Valence instability in an Anderson lattice system: CeAl2

We report the existence of a volume collapsed strongly mixed valent state at pressures above 65 K bars in the prototype “concentrated Kondo” system CeAl₂ and discuss the relevant energy scales and general phase diagram of CeAl₂. To our knowledge this is the first demonstrated example of what should be a large class of systems exhibiting the full diversity of ground states of an Anderson lattice.     

On the spin fluctuation approach to the anderson and Kondo hamiltonians

The free energy expression of the full Anderson model is derived in a similar way as has been done before for the Kondo model. Use is made of the “asymptotic time approximation” first invented to study the x-ray threshold singularity. Again the procedure leads to a classical Coulomb gas on a ring. The magnetic field is included and plays the role of an electric field for the Coulomb gas. Further it turns out that the “symmetric” Anderson model (2ε _d =?U) is identical to the antiferromagnetic Kondo model. The method and the results suggest the construction of a “polaron” model which in the approximation used is equivalent to the Kondo model as well as the Anderson model. From this a new picture of the “Kondo effect” in terms of spin fluctuations is developed.     

On the theory of superconductivity in Kondo lattice systems

An attempt is made to explain the occurrence of superconductivity in Kondo lattice systems with special reference to CeCu₂Si₂. Starting point is the Fermi liquid approach. It is generalized from a Kondo impurity to the Kondo lattice by means of the Korringa-Kohn-Rostocker method. From it a hybridization model is derived and discussed in detail. Two electron-phonon mechanisms are investigated which appear in Kondo lattices. One results from the additional phase shifts caused by the Kondo ions while the other is responsible for the so-called Kondo volume collapse. It is shown that the latter is sufficiently strong in order to explain why CeCu₂Si₂ is a superconductor while LaCu₂Si₂ is not. An estimate for the superconducting transition temperatureT _c produces the right order of magnitude.     

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.     

Kondo effect,spin dynamics and magnetism in anomalous rare earth and actinide compounds

The influence of spin dynamics on the Kondo effect manifestations in the Kondo lattices is investigated within perturbation theory with respect to thes-f interaction. It may give rise to Kondo-like divergencies in the electron self-energy already in the second order, resulting in an appreciable effective mass enhancement. As for usual Kondo contributions to thermodynamic and transport properties, the effect of spin dynamics reduces roughly to the replacement ln , with the characteristic spin-fluctuation energy. The thermoelectric power of dense Kondo systems is discussed. Singular contributions to the electron self-energies in the ferro-and antiferromagnetic state are considered. Kondo-like corrections to the intersite exchange interactions, saturation magnetic moment and total energy in a magnetically ordered state are calculated. The strong-coupling regionT<T _K is investigated within the Anderson lattice model. A decrease ofT _K due to spin fluctuations is demonstrated.     

Transport properties of the Anderson lattice

Transport properties including electrical resistivity, thermoelectric power, Lorenz number and a.c. conductivity are evaluated in an approximate fashion for the Anderson lattice model for six-fold degenerate Ce ions. Coherence (Bloch's theorem) is explicitly included while the effects of intersite interactions which may be responsible for magnetic and superconducting instabilities are neglected. The calculations utilize the AverageT-matrix Approximation (ATA) with the self-consistent Non-Crossing Approximation (NCA) perturbation theory employed to give the single siteT-matrix estimate. The resistivity peaks near the characteristic Kondo temperatureT ₀, with high temperature logarithmic decrease and low temperatureT ² behavior. The thermoelectric power is positive and similar to the impurity result except for low temperatures; sign changes in the thermopower are in principle possible with momentum dependent hybridization. Frequency and temperature dependent optical conductivity calculations are in qualitative agreement with experimental data, although a suitably defined optical effective mass and scattering rate do not agree at least for large orbital degeneracy. The behavior of these latter quantities is qualitatively different for twofold degeneracy. Unanswered questions arising from the experimental literature are summarized.     

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.     

Finite cell calculations on the periodic Anderson Hamiltonian

We report finite cell calculations on the one-dimensional periodic Anderson Hamiltonian. The ground state for two electrons per site is found to be an insulating non-magnetic singlet, which evolves continuously from the noninteracting U = 0 limit to the large U mixed valence and Kondo lattice regimes. The calculations for four sites given energy gaps which agree well with results for the infinite lattice in the few cases where they are known.     

自旋极化对Kondo系统基态的影响

Anderson模型中的自旋极化效应是一个普遍存在的问题.本文从Anderson杂质模型出发,利用变分及对角化方法分析了自旋极化所引起的系统基态性质的改变,分别研究了自旋极化对Kondo单态以及高温超导两分量模型中Zhang-Rice单态稳定性的影响问题.     

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationn _c (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosida's wavefunction which implies the existence of a large Fermi volume, in accordance with Luttinger's theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andn _c, and for the Kondo gap atn _c=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W forn _c 1/3.     

Volume collapse in the Kondo lattice

The α-γ transition of Ce and its compounds are explained within a compressible Kondo lattice model where the variation of |J|/D with volume is taken into account. We show that, contrary to the valence change model, the Kondo contribution is sufficient to induce a first order transition at low temperature from a magnetic to a Kondo phase. The disappearance of magnetism is then related to an extremely high Kondo temperature. Applications to Ce and CeAl₂ cases are given.     

Why could electron spin resonance be observed in a heavy fermion Kondo lattice?

We develop a theoretical basis for understanding the spin relaxation processes in Kondo lattice systems with heavy fermions as experimentally observed by electron spin resonance (ESR). The Kondo effect leads to a common energy scale that regulates a logarithmic divergence of different spin kinetic coefficients and supports a collective spin motion of the Kondo ions with conduction electrons. We find that the relaxation rate of a collective spin mode is greatly reduced due to a mutual cancellation of all the divergent contributions even in the case of the strongly anisotropic Kondo interaction. The contribution to the ESR linewidth caused by the local magnetic field distribution is subject to motional narrowing supported by ferromagnetic correlations. The developed theoretical model successfully explains the ESR data of YbRh₂Si₂ in terms of their dependence on temperature and magnetic field.     

Kondo lattice and heavy fermions in Heusler phases: CeInAg2−xCux

Magnetic properties, electrical resistivity, specific heat and magnetic excitations have been investigated in Heusler phases CeInAg_2–xCu_x. The hybridization continuously increases from CeInAg₂ (antiferromagnetic Kondo lattice) to CeInCu₂ (heavy fermion compound). The specific heat coefficient for this last compound is found to reach 1.2 J/mole. K² at 1.4 K, the Kondo temperature is 6 K and the Wilson ratio is close to 2.     

Interpretation of neutron magnetic scattering in the Kondo lattices YbPd2Si2 and YbAgCu4

We present an interpretation of published neutron inelastic scattering spectra in the Kondo lattices YbPd₂Si₂ and YbAgCu₄ obtained in terms of the Anderson impurity model, describing the hybridisation of the 4f Yb electrons with the band electrons, and also including the crystal electric field interaction. In YbPd₂Si₂, the tetragonal crystal field parameters were determined. In YbAgCu₄ the crystal field interaction was taken to exist by analogy with the isoelectronic compound YbAuCu₄ where it has been identified. Both compounds can be described by a Kondo temperature,T ₀=60 K and a Yb valency very close to 3.     

U-perturbation treatment of heavy fermion systems

Heavy fermion systems are described by the periodic Anderson Model (PAM), i.e. a lattice of localized, highly correlatedf-electron states hybridized with the delocalized states of a conduction band. We treat the PAM within the second orderU perturbation theory around the non-magnetic Hartree-Fock solution (U on site Coulomb correlation between thef-electrons). This treatment has the advantage that Fermi liquid relations (Luttinger theorem) are automatically fulfilled. Thef-electron selfenergy and spectral function are calculated for different temperatures, and, for the symmetric PAM, we obtain single-particle peaks near toE _f andE _f +U and in addition many-particle (Kondo) resonance peaks near to the chemical potential (E _f baref-electron energy). The resonance peaks are strongly temperature dependent and vanish on a characteristic temperature scaleT _K. For the symmetric PAM and a constant on-site hybridization the Fermi energy falls into a hybridization gap. A second, smaller characteristic temperature scaleT _coh (coherence temperature), on which the hybridization gap vanishes, is observed within this approach. For the non-symmetric PAM (i.e.E _f andE _f +U not symmetric around the chemical potential) we obtain a similar behaviour, but the single-particle peaks are no longer at the correct positionsE _f andE _f +U. The proper behaviour for the symmetric PAM but less satisfactory behaviour for the non-symmetric PAM can be understood from the fact that only for the symmetric PAM the exactly solvable limit of a vanishing hybridization is reproduced within this approach.     

Anomalous magnetic splitting of the kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in a finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for a nonzero magnetic field and the Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulas are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large- N approaches to spin- 1 / 2 impurities at finite magnetic field is suggested.     

Thermoelectric power of heavy-fermion compounds

We calculate the diffusion thermopower of the Anderson lattice as a model for heavyfermion compounds in a semi-phenomenological theory. In this theory, the thermopower is expressed by the dynamical susceptibility which describes spin fluctuations and can be measured by neutron scattering. The Kondo effect is taken into account for a singlef-electron spin which is coupled to all other spins and to the conduction electrons. This approach neglects multiple intesite-scattering of the conduction electrons. We obtain a Kondo termS ₍₁₎ ^d (T) (in which the thermopower of non-interacting spins is multiplied by a factor which describes the spin dynamics) and a resonance termS ₍₂₎ ^d (T) of opposite sign which vanishes for vanishing interactions. The superposition of both terms leads to a broad maximum of the thermopower roughly at the Kondo temperatureT _K and to an additional minimum belowT _K . ForT0 the termS ₍₁₎ ^d vanishes asT ² and the termS ₍₂₎ ^d becomes proportional toT. We also show that the Sommerfeld expansion leads to an incorrect result for the low temperature resistivity of the Anderson lattice and that the Gorter-Nordheim relation does not hold at low temperatures.     

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.