Abstract
Abstract Two methods for calculating the energy levels arising from the 5D multiplet and the zero-field splitting (ZFS) parameters for the ground orbital singlet of a 3d4 or 3d6 ion at tetragonal sites in crystals are considered. A superposition model is used to relate the changes in the structural parameter r = R 1 R 2 (where R2 is the in-plane and R1 is the out-of-plane ligand distance), which accounts for the elongation or compression of a perfect octahedron, with the tetragonal crystal field parameters B20, B40 and B44. By separating the cubic (Dq) component and the axial one (B20) the nature of the tetragonal distortion is related to the crystal structure. A matrix diagonalization (MD) method is used to determine numerically the ZFS parameters bkq. The matrix of Hamiltonian, which includes the tetragonal CF, spin-orbit (λ) and spin-spin (ρ) coupling, is obtained and its eigenvalues are related to bkq's. The results of the MD method are compared for a wide range of values of B20, Dq and r with those obtained from the microscopic spin Hamiltonian (MSH) theory developed earlier within the 5D approximation. The following contributions are taken into account in the MSH expressions: λ2, λ3, λ4, ρ, ρ2, and λρ. The MD and MSH methods together with the superposition model enable study of the variation of the energy levels and ZFS parameters with the crystal field (CF) parameters and the related crystal structure ones. The dependence of the energy levels and ZFS parameters b20, b40 and b44 on Dq, B20 and r resulting from both methods is presented in the form of diagrams. The ranges of validity of the MD and MSH approach are established. Numerical calculations are carried out for Fe2+ ion in the minerals FeSb2S4, BaFeSi4O10 and FeTa2O6 and for Cr2+ impurity in semiconductors CdS, ZnS and ZeSe. Good agreement with experimental data for the ZFS parameters bkq is obtained.
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