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.     

Crystal field and microscopic spin Hamiltonians approach including spin-spin and spin-other-orbit interactions for d and d ions at low symmetry C3 symmetry sites: V in Al2O3

A new module has been developed within the CFA/MSH computer package, which is applicable for d² and d⁸ ions at sites of trigonal symmetry type I (C_3v,D₃,D_3d) and type II (C₃,C_3i), including the ‘imaginary’ CF term. For the first time the spin-spin (SS) and spin-other-orbit (SOO) interactions have also been included in the Hamiltonian. This module enables to study the contributions to the energy levels and the spin Hamiltonian parameters, i.e. zero-field splitting D and g-factors: g_∥ and g_⊥. The contributions arising from the spin-orbit (SO), SS, and SOO interaction as well as those due to the low symmetry CF effects induced by the distortion angle ?, which describes the difference between C₃ and C_3v symmetry, can be studied. As an application of the new module, calculations have been carried out for V³⁺(3d²) ions in α-Al₂O₃ crystal, taking into account for the first time the SS and SOO interactions, and the low symmetry CF effects. The results show that (i) the contributions from the SS and SOO interactions to the energy levels are larger for free V³⁺ ions than those for V³⁺ ions in α-Al₂O₃ crystal, (ii) both the contributions to the SH parameters and the energy levels arising from the SOO interaction are larger than those arising from the SS interaction, (iii) the contributions due to the low symmetry CF effects induced by the distortion angle ? are in general significant, (iv) D and g_⊥ are sensitive to the distortion angle ?, whereas g_∥ is insensitive to ?, and (v) the influence of the lattice distortions on the spectroscopic properties of V³⁺ ion in α-Al₂O₃ is pronounced. It appears important for similar ion-crystal cases to consider the lattice distortions in detailed calculations, which take into account the relevant contributions from the SO, SS and SOO interactions. A good agreement between the theoretical and experimental results has been obtained.     

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.     

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.     

Electron paramagnetic resonance and optical absorption spectra of Cr ions in cadmium phosphate glass

EPR and optical absorption investigations of chromium doped cadmium phosphate glass are carried out. Crystal field, spin-Hamiltonian and bonding parameters are evaluated. From the results and analyses of the EPR and optical studies, the site symmetry of Cr³⁺ ion in the glass is ascribed to a distorted octahedron. The bonding parameters suggest the ionic nature of Cr³⁺ ion with the ligands.     

Spin Hamiltonian parameters and structural disorder analysis for Cr ion in YGG crystals

A new crystalline lattice distortion model has been proposed, on the basis of it, the relations between spin Hamiltonian parameters and crystal micro structure have been established. By taking into account slight magnetic interactions, including spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions, the local structure of Cr³⁺ ion in YGG crystal has been studied using complete diagonalization method (CDM). The studies show that the local structure in the YGG:Cr³⁺ crystal is of the compressed trigonal distortion. The ligand oxygen plane moved 0.0138 nm toward Cr³⁺ ion along C₃-axis. Accordingly, the SH parameters in YGG:Cr³⁺ crystal are explained successfully.     

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⁺.     

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.     

Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field

In this paper, a Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field is presented. For orbital doublet ²E, which is an orbital degenerate state in the cubic field and is a near-degenerate state in the tetragonal field, we obtain the cubic invariant form and the tetragonal invariant form of the Spin-Hamiltonian. In case of near-degeneracy (tetragonal splitting is very small) two additional g-factors are introduced to investigate Zeeman-splitting for tetragonal field. The two additional g-factors g_2z and g_2xy describe the magnetic interest between A_1g and B_1g states for a parallel magnetic field with z-axis and a perpendicular magnetic field with z-axis, respectively. The theory is based on the time-reversal invariant and the point-group symmetry invariant. The theoretical method can also be used for other orbital degenerate states ^2S+1Γ including and Γ=T₁ or T₂ and can be used for other point-group symmetry.     

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.     

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.     

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.     

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.     

ESR investigation of Cr diffusion in MgO powders

The electron spin resonance (ESR) technique was used to investigate the diffusion of Cr³⁺ in magnesium oxide (MgO) powders. The ESR absorption intensity was measured for several annealing times and four different temperatures of isothermal annealing: 1223, 1273, 1323 and 1373 K. The activation temperature for diffusion, calculated from the experimental data using a theoretical model based on the Fick equation, was found to be E_A=212±9 kJ mol⁻¹. This result is about 30% smaller than similar data obtained for single-crystal MgO using the radioactive-tracer sectioning technique. The difference is attributed to a higher concentration of defects in the powder relative to single crystals.     

Theoretical explanation of the g factor for Cr in Y2SiO5 crystal

The g factor of Cr⁴⁺ in Y₂SiO₅ crystal is calculated from a completed high-order perturbation formula, in which not only the conventional contribution to the g-shift Δg(=g−g_e) from the crystal-field mechanism, but also the contribution from the charge-transfer mechanism (which is neglected in the crystal-field theory) are considered. The calculated result shows good agreement with the observed value. It is found that the calculated Δg due to the charge-transfer mechanism is opposite in sign and about 38% in magnitude, compared with that due to the crystal-field mechanism. So, in the studies of the g factor for a 3dⁿ ion having high valence state in crystals, the contribution due to the charge-transfer mechanism should be taken into account.     

Studies of the zero-field splitting and g-factor for the defect model of Cr in α-LiIO3 crystals at low temperature

The EPR zero-field splitting parameters D and g-factors for Cr³⁺ in α-LiIO₃ 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 3d³ 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⁻¹g_∥=1.965±0.001, g_⊥=1.971±0.002). In addition, Macfarlane's perturbation expressions lead to results almost identical with the CDM for Cr³⁺ in an α-LiIO₃ single crystal.     

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.     

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.     

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.