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.     

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.     

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.     

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.     

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.     

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.     

Interpretation of charge transfer bands in Fe doped SrTiO3 crystals

The electronic structures of SrTiO₃ crystals doped with Fe³⁺, Fe⁴⁺ and Fe⁵⁺ ions have been investigated using the Xα cluster approach. The ground-state eigenvalues show the lower Fe acceptor level, of t_2g↓ symmetry, localized inside the SrTiO₃ band gap, respectively at 2.8 eV $\text{(}\text{Fe}{}^{\mathrm{3+}}\text{, S =}\text{5}\text{2}\text{), 1.6}\text{eV}\text{(}\text{Fe}{}^{\mathrm{4+}}\text{, S = 1)}\text{or}\text{1.1}\text{eV}\text{(}\text{Fe}{}^{\mathrm{4+}}\text{, S = 0)}\text{and}\text{1.1}\text{eV}\text{(}\text{Fe}{}^{\mathrm{5+}}\text{, S =}\text{3}\text{2}\text{)}$ above the valence band edge. Other acceptor levels, with eg↓ and eg↑ symmetries, appear inside the gap when the Fe nominal ionicity increases.The theoretical Xα excitation energies of O 2p-Fe 3d transitions confirms the experimental interpretations of acceptor charge transfer bands for the optical absorption spectra of SrTiO₃:Fe⁴⁺ and SrTiO₃:Fe⁵⁺ crystals.The large optical excitation energies compared with the thermal transitions are partly due to the O 2p band width.     

立方对称晶场中6S(3d5)态离子的磁相互作用及其自旋哈密顿参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶S(3d⁵)态离子在立方对称晶场中的磁相互作用,分析了自旋哈密顿参量(a, g,Δg)的微观起源.研究中除了考虑研究者通常考虑的SO(spin-orbit)磁相互作用外,同时考虑了SS(spin-spin),SOO(spin-other-orbit),OO(orbit-orbit)磁相互作用.研究表明：⁶S(3d⁵)态离子在立方对称晶场中的自旋哈密顿参量起源于五种机理,即SO机理,SS机理,SOO机理,OO机理以及SO-SS-SOO-OO联合作用机理.文中研究了五种机理的相对重要性,结果表明：SO机理与SO-SS-SOO-OO联合作用机理在五种机理中最为重要.尽管SS,SOO,OO磁相互作用单独作用时对自旋哈密顿参量的贡献很小,但它们的联合作用SO-SS-SOO-OO机理对自旋哈密顿参量的贡献非常可观.此外研究表明：零场分裂参量a主要来自纯自旋四重态及自旋二重态与自旋四重态联合作用的贡献,而Zeemang(或者Δg)因子主要来自纯自旋四重态的贡献.纯自旋二重态对自旋哈密顿参量a与g(或者Δg)的贡献为零.在我们所选择的晶场区域,发现下列关系始终成立：a>0,a(-|Dq|)<a(|Dq|),g(-Dq)=g(Dq),a(-Dq,-ξ_d,B,C)=a(Dq,ξ_d, B,C),Δg(-Dq,-ξ_d, B, C)=Δg(Dq,ξ_d, B, C).作为本文理论的应用,研究了四种典型的Mn²⁺掺杂晶体材料,即Mn²⁺:KZnF₃,Mn²⁺: RbCdF₃,Mn²⁺: MgO,Mn²⁺: CaO,理论与实验测量符合很好. 关键词： 自旋哈密顿参量 6S(3d⁵)态离子')" href="#">⁶S(3d⁵)态离子 磁相互作用 完全对角化方法(CDM)     

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.     

Fully relativistic analysis of the covalence effects for the isoelectronic 3d ions (Cr, Mn, Fe) in SrTiO3

Fully relativistic calculations of the energy levels, absorption spectra, molecular orbitals (MO) compositions, covalence effects and energies of the charge transfer (CT) transitions for three isoelectronic ions Cr³⁺, Mn⁴⁺, Fe⁵⁺ in the SrTiO₃ (STO) crystal have been performed. The recently developed first-principles approach to the analysis of the absorption spectra based on the first principles discrete variational multi-electron method (DV-ME) (K. Ogasawara et al., Phys. Rev. B 64 (2001) 115413) was used in the calculations. As a result, energy levels of the above ions, their absorption spectra and energies of the lowest CT transitions were all calculated. By performing analysis of the MO population, it was shown that the degree of covalence of the chemical bonds between 3d ions and oxygen ions in SrTiO₃ increases in the following order: Cr³⁺→Mn⁴⁺→Fe⁵⁺, whereas the CT energies monotonically decrease in the same order.     

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.     

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.     

EPR study of the impurity paramagnetic centres in (CaO−Ga2O3−GeO2) glasses

The X-band EPR spectra of Cr³⁺, Mn²⁺, and Fe³⁺ impurity ions in glasses of (CaO?Ga₂O₃?GeO₂) system are investigated in the 77÷300 K temperature range. The experimental data analysis yields the following results: (i) Impurity chromium ions are incorporated into the (CaO?Ga₂O₃?GeO₂) glasses network in Cr³⁺ (3d³,⁴F_3/2) paramagnetic valence state only and occupy the strong distorted oxygen coordinated octahedral sites. (ii) For all activated and non-activated (CaO?Ga₂O₃?GeO₂) glasses the iron impurity is present at concentration roughly 0.01 wt.%. Isotropic EPR signals atg _eff=4.29 andg _eff=2.00 are assigned to Fe³⁺ (3d⁵,⁶S_5/2) ions in the sites with strong rhombic distortion and in the sites with nearly cubic symmetry respectively. (iii) The manganese EPR spectrum in (CaO?Ga₂O₃?GeO₂) glasses is weakly dependent on temperature, doping procedure as well as manganese concentration. EPR spectra of impurity manganese ions in glasses with Ca₃Ga₂Ge₃O₁₂ and Ca₃Ga₂Ge₄O₁₄ compositions are virtually identical and belong to Mn²⁺ (3d⁵,⁶S_5/2) ions. Impurity manganese ions are incorporated into the (CaO?Ga₂O₃?GeO₂) glass network as isolated Mn²⁺ centres and clusters of Mn²⁺ ions.     

Nephelauxetic effect for the isoelectronic 3d-ions (Cr, Mn, Fe) in SrTiO3

The exchange charge model of crystal field theory has been used to analyze systematically the ground state absorption spectra of isoelectronic Cr³⁺, Mn⁴⁺, and Fe⁵⁺ ions in an octahedral coordination in the SrTiO₃ crystal. The parameters of the crystal field acting on the valence electrons of impurity ions are calculated from the available crystal structure data. A special attention is paid to the analysis of dependencies of the crystal field invariants and covalence effects on the impurity ion. It is shown numerically that the covalence effects between the above impurity ions and ligands increase with an increase of the 3d-ion oxidation state.     

Spectroscopic studies on Fe and Mn doped SrB4O7 glasses

EPR and optical absorption studies on Fe³⁺ and Mn²⁺ doped strontium tetraborate (SrB₄O₇) glasses are carried out at room temperature. The EPR spectrum of the Fe³⁺ doped glass consists of signals with g-values 9.04, 4.22 and 2.04, whereas the EPR spectrum of Mn²⁺ doped glass exhibits a characteristic hyperfine sextet around g=2.0. The spectroscopic analyses of the obtained results confirmed distorted octahedral site symmetry for the Fe³⁺ and Mn²⁺ impurity ions. Crystal field and Racah parameters evaluated from optical absorption spectra are: Dq=790, B=700 and C=3000 cm⁻¹ for Fe³⁺doped glass and Dq=880, B=700 and C=2975 cm⁻¹ for Mn²⁺ doped glass.     

Influence of chemical bond length changes on the crystal field strength and “ligand-metal” charge transfer transitions in Cs2GeF6 doped with Mn and Os ions

Detailed study of dependence of the crystal field strength 10Dq and lowest charge transfer (CT) energies for different interionic distances in Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺crystals is presented. The calculations were performed using the first-principles discrete-variational Dirac-Slater (DV-DS) method. As a result, the functional dependencies of 10Dq and lowest CT energy on the metal-ligand distance R were obtained without any fitting or semiempirical parameters. It was shown that 10Dq depends on R as 1/Rⁿ, with n=4.0612 and 4.3874 for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively. Two approximations (linear and quadratic) are obtained for the dependence of the lowest CT energy on R; CT energy decreases when R increases with dE(CT)/dR=−638 and −1080 cm⁻¹/pm for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively, if the linear approximation is used. These values can be used for estimations of the lowest CT energies for Mn⁴⁺ and Os⁴⁺ ions in other hosts with fluorine ligands. Estimations of the electron-vibrational interaction (EVI) constants, Huang-Rhys parameters, and Stokes shifts for all the above-mentioned crystals were performed using the obtained 10Dq and E(CT) functions.     

Identification of Fe4+ and Fe5+ charge-transfer photochromic absorption bands in SrTiO3

Optical absorption and the enhancement and bleaching of Fe³⁺ and Fe⁵⁺ electron paramagnetic resonance in SrTiO₃: Al measured as a function of wavelength and time show that the photochromic absorption bands are due to electron transfer from O^2- valence states to Fe⁴⁺ and Fe⁵⁺. They occur at 2.09 and 2.82 eV for Fe⁴⁺ and at 1.99 and 2.53 eV for Fe⁵⁺.     

四角对称晶场中4B1(3d3)态离子的磁相互作用及其自旋哈密顿参量研究

基于完全对角化方法，研究了⁴B₁(3d³)态 离子在四角对称晶场中的磁相互作用，分析了自旋哈密顿参量(b⁰₂, g_∥, g_⊥ , Δg)的微观起源.结果表明 ：在被考虑的大部分晶场区域，人们通常考虑的SO(spin-orbit)磁相互作用的贡献最为重要 ；然而，对于零场分裂参量b⁰₂而言，来自其他机理(包 括SS(spin-orbit)，SOO(sp in-other-orbit)，SO-SS-SOO)的贡献在大部分晶场区域超过了20％；在部分晶场区域，其 他机理的贡献甚至超过SO机理的贡献.详细地分析了Macfarlane 零场分裂参量b^{0₂ 近似三阶微扰理论的收敛性，结果表明：该理论在大部分晶场区域收敛性较差.讨论了3d3}态离子第一激发态²E_g分裂的微观起源.并利用 群论方法解 释了在C_4v和C_3v对称晶场中²E_{g< /sub>态分裂的不同机理. 关键词： 4B1(3d³)态离子')" href="#">⁴B1(3d³)态离子 磁相互作用 自旋哈密 顿参量 完全对角化方法(CDM) 微扰理论方法(PTM)}     

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.     

EPR parameters and defect structures of the off-center Ti ion on the Sr site in neutron-irradiated SrTiO3 crystal

The EPR parameters (g factors and hyperfine structure constants A) for the tetragonal Ti³⁺ center in cubic phase and the rhombic Ti³⁺ center in tetragonal phase in the neutron-irradiated SrTiO₃ crystals are calculated from the third-order perturbation formulas of EPR parameters for d¹ ions. These low-symmetry Ti³⁺ centers in both phases of SrTiO₃ are due to the Ti³⁺ ion at “off center” on the Sr²⁺ site. From the calculation, the defect models (including the direction and magnitude of the Ti³⁺ off-center displacement) of the two Ti³⁺ centers in SrTiO₃ are estimated and the EPR parameters of both Ti³⁺ centers are reasonably explained on the basis of the defect models. The results are discussed.