Ion In Trigonal Symmetry Research Articles

Studies of the EPR g factors and the local structure for the trigonal Nd 3+ center in LiNbO 3:Nd 3+ crystal

In this paper, the perturbation formulas of the EPR g factors g ∥ and g ⊥ for a 4f 3 ion in trigonal symmetry are established. In these formulas, the contributions to the g factors from the second-order perturbation terms, the admixtures of various states and covalency effect are taken into account. The above formulas are applied to the trigonal Nd 3+ center in LiNbO 3, with the related crystal-field parameters obtained from the local structural parameters of the impurity center. Based on the studies, one can find that the impurity Nd 3+ may not occupy the ideal Li + site, but undergo an off-center displacement Δ Z (≈−0.28 Å) away from the center of the oxygen octahedron along the C 3 axis. The above displacement Δ Z is comparable with that (≈−0.40 Å) obtained from Rutherford backscattering spectrometry (RBS) experiment. In addition, the calculated g factors (and also the anisotropy Δ g (= g ⊥− g ∥)) based on the Δ Z show reasonable agreement with the observed values. The contributions to the g factors and the local structure of this impurity center are also discussed.

Investigations of the electron paramagnetic resonance g factors for the trigonal Er3+−VK centers in KMF3 (M=Mg and Zn)

The electron paramagnetic resonance g factors gǁ and g⊥ for the trigonal Er3+−VK centers (where VK denotes K+ vacancy) in KMF3 (M=Mg and Zn) are theoretically investigated from the perturbation formulas of the g factors for a 4f11 ion in trigonal symmetry. In these formulas, the contributions to the g factors from the second-order perturbation terms and the admixture of various energy levels are taken into account. In the above trigonal centers, the impurity Er3+ resides in the octahedral M2+ site of both crystals, associated with one VK in the C3-axis due to charge compensation. By analyzing their g factors, we find that the impurity Er3+ in both centers would move towards the VK by an amount ΔZ along the C3-axis due to electrostatic attraction. The calculated g factors for the Er3+ centers based on the above displacements ΔZ show good agreement with the observed values. The validity of the results is discussed.

Theoretical investigations of the local structure and the EPR parameters for the trigonal Co 2+ center in K 4CdCl 6

The local structure and the electron paramagnetic resonance (EPR) g factors g ||, g ⊥ and the hyperfine structure constants A || and A ⊥ for the trigonal Co 2+ center in K 4CdCl 6 are theoretically investigated by using the perturbation formulas of the EPR parameters for a 3d 7 ion in trigonal symmetry based on the cluster approach. In these formulas, the contributions to the EPR parameters arising from the admixture of different energy levels, covalency effect and low symmetry distortion are included. The parameters related to the above effects are obtained from the optical spectral data and the local geometrical relationship of the studied system. By analyzing the EPR spectra, we find that the impurity–ligand bonding angle β (≈53.54°) related to the C 3-axis in the Co 2+ impurity center is smaller than the corresponding metal–ligand bonding angle β H (≈54.90°) in the host K 4CdCl 6. From the difference Δ β between the bonding angle β (or β H) and the corresponding angle β 0 (≈54.74°) in cubic symmetry, the chlorine octahedron changes from compression (Δ β H= β H− β 0>0) in the host to elongation (Δ β= β− β 0<0) in the impurity center. The calculated EPR parameters, especially the anisotropies of the g and A factors for K 4CdCl 6:Co 2+ based on the angle β show good agreement with the observed data. The theoretical studies on the local structure for Co 2+ in K 4CdCl 6 would be helpful to understand the structure properties for the equivalent octahedral transition-metal M site in the isostructural A 3M′MO 6 compounds.

Theoretical investigations of the local structure for the trigonal Co 2+ center in MgTiO 3 crystal

The local structure of the trigonal Co 2+ center in MgTiO 3 is theoretically investigated by using the perturbation formulas of the spin Hamiltonian parameters for a 3d 7 ion in trigonal symmetry based on the cluster approach. From the studies, it can be found that the impurity Co 2+ ion substitutes for Mg 2+ rather than Ti 4+ ion, and that the Co 2+ takes an outward displacement (≈0.02 Å) away from the center of the oxygen octahedron along the C 3 axis in MgTiO 3. The theoretical spin Hamiltonian parameters calculated from the above displacement show good agreement with the observed values. The validity of the results is discussed based on the impurity displacement model for corundum-type structures.

EPR g factors of trigonal Dy3+ center in ThO2 crystal

The perturbation formulas of EPR g factors g‖ and g⊥ for the lowest Kramers doublet of 6H15/2 of a 4f9 ion in trigonal symmetry are established in this paper. In these formulas, besides the contribution due to the interaction within the lowest 6H15/2 manifolds considered in the previous papers, the contributions due to the J-mixing among the 6H15/2, 6H13/2 (first excited state) and 6H11/2 (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 Γγ and other Kramers doublets ΓX within the states 6HJ (J=15/2,13/2,11/2) via crystal-field and orbital angular momentum interactions are included. From these formulas, the g factors g‖ and g⊥ for the trigonal Dy3+ center in ThO2 crystal are calculated. The results are discussed.

Theoretical investigation of EPR parameters for two trigonal Yb 3+ centers in LiNbO 3 and LiNbO 3:MgO crystals

The perturbation formulas of EPR parameters ( g factors g ∥, g ⊥ and hyperfine structure constants A ∥, A ⊥) for the lowest Kramers doublet Γ 6 or Γ 7 of 2F 7/2 of 4f 13 ion in trigonal symmetry are established. In these formulae, the contributions of the covalency effects, the admixture between J=7/2 and 5/2 states as well as the second-order perturbation (which is not considered in the previous works) are all included. From these formulae, the EPR parameters for two trigonal Yb 3+ centers in LiNbO 3 and MgO codoping LiNbO 3 crystals are reasonably explained by considering suitable defect structures of these centers. The results (including the relative importance of second-order perturbation contribution) 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 ‖, g ⊥ 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 defect structures for two trigonalEr3+centers inLiNbO3and MgO or ZnO codopedLiNbO3crystals

In this paper, the perturbation formulas of EPR parameters (g factors g(parallel to),g(perpendicular to) and hyperfine structural constants A(parallel to) and A(perpendicular to)) for the lowest Kramers doublet Gamma(6) or Gamma(7) of I-4(15/2) of 4f(11) ion in trigonal symmetry are established. In these formulas, the second-order perturbation contributions are considered in addition to the first-order perturbation contributions considered in the previous works. Based on these formulas, the EPR parameters and the defect structures of two trigonal Er3+ centers in LiNbO3 and MgO or ZnO codoped LiNbO3 crystals are studied. It is found that in order to reach a good fit between calculations and experiments, the Er3+ ions in centers I and II do not occupy exactly the Li+ and Nb5+ sites, respectively, but are displaced along the C-3 axis away from the center of oxygen octahedron by about 0.039 nm for center I and towards the center of octahedron by about 0.030 nm for center II. The reasonableness of the local lattice distortions and the contributions from the second-order perturbation terms are discussed.

EPR parameters and defect structure of paramagnetic Er3+ center in α-LiIO3 crystal

The EPR parameters (g factors g//, g⊥ and hyperfine structure constants A//, A⊥) of paramagnetic Er3+ centers in the α-LiIO3 crystal are studied from the perturbation formulas of EPR parameters for 4f11 ion in trigonal symmetry. In these formulas, besides the first-order perturbation contribution considered in previous papers, the second-order perturbation contribution is taken into account, and the crystal-field parameters are estimated from the structural data of Er3+ centers in α-LiIO3:Er3+ by using the superposition model. From the studies, it is found that in the Er3+ center the six O2− ions between the Er3+ ion and Li vacancies (VLi) are shifted away from the VLi by about 0.037 Å. The shift direction is in agreement with those of the trivalent iron-group ions Cr3+ and Fe3+ in α-LiIO3 as well as with the expectation based on the electrostatic interaction model. The EPR parameters g//, g⊥, A// and A⊥ for α-LiIO3: Er3+ are also reasonably well explained by considering the local lattice relaxation.

Spin-lattice Coupling Coefficient G44 of KMgF3:Mn2+ Calculated from Two Cases

Abstract The high (fourth) order perturbation formulas based on the dominant spin-orbit coupling mech­anism for the zero-field splittings Dtri of a 6S-state ion in trigonal symmetry and Erho in rhombic symmetry are derived from the strong field scheme. Two analytic expressions of the spin-lattice coupling coefficient G44 obtained from the formulas of and Erho are established by using a simple and uniform method. Based on the two expressions, the coefficients G44 for KMgF3:Mn2+ are calculated in two cases. The results show that the lowest (third) order perturbation formulas of D(3) tri and E(3) rho are too simple and too approximate to give reasonable and consistent values of G44, whereas when the fourth-order perturbation terms D(4) tri and E(4) rho are considered, the calculated values of G44 (= G(3) 44 + G(4) 44) in both cases are not only close to each other, but also in agreement with the observed value. So, the fourth-order perturbation terms cannot be neglected.

EPR studies of phase transitions in (NH4)3H(SO4)2single crystals

The successive phase transitions reported in triammonium hydrogen disulphate (TAHS) are investigated by EPR using Cu2+ and Mn2+ ions as probes. At room temperature, in the spontaneously strained monoclinic phase, Cu2+ and Mn2+ ions were found to be in two magnetically inequivalent sites. At the phase II (monoclinic) to (+140 degrees C) phase I (trigonal) transition the magnetic inequivalence of Cu2+ ions vanished, resulting in a broad single line at g=2.240+or-0.002 due to a possible dynamic Jahn-Teller effect that may be present for the 2E state of the Cu2+ ion in trigonal symmetry. This transition exhibited a hysteresis of about 45 degrees with the reverse transition appearing at +95 degrees C on cooling. The II to III transition resulted in the splitting of the Cu2+ resonance into two components with a temperature-dependent intensity ratio and separations. These results are consistent with the model that the Cu2+ ion occupies the NH4+ (I) position at room temperature, and takes an off-centred position in phase III with an associated electronic dipole moment, responding to the onset of antiferroelectric ordering.

Zero-Field Splitting of aS6Ion in Trigonal Symmetry

The expressions for various possible mechanisms under the point-multipole approximation which contribute to the zero-field splitting parameter $^{6}S$ in the spin Hamiltonian $D$ for a paramagnetic ${H}_{S}=D[3{S}_{z}^{2}\ensuremath{-}S(S+1)]$ ion in a trigonal symmetry have been derived. Important differences have been noticed in this axial symmetry in contrast with the results in the tetragonal symmetry considered previously. The applications of the expressions to two hypothetical cases and the real case of Cd${\mathrm{Cl}}_{2}$:${\mathrm{Mn}}^{2+}$ reveal that both the spin-spin and spin-orbit interactions are important. In the case of Cd${\mathrm{Cl}}_{2}$:${\mathrm{Mn}}^{2+}$, the spin-orbit contribution ${(\ensuremath{-}10.43\ifmmode\times\else\texttimes\fi{}10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$) cancels a large part of the spin-spin contribution (+15.35\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$), giving the value $D=+4.92\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. This compares favorably with the results (at room temperature) of +5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ for $D$ from experiments on single crystals and \ensuremath{\sim} + 1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ from experiments on powdered samples. The latter approximate result from powdered samples has been deduced by reducing the uncertainty in $D$ using the graph illustrating the experimental variation of $D$ with temperature. For ${\mathrm{CdCl}}_{2}$:${\mathrm{Mn}}^{2+}$ it has also been pointed out that the value of $D$ varies from -2.11\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ to + 10.49\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ if one considers the existing uncertainty in the crystal structure parameter obtained from x-ray diffraction. In the present study, the presence of higher multipoles because of the ions, and the distortion of the lattice surrounding the magnetic ion, have not been taken into account.