Lv He

Spin-Hamiltonian parameters and tetragonal distortion due to the Jahn-Teller effect for Cu2+centres in trigonal Zn(BrO3)center dot 6H2O crystal

The spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants 65A// and 65A⊥) for the tetragonal Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal are calculated from the complete diagonalization (of energy matrix) method (CDM) based on the cluster approach. In the CDM, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and the contributions to the spin-Hamiltonian parameters from both the spin-orbit coupling parameter of central d9 ion and that of ligand ion are included. The calculated spin-Hamiltonian parameters of Zn(BrO3)·6H2O: Cu2+ show good agreement with the experimental values and the tetragonal elongation (characterized by ΔR=R// − R ⊥, where R// and R ⊥ represent the metal-ligand distances parallel with and perpendicular to the C4 axis) due to the static Jahn–Teller effect is obtained from the calculations. The results are discussed.

Studies of the g factors for the tetragonally elongated and compressed CuIIN6 octahedra in image omitted (MI = K, Rb, Cs; MII = Ca, Sr, Ba, Pb) crystals

The EPR g factors, g / / and g ⊥, of tetragonally elongated and compressed CuIIN6 octahedral clusters (with the ground states |dx 2 − y 2 ⟩ and |d z 2 ⟩, respectively) in (MI = K, Rb, Cs; MII = Ca, Sr, Ba, Pb) crystals were calculated using a two-mechanism model. In the model, the contributions to the g-shifts, Δgi (= gi − gs , where i = // or ⊥; gs ≈ 2.0023 is the free-ion g value), from both the crystal-field (CF) mechanism related to CF excited states and the charge-transfer (CT) mechanism related to CT excited states, which is neglected in the widely-used CF theory, were considered. For the CF mechanism, two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM), were applied. The CF parameters used were calculated from the superposition model, in which the structural data for CuIIN6 clusters in crystals were measured exactly by X-ray diffraction. The calculated g factors for both the tetragonally elongated and compressed CuIIN6 octahedra are in reasonable agreement with the experimental values. For the strongly covalent CuIIN6 clusters in crystals with different ground states, both the PTM and CDM can be applied to calculate the g-shifts, , arising from the CF mechanism, but exact and reasonable calculations of g factors should take both CF and CT mechanisms into account.

A theoretical study on the temperature dependence of zero-field splitting for the tetragonal Cr3+ center in MgO crystal.

This paper reports a detailed theoretical calculation of the temperature dependence of zero-field splitting D (characterized by ΔD(T)=D(T)-D(0)) for the tetragonal Cr3+ center in MgO crystal by considering both the static contribution due to the thermal expansion of Cr3+ center and the vibrational contribution caused by electron-phonon (including the acoustic and optical phonons) interaction. The vibrational contribution due to the acoustic phonon is calculated using the long-wave approximation similar to the study on the specific heat of crystals and that due to optical phonon is estimated using the single-phonon model. The calculated results are in reasonable agreement with the experimental values. From the calculation, it is found that the static contribution ΔDstat(T) (which is often regarded as very small and is neglected in the previous papers) is larger than the vibrational contribution ΔDvib(T) and so the reasonable studies of temperature dependence of zero-field splitting should take both the static and the vibrational contributions into account.

A study of the spin-Hamiltonian parameters for Cr5+ at the rhombically-distorted tetrahedral P5+ site of Ca2PO4Cl crystal using a two-mechanism model

The complete high-order perturbation formulae of spin-Hamiltonian (SH) parameters (g factors gi and hyperfine structure constants Ai , where i = x, y, z) containing contributions from both the crystal-field (CF) and charge-transfer (CT) mechanisms (the latter mechanism is neglected in the widely-used CF theory) are established for d1 ions in rhombic tetrahedra. From these formulae, the SH parameters of Cr5+ ion at the rhombically-distorted tetrahedral P5+ site of Ca2PO4Cl crystal are calculated. The CF and CT energy levels used in the calculation are obtained from the optical spectra of the studied Ca2PO4Cl : Cr5+ crystal. The calculated results showed reasonable agreement with the experimental values. The signs of the hyperfine structure constants Ai and the relative importance of the CT mechanism to SH parameters are acquired from the calculations.

Theoretical Explanations of the g Factors for Ni(3+) Ions in KMgF(3) and CsCaF(3) Crystals

ABSTRACT By using the optical spectral parameters of (NiF6)3− clusters in KMgF3:Ni3+ and CsCaF3:Ni3+ crystals estimated from the observed values in pure K3NiF6 crystal, the electron paramagnetic resonance (EPR) g factors for KMgF3:Ni3+ and CsCaF3:Ni3+ are calculated from the second-order perturbation formula (with the high-spin ground orbital state) based on the cluster approach. The results are in reasonable agreement with the observed values. The spin transition from the low-spin state in pure K3NiF6 crystal to the high-spin state in KMgF3:Ni3+ and CsCaF3:Ni3+ crystals owing to the slight increase of Ni3+ – F− distance is discussed.

Investigation of the optical spectra and spin-Hamiltonian parameters for the rhombic Cu2+ center in β-Ca3(PO4)2

The four optical band positions and six spin-Hamiltonian parameters (the g factors g(i) and the hyperfine structure constants A(i), i = x, y, z) for the rhombic Cu(2+) center in fi-Ca(3)(PO(4))(2) are calculated by two theoretical methods: the complete diagonalization (of energy matrix) method and the perturbation theory method (PTM). Both methods are based on the cluster approach, in which the covalence due to admixture of ligands to the central metal ion is considered. The calculated results of the two methods are close to each other and agree with the experimental values. This suggests that both methods are effective in explaining the optical and electron paramagnetic resonance data for d(9) ions in crystals. The calculations also show that although the admixture of vertical bar d(z)(2)> to the ground state wave function is small, it should not be neglected in calculations of spin-Hamiltonian parameters. So, in PTM, the high-order perturbation formulae of spin-Hamiltonian parameters based on the cluster approach for d(9) ion in rhombic symmetry should be derived by taking into account the admixture of the vertical bar d(z)(2)> state to the vertical bar d(x2-y2)> ground state.

Spin-Hamiltonian parameters and off-center displacements for Rh4+ and Ir4+ ions in rhombohedral BaTiO3

By means of the formulae based on the first-order theory of resonance for a low-spin 2T2 term in trigonal symmetry, the spin-Hamiltonian parameters (g factors g //, g ⊥ and hyperfine structure constants A //, A ⊥) for Rh4+(4d5) and Ir4+(5d5) ions in the low-temperature rhombohedral phase of BaTiO3 are calculated. The calculated results are in reasonable agreement with the experimental values. From the calculations, the off-center displacements of Rh4+ and Ir4+ in the oxygen octahedra of BaTiO3 crystal are acquired. These impurity displacements are much smaller than that of the replaced host ion Ti4+. This point is analogous to the displacements of 3d n impurities Fe3+ and Co2+ in rhombohedral BaTiO3 obtained by analyzing their spin-Hamiltonian parameters.

Studies of the spin-Hamiltonian parameters and defect structures for the trigonal Mo3+ centers in Y3Al5O12 and Lu3Al5O12 crystals

The complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM) are applied to calculate the spin-Hamiltonian (SH) parameters (electron paramagnetic resonance g factors g //, g ⊥ and zero-field splitting D) of the trigonal Mo 3+ centers in Y 3Al 5O 12 and Lu 3Al 5O 12 crystals. Both methods are based on the cluster approach in which the covalence effect due to the admixture between the d orbitals of central d n ion and p orbitals of ligands is considered. The g factors calculated by both methods are close to each other and agree with the experimental values. However, the calculated zero-field splittings D from PTM for both crystals are about 84% those from CDM. The reasons that the CDM is preferable to the PTM in the calculations of SH parameters are discussed. The angular distortions of Mo 3+ centers in both garnet crystals are predicted.

Investigations on the g factors of the ground and excited states for Cu2+ions in ZnO crystal

The g factors g // and g ⊥ of the ground Γ6(2 T 2) and excited Γ4,5(2 E), Γ6(2 E) states for trigonal Cu2+ centres in ZnO crystals are calculated from three theoretical methods, the complete diagonalization (of the energy matrix) method, the second-order perturbation method (PTM-I) and the simplified second-order perturbation method (PTM-II, this method was described in an earlier paper). These methods are based on the cluster approach in which the spin-orbit coupling parameters ζ, ζ′ and the orbital reduction factors k, k′ are calculated from a semi-empirical molecular orbital method. The crystal-field parameters used in the calculations are obtained from the superposition model and so the defect structure of Cu2+ centres in ZnO can be acquired. The calculated g factors from the three methods are in reasonable agreement with the experimental values and the defect structure of Cu2+ centres in ZnO is acquired. It appears that in some cases the approximate PTM can be applied in the studies of g factors of various states. The conditions that the PTM are ineffective are discussed.

Studies of spin-Hamiltonian parameters and defect structures for two tetragonal Ir4+ centers in MgO and CaO crystals

By means of the resonance theory related to the low-spin 2T2 term for strong field d5 configuration in tetragonal symmetry, the spin-Hamiltonian parameters, g factors g |, g ⊥ and hyperfine structure constants 191 A |, 191 A ⊥, 193 A | and 193 A ⊥, for two tetragonal Ir4+ centers T and T′ in MgO and CaO crystals are calculated. The calculated results are in reasonable agreement with the experimental values. From the calculations, negative signs are suggested for the hyperfine structure constants A |, A ⊥, the defect models for the two tetragonal Ir4+ centers suggested in the earlier paper are confirmed and the defect structural data for both centers in MgO and CaO crystals are obtained. These results are discussed.