Trigonal Field Research Articles

Analysis of ground-state zero-field splitting for Mn 2+ in hexagonal ZnS:Mn 2+

The ground state splitting of d 5 configuration ion Mn 2+ in ZnS:Mn 2+ has been studied by diagonalizing the energy matrices for electron–electron repulsion, spin–orbit coupling and trigonal ligand field interactions. It is shown that in order to give a unified explanation for the EPR parameters a, D and ( a− F) for Mn 2+ in ZnS:Mn 2+, a positive Dq has to be employed. This means that in tetrahedral ZnS the sulfur ion has a positive effective charge. This unusual result supports the Pauling's speculation that the sulfur ion in ZnS may be looked upon as an electron donor that forms a quadricovalent argon state of S 2+ with sp 3 hybrid configuration.

Spectroscopic and structural characterization of the [Fe(imidazole)(6)](2+) cation.

Spectroscopic, structural, and magnetic data are presented for Fe(C(3)H(4)N(2))(6)(NO(3))(2), which facilitate a precise definition of the electronic and molecular structure of the [Fe(Im)(6)](2+) cation. The structure was determined at 120(1) K by X-ray diffraction methods. The salt crystallizes in the trigonal space group R3 with unit-cell parameters a = 12.4380(14) A, c = 14.5511(18) A, and Z = 3. All the imidazole ligands are equivalent with an Fe-N bond distance of 2.204(1) A. Variable-temperature inelastic neutron scattering (INS) measurements identify a cold magnetic transition at 19.4(2) cm(-1) and a hot transition at 75.7(6) cm(-1). The data are interpreted using a ligand field Hamiltonian acting in the weak-field (5)D basis, from which the diagonal trigonal field splitting of the (5)T(2g) (O(h)) term is estimated as approximately 485 cm(-1), with the (5)A(g) (S(6)) component lower lying. High-field multifrequency (HFMF) EPR data and measurements of the magnetic susceptibility are also reported and can be satisfactorily modeled using the energies and wave functions derived from analysis of the INS data. The electronic and molecular structures are related through angular overlap model calculations, treating the imidazole ligand as a weak pi-donor.

Optical absorption of octahedral ions Fe 2+, Fe 4+ and photoinduced effect in YIG single crystals

The peculiarities of optical absorption of octahedral ions Fe 2+ and Fe 4+ have been analyzed at various parameters of a trigonal and non-trigonal field by taking into account the transitions between levels of a split ground state. The spectral dependence of optical absorption coefficient on parameters of a crystal field has been constructed. The differences of optical absorption spectra that arise with redistribution and change of quantity of ions Fe 2+ and Fe 4+ have been considered. The explanation of experimental results on photoinduced changes of optical absorption in yttrium ferrite garnet single crystals has been proposed.

Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+ II: Energy Spectra at Normal Pressure, Low and Room Temperatures

With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr3+ at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperature-independent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of and . It is found that the contribution from EPI to R1 line of GSGG:Cr3+ with taking into account spin-orbit interaction (Hso) and trigonal field (Vtrig) is much larger than the one with neglecting Hso and Vtrig, and accordingly it is essential for the calculation of the EPI effect to take first into account Hso and Vtrig. The admixture of base-wavefunctions, and , the average energy separation and their variations with temperature have been calculated and discussed.

Orbital state and magnetic properties ofLiV2O4

LiV_2 O_4 is one of the most puzzling compounds among transition metal oxides because of its heavy fermion like behavior at low temperatures. In this paper we present results for the orbital state and magnetic properties of LiV_2 O_4 obtained from a combination of density functional theory within the local density approximation and dynamical mean-field theory (DMFT). The DMFT equations are solved by quantum Monte Carlo simulations. The trigonal crystal field splits the V 3d orbitals such that the a_{1g} and e_{g}^{pi} orbitals cross the Fermi level, with the former being slightly lower in energy and narrower in bandwidth. In this situation, the d-d Coulomb interaction leads to an almost localization of one electron per V ion in the a_{1g} orbital, while the e_{g}^{pi} orbitals form relatively broad bands with 1/8 filling. 2The theoretical high-temperature paramagnetic susceptibility chi(T) follows a Curie-Weiss law with an effective paramagnetic moment p_{eff}=1.65 in agreement with the experimental results.

Studies of the zero-field splitting and g-factor for the defect model of Cr 3+ in α-LiIO 3 crystals at low temperature

The EPR zero-field splitting parameters D and g-factors for Cr 3+ in α-LiIO 3 single crystal, taking into account both the effect of lattice distortion and two Li + vacancies, have been investigated using a complete diagonalization method (CDM) for 3d 3 ions in a trigonal symmetry crystal field. The theoretical results ( D=−0.60876 cm −1, g ∥=1.9641, g ⊥=1.9682) are in excellent agreement with experimental results ( D=−0.6099(3) cm −1 g ∥=1.965±0.001, g ⊥=1.971±0.002). In addition, Macfarlane's perturbation expressions lead to results almost identical with the CDM for Cr 3+ in an α-LiIO 3 single crystal.

Displaced Substitutional Phosphorus Acceptors in Zinc Selenide

Spin-flip Raman scattering experiments reveal that shallow phosphorus acceptors in ZnSe grown epitaxially on GaAs are subject to a local crystal field of trigonal symmetry. In relaxed layers, the trigonal field dominates the macroscopic biaxial tensile strain field. The trigonal field is also observed in pseudomorphic layers, where the sign of the overall macroscopic biaxial strain is reversed. In both cases, the wavefunction of the hole bound at the acceptor appears to be sufficiently localised for the effects of the macroscopic strain field to be severely reduced. This increased localisation relative to nitrogen acceptors and the appearance of the trigonal field are in excellent agreement with the results of previous total energy pseudopotential calculations, which predict that substitutional phosphorus acceptors should be displaced from selenium sites in 〈111〉 directions.

A novel binuclear copper(II) complex with fumarate and 1,10-phenanthroline

A MeOH solution of 1,10-phenanthroline reacts with Cu(fum)[fum = (OOCCH = CHCOO)2−] to yield a novel binuclear copper(II) unsaturated dicarboxylate complex of general formula [Cu2(fum)(phen)4](fum) · 11H2O, whose crystal structure has been determined by X-ray diffraction. Two copper(II) atoms are bridged by a fumarate group, and each copper(II) atom is coordinated to two 1,10-phenanthroline molecules in a distorted trigonal bipyramidal configuration. The i.r. spectrum shows the presence of the monodentate carboxylate ligand. The electronic reflectance spectrum in the solid state suggest that the d–d transitions of the complex is in a trigonal bipyramidal ligand field. The temperature-dependent magnetic susceptibility studies suggest that a weak ferromagnetic interaction exists between the two copper(II) atoms when the temperature exceeds 130 K.

Novel trinuclear copper(II) complexes with alpha,beta-unsaturated carboxylates and imidazole

A MeOH solution of imidazole reacts with Cu(2)A(4)(H2O)(2) [A = CH2=CHCO2-, CH2=C(Me)CO2-] to yield novel trinuclear copper(II) carboxylate complexes of general formula: Cu(3)A(5)(OH)(imH)(3) [(1) A=CH2=CHCO2-; (2) A = CH2=C(Me)CO2-; imH = imidazole]. The crystal structure of (2) has been determined. The geometry of one copper(II) atom is distorted trigonal bipyramidal, and the other two copper(II) atoms are distorted square-planar. The i.r. spectra show the presence of the absorption bands of both bidentate mu(2)-O,O' and monodentate carboxylate ligands. The electronic reflectance spectra in the solid state suggest that the d-d transitions of complexes are in a trigonal bipyramidal ligand field and a square-planar ligand field. Room temperature X-band e.s.r. spectra of powdered samples with g(av) = 2.140 for (1) and g(av) = 2.092 for (2), indicate that there is no spin coupling between the copper(II) atoms.

Direct evidence for the trigonal symmetry of shallow phosphorus acceptors in ZnSe

Spin-flip Raman scattering has been used to provide direct experimental evidence that shallow phosphorus acceptors in relaxed ZnSe epitaxial layers grown on GaAs lie at sites of predominantly trigonal local symmetry. As a consequence, the energy of the heavy-hole bound exciton is about 0.45 meV less than that of the light exciton. This splitting is significantly smaller than (and of opposite sign and different symmetry to) the valence-band splitting of 3 meV observed due to the macroscopic biaxial tensile strain in the same specimens. The behavior is in complete contrast to that of nitrogen acceptors, for which no trigonal field is observed. The experiments provide confirmation of the behavior predicted by previous pseudopotential total-energy calculations for the shallow acceptor states formed by these two different group-V dopants when substituting at selenium sites.

Local structure and the electron paramagnetic resonance parameters for the Cr 3+ ions at K +-vacancy site in Cr 3+:KZnF 3 laser crystal

The quantitative relationship between the electron paramagnetic resonance (EPR) parameters D, g ∥, g ⊥ and the local structure parameters of Cr 3+ ion in KZnF 3 crystals is established. The local structure for Cr 3+ paramagnetic center in KZnF 3:Cr 3+ crystal has been determined from EPR parameters of Cr 3+ ion. This work shows that the trigonal crystal field of Cr 3+ ion in KZnF 3 crystals comes from following two origins: (1) the nearest-neighbor K + vacancy caused by the charge compensation in the [1 1 1]-axis direction; and (2) the lattice distortions of the nearest-neighbor fluorine coordination caused by the K + vacancy and the differences in mass, charge, and radius between Cr 3+ ion and Zn 2+ ion. The unified calculation of the EPR zero-field splitting and g factors, taking into account the K + vacancy and the lattice distortions, has been carried out on the basis of the complete diagonalization procedure and the superposition crystal-field model, all calculation results are in excellent agreement with the experimental data. Although the main source of the trigonal crystal field comes from the K + vacancy caused by the charge compensation, the contribution of the lattice distortion cannot be neglected.

Calculations of the Spin-Lattice Coupling Coefficients Fij and Zij for MgO:Co2+ Crystal

According to a uniform and simple method of calculating spin-lattice coupling coefficients and the perturbation formulas of gi factors and hyperfine structure constants Ai based on the cluster approach for 3d7 ions in cubic, tetragonal and trigonal octahedral crystal fields, the spin-lattice coupling coefficients Fij (F11, F12, F44),Zij (Z11, Z12, Z44) and also g factor and hyperfine constant A for MgO:Co2+ are calculated by using the parameters obtained from the optical spectra without adjustable parameters. The calculated results show good agreement with the observed values. The difficulty in explaining the coefficients Fij and Zij is therefore removed.

Examination of the electron paramagnetic resonance parameters and their pressure-induced shifts for the Mn 2+ ion in Na 2ZnCl 4·3H 2O

In order to overcome the difficulties, which arose in previous works, in explaining the electron paramagnetic resonance (EPR) parameters and their pressure-induced shifts for the Na 2ZnCl 4·3H 2O:Mn 2+ crystal, in this work exact complete energy diagonalization calculations were completed based on the analytical expressions for the EPR parameters of 3d 5 ions in trigonal symmetry field proposed by Zhao. Results show that, in contrast with some authors, the local structure of Mn 2+ in Na 2ZnCl 4·3H 2O is C 3 v symmetry with four Cl − ligands instead of [MnCl 3·H 2O] −. The values of D and a and their pressure-induced shifts deduced are in good agreement with the experimental data.

Zeeman splitting factor of the Er3+ ion in a crystal field

Numerical computations are presented on the energy levels of the Er3+ ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet Γ8 states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian ℋ= gμBBJ+ uμBBJ3 with the parametersg andu calculated for mixed fourth- and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principalg tensor components g∥ and g⊥ were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g∥ + 2g⊥ is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors |g∥| + 2|g⊥| is not always equal to their real trace g∥ + 2g⊥. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values gx, gy and gz. A good agreement is obtained for the recently reportedg values of an erbium center in silicon.

Local structure and local compressibilities around Co 2+ impurity in ZnSiF 6·6H 2O crystal determined from electron paramagnetic resonance data

The perturbation formulas of g-factors g ‖, g ⊥ and hyperfine structure constants A ‖, A ⊥ for 3d 7 ion in trigonal octahedral crystal field are established on the basis of a cluster approach. These formulas consist of the contributions from configuration interaction and covalency effect and the parameters related to both effects can be estimated from the optical spectra and the structural data of the system under study. According to these formulas, the local trigonal distortion angle β at pressure P=0 and the local compressibilities d ln β/d P in two pressure regions around Co 2+ impurity in ZnSiF 6·6H 2O crystal are estimated by fitting the calculated electron paramagnetic resonance parameters g i , A i and their pressure coefficients to the observed values. The results show that these local values are different from those of the host crystal because of the influence of impurity.

Electronic Raman transitions from the vanadium(III) hexa-aqua cation, in guanidinium vanadium sulphate

Electronic Raman transitions ( 3 A→ 3 E( C 3) ) have been observed between the trigonally split components of the 3 T 1 g ( O h ) ground term of the vanadium(III) hexa-aqua cation in guanidinium vanadium sulphate hexa-hydrate. The magnitude of the trigonal field splitting is considerable, ∼2720 cm −1, which is consistent with expectations based on the stereochemistry of the [V(OH 2) 6] 3+ complex. It is shown that a satisfactory reproduction of the electronic Raman band profile can be obtained only by assuming a ( 3 A⊕ 3 E)⊗e vibronic coupling model.

Studies of the EPR Parameters gi and Ai for Co2+ in the Octahedral Sites of Y3Al5O12 and Y3Ga5O12 Crystals

The perturbation formulas of EPR g factors g∥, g⟂ and hyperfine structure constants A∥, A⟂ for the trigonal octahedral 3d7 cluster are derived considering not only the configuration interaction effect due to the admixture among ground and excited states, but also the covalency effect due to the admixture between the d electrons of the 3d7 ion and the p electrons of ligands. In these formulas, the parameters related to both effects and the trigonal field parameters are estimated from the optical spectra and the structural parameters of the studied system. According to these formulas, the EPR parameters g∥, g⟂, A∥ and A⟂ for Co2+ in the octahedral sites of Y3Al5O12 and Y3Ga5O12 garnets are satisfactorily explained from the optical spectra and the structure data. The role of the covalency effect is discussed.

Magnetic exchange interaction in a pair of orbitally degenerate ions: Magnetic anisotropy of [Ti2Cl9]−3

The theory of the kinetic exchange in a pair of orbitally degenerate ions developed by the authors [J. Phys. Chem. A 102, 200 (1998)] is applied to the case of face-shared bioctahedral dimer (overall D3h-symmetry). The effective kinetic exchange Hamiltonian is found for a T22–T22 system taking into account all relevant transfer pathways and charge-transfer crystal field states. The influence of different transfer integrals involved in the kinetic exchange on the energy pattern and magnetic properties of the system is examined. The role of other related interactions (trigonal crystal field, spin–orbit coupling) is also discussed in detail. Using the pseudoangular momentum representation and the technique of the irreducible tensor operators of R3-group we give a general outlook on the nontrivial symmetry properties of the effective Hamiltonian for the D3h-pair, and on the magnetic anisotropy arising from the orbital interactions specific for the case of orbital degeneracy. The magnetic properties of the binuclear unit [Ti2Cl9]−3 in Cs3Ti2Cl9 are discussed with a special emphasis on the magnetic anisotropy experimentally observed in this system. The existing exchange models for [Ti2Cl9]−3 and the concept of the effective Hamiltonian are discussed in the context of the present study.

On the nature of the trigonal fields in hexaaquachromium(III) in guanidinium aluminum sulfate hexahydrate.

Zeeman and site selective luminescence and excitation spectra in the region of the 2E<--4A2 transition are reported for the hexaaquachromium(III) complex in the trigonal ferroelectric guanidinium aluminum sulfate hexahydrate. The two prominent transitions are due to the R1 lines of the two sites of C3 and C3v point symmetry. The two R1 lines display g parallel = -3.1 and g parallel = -3.2, respectively, and show no measurable Zeeman shift or splitting with B perpendicular c. This behavior is consistent with the presence of a very large trigonal field. A peculiar feature of the present system is the conspicuous absence of any prominent R2 line. From the Zeeman data with B perpendicular c and a comparison of vibrational sidelines in excitation and luminescence it is concluded that the R2 level strongly interacts with vibrational levels.

Magnetic susceptibility and luminescence of α-ZnAl 2S 4 tiospinel doped with chromium

The magnetic susceptibility as well as the optical excitation and luminescence spectra of three samples of α-ZnAl 2S 4 tiospinel doped with Cr at various concentrations have been measured in the temperature range 77–300 K. The susceptibility has allowed us to estimate the concentration of Cr in the samples studied as lying in the range 0.01–0.06 at.%. Crystal-field theory, including spin–orbit coupling and the trigonal crystal field of the D 3d site has been used to fit the optical data. The best-fit parameters of the tiospinel crystal are B 20=4800 , B 40=32 500 , B 43=−28 500 , F (2)=58 800 , F (4)=40 500 and ξ D =300 cm −1. The computational procedure used gives excellent agreement between the experimental and calculated energy levels of the Cr 3+ ion in the α-ZnAl 2S 4 matrix.