Investigations of the EPR g factors and hyperfine structure constants for two trigonal Co2+ centers in Al2O3 crystals

The EPR g factors gparallel, gperpendicular and the hyperfine structure constants Aparallel, Aperpendicular for two trigonal Co2+ centers (i.e. Co2+(I) center at the substitutional site and Co2+(II) center at the interstitial site) in Al2O3 crystals are calculated from the second-order perturbation formulas based on the cluster approach. In these formulas, the contributions to EPR parameters from both the spin-orbit coupling parameter of central 3dn ion and that of ligand are included. The calculated results are in reasonable agreement with the observed values. Based on the calculations, the defect structures of both Co2+ centers in Al2O3 crystals are obtained and the negative sign of Aparallel for Co2+(I) center is suggested. The results are discussed.     

Studies of the g factors and zero-field splitting for the trigonal Ti(2+)(Ga)-S(p) defect center in GaP crystal

The EPR g factors g(parallel), g(perpendicular) and zero-field splitting D suggested to be caused by a donor-acceptor nearest-neighbour pair defect [Ti(Ga)(2+)-Sp] in GaP:Ti(2+) co-doped with sulphur are calculated from the high-order perturbation formulas based on a two spin-orbit coupling parameter model for the EPR parameters of 3d(2) ion in trigonal symmetry. The calculated results are close to the observed values. The suggestion of [Ti(Ga)(2+)-Sp] pair defect in GaP:Ti co-doped with sulphur is also confirmed from this calculation.     

EPR parameters and local geometry for Cr3+ and V2+ ions in HfS2 crystals

From the high-order perturbation formulas of EPR parameters (zero-field splitting D, g factors gparallel, gperpendicular and hyperfine structure constants Aparallel, Aperpendicular) based on the two spin-orbit coupling parameter model for 3d3 ions in trigonal symmetry, the EPR parameters of Cr3+ and V2+ ions in HfS2 crystals are calculated. From the calculations, it is found that the local trigonal distortion angle theta of impurity center in HfS2:Cr3+ is smaller than that in HfS2:V2+. The dominant cause of the small zero-field splitting |D| and g-anisotropy |Deltag|=|gparallel-gperpendicular| in HfS2:Cr3+ (compound to HfS2:V2+) is due to the small local trigonal distortion angle theta rather than to the small impurity-ligand distance R in HfS2:Cr3+.     

Ni2+掺杂到氟化物钙钛矿中的局域结构畸变和基态分裂的理论研究

By analyzing the optical spectra and electron paramagnetic resonance parameter D, the local structure distortion of (NiF₆)^4- clusters in AMF₃ (A=K, Rb; M=Zn, Cd, Ca) and K₂ZnF₄ series are studied using the complete energy matrix based on the double spin-orbit coupling parameter model for configuration ions in a tetragonal ligand field. The results indicate that the contribution of ligand to spin-orbit coupling interaction should be considered for our studied systems. Moreover, the relationships between D and the spin-obit coupling coefficients as well as the average parameter and the divergent parameter are discussed.     

Theoretical investigation of electron paramagnetic resonance spectra and local structure distortion for Mn2+ ions in CaCO3:Mn2+ system: a simple model for Mn2+ ions in a trigonal ligand field

This paper reports on a novel application of a ligand field model for the detection of the local molecular structure of a coordination complex. By diagonalizing the complete energy matrices of the electron-electron repulsion, the ligand field and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field, the local distortion structure of the (MnO6)10- coordination complex for Mn2+ ions doped into CaCO3, have been investigated. Both the second-order zero-field splitting parameter b(0)2 and the fourth-order zero-field splitting parameter b(0)4 are taken simultaneously in the structural investigation. From the electron paramagnetic resonance (EPR) calculations, the local structure distortion, DeltaR=-0.169 A to -0.156 A, Deltatheta=0.996 degrees to 1.035 degrees for Mn2+ ions in calcite single crystal, DeltaR=-0.185 A to -0.171 A, Deltatheta=3.139 degrees to 3.184 degrees for Mn2+ ions in travertines, and DeltaR=-0.149 A to -0.102 A, Deltatheta=0.791 degrees to 3.927 degrees for Mn2+ ions in shells are determined, respectively. These results elucidate a microscopic origin of various ligand field parameters which are usually used empirically for the interpretation of EPR and optical absorption experiments. It is found that the theoretical results of the EPR and optical absorption spectra for Mn2+ ions in CaCO3 are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the doped CaCO3, the theoretical values of the fourth-order zero-field splitting parameters b(0)4 for Mn2+ ions in travertines and shells are reported first.     

EPR g factors of trigonal Dy(3+) center in ThO(2) crystal

The perturbation formulas of EPR g factors g(parallel) and g( perpendicular ) for the lowest Kramers doublet of 6H(15/2) of a 4f(9) ion in trigonal symmetry are established in this paper. In these formulas, besides the contribution due to the interaction within the lowest 6H(15/2) manifolds considered in the previous papers, the contributions due to the J-mixing among the 6H(15/2), 6H(13/2) (first excited state) and 6H(11/2) (second excited state) via crystal-field interaction, the admixtures among the states with the same J value via spin-orbit coupling interaction and those between the lowest Kramers doublet Gammagamma and other Kramers doublets Gamma(X) within the states 6H(J) (J=15/2,13/2,11/2) via crystal-field and orbital angular momentum interactions are included. From these formulas, the g factors g(parallel) and g( perpendicular ) for the trigonal Dy(3+) center in ThO(2) crystal are calculated. The results are discussed.     

Theoretical studies of the spin Hamiltonian parameters and the local structures for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3

The spin Hamiltonian parameters (zero-field splitting D, g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3 are studied by using the perturbation formulas of the spin Hamiltonian parameters for 3dn (n=7, 5, 3, 8) ions in trigonal symmetry based on the cluster approach. In these formulas, the contributions to the spin Hamiltonian parameters from the admixture of d orbitals of the central ions with the p orbitals of the ligands and from the trigonal distortion are included and the parameters related to these effects can be obtained from the optical spectra and the local structures of the studied systems. Based on the studies, it is found that the local trigonal distortion angle beta in the M2+ impurity center is unlike that betaH (approximately 51.71 degrees) in the host CsMgCl3. The spin Hamiltonian parameters for these divalent ions in CsMgCl3 are also satisfactorily explained by using the local angle beta. The validity of the results is discussed.     

Tetragonal distortion of structural defects in Cr3+ doped in several perovskites calculated from the EPR and optical data: a complete energy matrix study

This paper describes a novel application of a ligand field model in the study of the local molecular structure of the (CrF 6) (3-) coordination complex. Based on the ligand field model, the complete energy matrix which contains the electron-electron repulsion interaction, the ligand field interaction, the spin-orbit coupling interaction, and the Zeeman interaction, has been constructed for a d (3) configuration ion in a tetragonal ligand field. In order to study the relation between the EPR, the optical spectra, and the local lattice structures around the centers with tetragonal symmetry in AMF 3 codoped with Cr (3+) and Li (+) ions, a three-layer-ligand model is proposed. By diagonalizing the complete energy matrix and employing the three-layer-ligand model, the variational ranges of the local structural parameters around the Cr (3+) ions are determined, respectively. The results show that the local lattice structures around the Cr (3+) ions in AMF 3 exhibit a compressed distortion, and the magnitude of distorted parameter Delta R 1 of the Cr (3+)-V M center is different from that of the Cr (3+)-Li (+) center in AMF 3. The compressed distortion is ascribed to the fact that the radius of the Cr (3+) ion is smaller than those of M (2+) (M = Cd, Mg, Zn). Moreover, a linear correlation between the difference in the magnitude of distortion parameterDelta R for two different defect centers and the difference in the corresponding values of the zero-field-splitting parameter Delta D are found first.     

Analysis of the uniaxial magnetic properties of high-spin d(6) ions at trigonal prism and linear two-coordinate sites: uniaxial magnetic properties of Ca(3)Co(2)O(6) and Fe[C(SiMe(3))(3)](2)

It was shown that high-spin d(6) ions at trigonal prism and linear two coordinate sites have uniaxial magnetic properties by calculating their low-lying eigenstates under the influence of crystal field and spin-orbit coupling and then determining their g-factors for the parallel and perpendicular directions. On the basis of our theoretical findings, we interpreted the uniaxial magnetic properties of Ca(3)Co(2)O(6) with high-spin Co(3+) (d(6)) ions at the trigonal prism sites and those of Fe[C(SiMe(3))(3)](2) with high-spin Fe(2+) (d(6)) ions at linear two-coordinate sites, and discussed why compounds with high-spin d(6) ions at octahedral sites cannot have uniaxial magnetic properties.     

Investigations of the EPR zero-field splitting and the defect structure for Mn(2+) and Fe(3+) ions in anatase crystals

The EPR zero-field splittings D of Mn(2+) and Fe(3+) ions in anatase crystals at room and low temperatures are calculated from the high-order perturbation formula of zero-field splitting D for 3d(5) ions in tetragonal symmetry based on the dominant spin-orbit coupling mechanism. The calculated results are consistent with the observed values. From the calculations, Mn(2+) and Fe(3+) ions are suggested to substitute for Ti(4+) ions in anatase (in the previous paper, Mn(2+) ion was suggested at an interstitial site rather than substitutional site) and the defect structures (characterized mainly by the local oxygen parameter u) for both tetragonal Mn(2+) and Fe(3+) impurity centers are estimated. The different zero-field splitting at room and low temperatures are due mainly to the change of local oxygen parameter u with the temperature. These results are discussed.     

Investigations of EPR parameters for the trigonal Ti3+-Ti3+ pair in beryl crystal

By using the complete diagonalization of energy matrix of 3d1 ions in trigonal symmetry, the EPR parameters (g factors g( parallel), g( perpendicular) and zero-field splitting D) of the trigonal Ti3+-Ti3+ pair in beryl crystal are calculated. In the calculations, the exchange interaction in the Ti3+-Ti3+ pair is taken as the perturbation and the local trigonal distortion in the defect center is considered. The results (which are in agreement with the experimental values) are discussed.     

Theoretical investigations of zero-field splitting of excited states for 3d3 ions in trigonal crystal fields

By taking into account slight interactions, i.e. spin-spin, spin-other-orbit and orbit-orbit interactions, in addition to spin-orbit interaction, the zero-field splitting of ground state and low excited states and g factors of ZnGa2O4:Cr3+ crystal have been interpreted systematically. And the contributions to zero-field splitting arising from slight magnetic interaction and trigonal crystal field are investigated. It is found that there exist combined mechanism between magnetic interactions and trigonal crystal field.     

Studies of EPR parameters for Mn5+ -doped Li3PO4 and Li3VO4 crystals

The EPR parameters (zero-field splitting D and g factors g parallel, g perpendicular) of Mn5+ -doped Li3PO4 and Li3VO4 crystals are calculated from the complete high-order perturbation formulas based on a molecular orbital scheme for a 3d2 ion in tetragonal MX4 clusters. These formulas include not only the contribution coming from crystal-field excitations, but also that arising from charge-transfer excitations (which is discarded in crystal field theory). The calculated results are in reasonable agreement with the observed values. The contributions to EPR parameters coming from the charge-transfer excitations are comparable with those arising from the crystal-field excitations. It appears that for a high valence state 3dn ion in crystals, the reasonable explanations of EPR parameters should take the contributions due to both crystal-field and charge-transfer excitations into account.     

Characterization of electronic transition energies and trigonal distortion of the (FeO6)9- coordination complex in the Al2O3:Fe3+ system: a simple method for transition-metal ions in a trigonal ligand field

A theoretical method for studying the inter-relationships between electronic and molecular structure has been proposed on the basis of the complete energy matrices of electron-electron repulsion, the ligand field, and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field. As an application, the local distortion structure and temperature dependence of zero-field splitting for Fe3+ ions in the Al2O3:Fe3+ system have been investigated. Our results indicate that the local lattice structure of the (FeO6)(9-) octahedron in the Al2O3:Fe3+ system has an elongated distortion and the value of distortion is associated with the temperature. The elongated distortion may be attributed to the facts that the Fe3+ ion has an obviously larger ionic radius than the Al3+ ion and the Fe3+ ion will push the two oxygen triangles upward and downward, respectively, along the 3-fold axis. By diagonalizing the complete energy matrices, we found that the theoretical results of electronic transition energies and EPR spectra for Fe3+ ions in the Al2O3:Fe3+ system are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the Al2O3, the theoretical values of the zero-field splitting parameters and the corresponding distortion parameters in the range 50 K 相似文献   

Ligand-field treatment for the optical and electron paramagnetic resonance spectra of ZnO:V(3+)

In this work, a full ligand-field energy matrix (45 x 45) diagonalization treatment for 3d(2) ions in trigonal symmetry C(3v) is performed on the basis of a central metal ion-ligand covalency model including the ligand spin-orbit (SO) coupling. Optical fine structure and electron paramagnetic resonance (EPR) spectra of ZnO:V(3+) are uniformly explained.     

Theoretical investigation of the EPR parameters and local structure for trigonal Yb3+ ion in Bi4Ge3O12 crystal

Bi4Ge3O12 single crystals are of great interest for science research and engineering applications. In this paper, the electron paramagnetic resonance (EPR) g factors g||, gperpendicular of Yb3+ and hyperfine structure constants A||, Aperpendicular of 171Yb3+ and 173Yb3+ isotopes in Bi4Ge3O12 crystal are calculated from the perturbation formulas of these parameters. The crystal-field parameters are obtained from the superposition model and the crystal structure data. The EPR parameters for trigonal Yb3+ centers in Bi4Ge3O12 are reasonably explained by involving the defect structures of impurity Yb3+ centers. Based on the calculations, Yb3+ ion is found not to occupy exactly the host Bi3+ site, but to shift away from the center of oxygen octahedron by a distance DeltaZ approximately 0.317 A along C3 axis. The results are discussed.     

Investigations of zero-field splitting (ZFS) and local distortion parameters of ZnAl2S4:Mn2+ by theoretical analysis

Fourth-order perturbation formula on the basis of the dominant spin-orbit coupling mechanism is employed to investigate the local environment around Mn2+ centers in ZnAl2S4 single crystals. The zero-field splitting (ZFS) parameter D is calculated for the Mn2+ ions at the Al3+ site with local symmetry D3d using the different orbital reduction factors. Both the contributions of the lattice distortions to the crystal-field (CF) parameters and the D are examined by means of different cases. The comparison between the calculated results in this study and the previous experimental and theoretical values reveals a good agreement and reasonable distortion parameters for Mn2+ ions at Al3+ sites.     

锰(Ⅱ)络合物零场分裂值的理论解释

利用非自由Mn(Ⅱ)的径向波函数讨论Mn(Ⅱ)络合物的零场分裂,证实了零场分裂主要来自低对称晶场和旋-轨耦合作用的贡献。定量计算了三角、四角畸变时的|D|值,计算结果与实验值符合。     

Investigations of EPR parameters and local lattice distortions for both Co2+ centers in La2Mg3(NO3)12.24H2O crystal

The EPR g factors, g parallel and g perpendicular, of Co2+ and hyperfine structure constants (A parallel, A perpendicular) of 59Co2+ and 60Co2+ isotopes in both trigonal Mg2+ sites of La2Mg3(NO3)12.24H2O crystal are calculated from the high-order perturbation formulas of EPR parameters based on the cluster approach for 3d7 ion. It is found that to explain reasonably all these EPR parameters, the local relaxation effects (particularly, those related to the trigonal distortion angles thetai) in the vicinity of both Co2+ impurities should be considered. The local angles thetai are obtained from the calculations and the results are discussed.     

Density functional theory analysis of the interplay between Jahn-Teller instability, uniaxial magnetism, spin arrangement, metal-metal interaction, and spin-orbit coupling in Ca3CoMO6 (M = Co, Rh, Ir)

In the isostructural oxides Ca(3)CoMO(6) (M = Co, Rh, Ir), the CoMO(6) chains made up of face-sharing CoO(6) trigonal prisms and MO(6) octahedra are separated by Ca atoms. We analyzed the magnetic and electronic properties of these oxides on the basis of density functional theory calculations including on-site repulsion and spin-orbit coupling, and examined the essential one-electron pictures hidden behind results of these calculations. Our analysis reveals an intimate interplay between Jahn-Teller instability, uniaxial magnetism, spin arrangement, metal-metal interaction, and spin-orbit coupling in governing the magnetic and electronic properties of these oxides. These oxides undergo a Jahn-Teller distortion, but their distortions are weak, so that their trigonal-prism Co(n+) (n = 2, 3) ions still give rise to strong easy-axis anisotropy along the chain direction. As for the d-state split pattern of these ions, the electronic and magnetic properties of Ca(3)CoMO(6) (M = Co, Rh, Ir) are consistent with d(0) < (d(2), d(-2)) < (d(1), d(-1)) but not with (d(2), d(-2)) < d(0) < (d(1), d(-1)). The trigonal-prism Co(3+) ion in Ca(3)Co(2)O(6) has the L = 2 configuration (d(0))(1)(d(2), d(-2))(3)(d(1), d(-1))(2) because of the metal-metal interaction between adjacent Co(3+) ions in each Co(2)O(6) chain, which is mediated by their z(2) orbitals, and the spin-orbit coupling of the trigonal-prism Co(3+) ion. The spins in each CoMO(6) chain of Ca(3)CoMO(6) prefer the ferromagnetic arrangement for M = Co and Rh but the antiferromagnetic arrangement for M = Ir. The octahedral M(4+) ion of Ca(3)CoMO(6) has the (1a)(1)(1e)(4) configuration for M = Rh but the (1a)(2)(1e)(3) configuration for M = Ir, which arises from the difference in the spin-orbit coupling of the M(4+) ions and the Co···M metal-metal interactions.