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.     

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.     

Crystal field investigations of Yb(C2H5SO4)3. 9H2O and Er: YA1G

Using the spectroscopically derived crystal field parameters for Yb(C₂H₅SO₄)₃. 9H₂O and Er³⁺: YA1G, the temperature dependence of Schottky specific heat, paramagnetic susceptibility, magnetic anisotropy and μ_eff has been calculated over a temperature range 5–400°K. The hyperfine interaction parameters for ¹⁷¹Yb³⁺, ¹⁷³Yb³⁺ and ¹⁶⁷Er³⁺ systems are also obtained and in turn used to estimate the nuclear specific heat. The nice agreement obtained for susceptibility and specific heat of Yb(C₂H₅SO₄)₃. 9H₂O at very low temperatures confirms the accuracy of CEF parameters employed and the neglect of exchange interaction. However, for Er³⁺: YA1G, the CEF parameters are adequate to explain the bulk thermal and magnetic properties but not the g-values.     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.     

Investigations of the spin-Hamiltonian parameters,optical absorption bands,and local structure for the tetragonal Cu2+ center in Cu2+-doped ZnCdO nanopowder

The spin-Hamiltonian (or EPR) parameters of tetragonal Cu²⁺ octahedral centers in ZnCdO nanopowders are calculated from the high-order perturbation formulas based on the cluster approach. In these formulas, the contributions to spin-Hamiltonian parameters due to the admixture between the d orbitals of dⁿ ion and the p orbitals of ligand ions via covalence effect are considered. The crystal field parameters are calculated from the superposition model and so the optical absorption bands (related to the crystal field energy levels) and local structure of Cu²⁺ octahedral centers in ZnCdO nanopowder are also studied. The calculated spin-Hamiltonian parameters and optical absorption bands are in reasonable agreement with the experimental values. The tetragonal elongation ΔR (=R_//−R_⊥) of Cu²⁺ octahedron in ZnCdO nanopowder due to Jahn–Teller effect is acquired from the calculations. The results are discussed.     

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.     

Influence of unstable valence of cerium ions on the crystal field in ReNi compounds

To examine the effect of hybridization of 4f electrons with conduction electrons on the crystal field potential using neutron spectroscopy, we studied the effects of the crystal electric field (CEF) in intermetallic compounds of the type ReNi, in which chemical substitution is followed by a transition of the cerium ions from an intermediate valence state to the Kondo state. Measurements were performed both on cerium ions in the compounds Ce_1−x La_xNi (x=0.5, 0.8), where they have a whole-number population of the 4f shell, and on the paramagnetic impurity ion Nd in the series of compounds Re_1−x Nd_xNi (Re=Ce, La, Y), in which the cerium ions are found either in an intermediate valence state or in the Kondo state. From the neutron inelastic magnetic scattering spectra on Nd ions, we have reconstructed the crystal field parameters in ReNi compounds and calculated the CEF level diagram of Ce ions in these compounds as functions of the interion distances Re-Ni. The results of our calculations are in good agreement with the experimentally determined splitting diagram of the ground-state multiplet of the Ce ions. We have determined that as the degree of hybridization with the conduction electrons grows the CEF potential varies considerably and the effective splitting of the 4f shell of the cerium ions increases. The estimated energy scale of the splitting of the ground-state multiplet of the Ce³⁺ ions in the ReNi CEF (Δ_CEF∼15 meV) turns out to be commensurate with the Kondo temperature (T _K ;140 K for CeNi. Analysis indicates that the CEF potential has a substantial effect on the formation of the valence-unstable ground state of the f shell in this compound. Zh. éksp. Teor. Fiz. 113, 1731–1747 (May 1998)     

低温高压下的Na5Eu(WO4)4的发光和晶体场参数

用低温金刚石对顶砧高压显微光谱系统在20—300K低温和0—10GPa高压范围内研究了白钨矿型化学计量的基质发光晶体四钨酸铕钠Na₅Eu(WO₄)₄中Eu³⁺的发光.确定了Eu³⁺荧光谱线和能级在低温下的压力移动率.它随温度变化,表明温度和压力对Eu³⁺谱线作用不是独立无关的.按晶体场理论简化方法推导了能级的晶体场参数表达式,并按实验数据拟合出在不同低温下晶体场参数随压力的移     

掺Gd3+钼酸盐AMoO4 (A=Ca,Sr, Ba,Pb)自旋哈密顿参量的理论计算

采用基于单电子晶体场机制的对角化能量矩阵方法, 计算了Gd³⁺在钼酸盐AMoO₄ (A=Ca, Sr, Ba, Pb)晶体中的自旋哈密顿参量(g因子g_//, g_⊥和零场分裂b₂⁰, b₄⁰, b₄⁴, b₆⁰, b₆⁴). 矩阵中的晶体场参量采用重叠模型计算. 计算结果显示, 应用三个合理的可调参量[即重叠模型中的内禀参量A₂ (R₀), A₄ (R₀)和A₆ (R₀)], 计算的七个自旋哈密顿参量与实验结果符合甚好, 表明该方法可用于计算或解释Gd³⁺在晶体中的自旋哈密顿参量. 关键词： AMoO₄ (A=Ca,Sr,Ba,Pb):Gd³⁺晶体')" href="#">AMoO₄ (A=Ca,Sr,Ba,Pb):Gd³⁺晶体 自旋哈密顿参量 晶体场理论 对角化能量矩阵     

A high‐level theoretical study into the atmospheric phase hydration,bond dissociation enthalpies,and acidity of aldehydes

CBS‐Q//B3, G4(MP2), and G4 composite method calculations were used to estimate atmospheric phase standard state (298.15 K, 1 atm) free energies of hydration (Δ_hydrG°_(g)), hydration equilibrium constants (log K_hydr,(g)), bond dissociation enthalpies (BDEs), and enthalpies (Δ_dH°_(g)) and free energies (Δ_dG°_(g)) of aldehydic proton acid dissociation for various substituted aldehydes with electron withdrawing and electron releasing groups. Good quality log K_hydr,(g) correlations with the Swain–Lupton resonance effect parameters R and R⁺ were found, allowing extension of the model to predict log K_hydr,(g) values for 487 substituted aldehydes having available R‐values and 108 substituted aldehydes having available R⁺ values. Good correlations were also found between experimental aqueous phase hydration equilibrium constants (log K_hydr,(aq)) and summative R/R⁺ values for peripheral substituents on a range of carbonyl derivatives (aldehydes, ketones, esters, and amides), suggesting that the structure–reactivity modeling approach can be extended to include all possible combinations of R₁C(O)R₂ carbonyl substitution in both gas and aqueous systems. Computationally derived BDEs and Δ_dH°_(g)/Δ_dG°_(g) were in good agreement with the limited experimental and theoretical datasets. BDEs did not generally correlate with any of the Hammett substituent constants or Swain–Lupton parameters considered. Gas phase acidities exhibited high correlation coefficients with Hammett inductive substituent constants (σ_I) and field effect parameters (F), allowing these to be employed as surrogates for estimating the gas phase aldehydic proton acidities of a larger potential compound range. The resulting models will be of use in predicting the environmental behavior for a broad range of environmentally relevant compounds containing carbonyl functionalities. Copyright © 2016 John Wiley & Sons, Ltd.     

CEF nature of the magnetic excitations in ordered HoNi B C

The magnetic excitations in the antiferromagnetic phase of HoNi₂B₂C are studied by inelastic neutron scattering on single crystals for the first time. Spectra measured at constant T = 2 K along symmetry directions of the reciprocal space are well explained in terms of crystal electric field (CEF) magnetic excitons within the J = 8 ground state multiplet of Ho³⁺. Very modest bandwidth with planar energy dispersion describes the magnetic exciton dynamics. A perturbative model approach consisting of the CEF states in the effective exchange mean-field provides a simple but applicable characterization of the experimental observations. The microscopic determination of the relevant exchange parameters is discussed in connection with previous works on the subject. Received 25 February 2002 / Received in final form 13 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: nordal.cavadini@psi.ch     

Magnetization measurements on some rare-earth iron garnets

The magnetic properties of Fe-based singlecrystal garnets have been studied. A magnetic field up to 55 kOe in the temperature range from 4.5 to 300 K has been used. The compensation temperature (T _comp) of the studied garnets has been determined. The compensation temperature increases with the increase of the rare-earth ions (Ho³⁺ or Gd³⁺) substituting Y³⁺ ions in thec sublattice of R₃Fe₅O₁₂. AboveT _comp, the magnetization was found to be linearly field dependent. The results are in good agreement with magnetization measurements performed on polycrystaline samples, and with calculations based on the crystal field parameters of the isostructural Holmium Gallium Garnet (HoGG).     

Gravitational Field Equations of Fourth Order and Supersymmetry

We discuss the field equations which stem from a variational principle containing the quadratic terms αR_μνR_μν and βR² besides the Einstein-Hilbert Lagrangian R. Comparison of this theory with a pure theory of fourth order shows that R must necessarily be included if we wish to interpret the field equations as gravitational equations. The Einstein-Bach-Weyl theory (α = ?3β) has the property of being a theory of “supergravitation”. Apart from gravitons without rest-mass, we have here only one additional kind of particles with rest-mass. Their mass may be determined by Planck' slength (hG/c³)^1/2. The occurrence of those particles results from the breakdown of a “supersymmetry”, that is of the conform invariance. The Einstein tensor E_μν ? R_μν ?1/2g_μνR can be regarded as a source of the gravitons without rest-mass.     

Magnetic properties of Nd3+ in Nd−Ba−Cu−O-compounds

Neutron diffraction, neutron spectroscopy and magnetization measurements have been employed to study the structural, electronic, and magnetic behavior of eleven compounds with the general formula Nd_1+y Ca _v Ba_2–y–v Cu₃O _x (0y0.5; 0v0.25; 6x7). The structure turned out to react to oxygen reduction similar as other 123-compounds, yielding discontinuities close to the metal-insulator-transition and the well-known relations of bond lengths as a function ofT _c. The crystalline electric field (CEF) interaction, splitting the 10-fold degenerate ground-state J-multiplet of the Nd³⁺-ions into five doublet states, was investigated by neutron spectroscopy. The derived CEF parameters have been used to determine changes in the electronic surroundings of the Nd³⁺ ions. In addition, with the help of the CEF parameters the thermodynamic magnetic properties of these compounds were calculated which turn out to be in good agreement with the experimental data.     

Molecular field theory analysis of R2Fe17C (R=PR,Nd, Gd,Tb, Dy,Ho, Er)

The temperature dependence of magnetization is analysed for R₂Fe₁₇C via the two-sublattice molecular field theory. The molecular field coefficients n_FF, n_RF and n_RR are obtained, by which T_C was calculated. Using the least-squares method, the fitted-form of H_R(T) varying with temperature for each compound is presented. The results are analysed. In addition, the parameters F=M_Fe²(0)n_FF/T_C was calculated for each R₂Fe₁₇C. By F, some phenomena different from the normal view were explained.     

四角或三角畸变立方晶场中(3d)1过渡金属离子的劈裂因子

对四角或三角畸变立方晶场中的(3d)¹离子,在已有的静电晶场理论的基础上,采用“集团模型”,进一步引入Γ_∥, Γ_⊥及K_∥, K_⊥,R_∥, R_⊥,并考虑E_g混入T_2g,导出适用于四角或三角畸变立方晶场各种可能情况的g_∥, g_⊥公式。讨论了g_∥, g 关键词：     

Additional raising of the degeneracy of CEF-split Ho3+ ions by antiferromagnetic spin-waves in Ho0.1Y0.9Ba2Cu3O6.13

Inelastic neutron scattering has been employed to study in detail the low-energy crystal-field (CEF) excitations of Ho³⁺ in tetragonal antiferromagnetic (AF) Ho_0.1Y_0.9Ba₂Cu₃O_6.13. We observe a splitting of the lowest excited ₅ doublet atT=1.5 K. This splitting is explained as resulting from the exchange interaction with the AF subsystem of copper spins. The corresponding susceptibility at the Ho³⁺ site has a symmetry lower than the tetragonal one of the CEF potential and, as a result, produces the splitting. The value of the coupling between Ho³⁺ and Cu²⁺ ionsJ _ex=2.4 meV is derived from the experimentally observed value of the splitting E=0.1 meV and parameters of the AF subsystem, known from the neutron scattering experiments. Some possible consequences of the rare-earth (RE)-copper exchange are discussed, including the interaction between RE ions via the virtual exchange by spin waves.     

Theoretical investigations of the local structure distortion and the spin Hamiltonian parameters of Cr ions at tetragonal charge-compensation defect CrF5O site in Cr: KMgF3 crystals

The local structure distortion and the spin Hamiltonian (SH) parameters, including the zero-field splitting (ZFS) parameter D and the Zeeman g-factors g_‖ and g_⊥, are theoretically investigated by means of complete diagonalization method (CDM) and the microscopic spin Hamiltonian theory for tetragonal charge compensation CrF₅O defect center in Cr³⁺:KMgF₃ crystals. The superposition model (SPM) calculations are carried out to provide the crystal field (CF) parameters. This investigation reveals that the replacement of O²⁻ for F⁻ and its induced lattice relaxation Δ₁(O²⁻) combined with an inward relaxation of the nearest five fluorine Δ₂(F⁻) give rise to a strong tetragonal crystal field, which in turn results in the large ZFS and large anisotropic g-factor Δg. The experimental SH parameters D and Δg can be reproduced well by assuming that O²⁻ moves towards the central ion Cr³⁺ by Δ₁(O²⁻)=0.172R₀ and the five F⁻ ions towards the central ion Cr³⁺ by Δ₂(F⁻)=0.022R₀. Our approach takes into account the spin-orbit (SO) interaction as well as the spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions omitted in previous studies. This shows that although the SO interaction is the most important one, the contributions to the SH parameters from other three magnetic interactions are appreciable and should not be omitted, especially for the ZFS parameter D.