Friedel oscillation about a Friedel-Anderson impurity

The Friedel oscillations in the vicinity of a Friedel-Anderson (FA) impurity are investigated numerically. For an FA impurity in the local moment limit the normalized amplitude A(ξ) is S-shaped, approximately zero at short distances, approaching two at large distances and crossing the value one at the characteristic length ξ _1/2. Surprisingly, the Friedel oscillations of a simple non-interacting Friedel impurity with a narrow resonance at the Fermi level show a very similar behavior of their amplitude A(ξ). A comparison correlates the resonance width and the Kondo energy of the FA impurity with the characteristic length ξ _1/2 of the Friedel oscillations.     

Superconducting and normal state properties of dilute alloys of LaSn3 containing Ce impurities

The dependence of the superconducting transition temperature T_c on Ce impurity concentration and the specific heat jump at T_c as a function of T_c are reported for the system ($\text{La}$Ce)Sn₃. The experimental results are analyzed using a theory due to Kaiser concerning the effect on superconductivity of nonmagnetic localized resonant impurity states This analysis yields values for the intraatomic Coulomb repulsion parameter U_eff and the Ce local density of states at the Fermi level N_? (E_F). The results of low temperature normal state heat capacity and magnetic susceptibility measurements which give independent estimates of N_? (E_F) are also reported. A large pressure dependence of the T_c of ($\text{La}$Ce)Sn₃ alloys was observed for pressures up to 20 kbar. This behavior is similar to that previously observed in several other superconducting matrix-Ce impurity systems in which the Ce solute 4f electron shell undergoes a continuous-pressure induced demagnetization.     

Kondo effect in spin glasses: Electrical resistivity

We investigate the influence of the Kondo effect on the electrical resistivity of spin glasses. Our approximation reduces in the limit of vanishing impurity concentrations to the Suhl-Nagaoka theory for the Kondo effect. The magnetic impurity interactions are taken into account in the form of time dependent two-spin correlation functions which can be measured by neutron scattering. The dynamics of the impurity spins leads to a partial destruction of the Kondo effect. For the resistivity this can be described by a temperature dependent effective spinS _eff ² (T) withS _eff ² 0 forT0 andS _eff ² S(S+1) forT, and by a reduction of the Kondo temperatureT _K. Sufficiently strong interactions lead toT _K=0. We obtain a resistivity maximum at a temperatureT _m due to the interplay of the Kondo effect and the spin dynamics;T _m depends onT _K and on the excitation spectrum, and therefore on parameters such as impurity concentration or pressure. The ratioT _m/T_f (T _f is the freezing temperature) is calculated for a single relaxation time and for a square density of relaxation modes and is compared with experimental data forAuCr,AuMn,AgMn, andCuMn. The influence of other possible modes on various spin glass properties is discussed.SFB 125 Aachen-Jülich-Köln     

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.     

Paramagnetic labeling as a method for the soft spectroscopy of electronic states

A self-consistent microscopic theory of the relaxation of the crystal-field levels of an impurity ion in a state with an integer valence implanted in a normal metal is devised. A microscopic approach based on the Coqblin-Schrieffer-Cooper approach, rather than the formal model of the sf exchange interaction, makes it possible to take into account the specific details of both the crystal-field states of the impurity ion and the electronic band spectrum of the metal. A new method for the soft spectroscopy of electronic states based on measurements of the temperature dependence of the width Γ_MM′(T) of transitions between the crystal-field states |M〉 of a paramagnetic ion implanted in the compound being studied is proposed. To make specific use of this method in neutron and optical spectroscopy, a classification of the types of temperature dependence of the natural relaxation width γ _M (T) of the levels is devised, and procedures for possible experimental methods are proposed. A nonzero value of the natural relaxation width γ _G (T) of the crystal-field ground state | G〉 of an impurity ion at zero temperature is obtained within the proposed self-consistent model, but is beyond the scope of perturbation theory. It is shown that the widely accepted estimate of the characteristic temperature of Kondo systems T*=Γ _G(T=0)/2 from the quasielastic scattering width at zero temperature Γ _G (T=0)/2 is incorrect in the case of strong relaxation in a system with soft crystal fields. The proposed model is applied to the quantitative analysis of the relaxation of the crystal-field levels of paramagnetic Pr³⁺ ions implanted in CeAl₃ and LaAl₃. The results of the calculations are in quantitative agreement with the experimental data. Zh. éksp. Teor. Fiz. 113, 1843–1865 (May 1998)     

The S-J exchange interaction under the influence of the crystalline field

A magnetic impurity, having the s-j interaction with conduction electrons, under the crystalline field of host metals is investigated. The Hamann integral equation for the t-matrix can be derived and solved by the method of Zittartz and Müller-Hartmann for the cases of (1) small splittings, yielding the Kondo anomaly and decrease of the Kondo temperatureT _K compared with no splittings, (2) a large splitting from the crystalline ground doublet state, producing the higherT _K by the exicited level, and (3) a large splitting from the ground singlet state giving no Kondo effect. The macroscopic properties are calculated for (1) and (2).     

Ground state properties of the two impurity Anderson model in a 1/N expansion

The intersite contribution to the ground state energy for the two impurity Anderson model is calculated to first order in 1/N. The dependence of this contribution on the interimpurity separation has an R^?1 or R^?3 envelope for distances smaller or larger than a length ν_F/T_A ranges from a value equal to the bare ?-level position (in the weak valent regime) to the Kondo temperature (in the local moment limit).     

Strong coupling in the Kondo problem in the low-temperature region

The magnetic field dependence of the average spin of a localized electron coupled to conduction electrons with an antiferromangetic exchange interaction is found for the ground state. In the magnetic field range μH∼0.5T _c (T _c is the Kondo temperature) there is an inflection point, and in the strong magnetic field range μH≫T _c , the correction to the average spin is proportional to (T _c /μ H)². In zero magnetic field, the interaction with conduction electrons also leads to the splitting of doubly degenerate spin impurity states. Zh. éksp. Teor. Fiz. 115, 1263–1284 (April 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor     

Isospin properties of () reactions for the formation of deeply-bound antikaonic nuclei

The formation of deeply-bound antikaonic nuclear states in nuclear (K⁻,N) reactions is investigated theoretically within a distorted-wave impulse approximation (DWIA), considering the isospin properties of the Fermi-averaged elementary amplitudes. We calculate the formation cross sections of the deeply-bound states by the (K⁻,N) reactions on the nuclear targets, ¹²C and ²⁸Si, at incident K⁻ lab momentum p_K⁻=1.0 GeV/c and θ_lab=0°, introducing a complex effective nucleon number N_eff for unstable bound states in the DWIA. The results show that the deeply-bound states can be populated dominantly by the (K⁻,n) reaction via the total isoscalar ΔT=0 transition owing to the isospin nature of the amplitudes, and that the cross sections described by ReN_eff and ArgN_eff enable to deduce the structure of the nuclear states; the calculated inclusive nucleon spectra for a deep -nucleus potential do not show distinct peak structure in the bound region. The few-body and states formed in (K⁻,N) reactions on s-shell nuclear targets, ³He, ³H and ⁴He, are also discussed.     

Small-x behavior of the structure function and its slope for “frozen” and analytic strong-coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F₂ and its slope ∂lnF₂/∂ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA.     

Two Anderson impurities in the framework of the non-crossing approximation: Spectral functions and spin correlations

Using a novel slave boson mapping, which was recently proposed by us for two Anderson impurities embedded in a metal, we present here spectral functions for all pseudoparticles involved in the mapping. These were numerically calculated in the framework of the Non-Crossing Approximation for different temperatures and inter-impurity distances, both for the degenerate (N_f = 6) and nondegenerate (N_f = 2) models. For the nondegenerate case, temperature dependencies of the partial occupancies and the spin-spin correlation function suggest that an antiferromagnetic (AFM)-like ground state is formed at suitable inter-impurity separation. By contrast, Kondo quenching of the impurity moments takes place for the isotropic N_f = 6 case even when a direct AFM interaction is introduced in order to amplify the indirect (inherent) one. Numerical calculations are in agreement with our previous prediction [Phys. Rev. B 47, 14,297 (1993)] that no AFM-like ground state can appear for two isotropic degenerate impurities.     

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.     

Determination of effective atomic number and electron density of heavy metal oxide glasses

The effective atomic number (Z_eff) and effective electron density (N_eff) of eight heavy metal oxide (HMO) glasses have been determined using the Monte Carlo simulation code MCNP for the energy range of 10?keV–10?MeV. The interpolation method was employed to extract Z_eff and N_eff values from the simulation and that calculated with the help of XCOM program. Comparisons are also made with predictions from the Auto-Z_eff software in the same energy region. Wherever possible, the simulated values of Z_eff and N_eff are compared with experimental data. In general, a very good agreement was noticed. It was found that the Z_eff and N_eff vary with photon energy and do not have extended intermediate regions where Compton scattering is truly dominating; only dips slightly above ～1.5?MeV were recorded. Z_eff and N_eff are found to increase with PbO and Bi₂O₃ contents. It was found that the Z_eff value rather than the N_eff value is a better indicator for PbO and/or Bi₂O₃ contents.     

An EPR study of the temperature dependence of the energy gap in ytterbium dodecaboride

An EPR study of ytterbium dodecaboride (YbB₁₂) showed the presence of an energy gap with a width of 2Δ=12 meV in the energy spectrum of this Kondo insulator. The temperature dependence of the energy gap was determined by interpreting the experimental data within the framework of the exciton dielectric model: Δ(T)=72 K at an absolute zero and Δ(T)=0 at ～115 K. The temperature dependence of the EPR line-width exhibits a feature at 13–15 K, which is indicative of a finite density of states inside the gap. This can be related to the presence of impurity states or bound polaron excitations in the electron spectrum of YbB₁₂.     

Influence of absorption in the zero effective phase gap in one-dimensional photonic crystals containing single-negative materials

The transmission properties of one-dimensional (1D) photonic crystals containing two kinds of single-negative (ENG and MNG) material are investigated theoretically. A type of photonic gap with zero effective phases (zero-φ_eff) and the effects of absorption on the properties of the zero-φ_eff gap were shown. Specifically, it is demonstrated that strong absorption creates photon states inside the gap and this makes the band gap to be of zero width.     

Impurity contribution to the specific heat in the Kondo model

Summary Using the Lanczos scheme (tridiagonalization) we investigate the impurity contribution to the single-impurity Kondo model. This is accomplished by obtaining the ground-state energy of aN-particle system and a (N+1)-particle system, and obtaining the functional dependence ofg(J) (whereJ is the strength of the interaction). Hereg(J) is the coefficient of a correction term which is of order 1/N. The density of states at the Fermi level is effectively changed by the factorg(J). The excess heat capacity associated with the impurity is then proportional tog(J). To speed up publication, the authors of this papers have agreed to not receive the proofs for correction.     

Intramolecular vibrational relaxation in aromatic molecules. 2: An experimental and computational study of pyrrole and triazine near the IVR threshold

The threshold region of vibrational energy redistribution (IVR) presents a great experimental and computational challenge for organic molecules with more than 10 degrees of freedom. The density of states ρ_tot is high and requires high resolution measurements over a wide range to cover all relevant timescales experimentally. Yet ρ_tot is sufficiently low that IVR quantities like the initial relaxation time τIVR or the number of participating states N_eff are very sensitive to the coupling structure. To highlight the competing effects of molecular symmetry and mode localization on the accessible density of states, this work complements a study of benzene (Callegari, A., Merker, U., Engels, P., Srivastava, H. K., Lehmann, K. K., and Scoles, G., 2000, J. chem. Phys., 113, 10583) by measuring the CH overtone spectra of pyrrole (C₄H₄NH) and 1,2,3-triazine (C₃N₃H₃) using eigenstate-resolved double-resonance spectroscopy. Large scale computations of IVR dynamics were undertaken, applying filter diagonalization to analytically fitted fourth-order ab initio force fields. With an overall adjustment to the anharmonicity of the potential, the modelled N_eff and τ_IVR agree with the experimental quantities within a factor of 2 to 3, which is reasonable for a rate theory in the threshold regime. The models also correctly predict the experimentally observed trends of τ_IVR and N_eff for the two molecules, and provide insight into the highly off-resonant coupling mechanism, which yields very sharp linewidths.     

On the behaviour of the new Kondo lattice CeCuAl3

The temperature dependence of the electrical resistivity, thermopower, specific heat, susceptibility and magnetization of CeCuAl₃ are presented. CeCuAl₃ behaves as a Kondo lattice system with antiferromagnetic ground state properties (T _N 2.8 K). The valency of Ce in this tetragonal compound is close to 3 and the overall crystal field splitting found from our results is about 150 K. The Kondo temperatureT _K in the crystal field ground state, estimated from the magnetic susceptibility and the specific heat, is of the order of 8 K.     

One-dimensional Anderson model with dichotomic correlation in the presence of external electric field

A one-dimensional diagonal tight binding electronic system with dichotomic correlated disorder in the presence of external d.c field is investigated. It is found numerically that the conductance distribution obeys fairly well to log-normal distribution in weak disorder strength in localized regime, which indicates validity of single parameter scaling theory in this limit. Contrary to the universal cumulant relation C ₁ = 2C ₂ in the absence of d.c. field, we demonstrated numerically that C ₁ ≫ 2C ₂ in the presence of the field in localized regime. We interpret this result as suppression of the fluctuation effects by the external field. In addition, it is obtained that the quantity NF _c , here N is the system size and F _c is the crossover field, decreases as the as the system energy E increases. Moreover, we find numerically a simple linear relation between the average logarithm of the conductance 〈ln(g)〉 and the field strength as 〈ln(g)〉 = C(N, λ)F, here C(N, λ) is a constant for particular values of N and λ, which is the Poisson parameter of the dichotomic process.