Wei-Qing Yang

Theoretical calculations of the spin-Hamiltonian parameters from a two-mechanism model for Cr5+ ions in MVO3 (M = Li, Na, K, Rb) crystals

The spin-Hamiltonian parameters (g factors g //, g ⊥ and hyperfine structure constants A //, A ⊥) of the approximately-tetragonal Cr5+ centers in MVO3 (M = Li, Na, K, Rb) crystals are calculated from the complete high-order perturbation formulas for d1 ions in tetragonal symmetry with the ground state . These formulas are based on a two-mechanism model, in which not only the contribution to spin-Hamiltonian parameters from the crystal-field (CF) mechanism concerning CF excitations, but also that from the charge-transfer (CT) mechanism concerning CT excitations (which is neglected in the widely-used CF theory) are included. The calculated results are in reasonable agreement with the experimental values and the signs of hyperfine structure constants are suggested. The calculations show that for a high valence state dn ion (e.g. Cr5+) in crystals, the exact calculation of spin-Hamiltonian parameters should take the contributions due to both CF and CT mechanisms into account.

Investigations of the optical spectra and EPR g factors for the tetragonal Cu2+ centers in trigonal ZnCO3 crystal

Two distinctive theoretical methods, the complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM), are employed to calculate the optical band positions and EPR g factors g(||), g(perpendicular) for the tetragonal Cu(2+) centers in trigonal ZnCO(3) crystal. The results from the two methods coincide and are also in good agreement with the experimental values. So both the CDM and PTM are adequate for the investigations of optical and EPR data for d(9) ions in crystals. The tetragonal distortion due to the static Jahn-Teller effect for the tetragonal Cu(2+) centers in trigonal Zn(2+) site of ZnCO(3) is also acquired from the calculations. The results are discussed.

Studies of the spin-Hamiltonian parameters and the Jahn-Teller distortions for tetragonal Cu(H(2)O)(6)(2+) clusters in trigonal A(2)Mg(3)(NO(3))(12)center dot 24H(2)O (A = La, Bi) crystals

The anisotropic and isotropic spin-Hamiltonian parameters (g factors and hyperfine structure constants) of tetragonal Cu(H(2)O)(6)(2+) clusters due, respectively, to the static and dynamic Jahn-Teller effects for Cu(2+) in trigonal A(2)Mg(3)(NO(3))(12).24H(2)O (A=La, Bi) crystals are calculated from the high-order perturbation formulas based on the cluster approach. In the approach, the admixture between the d orbitals of 3d(n) ion and the p orbitals of ligand ion via covalence effect is considered. All of the calculated results are in agreement with the experimental values. The tetragonal elongations (characterized by DeltaR=R(parallel)-R( perpendicular)) of Cu(H(2)O)(6)(2+) cluster due to the Jahn-Teller effect in A(2)Mg(3)(NO(3))(12).24H(2)O crystals are acquired from the calculations. The results are discussed.

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.

Investigations of the spin-Hamiltonian parameters for Er3+ions in AlN crystal

The spin-Hamiltonian parameters (g factor g //, g ⊥ and hyperfine structure constants A //, A ⊥) for Er3+ ion at the trigonal Al3+ site of AlN crystal are calculated by diagonalising the 52 × 52 energy matrix. The matrix are related to the ground mutiplet 4I15/2 and the first to third excited multiplets 4I13/2, 4I11/2 and 4I9/2 for 4f11 ions in trigonal crystal field under an external magnetic field. The crystal-field parameters used in the matrix are obtained from the superposition model and the local lattice relaxation due to the substitution of Er3+ for Al3+ is considered. The calculated spin-Hamiltonian parameters are in reasonable agreement with the experimental values and the signs of hyperfine structure constants are suggested. The results are discussed.

A study of the spin-Hamiltonian parameters for the trigonal Sm3+ center in La2Mg3(NO3)12·24H2O crystal

This paper reports a theoretical calculation of spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants 147A//, 147A⊥, 149A//, 149A⊥) for 147Sm3+ and 149Sm3+ isotopes in the trigonal La3+ site of La2Mg3(NO3)(12)·24H2O crystal from a diagonalization (of energy matrix) method. In the method, the Hamiltonian concerning the energy matrix includes the Zeeman and hyperfine interaction terms and so there is no perturbation calculation in it. The crystal-field parameters in the energy matrix are calculated using the superposition model, in which the structural data of 12-fold coordinated site rather than those of the incorrect 6-fold coordinated site given in the previous paper are applied. The calculated results are in reasonable agreement with the experimental results. The results are discussed.

Studies of the spin-Hamiltonian parameters and defect structures for Gd3+ ions in zircon-structure silicates MSiO4 (M = Zr, Hf, Th)

The spin-Hamiltonian parameters (g factors g∥, g⊥ and zero-field splittings b2(0), b4(0), b4(4), b6(0), b6(4)) for 4f7 ion Gd3+ at the tetragonal M4+ site of zircon-structure silicates MSiO4 (M=Zr, Hf, Th) are calculated from a diagonalization (of energy matrix) method. The Hamiltonian concerning this energy matrix contains the free-ion, crystal-field interaction and Zeeman interaction terms and the 56×56 energy matrix is constructed by considering the ground multiplet 8S7/2 and the excited multiplets 6L7/2 (L=P, D, F, G, H, I). The defect structures of Gd3+ centers in the three MSiO4 crystals are yielded from the calculation. The results are discussed.

Spin-Hamiltonian parameters and defect structure for the rhombic Dy3+ center in AgCl crystal.

Based on the defect model that the rhombic Dy(3+) center in AgCl crystal is formed by substitutional Dy3+ ion associated with two nearest Ag+ vacancies (VAg) along the <110> and <110> axes owing to charge compensation, the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants 161Ai and 163Ai, where i=x, y, z) of this rhombic Dy3+ center are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman (or magnetic) and hyperfine interaction terms are attached to the classical Hamiltonian used in the calculation of crystal-field energy levels and a 66×66 energy matrix concerning this Hamiltonian is constructed by taking all the ground-term multiplets 6HJ (J=15/2, 13/2, 11/2, 9/2, 7/2, 5/2) into account. The calculated results (g factors gi and average |A(161Dy3+)| and |A(163Dy3+)|) are in reasonable agreement with the experimental values. From the calculations, the above defect model of rhombic Dy3+ center is confirmed, the defect structure of this Dy3+ center (characterized by the displacement of Cl- ligand caused by VAg) is obtained and the components of hyperfine structure constants Ai(161Dy3+) and Ai(163Dy3+) are predicted. The results are discussed.

Studies of the EPR parameters and defect models for three Er3+ impurity centers in ThO2 crystals.

The electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants of the ground state, and g factors of the first excited state) of three (one cubic and two trigonal) Er(3+) centers in fluoride-type ThO(2) crystal are studied from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are added to the classical Hamiltonian, and a 52 x 52 energy matrix concerning the ground multiplet (4)I(15/2) and the first to third excited multiplets (4)I(13/2), (4)I(11/2) and (4)I(9/2) is established for a 4f(11) ion in trigonal crystal field and under an external magnetic field. From the studies, the EPR parameters for three Er(3+) centers in ThO(2) are reasonably explained, the defect models for the two trigonal Er(3+) centers suggested in the previous paper are confirmed and the defect structures of the two trigonal centers are obtained. The results are discussed.

STUDIES OF THE SPIN-HAMILTONIAN PARAMETERS AND OPTICAL SPECTRUM BAND POSITIONS FOR THE Yb(3+) ION IN Tm(3)Al(5)O(12) CRYSTALS

The spin-Hamiltonian parameters (g factors g(i) and hyperfine structure constants A(i), where i = x, y, z) and optical spectrum band positions of the Yb(3+) ion in the rhombically-distorted Tm(3+) site of Tm(3)Al(5)O(12) garnet crystal are calculated by a complete diagonalization (of the energy matrix) method, in which the Zeeman and hyperfine interaction terms are also included in the conventional Hamiltonian. From the calculations, the observed spin-Hamiltonian parameters of Tm(3)Al(5)O(12):Yb(3+) are explained reasonably and the optical spectrum band positions are suggested. The rationality of these suggested optical spectrum band positions is discussed by comparing them with the observed values of Yb(3+) ions in similar aluminum garnet (Yb(3)Al(5)O(12), Y(3)Al(5)O(12) and Lu(3)Al(5)O(12)) crystal.