Periodic Anderson Hamiltonian Research Articles

Interplay of magnetism and valence instabilities in lanthanide systems

Abstract The valence instability in lanthanide systems is described within an extended periodic Anderson Hamiltonian (EPAM) which includes Coulomb repulsion between f- and conduction- electrons, allowing to describe both discontinuous and continuous valence variations. We investigate the connection between valence and magnetism in this model and show that it can be applied to several lanthanide compounds showing both magnetic and valence instabilities.

Pressure induced valence transitions in the Anderson lattice model

Abstract 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 .

Transport properties of Kondo-insulator alloys

We study the transport properties of disordered Kondo insulators. The compound $({\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{)}_{3}{\mathrm{Bi}}_{4}{\mathrm{Pt}}_{3}$ is taken as a paradigmatic example to study the properties of these systems. The metal-nonmetal transition is analyzed as a function of the impurity concentration x. The system is described by a periodic Anderson Hamiltonian. The many-body effects are treated by diagonalizing the site Hamiltonian and embedding this solution into the lattice, using a cumulant expansion calculated in the chain approximation. The disorder is treated through a numerical simulation. We calculate the position of the Fermi level and the mobility edges as a function of concentration, temperature, and the external applied potential. We propose a scenario where the metal-insulator transition, driven by the impurity concentration x, occurs when the Fermi level is inside the conduction band. The results are discussed under the light of several experimental results.

Itinerant electrons and local moments in high and low magnetic fields: theoretical analysis of metamagnetism and paramagnetic susceptibility

Starting from a periodic Anderson Hamiltonian in the presence of an applied magnetic field, we present a model of the field-induced metamagnetism. Equations of motion for the magnetization and spin-fluctuation amplitudes are derived using Heisenberg's equation. A non-linear equation is set up, which connects the applied field ( h) with magnetization ( m). Spin fluctuation and magnetization dampings are considered phenomenologically. Metamagnetism is shown to be driven by the transverse part of the applied field and strong electron correlations are found to be important in the high field state. The low-field paramagnetic susceptibility is also analyzed for an itinerant electron system in the presence of conduction electron moment and localized moment (c-l) hybridization. In the process we derive an expression for the spin susceptibility of an itinerant electron system and express it as a sum of exchange enhanced Pauli spin susceptibility and a part which is written as a product of the electron paramagnetic resonance (EPR) shift and the Curie–Weiss susceptibility. The EPR shift is very much similar to the Knight shift, if a contact interaction for the c-l hybridization is assumed. The agreement with experimental observation in CeRu 2Si 2 is good on qualitative grounds.

Magnetic and Thermodynamic Properties of the Three-Dimensional Periodic Anderson Hamiltonian

The three-dimensional periodic Anderson model is studied with the quantum Monte Carlo method. We find that the crossover to the Kondo singlet regime is remarkably sharp at low temperatures, and that the behavior of magnetic correlations is consistently reflected in both the thermodynamics and the density of states. The abruptness of the transition suggests that energy changes associated with the screening of local moments by conduction electrons might be sufficient to drive large volume changes in systems where applied pressure tunes the ratio of interband hybridization to correlation energy.

Theory of Anomalous Hall Effect in Heavy Fermion System

The theory of the anomalous Hall effect in the heavy fermion system in the coherent regime is developed on the basis of the periodic Anderson Hamiltonian with degenerate orbitals. The anomalous Hall conductivity arises from the skew-scattering due to the orbital momenta of f -electrons in the presence of magnetic field. By a newly developed analysis based on the phase factor of the f -electron wavefunction in x - y plane, a simple expression for the Hall conductivity σ x y is derived. It makes possible to understand clearly the mechanism and to estimate the sign and the magnitude of the anomalous Hall coefficient. Our theory explains well experimental results in the heavy fermion systems. Finally, we discuss the extension of this theory to explain the temperature dependence of the Hall coefficient in the cuprate high- T c superconductors.

Field dependence of the anomalous Hall resistance of the heavy-fermion compounds

Abstract Considering the fact that the hybridization bands of the two spins are shifted differently by the Zeeman energy, we adopt a two-“band” model to study the field dependence of the anomalous Hall resistance of the heavy-fermion compounds. Starting from the periodic Anderson Hamiltonian, we use the standard large-degeneracy expansion for the slave-boson technique. At the mean-field level, we find that the anisotropyof the hybridization matrix element is crucial in reproducing the correct field dependence of the Hall resistance. This provides further evidence for the feasibility of our previously proposed mechanism for the metamagnetic-like transition.

Heavy Fermion Superconductor Order Parameter in High Magnetic Field

We consider the influence of a uniform high magnetic field B on the superconducting order parameter of heavy fermion II-type superconductors at T = O. The system is described in the slave boson mean field approach to the periodic Anderson Hamiltonian. We assume that the heavy fermion quasiparticles are caused by the 4f electrons hybridization with conducting ones in the Landau states [1]. Moreover, the applied field is sufficiently high to take into account only the lowest occupied Landau level. Thus we can start with the following effective Hamiltonian of the quasiparticles in strong magnetic field:

Anomalous Hall Coefficient in Heavy Electron Systems

The anomalous Hall effects at low temperatures in the heavy electron system are discussed on the basis of the periodic Anderson Hamiltonian with degenerate orbitals. We take into account the skew scattering through the spin-orbit coupling of the f-orbitals. Following the Fermi liquid theory, we derive the general expression for the anomalous Hall coefficient in the coherent regime. The expression shows that the anomalous Hall coefficient, which is added to the ordinary Hall coefficient, is proportional to the product of the susceptibility and the square of the resistivity at low temperatures. This behavior is confirmed to be in good agreement with the experimental results. The extension of this theory to the cuprate high temperature superconductor is also discussed shortly

Magnetic susceptibility and specific heat of the Anderson lattice: Perturbative expansion around the atomic limit.

The Green's functions relevant to the periodic Anderson Hamiltonian are calculated via perturbation theory around the atomic limit. The approximation reproduces exact results in three different limits: zero bandwidth, zero hybridization, and zero Coulomb correlation. The density of states, the magnetic susceptibility, and the electronic specific heat are calculated and discussed in both the Kondo and intermediate-valence regimes for different values of hybridization and Coulomb repulsion. The results are in qualitative agreement with experiments and are related to other theoretical calculations.

Anisotropic transport properties of cerium Kondo compounds.

The anisotropy of transport properties, i.e., the electrical resistivity, the thermoelectric power, and the thermal conductivity, observed experimentally in single crystals of noncubic cerium Kondo compounds, is studied here theoretically in a model that takes into account both crystal-field and Kondo effects. At temperatures that are high compared with the Kondo temperature, we use perturbation theory on the Coqblin-Schrieffer Hamiltonian, and at low temperatures we use the slave-boson technique on the periodic Anderson Hamiltonian. We study also the effect of disorder and the resulting relation between the residual resistivity and the coefficient of the resistivity ${\mathit{T}}^{2}$ law. Detailed comparison with experiment is finally given and a reasonable agreement is obtained for cerium Kondo compounds, such as ${\mathrm{CePt}}_{2}$${\mathrm{Si}}_{2}$, ${\mathrm{CeCu}}_{6}$, or ${\mathrm{CeAl}}_{3}$.

Magnetic correlations in Kondo lattice problem

Encouraged by the recent developments in the t - J model of high- T c problem we try to make connections to the Kondo lattice problem with special attention to its ground-state magnetic properties. Starting from the periodic Anderson Hamiltonian we integrate out the conduction-electron Grassmann variables and obtain an effective action for the f-level electrons, which is similar to the Hubbard model except that the hopping amplitude ( t) is long-ranged, sinusoidal in space are retarded in time. Close to the Kondo limit in the lattice case the mean occupation number of f-level electrons is close to one, corresponding to low doping limit. Some lessons can be borrowed from the t - J model. Mainly the special feature of t makes the Kondo problem much more difficult.

Local approach to the magnetic susceptibility and specific heat of the Anderson lattice

Green's functions relevant to the periodic Anderson Hamiltonian are evaluated via perturbation theory around the atomic limit, within an approximation that reproduces exact results in three different limits: zero band width, zero hybridization and zero Coulomb correlation. The magnetic susceptibility and the electronic specific heat are calculated for both Kondo and intermediate valence regimes. The results are in qualitative agreement with experiments and can be related to other theoretical calculations.

Fermi Liquid Theory on Heavy Electron Systems

Theory of heavy electron is reviewed on the basis of the Fermi liquid theory. The importance of the orbital degeneracy in realizing the heavy electrons is stressed by using the scaling theory on the Kondo temperature. With use of the periodic Anderson Hamiltonian, the expressions for the physical quantities, such as electronic specific heat, magnetic susceptibility, conductivity, relaxation time of nuclear spin and anomalous Hall coefficient are derived. These results explain the essential properties of heavy electrons. For further development the extension to the orbital degenerate case is essential and discussed mainly on the specific heat and the susceptibility. At the end the relation between the Fermi liquid state and spin fluctuation is discussed with use of the orthogonality theorem.

Anomalous Hall effect in the coherent regime

General expressions for transport coefficients and T 1 −1 are derived on the basis of the diagrammatic perturbation theory. The anomalous Hall effect observed in heavy fermion systems in the coherent regime is discussed on the basis of the periodic Anderson Hamiltonian.

Perturbation Approach to the Periodic Anderson Hamiltonian with k‐Dependent Hybridization

Calcul de l'approximation de second ordre en U pour l'autoenergie des electrons d'impuretes, afin d'etudier les modifications introduites par une dependance en K des elements de la matrice d'ybridation. Cette dependance du terme d'hybridation introduit des changements drastiques dans le comportement de plusieurs quantites physiques, plus specialement des energies proches du potentiel chimique

Kinetic equations for electron and heavy fermion excitations

A system of kinetic equations describing the relaxation of electron and heavy quasy-particle excitations in the periodic Anderson Hamiltonian model is obtained. It is shown that a complete system of equations in the second and higher orders of perturbation theory in the spatially homogeneous case includes, in addition to kinetic equations for “light” and “heavy” quasi-particle, also a system of equations for the nonequilibrium spectrum of quasi-particles, the nonequilibrium renormalization parameter and the f-level of local electrons.

Dynamical and static susceptibility of anomalous rare-earth systems

Dynamical and static susceptibility of anomalous rare-earth systems are computed within the atomic limit of the periodic Anderson Hamiltonian in both Kondo and intermediate valence regimes. The model can give an explanation of the inelastic peaks observed by neutron scattering measurements in CeSn 3 or CePd 3.

Electronic structure of the Anderson lattice with finite Coulomb interaction

An approximate diagrammatic technique is applied to the periodic Anderson Hamiltonian with finite Coulomb interaction. A Kondo peak at the Fermi level is obtained, it is split by the hybridization gap. We investigate the dependence of the gap and of the density of states as functions of the parameters of the Hamiltonian: the hybridization, the Coulomb repulsion and the energy of the ƒ-level.

A Green function approximation solution of the Kondo lattice

A Green function diagrammatic approach is utilised to calculate the density of states of a Kondo lattice described by a periodic Anderson Hamiltonian. The hybridisation between f and conduction electrons is included in the atomic term of the Hamiltonian, which can be solved exactly. The hopping terms are considered through an approximate Dyson equation, equivalent to a generalised Hubbard I scheme. The results at T=0 K indicate the existence of a 'Kondo peak' at the Fermi level. Metallic or insulating phases are obtained for different occupations of the f and conduction states.