Validity of the Anderson and Hubbard models for the description of metallic Ce and cerium heavy fermion compounds

The importance of the inclusion of inter-site f-f hybridization in electron structure calculations for metallic Ce and cerium heavy fermion compounds was studied. We demonstrate that for heavy-fermion systems such as cerium compound CeCu₂Si₂ f-f hybridization can be neglected and Anderson model application is well justified. On another hand for cerium metal f-f hybridization is strong enough to provide the contribution to hybridization function comparable to hybridization between 4f and itinerant electrons. We argue that in the case of Ce only the most general Hamiltonian combining the Hubbard and Anderson models should be used.     

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.     

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.     

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.     

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.     

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.     

Pressure induced valence transitions in the Anderson lattice model

We apply the equation of motion method to the Anderson lattice model, which describes the physical properties of heavy fermion compounds. In particular, we focus here on the variation of the number of f electrons with pressure, associated to the crossover from the Kondo regime to the intermediate valence regime. We treat here the non-magnetic case and introduce an improved approximation, which consists of an alloy analogy based decoupling for the Anderson lattice model. It is implemented by partial incorporation of the spatial correlations contained in higher-order Green's functions involved in the problem that have been formerly neglected. As it has been verified in the framework of the Hubbard model, the alloy analogy avoids the breakdown of sum rules and is more appropriate to explore the asymmetric case of the periodic Anderson Hamiltonian. The densities of states for a simple cubic lattice are calculated for various values of the model parameters V, t, E_f, and U.     

Superconducting gap anomaly in heavy fermion systems

The heavy fermion system (HFS) is described by the periodic Anderson model (PAM), treating the Coulomb correlation between the f-electrons in the meanfield Hartree-Fock approximation. Superconductivity is introduced by a BCS-type pairing term among the conduction electrons. Within this approximation the equation for the superconducting gap is derived, which depends on the effective position of the energy level of the f-electrons relative to the Fermi level. The latter in turn depends on the occupation probability n ^f of the f-electrons. The gap equation is solved self-consistently with the equation for n ^f; and their temperature dependences are studied for different positions of the bare f-electron energy level, with respect to the Fermi level. The dependence of the superconducting gap on the hybridization leads to a re-entrant behaviour with increasing strength. The induced pairing between the f-electrons and the pairing of mixed conduction and f-electrons due to hybridization are also determined. The temperature dependence of the hybridization parameter, which characterizes the number of electrons with mixed character and represents the number of heavy electrons is studied. This number is shown to be small. The quasi-particle density of states (DOS) shows the existence of a pseudo-gap due to superconductivity and the signature of a hybridization gap at the Fermi level. For the choice of the model parameters, the DOS shows that the HFS is a metal and undergoes a transition to the gap-less superconducting state.      

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：     

Heavy fermions in high magnetic fields

A qualitative picture of the metamagnetic transition in the Anderson lattice model of heavy fermion Ce compounds is described and a strong coupling spin fluctuation theory of the high field state is presented. The field dependence of the minority spin quasiparticle mass is calculated and the onset of the metamagnetic transition with decreasing field is discussed. The theory of the high field state is extended to include Landau levels and the oscillatory behaviour of the spin self-energy as a function of the inverse applied field is investigated. For the heavy fermion model considered such oscillations of the self-energy lead to significant modifications in the standard theory of the de Haas - van Alphen effect. The possible relevance to anomalous experimental results on CeRu₂Si₂ is discussed.     

Crystal-field effects in the intermediate-valence compound YbCu2Si2

Inelastic thermal-neutron scattering is used to study the intermediate-valence system YbCu₂Si₂. The magnetic scattering in two nonoverlapping ranges of transfer energies, 2<ε<5 meV and 5<ε<100 meV, is analyzed under the assumption that the regions influence each other only weakly. As a result, two sets of phenomenological crystal-field parameters are established, and their difference constitutes the experimental error in determining these parameters. A comparison of the fourth-order crystal field with other compounds belonging to the RCu₂Si₂ series (R stands for a rare-earth element) suggests that in YbCu₂Si₂ hybridization occurs between f electrons and copper electrons, in contrast to the heavy-fermion system CeCu₂Si₂, for which it was established earlier that hybridization occurs between f electrons and Si p electrons. Zh. éksp. Teor. Fiz. 114, 291–314 (July 1998)     

Electronic structure and magnetism of YbRhSn

The electronic band structure of YbRhSn has been calculated using the self-consistent full potential nonorthogonal local orbital minimum basis scheme based on the density functional theory. We investigated the electronic structure with the spin-orbit interaction and on-site Coulomb potential for the Yb-derived 4f orbitals to obtain the correct ground state of YbRhSn. The exchange interaction between local f electrons and conduction electrons play an important role in the heavy fermion characters of them. The fully relativistic band structure scheme shows that spin-orbit coupling splits the 4f states into two manifolds, the 4f_7/2 and the 4f_5/2 multiplet.     

Localization for 4f electrons in a heavy fermion compound CeCu2Si2: Insights from dynamical mean-field theory

A first principles calculation is carried out on a typical heavy fermion system-CeCu₂Si₂ by using a many-body method combing density functional theory (DFT) and dynamical mean-field theory (DMFT) along with the on-site Coulomb repulsion (represented by the Hubbard U parameter) for capturing the electronic correlation due to the incompletely filled Ce 4f orbitals. The results establish that the average occupation of Ce 4f electrons n_f is about 1.02 (mainly 4f¹ atomic configuration), close to the nominal occupation in pure Ce metal and in good agreement with the spectrum function in this work and the available experimental observations. The imaginary part of the impurity Green function indicates that the Ce 4f j = 5/2 and j = 7/2 states have metallic and insulating behavior, respectively. The dehybridization between the Ce 4f orbitals and ligand valence orbitals in the vicinity of the Fermi level is responsible for the localized 4f state and heavy fermionic behavior in this system.     

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.     

Phonon induced instabilities in intermediate valence compounds

The coupling of 4f electrons and longitudinal optical phonons and its implications on different types of structural phase transitions in intermediate valence compounds is discussed within the framework of the periodic Anderson model. Two types of interactions are considered. First, the usual density type of coupling of 4f electrons and phonons leads to a weakly temperature dependent renormalization of the positionE ₀ of the 4f level with respect to the 5d band. Secondly, phonon induced 4f–5d interband transitions lead to a renormalization of the hybridization energyV of 4f and conduction electrons. For appropriate parameter values the latter effect gives rise to discontinuous changes of the occupation of the 4f state.The tendency towards a ferromagnetic or antiferromagnetic instability is essentially suppressed by the presence of phonons.The dependence of the susceptibility on temperature and onE ₀ is calculated and a jump is found whenever a discontinuous change of the occupation of the 4f state occurs.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Pressure-induced valence and crystal field shifts in YbCu2Si2 and TmTe by neutron scattering

We present the quasielastic and inelastic neutron scattering of YbCu₂Si₂ and TmTe at high pressure and compare the results to those at ambient pressure performed at the same samples. In both cases we found variations of the quasielastic line width due to a pressure-induced 4f valence shift. The observations are shown to be in a gross quantitative agreement with theory as based on the Anderson model and therefore comply with the common picture of a dynamic 4f valence fluctuation. A measured variation of the crystal field parameters in YbCu₂Si₂ indicates a dominant contribution of the conduction electrons to the crystal field rather than the applicability of the Point Charge Model. As a by-product, very general theoretical expressions are provided for the pressure variation of crystal field parameters.This work is faithfully dedicated to Dieter Wohlleben whose tireless scientific truth and enthusiastic visions of the rules of nature will inspire us all forever.     

μ+SR study of LaNi2As2, URh2Si2 and CeRh2Si2

Muon spin relaxation experiments have been carried out in the paramagnetic and magnetically ordered states of URh₂Si₂ and CeRh₂Si₂. As the magnetic structure of these compounds is well known, these measurements can help to characterise their magnetic properties probed by μSR and to understand the μSR results of the heavy fermion compounds of the same crystallographic family. Our measurements show that the muons occupy two different crystallographic sites. The spectra of URh₂Si₂ and CeRh₂Si₂ in the magnetically ordered states are very different, probably reflecting their different magnetic structures. The spectra obtained on CeRh₂Si₂ are similar to the published spectra of the heavy fermion compound CeCu_2.1 Si₂. Muon spin rotation measurements on LaNi₂As₂ indicate that the muon is diffusing at 150 K.     

Electronic structure and magnetism of CeCoGe3

The electronic band structure of CeCoGe₃ has been calculated using the self-consistent full potential nonorthogonal local orbital minimum basis scheme based on density functional theory. We investigated the electronic structure with the spin-orbit interaction and on-site Coulomb potential for the Ce-derived 4f orbitals to obtain the correct ground state of CeCoGe₃. The exchange interaction between local f electrons and conduction electrons play an important role in their heavy fermion characters. The fully relativistic band structure scheme shows that spin-orbit coupling splits the 4f states into two manifolds, the 4f_7/2 and the 4f_5/2 multiplets.     

XPS and thermomagnetic characterization of the CeNi4Cr compound

The magnetic, thermodynamic and electronic structure properties are discussed for the CeNi₄Cr compound. The X-ray photoemission spectra (XPS) provide an evidence of a mixed valence behavior with the occupancy of the f states n_f=0.89 and their hybridization with the conduction electrons Δ=30 meV. These values reproduce well the magnetic susceptibility χ(T=0), which is enhanced compared to similar CeNi₄M (M=Al, B, Cu) compounds. In combination with a slightly increased electronic specific heat coefficient (up to 100 mJ mol⁻¹ K⁻²), this compound can be classified as being on the border of the heavy fermion and mixed valence behavior. Using a small magnetic field in the χ(T) measurements reveals a presence of magnetically ordered impurity phase, which is easily damped by higher fields and it is shown that the contribution of this phase is minor. The question of the dependence of the electronic specific heat coefficient on the magnetic field is also addressed and the observations agree well with theoretical predictions based on the Anderson model.     

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.