Investigations of EPR Parameters of MgTiO3:Cr3+, SrTiO3:Cr3+, and SrTiO3:Mn4+ Crystals

Complete high-order perturbation formulas are established based on charge-transfer (CT) and crystal-field (CF) mechanisms. The electron paramagnetic resonance (EPR) g-factors of MgTiO₃:Cr³⁺, SrTiO₃:Cr³⁺, and SrTiO₃:Mn⁴⁺ crystals are calculated from the formulas. The calculations of the EPR g-factors agree well with the experimental values. The contribution rate of the CT mechanism to EPR parameters increases with increasing valence state of the 3d ⁿ ions in the crystals. For the higher-valence state 3d ³ Mn⁴⁺ ion in the crystals, the elucidation of the EPR parameters rationally involves both CF and CT mechanisms.     

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.     

Theoretical studies of the defect structures and spin Hamiltonian parameters for manganese(II) and nickel(II) doped Zn(en)3(NO3)2 single crystals

The spin Hamiltonian parameters (g factors, hyperfine structure constants and zero-field splittings D and E) and local structures for Mn²⁺ and Ni²⁺ in [Zn(en)₃](NO₃)₂ single crystal are theoretically investigated from the perturbation calculations for trigonally distorted 3d⁵ and trigonally (or orthorhombically) distorted 3d⁸ cluster. The trigonal Mn²⁺ and Ni²⁺ centres are found to undergo the moderate angular variations Δβ of 4.5° and 5.2°, respectively, related to host Zn²⁺ site due to size mismatch. The orthorhombic Ni²⁺ centre shows the relative axial elongation ratio ρ (≈ 2.5%) and the relative perpendicular bond length variation ratio τ (≈0.2%). For Mn²⁺ centre, the contributions to g-shifts Δg_CT (or hyperfine structure constants A_CT and zero-field splitting D_CT) from charge-transfer (CT) mechanism are opposite in sign and five times (or 5% and 8%) in magnitude compared with those from crystal-field (CF) mechanism. For the trigonal Ni²⁺ centre, Δg_CT (or D_CT) are the same (or opposite) in sign and 17% (or 2%) in magnitude related to those from CF mechanism. For the orthorhombic Ni²⁺ centre, Δg_CT and E_CT (or D_CT) are same (or opposite) in sign and 16% and 48% (or 442%) in magnitude with respect to those from the CF mechanism. The signs and magnitudes of the trigonal distortion angles δβ (≈ ?0.3 and 0.4°) related to an ideal octahedron and the local angular variations Δβ related to the host bond angle are suitably illustrated by those of the axial distortion degree (ADD) and the angular variation degree (AVD) of the systems, respectively.     

Study of EPR parameters and defect structure for two tetragonal impurity centers in MgO:Cr<Superscript>3+</Superscript> and MgO:Mn<Superscript>4+</Superscript> crystals

The electron paramagnetic resonance (EPR) parameters (g-factors g _‖, g _⊥ and zero-field splitting D) of two tetragonal 3d³ impurity centers M_3d-V_Mg and M_3d-Li⁺ (where M_3d = Cr³⁺ or Mn⁴⁺, V_Mg is the Mg²⁺ vacancy) in M_3d-doped MgO crystals are calculated from the high-order perturbation formulas including both the crystal-field (CF) and the charge-transfer (CT) mechanisms for 3d³ ions in the tetragonal symmetry. The calculated results are in reasonable agreement with the experimental values. From the calculations, it can be found that the relative importance of the CT mechanism for EPR parameters increases with increasing valence state of the 3d³ ion. So, for the high-valence 3d ⁿ ions in crystals, a reasonable explanation of EPR parameters should take into account both CF and CT mechanisms. The defect structures (characterized by the displacement ΔR of O²⁻ in the intervening M_3d and V_Mg or Li⁺ at the Mg²⁺ site) for these tetragonal impurity centers are obtained from the calculations. The results are consistent with the expectations based on the electrostatic interactions.     

Investigations of the Spin-Hamiltonian Parameters for the Rhombic Mo5+ Centers in Ca1−x Y x MoO4 Crystal

The spin-Hamiltonian parameters (g factors g _i and hyperfine structure constants A _i , where i = x, y, z) of the rhombic Mo⁵⁺ center in Ca_1?x Y _x MoO₄ crystal are calculated from the high-order perturbation formulas based on the two-mechanism model for the rhombic d¹ tetrahedral clusters with the ground state |d _z 2〉. In these formulas, besides the contributions due to the widely applied crystal-field (CF) mechanism concerning CF excited states, those due to the charge-transfer (CT) mechanism (which is omitted in CF theory) concerning CT excited states are considered. The calculated results are in reasonable agreement with the experimental values. The calculations show that because of the great relative importance of CT mechanism for the components of spin-Hamiltonian parameter along x and y axes, the accurate and complete calculations of spin-Hamiltonian parameters for Mo⁵⁺ and other high valence state dⁿ ions in crystals should take account of both the CF and CT mechanisms. The defect model of the rhombic Mo⁵⁺ center is also confirmed from the calculations.     

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.     

Theoretical investigation of the optical and EPR parameters for VOion in some complexes

The molecular orbital coefficients and the EPR parameters of trisodium citrate dihydrate, sodium hydrogen oxalate monohydrate, potassium d-gluconate monohydrate and L-Alanine vanadyl complexes are calculated theoretically. Two d-d transition spectra and EPR parameters for the VO²⁺ complex are calculated theoretically by using crystal-field theory. The calculated g and A paramaters have indicated that paramagnetic center is axially symmetric. Having the relations of g_∥〈g_⊥〈g_e and A_∥〉A_⊥ for VO²⁺ ions, it can be concluded that VO²⁺ ions are located in distorted octahedral sites (C_4v) elongated along the z-axis and the ground state of the paramagnetic electron is d_xy.     

EPR g factors and tetragonal distortion for the isoelectronic Ni and Cu centers in the CuGaSe2 crystal

The EPR g factors, g_|| and g_⊥, for the isoelectronic 3d⁹ ions Ni⁺ and Cu²⁺ at the tetragonal Cu⁺ site of the CuGaSe₂ crystal are calculated from the high-order perturbation formulas based on a two-spin-orbit-parameter model. In the model, both the contributions to g factors from the spin-orbit parameter of central 3d⁹ ion and that of ligand ion are contained. The calculated results appear to be consistent with the experimental values. The tetragonal distortions (characterized by θ−θ₀, where θ is the angle between the metal-ligand bond and C₄ axis, and θ₀≈54.74° is the same angle in cubic symmetry) of Ni⁺ and Cu²⁺ centers, which are different from the corresponding angle in the host CuGaSe₂ crystal and from impurity to impurity, are obtained from the calculations. The difference of the sign of g_||−g_⊥ between the isoelectronic Ni⁺ and Cu²⁺ centers is found to be due to the different tetragonal distortions of both centers in the CuGaSe₂ crystal.     

Calculations of the Spin-Hamiltonian Parameters for the Trigonal Cr3+ and Mn4+ Centers in Ca3Ga2Ge3O12 (CGGG) Garnet Crystal

The spin-Hamiltonian parameters (zero-field splitting D, g-factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) of Cr³⁺ and Mn⁴⁺ ions at the trigonal Ga³⁺ site of Ca₃Ga₂Ge₃O₁₂ (CGGG) garnet crystals are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, besides the contributions to spin-Hamiltonian parameters from the crystal-field (CF) mechanism in the frequently applied CF theory, those from the charge-transfer (CT) mechanism (which is neglected in CF theory) are taken into account. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr³⁺ and Mn⁴⁺ impurity centers in CGGG crystals are also obtained from the calculations. The calculations show that the relative importance of CF mechanism (characterized by $ \left| {{{Q^{\text{CT}} } \mathord{\left/ {\vphantom {{Q^{\text{CT}} } {Q^{\text{CF}} }}} \right. \kern-0pt} {Q^{\text{CF}} }}} \right| $ , where $ Q = D,\;\Delta g_{\rm{//}} ,\;\Delta g_{ \bot } ,\;A_{\rm{//}}^{(2)} or\;A_{ \bot }^{(2)} $ ) for Mn⁴⁺ center in CGGG is larger than that for Cr³⁺ center. So, for the high valence state dⁿ ions in crystals, the reasonable calculations of spin-Hamiltonian parameters should consider the contributions due to both the CF and CT mechanisms.     

EPR parameters and local lattice structure study of V ions in CdCl2 and CsMgCl3 crystals

The local lattice structure and EPR parameters (D, g_‖, g_⊥) have been studied systematically on the basis of the complete energy matrix for a d³ configuration ion in a trigonal ligand field. By simulating the calculated optical and EPR spectra data to the experimental results, the local distortion parameters (ΔR, Δθ) are determined for V²⁺ ions in CdCl₂ and CsMgCl₃ crystals, respectively. The results show that the local lattice structure of CdCl₂:V²⁺ system exhibits a compression distortion (ΔR=−0.0868 Å) while that of CsMgCl₃:V²⁺ system exists an elongation distortion (ΔR=0.0165 Å). The different distortion may be ascribed to the fact that the radius of V²⁺ ion is smaller than that of Cd²⁺ ion or larger than that of Mg²⁺ ion. Moreover, the relationships between EPR parameter D and local structure parameters (R, θ) as well as the orbital reduction factor k and g‐factors (g_‖, g_⊥) are discussed.     

Theoretical study of EPR spectra and local structure for (NiO6) cluster in LiNbO3:Ni and Al2O3:Ni systems

For a d⁸ configuration ion, the 45×45 complete energy matrix, which contains the electron-electron repulsion interaction, the ligand-field interaction, the spin-orbit coupling interaction as well as the Zeeman interaction, has been established. By diagonalizing the complete energy matrix, the local lattice structure, EPR parameters (D, g_//, g_⊥) and optical absorption spectra for Ni²⁺ ions doped in LiNbO₃ and Al₂O₃ have been investigated. The local structure distortion parameters ΔR, Δθ₁ and Δθ₂ are determined for LiNbO₃:Ni²⁺ and Al₂O₃:Ni²⁺ systems, simultaneously. These results show that local structure of (NiO₆)¹⁰⁻ cluster exhibits an elongation distortion in both LiNbO₃:Ni²⁺ and Al₂O₃:Ni²⁺ systems, in spite of the different reasons of the elongation in both systems. In addition, we have found that the orbit reduction effect is very important to understand the anisotropic g-factors for Ni²⁺ ions doped in LiNbO₃ and Al₂O₃ crystals.     

Theoretical explanation of absorption spectra and ESR parameters of Cu in shattuckite

The optical absorption spectra and electronic spin resonance parameters (ESR g factors g_‖, g_⊥ and hyperfine structure constants A_‖, A_⊥) for Cu²⁺ in shattuckite crystal are calculated from the two spin–orbital coupling parameters model, high-order perturbation formulas and complete diagonalization (of energy matrix) method (CDM) of 3d⁹ ion in tetragonal symmetry. The calculated results are in good agreement with the observed values. Since the ESR parameters are sensitive to the local structure of a paramagnetic impurity center, the defect structure of Cu²⁺ center in shattuckite crystal is estimated. The results are discussed.     

Electron paramagnetic resonance parameters of Mn<Superscript>4+</Superscript> ion in h-BaTiO<Subscript>3</Subscript> crystal from a two-mechanism model

The EPR parameters (g factors g _‖, g _⊥ and zero-field splitting D) of Mn⁴⁺ ion in h-BaTiO₃ crystal are calculated from the complete high-order perturbation formulas based on a two-mechanism model for the EPR parameters of 3d ³ ions in trigonal symmetry. In the model, not only the widely used crystal-field mechanism, but also the charge-transfer mechanism (which is not considered in crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values. The relative importance of charge-transfer mechanism to EPR parameters and the defect structure of Mn⁴⁺ centre in h-BaTiO₃ crystal obtained from the calculations are discussed.      

Studies of the defect structure from the calculations of optical and electron paramagnetic resonance spectra for Ni<Superscript>2+</Superscript> centre in <Emphasis Type="Italic">α</Emphasis>-LiIO<Subscript>3</Subscript> crystal

By calculating the optical spectrum band positions and EPR parameters (g factors, g‖, g⊥ and zero-field splitting D) by diagonalizing the complete energy matrix of 3d⁸ ions in trigonal symmetry, the defect structure of Ni²⁺ centre in α-LiIO₃ crystal is studied. It is found that to reach the good fits of optical and EPR data between calculation and experiment, the Ni²⁺ ion should shift by Δz ≈ 0.298 Å along C₃-axis and the O^2? ions between the Ni²⁺ ion and Li⁺ vacancy (V _Li) should be displaced away from the V _Li by Δx ≈ 0.097 Å because of the electrostatic interaction. The results are discussed.     

Research of the Spin-Hamiltonian Parameters and Defect Structure for the Trigonal Mn<Superscript>4+</Superscript> Centers in Y<Subscript>2</Subscript>Ti<Subscript>2</Subscript>O<Subscript>7</Subscript>:Mn<Superscript>4+</Superscript> Crystal

The high-order perturbation formulas founded on the two-mechanism model are applied in this paper to compute the spin-Hamiltonian parameters (g factors g _//, g _⊥ and zero-field splitting D) of the trigonal Mn⁴⁺ centers in Y₂Ti₂O₇:Mn⁴⁺ crystal. In this model, besides the contributions from the traditional crystal-field (CF) mechanism (in the CF theory) related to CF excited states, those from the charge-transfer (CT) mechanism connected with CT excited states are contained. The calculated results are reasonably coincident with the observed values. The calculations show that the contributions of CT mechanism to spin-Hamiltonian parameters (in particular, the g factors) for (MnO₆)^8? clusters are large and cannot be neglected. The defect structure of trigonal (MnO₆)^8? clusters in Y₂Ti₂O₇:Mn⁴⁺ crystals is also evaluated. The results are discussed.     

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.     

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.     

Investigation of the EPR g factors and defect structure for the Cu-VNa center in the X-irradiated NaCl: Cu crystal

The g factors of a tetragonally-compressed Cu²⁺ center in NaCl: Cu⁺ crystal X-irradiated at room temperature are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, the contribution to g factors from both crystal-field (CF) and charge-transfer (CT) mechanisms are included. The calculations are based on the defect model that the tetragonally-compressed Cu²⁺center is assigned to the Cu²⁺ ion (which is caused by Cu⁺ ion (at the Na⁺ site) irradiated by X-ray) associated with a nearest Na⁺ ion vacancy V_Na along C₄ axis due to charge compensation. From the calculations, the g factors g_|| and g_⊥ are explained and the defect structure (charactering by the displacement ΔZ of the Cl⁻ ion intervening in Cu²⁺ and V_Na) of the Cu²⁺ (or Cu²⁺-V_Na) center is obtained. The results are discussed.     

Study of the electron paramagnetic resonance spectra of Zn(antipyrine)2(NO3)2:VO

In this work, a full ligand-field energy matrix (10×10) diagonalization treatment for 3d¹ ions in tetragonal symmetry is developed on the basis of the two-s.o.-coupling-parameter model. Spin Hamiltonian parameters (g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) of the tetragonal V⁴⁺ center in Zn(antipyrine)₂(NO₃)₂ are calculated from the complete energy matrix diagonalization method and the perturbation theory method. The calculated results from both methods are not only close to each other but also in good agreement with the experimental values. Furthermore, the compressed defect structure of V⁴⁺ center is discussed.