Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Yb at the tetragonal Y site of KY3F10 crystal

The six optical band positions and six spin-Hamiltonian parameters [g factors g_∥, g_⊥ and hyperfine structure constants A_∥(¹⁷¹Yb³⁺), A_⊥(¹⁷¹Yb³⁺), A_∥(¹⁷³Yb³⁺), A_⊥(¹⁷³Yb³⁺)] for Yb³⁺ ion at the tetragonal Y³⁺ site of KY₃F₁₀ crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14×14 complete energy matrix for 4f¹³ ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A_∥, A_⊥ for the isotopes ¹⁷¹Yb³⁺ and ¹⁷³Yb³⁺ in KY₃F₁₀ are suggested. The results are discussed.     

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Cr ions in Y2Ti2O7 crystal

The optical band positions and spin-Hamiltonian parameters (g factors g_g_? and zero-field splitting D) for the trigonal Cr³⁺ centers in Y₂Ti₂O₇ crystal are calculated from the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. In the calculations, the contributions to spectral data from both the spin-orbit parameter of central dⁿ ion and that of ligand ion are considered and the crystal field parameters used are estimated from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr³⁺ center is suggested.     

Studies of the crystal field energy levels and g factors for Ce in LiYF4 crystal

The five observed crystal field energy levels and EPR g factors g_//and g_⊥ for Ce³⁺-doped LiYF₄ crystal are calculated together from a complete diagonalization (of energy matrix) method. In the method, the contributions to g factors of ground Kramers doublet from all the rest doublets within the ground and excited manifolds ²F_5/2 and ²F_7/2 are included. The calculated results show reasonable agreement with the experimental values. The calculations suggest that the crystal field parameter B₂₀ > 0 in LiYF₄: Ce³⁺ crystal. The opinion of the parameter B₂₀ < 0 in the previous paper is not correct. Since this opinion is based on the calculation of g factors using a very simple method where only the contributions to g factors from the doublets within the ground manifold ²F_5/2 are considered, it is suggested that this simple method is not effective in the calculation of g factors for 4f¹ ions in crystals.     

Studies of the optical spectra and spin-Hamiltonian parameters for the trivalent ytterbium ions in lithium yttrium fluoride crystals

In this paper, the crystal field (CF) levels and spin-Hamiltonian (SH) parameters (g factors g _∥ and g _⊥ and hyperfine structure constants A _∥ and A _⊥) of the rare-earth ion Yb³⁺ in lithium yttrium fluoride crystals are calculated under D _2d point symmetry assumption. Two main methods are used in the calculation to study the SH parameters: one is the perturbation theory method and the other is the complete diagonalization (energy matrix) method (CDM). Comparing the calculated results with the experimental data, we can see that the CDM is more effective to calculate the SH parameters. In addition, the CF J-mixing of all excited-state multiplets into the ground-state multiplet ²F_7/2 is considered. The validity of the calculated results is discussed.     

Unified calculations of spin-Hamiltonian parameters and optical band positions for Ni+ ion in AgGaSe2 crystal

The complete diagonalisation (of energy matrix) method based on the two-spin-orbit-parameter model is applied to unifiedly calculate the spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) and optical band positions for Ni⁺ ion in silver gallium selenide (AgGaSe₂) crystal. In the model, besides the contribution due to the spin-orbit parameter of central dⁿ ion (i.e., the one-spin-orbit-parameter model in the traditional crystal-field theory), that of ligand ions are taken into account. The calculated results are reasonably consistent with the experimental values. The local structure of Ni⁺ centre in AgGaSe₂ is estimated through the calculation. The complete diagonalisation method based on the one-spin-orbit-parameter model is also applied to calculate these electron paramagnetic resonance and optical data. It is found that although the calculated optical band positions are close to those based on the two-spin-orbit-parameter model and hence to the experimental values, the calculated spin-Hamiltonian parameters (in particular, the g factors) are in disagreement with the experimental values. The latter point is further confirmed from the calculations with the perturbation method. So, for the rational calculations of spin-Hamiltonian parameters of dⁿ clusters with ligand having large spin-orbit parameter, the contributions due to spin-orbit parameters of both the central dⁿ ion and ligand ion should be contained.     

Defect model and spin-Hamiltonian parameters for the tetragonal Nd center in the tetragonal phase of SrTiO3 crystal

The spin-Hamiltonian parameters (g factors g_∥, g_⊥ and hyperfine structure constants ¹⁴³A_∥, ¹⁴³A_⊥, ¹⁴⁵A_∥ and ¹⁴⁵A_⊥) of the tetragonal Nd³⁺ center in the low-temperature (T≈4.2 K) tetragonal phase of SrTiO₃ are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are attached to the conventional Hamiltonian and a 52×52 energy matrix concerning the ground term ⁴H_J (J=9/2, 11/2, 13/2, 15/2) is constructed. The Nd³⁺ center is attributed to Nd³⁺ occupying the 12-fold coordinated Sr²⁺ site in SrTiO₃. Differing from the defect model assumed in the previous paper that the tetragonal distortion of this Nd³⁺ center is due to the association of one interstitial oxygen ion at a nearest neighborhood of Nd³⁺ and the Nd³⁺ displacement Δz along C₄ axis, we suggest that it is due to the distortion of SrTiO₃ lattice in the tetragonal phase. The calculated g factors g_∥ and g_⊥ show good agreement with the experimental values, suggesting that our defect model of Nd³⁺ center in SrTiO₃ is reasonable. The experimental hyperfine structure constants were not reported and so our calculated results remain to be checked by EPR experiment.     

Spin-Hamiltonian parameters and local rotational order parameters for Gd ion in the tetragonal phase of SrTiO3 crystal

Using a diagonalization method, the spin-Hamiltonian parameters (g factors g_||, g_⊥ and zero-field splittings b₂⁰, b₄⁰, b₂⁴, b₆⁰, b₆⁴) for Gd³⁺ ion at the 12-fold coordinated Sr²⁺ site in the tetragonal phase of SrTiO₃ at T≈4.2 and 77 K are calculated in a unified way. The calculated results are in reasonable agreement with the experimental values. The local rotational order parameters ?_l of Gd³⁺ center at the two temperatures are also obtained from the calculations. It is found that the local rotational order parameters ?_l of Gd³⁺ impurity center at both temperatures are different from the corresponding parameters ?_h in the host SrTiO₃ crystal and the changes of spin-Hamiltonian parameters with temperature are caused by the change of local rotational order parameter?_l with temperature. The results are discussed.     

Investigations of the spin-Hamiltonian parameters and defect structures for Gd ions in YMO4 (M=V, P, As) crystals

A 56×56 energy matrix containing the ground multiplet ⁸S_7/2 and the excited multiplets ⁶L_7/2 (where L=P, D, F, G, H, I) for 4f⁷ ion Gd³⁺ at a tetragonal crystal field and under an external magnetic field is constructed. By diagonalizing the energy matrix, the spin-Hamiltonian parameters (g factors g_‖, g_⊥ and zero-field splittings b₂⁰, b₄⁰, b₄⁴, b₆⁰, b₆⁴) for Gd³⁺ ion at the tetragonal Y³⁺ site of YMO₄ (M=V, P, As) crystals are calculated. The calculated results are in reasonable agreement with the experimental values. The defect structures of Gd³⁺ centers in YMO₄ crystals are estimated from the calculation. The results are discussed.     

Theoretical studies of spin-Hamiltonian parameters for Ni ions in CsMgX3 (X=Cl, Br, I) crystals from the two-mechanism model

In this paper, the high-order perturbation formulas of spin-Hamiltonian (SH) parameters (g factors g, g and zero-field splitting D), including both the crystal-field (CF) and for the first time charge-transfer (CT) mechanisms, are established for 3d⁸ ions in trigonal octahedral clusters. By using these formulas, the SH parameters of Ni²⁺ ions in CsMgX₃ (X=Cl, Br, I) crystals are calculated. The results are consistent with the experimental values. The calculations suggest that the sign of Q^CT (Q=Δg, Δg or D, where the g-shift Δg_i=g_i−g_e, g_e≈2.0023 is the value of free-electron) due to CT mechanism is the same as 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 the increasing atomic number of ligand X. So, for the 3dⁿ ML_m clusters with ligand having large atomic number, the reasonable theoretical explanations of all SH parameters should take both CF and CT mechanisms into account. The defect structure of (NiX₆)⁴⁻ impurity centers in CsMgX₃:Ni²⁺ crystals is also considered in our model.     

Unified calculations of the optical and electron paramagnetic resonance spectral data for Ce ion in Y3Ga5O12 crystal

Seven crystal field energy levels (obtained from the optical spectra) and three g factors g_x, g_y and g_z (obtained from electron paramagnetic resonance (EPR) spectra) for Ce³⁺ ion in Y₃Ga₅O₁₂ crystal are calculated together by diagonalizing a complete energy matrix. The Hamiltonian of this energy matrix includes all the interactions for 4f¹ ion Ce³⁺ in rhombic crystal field and under an external magnetic field, and so the optical and EPR data can be studied in a unified way. The calculated crystal field energy levels are in better agreement with the experimental values than the calculated values in the previous paper, and the g factors (which have not been calculated previously) are explained reasonably. The results are discussed.     

Unified calculations of the optical band positions and spin-Hamiltonian parameters for V2+ ions in CdCl2 crystal

The eight optical spectral band positions and three spin-Hamiltonian parameters (g factors g_//, g_⊥ and zero-field splitting D) of V²⁺ ions in trigonal CdCl₂ crystal are calculated together from the complete diagonalisation (of energy matrix) method (CDM) based on the two-spin-orbit-parameter model (also called the cluster approach). In the model, differing from the usual one-spin-orbit-parameter model in the conventional crystal-field theory (where only the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central dⁿ ion is considered), both the contributions from the spin-orbit parameter of central dⁿ ion and that of ligand ions are taken into account. The calculated results show reasonable agreement with the experimental values. The local lattice relaxation in the vicinity of V²⁺ ion due to the introduction of V²⁺ impurity is acquired from the calculations. The calculations of spin-Hamiltonian parameters from the CDM based on the one-spin-orbit-parameter and those from the perturbation theory method based on the two-spin-orbit-parameter model are also made for comparison. The results are discussed.     

Growth and optical properties of Yb and Tb codoped BaB2O4 crystals

Optical absorption and luminescence spectra of ytterbium and terbium codoped BaB₂O₄ (β-BBO and α-BBO) crystals grown in different conditions have been studied. Low-temperature absorption peaks were observed in all samples. Features related to rare earth ions were observed in absorption and luminescence spectra. Absorption and emission in the range 860-1000 nm are caused by ²F_5/2↔²F_7/2 transitions in Yb³⁺ ions. Emission peaks at 500, 550, 590 and 630 nm correspond to ⁵D₄→⁷F₆, ⁷F₅, ⁷F₄, and ⁷F₃ transitions of Tb³⁺ ions, respectively. The probable reasons of variations in spectroscopic features related to Yb in BBO host are discussed. It has been shown that the replacement of Ва²⁺ by Yb³⁺ in the lattice of ВаВ₂О₄ results in the decrease in the symmetry of oxygen surrounding of Yb³⁺.     

Theoretical investigation of EPR and optical spectra of Mo(V) in [Mo6O19][N(C4H9)4]3 salt

The electron paramagnetic resonance (EPR) spectral data (the g factors and hyperfine structure constants) and d–d transition spectra for the tetragonal Mo⁵⁺ centre in [Mo₆O₁₉][N(C₄H₉)₄]₃ salt are theoretically investigated from the complete diagonalization method (CDM) for a 4d¹ ion in tetragonally compressed octahedron. The theoretical results are in good agreement with the experimental data. The dependency of the g factors of the ground state on the R_∥(MoO bond length) has been studied. It is shown that the g factors varied with the R_∥ approximately in a linear way.     

Theoretical investigations of the spin Hamiltonian parameters for the tetragonal [Rh(CN)4Cl2] complex in KCl

The spin Hamiltonian parameters (g factors, hyperfine structure constants and superhyperfine parameters) for the tetragonal [Rh(CN)₄Cl₂]⁴⁻ complex in KCl are theoretically investigated from the perturbation formulas of these parameters for a 4d⁷ ion in a tetragonally elongated octahedron. This center can be assigned to the substitutional Rh²⁺ on host K⁺ site reduced from Rh³⁺ by capturing one electron during the electron irradiation, associated with the two axial ligands CN⁻ replaced by two Cl⁻. The crystal-fields of the two axial Cl⁻ are weaker than those of the four planar CN⁻, yielding the tetragonal elongation distortion. This system belongs to the case of low spin (S = 1/2) under strong crystal-fields, different from that of high spin (S = 3/2) under weak and intermediate crystal-fields (e.g., 3d⁷ ions such as Fe⁺ and Co²⁺ in conventional chlorides). The calculated spin Hamiltonian parameters show good agreement with the experimental data. The above [Rh(CN)₄Cl₂]⁴⁻ complex due to the different axial and perpendicular ligands is unlike the tetragonally elongated [RhCl₆]⁴⁻ complex due to the Jahn–Teller effect in the similar NaCl:Rh²⁺ crystals.     

Theoretical explanation of g factors for Ti ions in LiNbO3 and LiTaO3 crystals

The EPR g factors g_// and g_⊥ for Ti³⁺ ions at the trigonal octahedral Li⁺ sites of LiNbO₃ and LiTaO₃ crystals are calculated from the third-order perturbation formulas of g factors for 3d¹ ion in trigonal symmetry. In the calculations, the crystal-field parameters are obtained from the structural data by using the superposition model. The calculated values are in reasonable agreement with the observed values. The results are discussed.     

Blue luminescence in Tm-doped KGd(WO4)2 single crystals

Up-conversion blue emissions of trivalent thulium ions in monoclinic KGd(WO₄)₂ single crystals at 454 and 479 nm are reported for a single pump laser source at 688 nm. We grew thulium-doped KGd(WO₄)₂ single crystals at several concentrations from 0.1% to 10%. We recorded a polarized optical absorption spectrum for the ³F₂+³F₃ energy levels of thulium at room temperature and low temperature (6 K). From the low temperature emission spectra we determined the splitting of the ³H₆ ground state. The blue emissions are characterized as a function of the dopant concentration and temperature from 10 K to room temperature. To our knowledge, this is the first time that sequential two-photon excitation process (STEP) generated blue emissions in thulium-doped single crystals with a single excitation wavelength.     

Theoretical examination of optical and EPR spectra for Cu ion in K2PdCl4 crystal

In this work, two d-d transition spectra and four EPR parameters g_∥, g_⊥, A_∥, A_⊥ of K₂PdCl₄/Cu²⁺ are uniformly interpreted based on Zhao's crystal-field model. The calculation result is in good agreement with the experiment findings. The ligand spin-orbit coupling is neglected on the calculation, which is consistent with the ab initio result by Hillier et al. [J. Am. Chem. Soc. 98 (1976) 95]     

Studies of the spin-Hamiltonian parameters, d–d transitions and defect structures for two tetragonal Cu centers in Ba2ZnF6:Cu crystal

Two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM), are applied to calculate the spin-Hamiltonian parameters (g-factors g, g and hyperfine structure constants A, A, obtained from electron paramagnetic resonance (EPR) spectra) and d–d transitions (obtained from optical spectra) for two tetragonal Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ crystals. The Cu²⁺(I) ion replaces the Zn²⁺ ion at tetragonally compressed octahedral coordination and has the ground state ²A₁(|d_z²), whereas the Cu²⁺(II) ion is at an interstitial site with a square-planar F⁻coordination and has the ground state ²B₂(|d_x²-y²). The calculated spin-Hamiltonian parameters and d–d transitions from the PTM and CDM coincide and are in reasonable agreement with the experimental values. This suggests that both methods are effective for the theoretical studies of EPR and optical spectral data for 3d⁹ ions in tetragonal symmetry with different ground states. The defect structures of the two Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ are also estimated.     

Optical characterization of fourfold (Td)- and sixfold (Oh)-transition-metal species in MgAl2O4:Co by time-resolved spectroscopy

This work investigates the origin of novel visible photoluminescence (PL) bands observed in the spinel MgAl₂O₄:Co²⁺. Besides the well-known fourfold-coordinated Co²⁺(T_d) PL at 670 nm [N.V. Kuleshov, V.P. Mikhailov, V.G. Scherbitsky, P.V. Prokoshin and K.V. Yumashev, J. Lumin. 55 (1993) 265.], a rich structured PL band at 686 nm was also observed that we associate with uncontrolled impurities of sixfold coordinated Cr³⁺(O_h) by time-resolved spectroscopy and lifetime measurements and their variation with temperature. We also show that the lifetime of the Co²⁺(T_d) emission at 670 nm varies from τ=6.7 μs to 780 ns on passing from T=10 to 290 K. This unexpected behaviour for T_d systems is related to the excited-state crossover (⁴T₁↔²E), making the emission band to transform from a narrow-like emission from ²E at low temperature to a broad structureless band from ⁴T₁ at room temperature.