CRYSTAL FIELD AND EPR ANALYSIS FOR D-5 (3D(4) AND 3D(6)) IONS AT TETRAGONAL SITES - APPLICATIONS TO FE2+ IONS IN MINERALS AND CR2+ IMPURITIES IN SEMICONDUCTORS

摘要

Two methods for calculating the energy levels arising from the D-5 multiplet and the zero-held splitting (ZFS) parameters for the ground orbital singlet of a 3d(4) or 3d(6) 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 R(2) is the in-plane and R(1) is the out-of-plane ligand distance), which accounts for the elongation or compression of a perfect octahedron, with the tetragonal crystal held parameters B-2(0), B-4(0) and B-4(4). By separating the cubic (Dq) component and the axial one (B-2(0)) 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 b(k)(q). The matrix of Hamiltonian, which includes the tetragonal CF, spin-orbit (lambda) and spin-spin (rho) coupling, is obtained and its eigenvalues are related to b(k)(q)'s. The results of the MD method are compared for a wide range of values of B-2(0), Dq and r with those obtained from the microscopic spin Hamiltonian (MSH) theory developed earlier within the D-5 approximation. The following contributions are taken into account in the MSH expressions: lambda(2), lambda(3), lambda(4), rho, rho(2), and lambda rho. 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 b(2)(0), b(4)(0) and b(4)(4) on Dq, B-2(0) 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 b(k)(q) is obtained. [References: 57]