Local structure and the electron paramagnetic resonance parameters for the Cr3+ ions at K+-vacancy site in Cr3+:KZnF3 laser crystal

The quantitative relationship between the electron paramagnetic resonance (EPR) parameters D,g_∥,g_⊥ and the local structure parameters of Cr³⁺ ion in KZnF₃ crystals is established. The local structure for Cr³⁺ paramagnetic center in KZnF₃:Cr³⁺ crystal has been determined from EPR parameters of Cr³⁺ ion. This work shows that the trigonal crystal field of Cr³⁺ ion in KZnF₃ crystals comes from following two origins: (1) the nearest-neighbor K⁺ vacancy caused by the charge compensation in the [1 1 1]-axis direction; and (2) the lattice distortions of the nearest-neighbor fluorine coordination caused by the K⁺ vacancy and the differences in mass, charge, and radius between Cr³⁺ ion and Zn²⁺ ion. The unified calculation of the EPR zero-field splitting and g factors, taking into account the K⁺ vacancy and the lattice distortions, has been carried out on the basis of the complete diagonalization procedure and the superposition crystal-field model, all calculation results are in excellent agreement with the experimental data. Although the main source of the trigonal crystal field comes from the K⁺ vacancy caused by the charge compensation, the contribution of the lattice distortion cannot be neglected.     

Optical properties of trivalent chromium ions in the LiNbO<Subscript>3</Subscript> crystal

The formulas of the crystal-field theory have been adapted to a system with the symmetry group C _3v. A simple method has been proposed for including the polarization of the local environment of the Cr³⁺ impurity ion in LiNbO₃. A model dependent on one parameter has been proposed for a distortion of the niobium octahedron due to the incorporation of the trivalent chromium ion. This parameter has been determined from experimental data. The parameters of the intraionic and interionic interactions have been obtained for the Cr³⁺ ion in the lithium and niobium positions of the crystal lattice of lithium niobate.     

Local structure distortion and spin Hamiltonian parameters for Cr3＋-Vzn tetragonal defect centre in Cr3＋ doped KZnF3 crystal

The quantitative relationship between the spin Hamiltonian parameters (D, g_‖, Δg) and the crystal structure parameters for the Cr³⁺—V_Zn tetragonal defect centre in a Cr³⁺:KZnF₃ crystal is established by using the superposition model. On the above basis, the local structure distortion and the spin Hamiltonian parameter for the Cr³⁺—V_Zn tetragonal defect centre in the KZnF_3 crystal are systematically investigated using the complete diagonalization method. It is found that the V_Zn vacancy and the differences in mass, radius and charge between the Cr³⁺ and the Zn²⁺ ions induce the local lattice distortion of the Cr³⁺ centre ions in the KZnF₃ crystal. The local lattice distortion is shown to give rise to the tetragonal crystal field, which in turn results in the tetragonal zero-field splitting parameter D and the anisotropic g factor Δg. We find that the ligand F^- ion along [001] and the other five F^- ions move towards the central Cr³⁺ by distances of Δ₁ = 0.0121 nm and Δ₂ = 0.0026 nm, respectively. Our approach takes into account the spin—orbit interaction as well as the spin—spin, spin—other-orbit, and orbit—orbit interactions omitted in the previous studies. It is found that for the Cr³⁺ ions in the Cr³⁺:KZnF₃ crystal, although the spin—orbit mechanism is the most important one, the contribution to the spin Hamiltonian parameters from the other three mechanisms, including spin—spin, spin—other-orbit, and orbit—orbit magnetic interactions, is appreciable and should not be omitted, especially for the zero-field splitting (ZFS) parameter D.     

Investigation of local lattice structure around Cr3+ ions at the trigonal and tetragonal sites in RbCdF3: Cr3+ crystal

The local lattice structure and EPR, optical spectra for Cr³⁺ doped in RbCdF₃ crystal have been studied by diagonalizing the complete energy matrices. The results show that the local structure of the Cr³⁺ ions in RbCdF₃ exhibits a compressed distortion at the trigonal and tetragonal sites. The compressed distortion can be ascribed to the fact that the radius of Cr³⁺ ion is smaller than that of Cd²⁺ ion, and therefore Cr³⁺ ion will draw the fluorin ligands inwards. The variational ranges of the local structural parameters for Cr³⁺ doped in RbCdF₃ crystal R =?1.9491 Å ～?1.9814 Å, θ?= 55.234° ～?55.286° at the trigonal site and R ₁ =?1.8617 Å ～?1.8928 Å, R ₂ =?1.9527 Å ～?1.9851 Å at tetragonal site are obtained respectively, and the EPR and optical spectra agree well with the experimental results.     

EPR theoretical study of local lattice structure in ZnS:Cr system

By analyzing the EPR parameters a, D and F of Cr²⁺ ion located at tetrahedral site in ZnS, the local structure around Cr²⁺ in the crystal has been investigated on the basis of the complete energy matrix for a d⁴ configuration in a tetragonal ligand-field within a strong-field-representation. It is shown that there exists an expansion distortion in the local lattice structure. From EPR calculation, the distortion parameters ΔR=0.13 Å and Δθ=1.417° are determined.     

Al2O3:V3+晶体局域结构及其自旋哈密顿参量研究

提出了解释掺杂离子局域结构畸变的配体平面移动模型，建立了此模型下晶体微观结构与自旋哈密顿参量之间的定量关系.在考虑自旋与自旋、自旋与另一电子轨道和轨道与轨道作用等微小磁相互作用的基础上，采用全组态完全对角化方法，对Al₂O₃晶体中V³⁺的局域结构和自旋哈密顿参量进行了系统的研究.结果表明，V³⁺掺入Al₂O₃晶体后，上下配体氧平面间距离增大了0.0060 nm.从而成功地解释了Al₂O₃:V³⁺晶体的自旋哈密顿参量.在此基础上，研究了三角晶场下3d²离子自旋哈密顿参量的微观起源.研究发现，自旋三重态对自旋哈密顿参量的贡献是主要的，微小磁相互作用对自旋哈密顿参量的贡献只与自旋三重态有关.     

Spectroscopic properties of trivalent chromium ion in lithium niobate crystals

The formulas of crystal field theory are derived for a particular case of the C _3v symmetry group. Convenient and numerically simple methods are proposed to take into account the polarization of the local environment of the Cr³⁺ impurity ion in LiNbO₃. The parameters of intraion interactions for Cr³⁺ in lithium and niobium positions in the lithium niobate lattice and the distortion of the niobium octahedron in lithium niobate, which is caused by the incorporation of trivalent chromium ion, are determined.     

Theoretical investigations of the local structure distortion and the spin Hamiltonian parameters of Cr ions at tetragonal charge-compensation defect CrF5O site in Cr: KMgF3 crystals

The local structure distortion and the spin Hamiltonian (SH) parameters, including the zero-field splitting (ZFS) parameter D and the Zeeman g-factors g_‖ and g_⊥, are theoretically investigated by means of complete diagonalization method (CDM) and the microscopic spin Hamiltonian theory for tetragonal charge compensation CrF₅O defect center in Cr³⁺:KMgF₃ crystals. The superposition model (SPM) calculations are carried out to provide the crystal field (CF) parameters. This investigation reveals that the replacement of O²⁻ for F⁻ and its induced lattice relaxation Δ₁(O²⁻) combined with an inward relaxation of the nearest five fluorine Δ₂(F⁻) give rise to a strong tetragonal crystal field, which in turn results in the large ZFS and large anisotropic g-factor Δg. The experimental SH parameters D and Δg can be reproduced well by assuming that O²⁻ moves towards the central ion Cr³⁺ by Δ₁(O²⁻)=0.172R₀ and the five F⁻ ions towards the central ion Cr³⁺ by Δ₂(F⁻)=0.022R₀. Our approach takes into account the spin-orbit (SO) interaction as well as the spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions omitted in previous studies. This shows that although the SO interaction is the most important one, the contributions to the SH parameters from other three magnetic interactions are appreciable and should not be omitted, especially for the ZFS parameter D.     

Calculations of the optical and EPR spectral data for Cr3+ ion in Y3Ga5O12 crystal from the complete diagonalisation method

The complete diagonalisation (of energy matrix) method is applied in this paper to calculate together the optical and electron paramagnetic resonance (EPR) spectral data for Cr³⁺ ion at the trigonal Ga³⁺ site of Y₃Ga₅O₁₂ crystal. The method is founded on the two-spin-orbit-parameter model where in addition to the contributions from the spin-orbit parameter of central dⁿ ion (i.e., one-spin-orbit-parameter model) in the traditional crystal field theory, those from the spin-orbit parameter of ligand ion via covalence effect is also considered. The calculated results propose that by using only four adjustable parameters, the 12 observed spectral data (nine optical band positions and three EPR parameters g_//, g_⊥ and D) in Y₃Ga₅O₁₂: Cr³⁺ are reasonably explained. The impurity-induced local lattice distortion of Cr³⁺ in Y₃Ga₅O₁₂ crystal is also estimated through the calculations. The results are discussed.     

Lattice dynamics of ZnSe x S1 − x semiconductor crystals

Recently ultrabroadband infrared solid state lasers based on a new vibronic material Cr²⁺:ZnSe _x S_1–x were demonstrated [1–3]. Cr²⁺ ion substitutes the metal ion (tetrahedral sites), the crystal field of the solid solution is responsible for large inhomogeneous broadening of Cr²⁺ electron states. The crystal field can be reconstructed by investigation of lattice dynamics — optical phonon parameters and dielectric function in IR. We paid special attention to investigation of vibrational and infrared spectroscopic properties of ZnSe _x S_{1 ? x} crystals. A very interesting and somewhat unexpected result of these studies was the existence in the crystals of effective S-Se dipoles, which generate an additional deep dynamically charged level in the forbidden gap of the semiconductors. The results of the first-principles calculations of both the phonon structure and the electron localization in ZnSe _x S_1–x crystals as well as acceptor levels in Cr²⁺: ZnSe crystal are discussed.     

Optical spectrum, local lattice structure and EPR g factors for Cr impurity ions in MgTiO3 and LiTaO3

On the basis of the 120×120 complete energy matrices for a d³ configuration ion in a trigonal ligand field, for Cr³⁺ ions doped in MgTiO₃ and LiTaO₃, the local structures and EPR g factors of the octahedral (CrO₆)⁹⁻ clusters have been studied, respectively. By simulating the calculated optical spectra and the EPR spectra data to the experimental results, local structure parameters are obtained. The calculated results show that although the local lattice structures around the M (M=Mg²⁺, Ta⁵⁺) ions are obviously different, after Cr³⁺ replacing the M, the local lattice structures around the Cr³⁺ ions are quite similar and close to those of the Cr₂O₃. This may be ascribed to the fact that the octahedral Cr³⁺ center in MgTiO₃:Cr³⁺ and LiTaO₃:Cr³⁺ systems and that in Cr₂O₃ exhibit similar octahedral (CrO₆)⁹⁻ clusters. Moreover, the corresponding theoretical values of the optical spectra have been reported. It is also found that the orbital reduction factor k is very important to understand the EPR g factors for Cr³⁺ ions doped in MgTiO₃ and LiTaO₃.     

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.     

KZnF3:Cr3+和KMgF3:Cr3+四角对称电子顺磁共振参量与晶格缺陷的研究

用Newman叠加模型研究了KZnF₃:Cr³⁺四角对称基态的零场分裂,证实了Zn²⁺空位和畸变的存在;并指出,空位对晶场的贡献不可忽略。计算得到:KZnF₃:cr³⁺晶体[0,01]方向的一个F^-配体向Cr³⁺移动Δ(KZnF₃)=0.0029-0.0043nm。还研究了KMgF₃:Cr^{3+关键词：}     

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 studies of the optical and EPR spectra for Fe ion in the MF3:Fe (M=Al, Ga) systems

By analyzing the EPR spectra of Fe³⁺ ion in the fluorinde glasses, the local lattice structures around impurity Fe³⁺ ion in MF₃:Fe³⁺ (M=Al, Ga) systems have been studied by means of diagonalizing the complete energy matrices of the electron-electron repulsion, the ligand-field and the spin-orbit coupling for a d⁵ configuration ion in a trigonal ligand-field. Both the second-order and fourth-order EPR parameters D and (a−F) are taken simultaneously in the structural investigation. The results indicate that the local lattice structure around octahedral Fe³⁺ center has an expansion distortion for Fe³⁺ in MF₃:Fe³⁺ (M=Al, Ga). The expansion distortion may be ascribed to the fact that the radius of Fe³⁺ ion is larger than that of Al³⁺ ion and Ga³⁺ ion, and the Fe³⁺ ion will push the fluoride ligands upwards and downwards, respectively. The local lattice structure parameters R=1.927 A, θ=55.538° for Fe³⁺ in AlF₃:Fe³⁺ and R=1.931 A, θ=56.09° for Fe³⁺ in GaF₃:Fe³⁺ are determined, respectively, and the EPR spectra of the MF₃:Fe³⁺ (M=Al, Ga) systems are satisfactorily explained.     

YGG:Cr3+晶体的光谱特性

本文通过实验研究了YGG:Cr³⁺晶体的光谱特性,报道了室温下的吸收谱,10,133,300K的荧光谱,以及荧光寿命、无辐射跃迁几率、辐射量子效率与温度之间的依赖关系。从吸收谱及荧光谱中确定在C_3i(S₆)低对称场微扰下,Cr³⁺离子在基质YGG中²T₁能级分裂的子能级及基态⁺A₂→²E零声子跃迁R线的位置。 关键词：     

掺入Ni2+和V3+对α-Al2O3晶体光谱精细结构、晶体局域结构和零场分裂参量的影响

应用晶体场理论和不可约张量算符方法构造了3d2/3d8态离子在C3v对称晶场中包含自旋-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用和其它轨道-其它轨道相互作用四种微观磁效应的45阶可完全对角化的能量哈密顿矩阵.利用该矩阵,计算了V³⁺∶α-Al₂O₃和Ni²⁺∶α-Al₂O₃晶体的光谱精细结构、晶体局域结构和零场分裂参量,研究了掺入两种互补态离子Ni²⁺和V³⁺对同种晶体的光谱精细结构、晶体局域结构和零场分裂参量的影响,理论计算值和实验值相符.研究发现：掺杂没有改变晶体的光谱精细结构和能级分裂条数,但改变了能级间距|掺杂也没有改变晶体的对称性,但使晶体局域结构发生了一定程度的畸变| Ni²⁺∶α-Al₂O₃晶体局域结构的伸长畸变量大于V³⁺∶α-Al₂O₃晶体,键角的变化量小于V³⁺∶α-Al₂O₃晶体.     

Theoretical study of trigonal Fe center in SrCl2:Fesystem

The presence of Fe³⁺ centers with trigonal symmetry in chlorinated SrCl₂ crystal is an interesting phenomenon. By diagonalizing the complete energy matrices for a d⁵ configuration ion in a trigonal ligand-field and simulating the EPR low-symmetry parameters D and (a−F) simultaneously, the local lattice structure around trigonal Fe³⁺ center in SrCl₂:Fe³⁺ system has been studied. It is shown that Nistor et al.'s viewpoint about replacement is right, but the Cl⁻ ion along 〈111〉 axis around the Fe³⁺ center is replaced not by an O²⁻ ion but by some negative ion with effective charge to be less than that of Cl⁻ ion. Our results indicate that when the ratio of the effective charge of the negative ion to that of Cl⁻ ion is 0.8 as well as the distortion angle of the upper triangle is Δθ=−4.682°, the EPR parameters D and (a−F) can be explained satisfactorily.     

Theoretical investigation of the EPR parameters and the crystal lattice defects of the trigonal symmetry in RbCdF3:Cr3+

In this paper, the electron paramagnetic resonance (EPR) parameters in RbCdF₃:Cr³⁺ have been studied by means of energy matrices and the Newman superposition model, the theoretical results are in excellent agreement with the experimental ones. The existence of Rb⁺ vacancy and the lattice distortion have been verified. The EPR parameters arising from the Rb⁺ vacancy itself and the crystal lattice distortion are analyzed and calculated. We obtain that the six ligand F⁻ ions move to the central Cr³⁺ ion by Δ = 0.0013 nm, and the front three F⁻ ions rotate 2.98° away from the [111] axis while the back three F⁻ ions rotate 1.016° toward it.     

Optical spectra and energy levels of the Cr ions in MWO4 (M=Mg, Zn, Cd) and MgMoO4 crystals

Single crystals of MWO₄ (M=Mg, Zn, Cd) and MgMoO₄ doped with Cr³⁺ have been grown by the flux growth method. Their optical spectra have been systematically measured and assigned on the basis of the classical Ligand Field Theory. The exchange charge model of the crystal field has then been applied to calculate the crystal field parameters (CFPs) and the energy levels of the Cr³⁺ ion in all studied crystals. These are in reasonable agreement with the experimental data. Systematic trends in the CFPs values, crystal field splittings and Racah parameters have been evidenced and their relation with sizes and symmetry properties of the host cavities occupied by Cr³⁺ has been pointed out.