Crystal-field hamiltonian and spin-orbit interaction for d and d ions at low C3 symmetry sites: V:Al2O3 and Ni:LiNbO3

The experimental studies have provided evidence of the occurrence of transitions from the ³T_1g(³F) ground state to the crystal-field levels ³T_2g(³F), ³T_1g(³P) and ³A_2g(³F) for the V³⁺ centres in Al₂O₃ crystal; and from the ³A_2g(³F) ground state to the crystal-field levels ³T_2g(³F), ³T_1g(³F) and ³T_1g(³P) for the Ni²⁺ centres in LiNbO₃ crystal (levels are assigned to irreps of the O_h point symmetry group). Using the experimental spectroscopic data, theoretical calculations of the crystal-field levels of V³⁺:Al₂O₃ and Ni²⁺:LiNbO₃ are carried out based on the Racah theory. The observed crystalline-field splittings of the V³⁺ and Ni²⁺ terms were accounted for using a C₃ symmetry Hamiltonian. The spin-orbit interaction was taken into account in this work. The Racah, crystal-field and spin-orbit parameters, which fit experimental and theoretical energy levels, have been reliably obtained. A good agreement between the theoretical and experimental results for the energy levels of V³⁺:Al₂O₃ and Ni²⁺:LiNbO₃ has been obtained.     

Spin-spin and spin-other-orbit effects of optical spectra and the spin-Hamiltonian parameters for Cr ions in MgO crystals

An extended complete diagonalization method/microscopic spin-Hamiltonian (CDM/MSH) program has been developed, which is applicable for d³ ions at sites of tetragonal symmetry type I (C_4v, D_2d, D₄, D_4h) and trigonal symmetry type I (C_3v, D₃, D_3d). The Hamiltonian includes the spin-spin (SS) and spin-other-orbit (SOO) magnetic interactions besides the spin-orbit (SO) magnetic interaction usually taken into account. Utilizing the extended CDM/MSH program, the optical spectra, the spin-Hamiltonian (SH) parameters of the ground state ⁴B₁, and the splitting δ(²E) of the first excited ²E state for Cr³⁺ (3d³) ions at C_4v symmetry sites in MgO crystals have been successfully investigated. It is found that although the SO magnetic interaction is the most important one, the contributions to the SH parameters and the optical spectra from the SS and SOO magnetic interactions for Cr³⁺:MgO crystals are appreciable and should not be omitted, especially reaching 27.8% for the zero field splitting parameter D.     

Investigations of the electron paramagnetic resonance parameters and defect structures for Ni ions in CdX2 (X=Cl,Br) crystals

The high-order perturbation formulas of electron paramagnetic resonance (EPR) parameters (g factors g_∥,g_⊥ and zero-field splitting D) for 3d⁸ ions in trigonal octahedral clusters are established. These formulas contain the contributions not only from the crystal-field (CF) mechanism, but also from the charge-transfer (CT) mechanism (which is not considered in the widely used CF theory). From these formulas, the EPR parameters and the impurity-induced defect structures for Ni²⁺ ions in CdX₂ (X=Cl, Br) crystals are studied. The calculated EPR parameters are coincident with the experimental values, and the defect structure of Ni²⁺ impurity center obtained from the calculation is different from the corresponding structure in the host crystal. The sign of Q^CT (Q=Δg_∥, Δg_⊥, or D) due to CT mechanism agrees with that of the corresponding Q^CF due to CF mechanism and the relative importance of CT mechanism (characterized by Q^CT/Q^CF) increases with increasing covalence of 3d⁸ clusters and hence with raising atomic number of ligand X. So, in the explanations of the EPR parameters of 3d⁸ (or other 3dⁿ) ions in crystals with the heavy-element ligand ion (e.g., Br⁻), the calculated formulas based on the two-mechanism (CF and CT mechanisms) model are preferable to those based on only the CF mechanism in the CF theory.     

Investigations of the optical and EPR spectra for (NiX6) (X=Cl, Br, I) clusters

In this paper, the formulae of optical spectral levels and electron paramagnetic resonance (EPR) spectra in trigonal symmetry of 3d⁸ ions are established on the basis of strong field mechanism and a two spin-coupling (SO) parameters model. Unlike the classical crystal-field approach which has only taken the SO coupling of the central metal ions into account, the contribution of the SO coupling of the ligand ions to the optical and EPR spectra has been included in these formulae. When the optical and EPR spectra of the strong covalent crystals are calculated, the reasonable results can be obtained if the two SO parameters model has been put into action. As an application, the optical and EPR spectra of the (NiX₆)⁴⁻ clusters in CsMgX₃:Ni²⁺ (X=Cl, Br, I) crystals have been studied by the complete diagonalization (of energy matrix) method (CDM). The calculated results agree well with experimental findings. From the investigations, a more valid method to calculate the optical and EPR spectra for 3d⁸ ions clusters is provided.     

Theoretical studies of the optical and EPR spectra for V in Y2O3 crystal

In this paper, we give an alternative suggestion that both the observed optical and electron paramagnetic resonance (EPR) spectra of Yttrium oxide (Y₂O₃):V³⁺ are attributed to V³⁺ ions at the S₆ site of Y₂O₃. This suggestion is different from the opinion in the previous paper that the optical and EPR spectra are attributed to V³⁺ ions at the C₂ and S₆ sites, respectively. From the suggestion, the optical band positions and spin-Hamiltonian parameters are calculated by diagonalizing the complete energy matrix for 3d² ions in trigonal symmetry. The results are in good agreement with the experimental values, suggesting that both the observed optical and EPR spectra in Y₂O₃:V³⁺ may be due to V³⁺ at S₆ site of Y₂O₃ crystal.     

Crystal-field analysis for d ions at D4h symmetry sites: Electronic states in trans-NiCl2(H2O)4 complex

The polarized absorption spectra of trans-NiCl₂(H₂O)₄ complex were measured by Bussière et al. [Coord. Chem. Rev. 219-221 (2001) 509-543] at low-temperature. Using the experimental spectroscopic data, semiempirical calculations of the crystal-field levels of trans-NiCl₂(H₂O)₄ chromophore are carried out, based on the Racah theory. We used idealized D_4h point group symmetry to analyse the observed crystalline-field splitting of this chromophore. As a result, Racah and crystal-field parameters have been reliably obtained. A good agreement between the theoretical and experimental energy levels of trans-NiCl₂(H₂O)₄ complex has been obtained. The region of ³T_1g/¹E_g(O_h) bands is of great interest and it is useful to use the tetragonal symmetry to understand the features of this spectral region.     

Electronic structure of V in NaMgAl(ox)3·9H2O probed by Fourier transform spectroscopy

High-resolution Fourier transform absorption and luminescence spectroscopy reveal axial and rhombic zero-field splittings of the spin-forbidden electronic origins of V³⁺ in NaMgAl(ox)₃·9H₂O (ox=oxalate) single crystals below 25 K. The temperature dependence of the integrated absorption of the split features display behavior consistent with a Boltzmann distribution within the zero-field split ³Â₂ ground state of V³⁺. Weak luminescence is observed in the near-IR from the lowest energy spin-forbidden transition with a luminescence lifetime of less than 0.5 μs at 11 K and an estimated quantum efficiency of the order of 10⁻⁵.     

EPR spectra of Fe centers in layered TlGaSe2 single crystal

A single-crystal TlGaSe₂ doped by paramagnetic Fe ions has been studied at room temperature by electron paramagnetic resonance (EPR) technique. The fine structure of EPR spectra of paramagnetic Fe³⁺ ions was observed. The spectra were interpreted to correspond to the transitions among spin multiplet (S=5/2, L=0) of Fe³⁺ ion, which are splitted by the local ligand crystal field (CF) of orthorhombic symmetry. Four equivalent Fe³⁺ centers have been observed in the EPR spectra and the local symmetry of crystal field at the Fe³⁺ site and CF parameters were determined. Experimental results indicate that the Fe ions substitute Ga at the center of GaSe₄ tetrahedrons, and the rhombic distortion of the CF is caused by the Tl ions located in the trigonal cavities between the tetrahedral complexes.     

Theoretical interpretation of optical and EPR spectra and the substitutional site of ferroelectric LiNbO3:Ni crystal

The optical absorption spectrum, zero-field splitting (ZFS) and EPR g factor of LiNbO₃:Ni²⁺ are explained uniformly on the basis of complete energy matrix diagonalization procedure (CDP) and Zhao's self-consistent field (SCF) d-orbit of free Ni²⁺ ions. The agreement between the calculated results and the experimental data shows quantitatively that impurities Ni²⁺ replace the Nb⁵⁺ rather than Li⁺ sites in LiNbO₃:Ni²⁺.     

Twinned EPR spectra of Fe centers in ternary layered TlGaS2 crystal

TlGaS₂ single crystal doped by paramagnetic Fe³⁺ ions has been studied by electron paramagnetic resonance (EPR) technique. The fine structure of EPR spectra of paramagnetic Fe³⁺ ions was observed. The spectra reveal a nearly orthorhombic symmetry of the crystal field (CF) on the Fe³⁺ ions. Two groups each consisting of four equivalent Fe³⁺ centers were observed in the EPR spectra. The local symmetry of the crystal field on the Fe³⁺ centers and CF parameters were determined. Experimental results indicate that the Fe ions substitute Ga at the center of the GaS₄ tetrahedrons. The rhombic distortion of the sulfur ligand CF is attributed to the effect of Tl ions located in the trigonal cavities between the tetrahedral complexes. The observed twinning of the resonance lines indicates a presence of two non-equivalent positions of Tl ions that confirms their zigzag alignment in the TlGaS₂ crystal structure.     

Theoretical study of local lattice structure of Fe-V cd and Fe-Li systems in RbCdF3 and CsCdF3 crystals

A theoretical method for investigating the inter-relation between the electronic and the molecular structures of a 3d⁵ ion in a tetragonal ligand-field has been established on the basis of a 252×252 complete energy matrix. By means of this method, the local structure of the Fe³⁺-V _cd and Fe³⁺-Li⁺ systems in RbCdF₃:Fe³⁺ and CsCdF₃:Fe³⁺ crystals are determined by the experimental EPR spectrum. Our calculation show that the local lattice structure around an octahedral Fe³⁺ center has a compression distortion along the crystalline axis in RbCdF₃ as well as in CsCdF₃ crystals, and that the compression magnitude of a tetragonal Fe³⁺-Li⁺ system is larger than that of the Fe³⁺-V _cd system. This may be ascribed to the fact that a Fe³⁺ ion replaces a Cd²⁺ ion and a Li⁺ ion substitutes for another Cd²⁺ ion next to the Fe³⁺ ion in the Fe³⁺-Li⁺ system, and the Li⁺ ion will shift to the Fe³⁺ ion, which pushes the F₁ ion toward the Fe³⁺ ion. Using this method, the experimental EPR parameters , and are also interpreted simultaneously.     

Crystal field analysis of energy level structure of the Cr2O3 antiferromagnet

A detailed analysis of the energy level structure of the six-fold coordinated Cr³⁺ ion in the chromium oxide Cr₂O₃ is performed using the exchange charge model of the crystal field theory. Parameters of the crystal field acting on the Cr³⁺ optical electrons are calculated from the crystal structure data for the [CrO₆]⁹⁻ impurity center. The energy levels obtained are compared with the experimental absorption spectra for the considered crystal; a good agreement with experimental data is demonstrated. One possible explanation for the ultraviolet p₁ absorption band is proposed based on the results of crystal field calculations.     

Growth, EPR and optical absorption spectra of l-threonine single crystals doped with Cu ions

We investigated the crystal growth, electron paramagnetic resonance (EPR) and optical absorption spectra of l-threonine doped with Cu²⁺. The quality, size and habit of the single crystals grown from aqueous solution by the slow solvent evaporation and by the cooling methods vary when the impurities are introduced during the growth process. The variations with the magnetic field orientation of the EPR spectra of single-crystal samples at room temperature and 9.77 GHz in three crystal planes (ab, bc and ac) show the presence of copper impurities in four symmetry-related sites of the unit cell. These spectra display well resolved hyperfine couplings of the of Cu²⁺ with the I_Cu= of the copper nuclei. Additional hyperfine splittings, well-resolved only for specific orientations of the magnetic field, indicate that the copper impurity ions in the interstitial sites have two N ligands with similar hyperfine couplings. The principal values of the g and A_Cu tensors calculated from the EPR data are g₁=2.051(1), g₂=2.062(2), g₃=2.260(2), A_Cu,1=16.9(5)×10⁻⁴ cm⁻¹, A_Cu,2=21.8(6)×10⁻⁴ cm⁻¹, A_Cu,3=180.0(5)×10⁻⁴ cm⁻¹. The principal directions corresponding to g₃ and to A_Cu,3 are coincident within the experimental errors, reflecting the orientation of the bonding planes of the copper ions in the crystal. The values of the crystal field energies are evaluated from the optical absorption spectrum, and the crystal field and bonding parameters of the Cu impurities in the crystal are calculated and analyzed. The EPR and optical absorption results are discussed in terms of the crystal structure of l-threonine and the electronic structure of the Cu²⁺ ions, and compared with data reported for other systems. The effects of the impurities in the growth and habit of the crystals are also discussed.     

Crystal field interactions in DyFe2Si2 and DyFe2Ge2

Two sets of crystal field (CF) parameters have been proposed for DyFe₂Si₂, none of which could provide a simultaneous explanation of the available experimental data, particularly at low temperatures (below 100 K). The set derived from magnetic studies could not even explain the thermal variation of the magnetic specific heat reported in the same work. Although the set of CF parameters, obtained from a fit to the Mossbauer spectra, could provide a fairly good explanation of the thermal variation of the magnetic susceptibilities along the c-axis, it could not explain the observed thermal variation of other reported experimental findings. In the present work, an appraisal of the CF parameters proposed earlier has been done and a set of CF parameters has been derived, which provide a simultaneous explanation of all the available experimental data. The effect of substitution of Ge for Si on the magnetic properties and the magnetic specific heat of DyFe₂Si₂ has been studied in the framework of one electron crystal field model. The inelastic neutron scattering studies and EPR measurements are required to check the predicted Stark energies and the paramagnetic resonance g-values.     

Studies of EPR g factors of the isoelectronic 3d series Cr, Mn and Fe in SrTiO3 crystals

The g-shifts Δg(=g−g_s, where g_s≈2.0023 is the free-ion value) of the isoelectronic 3d³ series Cr³⁺, Mn⁴⁺ and Fe⁵⁺ in SrTiO₃ crystals are calculated from the high-order perturbation formula based on the cluster approach for 3d³ ion in cubic octahedral site. The formula includes not only the contribution from the crystal-field (CF) mechanism, but also that from the charge-transfer (CT) mechanism (which is omitted in the CF theory). From the calculations, it is found that the contribution Δg_CT from the CT mechanism in sign is contrary to the corresponding Δg_CF from the CF mechanism and the relative importance of CT mechanism (characterized by |Δg_CT/Δg_CF|) increases with the increasing valence state (and hence the atomic number) of 3d³ ion. The positive g-shift Δg of SrTiO₃:Fe⁵⁺ is due mainly to the contribution of CT mechanism. So, for the explanations of g factors of the high valence state 3dⁿ ions (e.g. Mn⁴⁺ and Fe⁵⁺) in crystals, the contributions from both CF and CT mechanisms should be taken into account.     

Correlation between Zero-Field Splitting and Site Distortions of Cr^3＋ Ions in NH4Cl：Cr^3＋ System： a Complete Energy Matrix Study

A theoretical method for investigating the inter-relation between the electronic and molecular structures of 3d^3 configuration ions in a tetragonal ligand field is established on the basis of the 120 × 120 complete energy matrices. Using this method, the local structure parameters of two tetragonal Cr^3＋ centers in the NH4 Cl：Cr^3＋ system are determined, Furthermore, the relations between the molecular symmetry and the ligand field symmetry are discussed.     

Optical and crystal-field analysis of Er ion in Y2O3-P2O5 thin films

Luminescence spectra of erbium ions doped in Y₂O₃-P₂O₅ thin films, with different P₂O₅ content (from 3% to 47%), were analysed with crystal-field Hamiltonian model with D_2d symmetry including J-mixing effect. The empirical crystal-field parameters (CFPs) obtained for the best fit of calculated to experimental energy levels allows us to confirm the well-established YPO₄ phase for 47% of P₂O₅. The CFPs are compared to those calculated for Ce³⁺, Nd³⁺ and Dy³⁺ in the YPO₄ host. This work is a continuation of our previous results for erbium-doped Y₂O₃ thin films.     

Crystal growth, spectroscopic and crystal field studies of [N(CH3)4]2MnCl4 and [N(CH3)4]2CoCl4 single crystals in the paraelectric phase

Single crystals [N(CH₃)₄]₂MnCl₄ and [N(CH₃)₄]₂CoCl₄ were grown by the slow evaporation technique from the super-saturated solutions. The samples obtained were undergone the X-ray and spectroscopic studies. Absorption spectra in the paraelectric phase at T=303 K have been recorded using the Shimadzu 160A double beam automatic scanning spectrophotometers. On the basis of the exchange charge model and Racah theory the crystal field parameters and Racah parameters have been calculated; all absorption bands for both crystals were given an assignment.