SPIN-TRIPLET CONTRIBUTION TO ZERO-FIELD SPLITTINGS FOR 3D(4) AND 3D(6) IONS AT TETRAGONAL SITES

The energy levels (EL) and the zero-field-splitting (ZFS) parameters b2(0), b4(0), and b4(4) for a 3d4 and 3d6 ion at tetragonal sites in crystals are considered. Results are presented in the form of useful diagrams depicting the variation of the EL and the ZFS parameters with the crystal-field (CF) parameters. To determine the EL and the ZFS parameters b(k)q, the Hamiltonian matrix including the electrostatic, tetragonal CF, spin-orbit (SO), and spin-spin (SS) interactions as well as Trees' correction is introduced. By separating the cubic CF parameter Dq from the axial parameters B20 and B40', the nature of the tetragonal distortion is related to the crystal structure, and the variation of the EL and the ZFS parameters b(k)q with D(q), B20, and B40' are studied. Numerical calculations of the ZFS parameters are carried out for the Cr2+ ion in GaAs:Cr2+ and CrSO4.5H2O and for the Fe2+ ion in K2FeF4, Cu2FeGeS4, and FeV2O4. The results show that the spin-triplet contributions to the ZFS are important; however, most of previously theoretical study of the ZFS for 3d 4 and 3d 6 ions in crystals were based on the spin quintet 5D approximation. The present results may be of interest to researchers in other fields relating to the fine-structure splitting of the ground state for these ions.