₂ system. Results of X-ray diffraction indicate that the tetragonal region of the CePt₂(Si_1−xSn_x)₂ alloy system that is amenable for study only extends up to x=0.3. The resistivity maximum characteristic of a Kondo lattice is observed at a temperature T_max=63 K for the parent compound CePt₂Si₂ and shifts to lower temperatures with increase in Sn content. The compressible Kondo lattice model is applied to describe the results of T_max in terms of the on-site Kondo exchange interaction J and the electron density of states at the Fermi level N(E_F). A value of |JN(E_F)|=0.060±0.009 for the parent compound is obtained from the experimental results.     

EPR study of exchange interactions in the nonmagnetic Kondo system La1−x CexCu6

The EPR of paramagnetic impurities Gd³⁺ and Mn²⁺ was studied in nonmagnetic Kondo system La_1−x Ce_xCu₆ containing in the 1.6–200 K range. The exchange interaction parameters of gadolinium and manganese ions with conduction electrons, of cerium ions with conduction electrons and with one another, the Kondo temperature of cerium ions, and the temperature behavior of cerium-ion spin-fluctuation rate have been determined. A pseudogap in the density of states at the Fermi level has been detected in the CeCu₆ regular system, which is apparently due to s-f hybridization. This pseudogap can be destroyed by introducing an aluminum impurity, which induces strong conduction-electron scattering. It was also found that RKKY interaction among manganese ions in CeCu_6−y Mn_y is considerably stronger than it is in LaCu_6−y Mn_y, which implies enhancement of nonlocal spin susceptibility due to an f band contribution to conduction-electron states. Fiz. Tverd. Tela (St. Petersburg) 40, 593–599 (April 1998)