Valence transition in the periodic Anderson model

A very rich phase diagram has recently been found in CeCu₂Si₂ from high pressure experiments where, in particular, a transition between an intermediate valence configuration and an integral valent heavy fermion state has been observed. We show that such a valence transition can be understood in the framework of the periodic Anderson model. In particular, our results show a breakdown of a mixed-valence state which is accompanied by a drastic change in the f occupation in agreement with experiment. This valence transition can possibly be interpreted as a collapse of the large Fermi surface of the heavy fermion state which incorporates not only the conduction electrons but also the localized f electrons. The theoretical approach used in this paper is based on the novel projector-based renormalization method (PRM). With respect to the periodic Anderson model, the method was before only employed in combination with the basic approximations of the well-known slave-boson mean-field theory. In this paper, the PRM treatment is performed in a more sophisticated manner where both mixed as well as integral valent solutions have been obtained. Furthermore, we argue that the presented PRM approach might be a promising starting point to study the competing interactions in CeCu₂Si₂ and related compounds.     

Functional integral approach to the single impurity Anderson model

Recently, a functional integral representation was proposed by Weller [1], in which the fermionic fields strictly satisfy the constraint of no double occupancy at each lattice site. This is achieved by introducing spin dependent Bose fields. The functional integral method is applied to the single impurity Anderson model both in the Kondo and mixed-valence regime. Thef-electron Green's function and susceptibility are calculated using an Ising-like representation for the Bose fields. We discuss the difficulty to extract a spectral function from the knowledge of the imaginary time Green's function. The results are compared with NCA calculations.     

Mössbauer and magnetic studies of mixed-valence linear chain compounds: Na3Fe2S4 and Na3Fe2Se4

Mössbauer and magnetic data establish the two compounds Na ₃ Fe ₂ X ₄ (X=S, Se) as mixed-valence linear chain compounds with rapid valence fluctuation. The compounds exhibit 1-dimensional antiferromagnetic coupling within the chains, and below a critical temperature a 3-dimensional ferrimagnetic ordering between the chains.     

Pressure- and photo-induced phase transition in mixed-valence gold complexes

The pressure- and photo-induced phase transition in mixed-valence gold complexes of Cs₂Au₂X₆ (X = Cl, Br, and I) has been investigated by means of the Raman scattering. The Raman-active Au-X stretching modes were deactivated by the pressure, which indicates a pressure-induced phase transition from the mixed-valence (MV) state to the single-valence (SV) state. The electronic phase diagrams of Cs₂Au₂X₆ (X = Cl and Br) as a function of pressure and temperature have been derived. A photoinduced phase transition from the MV state to the SV state has been found for Cs₂Au₂Br₆. The observed time behavior accompanying this phase transition is successfully interpreted by the Avrami model, indicating the three-dimensional character of the MV cluster growth.     

Electric-dipole increase in NMR intensity in mixed-valence complexes

The possibility of a considerable increase in NMR intensity has been shown for absorption on mixed-valence 3d ions in magnetically ordered crystals. This effect is determined by the high intensity of electric dipole transitions between the ground and low excited levels of a mixed-valence complex, as well as by the existence of the unfrozen orbital angular momentum in such complexes, which mixes nuclear and electron states.     

Dielectric properties of PbBO3 perovskites with mixed-valence substitution in the B position

This paper reports on the synthesis of PbBO₃ perovskites with mixed-valence substitution in the B position in which the number of ions n in different valence states occupying oxygen octahedra varies from 2 to 6. The dielectric properties of ceramic samples have been studied at frequencies in the range from 12 Hz to 100 kHz and in the temperature interval 77–450 K. The new compounds have been shown to possess relaxor properties.     

Fermi liquid theory of the impurity-lattice relaxation for a simple mixed-valence impurity model

Ward identities are used to relate the charge relaxation of a simple spinless mixed-valence impurity with its charge susceptibility at low temperatures. The result is compared with the Korringa relation for the Anderson model and the Kondo problem.     

Lattice vibrational properties of uranium pnictides

Lattice vibrational properties of uranium pnictides have been studied using breathing shell model (BSM) which includes breathing motion of electrons of the U-atoms due tof−d hybridization. The phonon dispersion curves of U-pnicitides calculated from the present model agree reasonably well with the measured data. A comparison has been made between BSM and our results reported earlier obtained from three-body force rigid ion model to reveal the importance of the short-range electron-phonon interactions in these compounds. We also report, for the first time, the two phonon density of states and specific heat for these compounds.     

EPR investigations ofS-state impurities with large hyperfine interaction in zinc and cadmium chalcogenides

A complete set of EPR data of paramagneticS-state impurity centers in the sulphur, selenium and tellurium compounds of zinc and cadmium has been given. New results mainly of gallium, thallium and lead have been included as well as former results which have partly been remeasured in order to obtain more precise data. The defects exhibit large hyperfine interaction with the impurity nucleus as well as EPR-resolved superhyperfine interaction with chalcogen and metal neighbours. These interactions decrease with increasing temperature due to coupling with localized vibrations. Formerly unidentified signals have been assigned to arise from associated or distorted centers. Systematic variations of the EPR-parameters with varying host lattice have been discussed in the frame of a phenomenological model making use of quantum defect electronegativity. Thus quantitative agreement of the EPR-parameters with experiment has been obtained.     

Diamagnetic susceptibility of hydrogenic donor impurity in low-dimensional semiconducting systems

The binding energies of a hydrogenic donor both in the parabolic and non-parabolic conduction band model within the effective mass approximation have been computed for the low-dimensional semiconducting systems (LDSS) like quantum well, quantum well wire and quantum dot taking GaAs/Al_xGa_1−xAs systems as an example. It is observed that the effect of non-parabolicity is not effective when the system goes to lower dimensionality. The diamagnetic susceptibility of a hydrogenic donor impurity has also been computed in these LDSS in the infinite barrier model. Since no theoretical or experimental works on the diamagnetic susceptibility of LDSS are available in the literature, as a realistic case the diamagnetic susceptibility has been computed in the finite barrier model (x=0.3) for a quantum well and the results are discussed in the light of semiconductor-metal transition.     

The asymmetric single-impurity Anderson model – the modified perturbation theory

We investigate the single-impurity Anderson model by means of the recently introduced modified perturbation theory. This approximation scheme yields reasonable results away from the symmetric case. The agreement with exactly known results for the symmetric case is checked, and results for the non-symmetric case are presented. With decreasing conduction band occupation, the breakdown of the screening of the local moment is observed. In the crossover regime between Kondo limit and mixed-valence regime, an enhanced zero-temperature susceptibility is found.     

Theory of substitutional alloys of intermediate valence systems: Concentration and temperature dependence of the static magnetic susceptibility

The effect of alloying in intermediate valence compounds is studied within an extended version of the Anderson model which takes into account substitutional disorder of the rare earth ions. In particular, we concentrate on modifications of the conduction band, describe them by an effective shift in the Fermi energy, and consider its influence on the mixed valence behaviour. By applying the alloy analog approximation to the manyparticle Hamiltonian describing the local magnetic 4f shells, the complete effective Hamiltonian is that of a ternary alloy. This problem is solved within the coherent potential approximation and the static magnetic susceptibility is calculated as a function of temperature and disorder. Depending on the shift of the Fermi energy with respect to the 4f levels, qualitatively different behaviour is obtained which corresponds very well with magnetic measurements on different Yb alloys. The model yields an inverse proportionality between the susceptibility atT=0 and the temperatureT _M of the susceptibility maximum as functions of the disorder.Work performed within the research program of the Sonderfor-schungsbereich 125 Aachen-Jülich-Köln     

Thermoelectric properties of a single quantum dot in mixed-valence regime

We study thermoelectric effects in correlated quantum dot coupled to ferromagnetic electrodes by calculating thermal conductance κ, thermopower S and Figure of merit ZT in the mixed-valence regime as function of on-dot energy level and temperature. The system is represented by the Anderson model and the results agree well with those recently experimental measured for a quantum dot coupled to two leads.     

Monte Carlo investigation of phase transitions in the frustrated Heisenberg model on a triangular lattice

The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants. A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ _k , the magnetization β and β _k , the correlation length ν and ν _k , as well as the Fisher exponents η and η _k , have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior.     

Magnetoresistance and magnetic ordering in praseodymium and neodymium hexaborides

The magnetoresistance Δρ/ρ of single-crystal samples of praseodymium and neodymium hexaborides (PrB₆ and NdB₆) has been measured at temperatures ranging from 2 to 20 K in a magnetic field of up to 80 kOe. The results obtained have revealed a crossover of the regime from a small negative magnetoresistance in the paramagnetic state to a large positive magnetoresistive effect in magnetically ordered phases of the PrB₆ and NdB₆ compounds. An analysis of the dependences Δρ(H)/ρ has made it possible to separate three contributions to the magnetoresistance for the compounds under investigation. In addition to the main negative contribution, which is quadratic in the magnetic field (−Δρ/ρ ∝ H ²), a linear positive contribution (Δρ/ρ ∝ H) and a nonlinear ferromagnetic contribution have been found. Upon transition to a magnetically ordered state, the linear positive component in the magnetoresistance of the PrB₆ and NdB₆ compounds becomes dominant, whereas the quadratic contribution to the negative magnetoresistance is completely suppressed in the commensurate magnetic phase of these compounds. The presence of several components in the magnetoresistance has been explained by assuming that, in the antiferromagnetic phases of PrB₆ and NdB₆, ferromagnetic nanoregions (ferrons) are formed in the 5d band in the vicinity of the rareearth ions. The origin of the quadratic contribution to the negative magnetoresistance is interpreted in terms of the Yosida model, which takes into account scattering of conduction electrons by localized magnetic moments of rare-earth ions. Within the approach used, the local magnetic susceptibility χ_loc has been estimated. It has been demonstrated that, in the temperature range T _N < T < 20 K, the behavior of the local magnetic susceptibility χ_loc for the compounds under investigation can be described with good accuracy by the Curie-Weiss dependence χ_loc ∝ (T − Θ _p )⁻¹.     

Neutron diffraction study of quasi-one-dimensional spin-chain compounds Ca<Subscript>3</Subscript>Co<Subscript>2–<Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>6</Subscript>

We report the results of the DC magnetization, neutron powder diffraction and neutron depolarization studies on the spin-chain compounds Ca₃Co_2–x Fe _x O₆ (x = 0, 0.1, 0.2 and 0.4). Rietveld refinement of neutron powder diffraction patterns at room temperature confirms the single-phase formation for all the compounds in rhombohedral structure with space group Rc. Rietveld refinement also confirms that Fe was doped at the trigonal prism site, 6a (0, 0, 1/4) of Co. The high temperature magnetic susceptibility obeys the Curie-Weiss law; the value of the paramagnetic Curie temperature (θ _p) decreases as the concentration of iron increases and it becomes negative for x = 0.4. No extra Bragg peak as well as no observable enhancement in the intensity of the fundamental (nuclear) Bragg peaks has been observed in the neutron diffraction patterns down to 30 K. No depolarization of neutron beam has been observed down to 3 K confirming the absence of ferro- or ferrimagnetic-like correlation.      

On the pressure-temperature phase diagram of intermediate valence compounds

The pressure-temperature (P, T) phase diagram of intermediate valence compounds has been calculated on the basis of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. It is shown that the positive slope (dP/dT>0) of the phase boundary between the insulating and the mixed valence phase as observed experimentally in Sm S and many other systems is determined by the behaviour of the electronic density of states of the interacting system as function ofP. Moreover, the observed anomalous thermal contraction in the insulating phase near the phase boundary and the anomalously large thermal expansion in the metallic phase are well described by numerical results for the extended periodic Anderson model.     

Vortex phase diagram studies in the weakly pinned single crystals of YNi2B2C and LuNi2B2C

We present a study of magnetization measurements performed on the single crystals of YNi₂B₂C and LuNi₂B₂C. For both the compounds, we find flux jumps in magnetisation values in the respective field regions, where the structural transitions in the flux line lattice symmetry have been reported in these systems via the small angle neutron scattering experiments. The magnetisation hysteresis loops and the AC susceptibility measurements show pronounced peak effect as well as second magnetisation peak anomaly for both YNi₂B₂C and LuNi₂B₂C. Based on these results, a vortex phase diagram has been constructed for YNi₂B₂C forH∥c depicting different glassy phases of the vortex matter.     

Role of rotational symmetry in magnetism of multiband models

The role of the complete Coulomb interaction matrix in the determination of the magnetic susceptibility of the two-band Hubbard model has been investigated in the dynamical mean-field theory. The off-diagonal component of the U-matrix has been found to reduce the Néel temperature, which agrees with the available experimental data. The magnitude of the effect upon a change in the dimension of the U-matrix is discussed. The results have been compared with the thermodynamic characteristics of an isolated Hubbard atom.     

Magnetic properties and energy transfer in the luminophors CaS:Eu,Cl

Studies have been performed on the magnetic properties and electron paramagnetic resonance (EPR) spectra of the small-crystal luminophors CaS:Eu,Cl. By comparing the EPR and magnetic susceptibility data we have determined that Eu enters into the CaS matrix primarily in the trivalent state Eu³⁺. We have found that the magnetic susceptibility of the sample with the lowest europium content (5×10⁻³ at. %) has a sharp peak at T≈5 K. A model is proposed of clusters into which the europium ions in these luminophors can associate. On the basis of this model an explanation is given for the anomalous temperature dependence of the magnetic susceptibility as well as a long list of other experimental facts (including peculiarities of the thermal luminescence). Zh. éksp. Teor. Fiz. 113, 1698–1707 (May 1998)