Molecular-field theory of moment reduction in Kondo systems with crystal-field effects

Several dense Kondo compounds have a low-temperature ordered phase in which the magnetic moments are reduced with respect to the values expected for the crystal-field (CEF) ground state. In the present work the phenomenon of moment reduction is studied within a molecular-field theory combined with a variational solution of the one-impurity Anderson model with CEF effects. The calculated zero-temperature magnetization and susceptibility agree well with available exact results; the present method is easily applied to systems of any symmetry. We first study the f ¹ configuration in cubic symmetry, for small values of the ratio T _K/Δ between Kondo temperature and CEF splitting. With a Γ _∞ ground state and a field along a 〈100〉 direction, an inflection point occurs in the magnetization curve, which gives rise to a first order transition in the zero-temperature phase diagram. This feature is not found for a field along 〈110〉 or 〈111〉, for which the transition is second order. For a Γ ₇ ground state and small values of T _K/Δ, the magnetic-nonmagnetic transition is second order for all field directions. On increasing T _K/Δ an inflection point in the magnetization curve appears first for a field along 〈111〉. The theory is applied to a study of cubic CeAg, CeAl₂, CePb₃, CeIn₃, CeTe, and hexagonal CePd₂Ga₃. The bare value of the moment is found to be strongly increased by exchange coupling to excited CEF states, and the amount of Kondo reduction is found to be substantial, confirming the importance of the Kondo effect in these compounds.     

Magnetic interactions in RECu2Si2 compounds (RE = Tb-Tm)

The RKKY theory and the molecular field model including CEF effects (by Noakes and Shenoy) are applied for the explanation of magnetic interactions in the RECu₂Si₂ family (RE = Tb-Tm). The negative sign of the obtained exchange integral J_sf may point to the presence of interband mixing. The predicted magnetic anisotropy and enhancement of ordering temperatures T_N-5 above the de Gennes values are consistent with experimental ones only on the basis of the B⁰₂ model with parameter A⁰₂ as for CdCu₂Si₂. They are not consistent if one uses the full CEF Hamiltonian with 5 A^m₁ parameters as for TmCu₂Si₂. A short discussion about the role of magnetic interactions other than the simple RKKY exchange is also given.     

μ+SR frequency shifts in the van‐Vleck paramagnet PrIn3

As part of an ongoing μ⁺SR study on cubic van‐Vleck paramagnets of the PrM₃ series ( M\ =\ In,Pb,Tl,Sn), in which the CEF level scheme varies systematically, we present preliminary static μ⁺SR results on a single crystal of PrIn₃. From the angular dependence and from the appearance of the μSR spectra, we could determine that stopped μ⁺ occupy octahedral sites of the (1/2, 0, 0) type, i.e. sites with 2 Pr and 4 In atoms as neighbors. The spectral frequency shifts can be accounted for by assigning to the Pr sites essentially unperturbed 4f dipole moment values, as derived from bulk magnetization measurements. The temperature dependence of the shifts scales to a good accuracy with the bulk susceptibility. It is concluded that unlike previous observations with PrNi₅, the local perturbations induced by an interstitial μ⁺ on the CEF levels of neighboring Pr in the PrIn₃ system are small compared with the unperturbed level splitting itself. This revised version was published online in July 2006 with corrections to the Cover Date.     

Jordan-Wigner approach to the frustrated spin one-half XXZ chain

The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the J₁-J₂ XXZ chain. We consider different solutions of the mean-field approximation for the transformed Hamiltonian. Ground state energy and the static structure factor are compared with complementary exact diagonalization and good agreement is found near the limit of the Majumdar-Ghosh model. Furthermore, the ground state phase diagram is discussed within the mean-field theory. In particular, we show that an incommensurate ground state is absent for large J₂ in a fully self-consistent mean-field analysis.     

Nonradiative multiphonon transitions described by static versus adiabatic coupling scheme in comparison with Landau-Zener's theory

A generalized coupling scheme for nonradiative multiphonon transitions is presented, which comprises both the static and the adiabatic scheme as essential alternatives. The perturbational rate expressions due to both coupling schemes are specialized for a two-level-one-mode system. A nonperturbational rate expression is derived by averaging the corresponding quasiclassical transition probability due to Landau-Zener's theory. The static limit of this quasiclassical theory is shown to give precisely the same result as the quasiclassical limit of the static coupling scheme. At variance to this, the adiabatic limit of the quasiclassical theory yields an adiabatic-gap tunneling factor exp [–3(T _c T)^1/3], for a certain parameterT _c larger than lattice temperatureT, which was obtainable so far neither from the familiar Condon approximation nor from certain non-Condon approximations of the adiabatic scheme. Causes of this repeated failure of the adiabatic scheme are discussed.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.Editorial notice: We regret to record the death of Professor Trlifaj on 10. 2. 1982.In concluding this paper I would like once more to give my sincere thanks to Prof. M. Trlifaj for having introduced me years ago into important problems of the theory of nonradiative transitions and for his support particularly as referee of our first publications on this controversial subject.     

Evaluation of LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript>-LiNi<Subscript>0.80</Subscript>Co<Subscript>0.15</Subscript>Al<Subscript>0.05</Subscript>O<Subscript>2</Subscript> hybrid material as cathode in soft-packed lithium ion battery

The major electrochemical performances of LiMn₂O₄ (LMO)-LiNi_0.80Co_0.15Al_0.05O₂ (NCA) blending cathodes with full-range ratios are evaluated in industrial perspective. The results indicate that the reversible lithium ions can be fully utilized when NCA percentage reaches up to 50 %. The median voltages of blends are higher than the value calculated from a linear relationship of the two pristine cathodes, which is beneficial to energy density. But a synergy effect on room-temperature cycle performance is not observed for the hybrid cathode. However, the high-temperature (45 °C) capacity retention with 70 % NCA is 97.9 % after 100 cycles, higher than both pristine cathodes. It is not until NCA content increases to more than 50 % that the high-rate performance is much deteriorated. Additionally, the swelling of fully charged pouch-type battery after 4 h storage at 85 °C disappears when NCA percentage is less than 50 %. Hence, it is practically manifested that critical flaws of NCA and LMO can be compromised by blending with each other in a critical ratio. In this way, NCA can be practically used in soft-packed battery.     

Neutron scattering studies of Bi2Sr2Ca0.5Ho0.5Cu2O8+x

Neutron scattering has been employed to study the crystalline electric field (CEF) interaction at the Ho³⁺ site in Bi₂Sr₂Ca_0.5Ho_0.5Cu₂O_8+x. The observed energy spectra exhibit a large number of broad but well-resolved CEF transitions between 1.2 and 73 meV, so that we have been able to unambiguously determine all nine CEF parameters required for the average orthorhombic symmetry. The unusually large line widths of the CEF transitions are shown to be related to the modulated structure. The CEF potential is essentially governed by the charge distribution of the CuO₂ planes which turns out to be very similar as in HoBa₂Cu₃O_7-x.     

铜纳米阵列高效电解水产氧催化剂的制备

本文报道了一种利用简单的两步牺牲模板法,在泡沫铜基底表面完成了三维氧化铜纳米晶阵列的生长. 氧化铜纳米晶阵列具有良好的导电性,稳定性,在碱性溶液中有着优秀的电解水产氧催化性能. 氧化铜纳米晶阵列催化水的电化学氧化只需400 mV的过电势即可达到100 mA/cm²的电流密度,与其它铜基电解水产氧催化剂以及贵金属IrO₂相比都有着明显的优势. 氧化铜纳米晶阵列在270 mA/cm²左右的工作电流下连续工作10 h依然可以保持良好的稳定性,是相同的工作电压下IrO₂工作电流的10倍(约25 mA/cm²).     

Transport,thermal, and magnetic properties in heavy-fermion superconductor Ce2CoIn8

We have grown high purity single crystals of Ce₂CoIn₈ using the self-flux technique, and have investigated its transport, thermal, and magnetic properties, including the anisotropic features. Single crystals of Ce₂CoIn₈ were grown in the lower temperature region to avoid the formation of un-wanted phases such as CeCoIn₅ and CeIn₃ impurities. The results of the structural and physical measurements imply that the present single crystals have high purity. The electrical resistivity and specific heat measurements demonstrate that Ce₂CoIn₈ has a superconducting ground state with a distinct non-Fermi liquid character. This indicates that the superconductivity in Ce₂CoIn₈ arises out of the verge of the underlying quantum critical instability mediated by the antiferromagnetic correlations. Additionally, we investigate the crystalline electric field (CEF) energy scheme based on the temperature dependence of the specific heat and the anisotropic features in the susceptibility. We propose one of the CEF level schemes calculated on the basis of the CEF model that the first and second CEF states are located at Δ₁ = 82 K and Δ₂ = 102 K above the ground state doublet, respectively.     

Application of Regression Analysis in spectroturbidity size-characterization methods

The possibilities of applying specific turbidity and turbidity theoretical computations of light-scattering characteristics, the ratio methods in the distributional analysis of PVC and SiO₂ exact Lorenz-Mie theory was applied. A good correlation with dispersions with spherical particles are discussed. The calculation of the best estimates of distribution function parameters was found were performed numerically using the simplex method. For theoretical computations of light-scattering characteristics, th exact Lorenz-Mie theory was applied. A good correlation with the results of angular light scattering and electron microscopy was found.     

An accurate approximation to the diffusivity factor

A new analytical approximation for diffusivity factor has been developed to deal with the angular integration of the diffuse transmission function for infrared radiation. The method is based on the bridging function theory which connects the exact results at both of the transparent and opaque limits. It is shown that the new scheme is much more accurate than any previously proposed schemes. By implemented into a one-dimensional radiative model, it is found that the new diffusivity factor can produce very accurate results in flux and cooling rate in the main spectral ranges for CO₂, O₃, and H₂O. Also, the new proposed diffusivity factor is efficient in computing.Therefore, the new scheme is a proper choice to replace the constant diffusivity factor of 1.66 currently used in radiative transfer models.     

The effect of a crystalline electric field on the magnetic transition temperatures of rare-earth rhodium borides

A simple molecular field model is presented for the prediction of magnetic transition temperatures of rare-earth (RE) compounds when crystalline electric field (CEF) splittings are significant. The model is applied to the RERh₄B₄ (RE=Gd?Tm) series, using what is known about the crystal field in these materials.     

Crystalline-electric-field level scheme of NdB6

We have determined the crystalline-electric-field (CEF) level scheme of NdB₆ by means of Raman spectroscopy. We could resolve two CEF-transitions at 92 cm^–1 and 98 cm^–1 due to the spectral resolution of 2 cm^–1 (=0.25 meV). The temperature dependent Raman scattering reveals the two transitions to be on top of one another, in agreement with fits of the temperature dependence of the magnetic susceptibility. The spectroscopically determined CEF level scheme yields a good fit of the elastic constants and hence the mean field prediction of a ferroquadrupolar ordering near 6 K. This result sheds new light on the phase transition in NdB₆ nearT _N =8.6 K which has so far been interpreted only in terms of antiferromagnetic ordering.Work supported by Deutsche Forschungsgemeinschaft, SFB 125Work supported by Deutsche Forschungsgemeinschaft, SFB 126     

Neutron crystal-field spectroscopy of RNi 2 11 B2C (R = Ho,Er, Tm)

Inelastic neutron scattering experiments of the crystal-field (CEF) splitting of the R³⁺ ions (R = Ho, Er, Tm) in the superconductor RNi ₂ ¹¹ B₂C have been performed in the paramagnetic as well as in the magnetically ordered state in order to deduce the CEF parameters which in turn determine the thermodynamic magnetic properties of these systems. The calculated ordered magnetic moments are in agreement with magnetic neutron diffraction results, i.e. both the easy axis and the size of the zero-field moments are correctly reproduced. In addition, the entropy involved in the magnetic ordering obtained from specific heat measurements is in correspondence with the number of low-lying CEF states observed in this study. Our CEF parameter set also reproduces both the behavior and the anisotropy in M/H measured for single crystals.     

Crystal field states in CeCu4Al

Heavy fermion CeCu₄Al compound has been studied by inelastic neutron diffraction (INS), heat capacity and magnetic susceptibility measurements. A single Crystal Electric Field (CEF) peak has been detected in the INS spectra, which may be explained by a quasi-quartet state suggested by the analysis of the Schottky anomaly contributing to the magnetic part of the specific heat. The Kondo interactions have been included in the analysis of the magnetic part employing the simplified resonance level model. The resulting Kondo temperature of about 5–10 K is somewhat larger than in the previous studies. The magnetic susceptibility confirms the CEF level scheme of the type 0–93 K and provides the values of the CEF parameters.     

Approximate and exact photon-maxwellian electron cross-sections and a Monte Carlo sampling scheme

Fast and accurate approximate methods for computing temperature-corrected photon-Maxwellian electron cross-sections, using distribution averaged electron energies and scattering angles, are presented. Use is made of the covariant (frame independent) picture of scattering for relativistic electrons. The schemes are motivated and detailed, predictions are obtained and compared with exact values, and appropriate limiting forms that retain the Thomson and Klein-Nishina cross-section structure are also recovered. A two-parameter fit to the total cross-sections in a Klein-Nishina picture is detailed using an invariant scattering kernel. This particular fit is useful in extending existing sampling schemes which employ the static probability density. Extensions of Kahn's technique (for sampling the Klein-Nishina density) arepresented for a temperature-corrected set of probability densities obtained from the fitted cross-sections. The methods are amenable to further pointwise (Monte Carlo) or multigroup (S_n) cross-section processing. An exact numerical scheme employing adaptive quadrature techniques, as implemented in the production code module MAXWELL is also described.     

Discrete ordinates interpolation method for radiative heat transfer problems in three-dimensional enclosures filled with non-gray or scattering medium

The discrete ordinates interpolation method (DOIM) is applied to three groups of problems of radiative heat transfer in three-dimensional rectangular enclosures containing non-gray or scattering medium. The original DOIM is first extended to a gray gas model using a new geometric interpolation scheme. It is applied to participating media for different scattering phase functions and optical thicknesses. For the non-gray gas model, the DOIM coupled with the narrow band-based weighted-sum-of-gray-gases (WSGG) model is developed. A few test problems with real gases such as pure H₂O and a mixture of CO₂, H₂O and N₂ are taken. The wall heat flux is calculated and compared with the exact solutions or reference values. All results of test problems are found to be reliable in this study. The DOIM closely reproduces the Monte Carlo reference solutions for different scattering phase functions and optical thicknesses. The non-gray gas results are compared with reference calculations based on the statistical narrow band model and they also show good agreements. The DOIM shows a remarkable merit in the computation time and the grid compatibility, to prove its usefulness for engineering applications.     

Large-scale atomistic simulations of nanostructured materials based on divide-and-conquer density functional theory

A linear-scaling algorithm based on a divide-and-conquer (DC) scheme is designed to perform large-scale molecular-dynamics simulations, in which interatomic forces are computed quantum mechanically in the framework of the density functional theory (DFT). This scheme is applied to the thermite reaction at an Al/Fe₂O₃ interface. It is found that mass diffusion and reaction rate at the interface are enhanced by a concerted metal-oxygen flip mechanism. Preliminary simulations are carried out for an aluminum particle in water based on the conventional DFT, as a target system for large-scale DC-DFT simulations. A pair of Lewis acid and base sites on the aluminum surface preferentially catalyzes hydrogen production in a low activation-barrier mechanism found in the simulations.