Theoretical Investigations Of Zero-field Splitting Parameters And Local Structure Of D～4 (Cr～(2+)) Ion In Tetragonal Field

The crystals doped with transition metal ions are extensively applied as optoelectronic and nonlinear optical materials, because they have special optical, magnetic and electric properties. As is known, the local structure of the doped crystal will have a distortion, because there are differences in the radii or charges between the impurity ions and the host ions. The optical, magnetic, electric and electron paramagnetic resonance (EPR) spectrum are very closely related to the local structure. Especially, the EPR zero field splitting (ZFS) parameters are very sensitive to the local structure distortion, so the local structure can be studied by analyzing the experimental zero field splitting parameters. These studies are very significant for understanding the interaction between impurity ions and host crystals and realizing the doped microscopic mechanism. Furthermore, it may be helpful to material designers.The systems of the d⁴ ions have larger ZFS values, so there are no EPR signals in the conventional EPR experiments. In recent years, the EPR studies of d⁴ ions become feasible because of the advances in the HF-EPR technology. In the previous theoretical works, the calculations are not complete because the contributions of the spin singlets are not considered. If the spin singlets are neglected, the important spin transitions can not be studied. So, for the complete calculation, all spin states should be considered. Thus, it will be very difficult to construct the complete energy matrix, because the Hamiltonian matrix has a dimension of 210 if including all the spin states. Considering this, we do the following works:(1) The concept of the standard basis adapted to the double group chain presented by Zhou Kang-Wei is adopted. This concept emphasizes the standardization of the basis of the whole d^N configuration space. From this, the basis functions can be constructed for each irreducible representation of the double group and each basis function has certain expression. Each standard basis adapted to the double group chain can be got from the former by a linear transformation, which forms a basis chain. Thus, it will be convenient to construct the complete energy matrix by the wave-function and operator methods in this standard basis chain.(2) We successfully constructed the complete energy matrix of d⁴ ions in tetragonal field by the UCFC (Unified Crystal Field Coupling) scheme crystal field method suggested by Zhou Kang-Wei. The Hamiltonian matrix with respect of the corresponding basis functions will become a block diagonal form. Especially, as for the lower symmetry field, its energy matrix can be easily constructed from the cubic field matrix. Each matrix block of the cubic matrix can be directly added into the matrix of the lower symmetry field, thus the cubic component needs not to be calculated. The electrostatic component forms a block diagonal matrix in the cubic standard basis. In each block, the matrix elements are just the same as the electrostatic matrix in the tables of Griffith's book. The matrix of the cubic crystal field will be fully diagonal and the diagonal elements can be easily obtained. UCFC method is not only a complete calculation method considering all multiplets, but also a unified, standardization and terse theoretical method system. It overcomes the limitations of the traditional strong field method, weak field method, and needs not to distinguish the crystal field strength, thus can be applied to arbitrary transition metal complexes in principle. With this standard basis and matrix, it is very convenient to assign energy levels, analyze d-d transition probability, elucidate the influence of the spin multiplets and symmetry on spectrum data and track down the subjection relationship of the energy states by the group chain.(3) The contributions of the spin singlets to zero field splitting are investigated for the first time with the above matrix. Our calculations show that the contributions of spin singlets to the zero field splitting parameters a and P are so large that neglecting this contribution one cannot obtain more accurate values of zero field splitting parameters. The contributions arise from the interaction of the spin quintuplets with both spin triplets and spin singlets via spin-orbit coupling. However, the selection rule of spin-orbit coupling shows that the spin singlets do not affect the quintuplets directly but indirectly via the spin triplets.(4) The local structure of ZnS:Cr²⁺ Jahn-Teller system is studied by diagonalizing the complete matrix. By analyzing the experimental zero field splitting parameters, the local structure parameters are obtained. The results show that the local structure of ZnS:Cr²⁺ system has an expansion distortion. The expansion distortion may be ascribed to the fact that the radius of Cr²⁺ is bigger than that of Zn²⁺. Thus, the Cr²⁺ will push the ligands outward when it is doped into the crystal. ZnS:Cr²⁺ system undergoes a static Jahn-Teller distortion, then we obtain the Jahn-Teller energy which is in good agreement with the experiments.(5) The substitution position and the local lattice structure of CdGa₂S₄:Cr²⁺ system are investigated on the basis of the complete energy matrix. There are two tetrahedrally coordinated cation positions in the crystal and they both show D_2d symmetry. Therefore, the problem of determining the position of Cr²⁺ becomes quite important. By computing the zero field splitting parameters at different positions, we can determine the substitution position. Our results show that the Cd²⁺ site is the only subgtitutional position for Cr²⁺. From our calculations, the lattice structure parameters of this system are also determined. It has a compression distortion, which may be ascribed to the fact that the radius of Cr²⁺ is smaller than that of Cd²⁺ and the Cr²⁺ ion will pull the ligands inward.