Computer package for microscopic spin Hamiltonian analysis of the 3d⁴ and 3d⁶ (spin S = 2) ions at orthorhombic and tetragonal symmetry sites

Authors:

• Czesław Zygmunt Rudowicz,
• Yi-Yang Zhou

Abstract

A FORTRAN package based on the microscopic spin Hamiltonian expressions derived by computer algebra (ALTRAN) for the high spin (S = 2) 3d⁴ and 3d⁶ ions with an orbital singlet ground state at orthorhombic (point groups: C_2v, D₂, D_2h) and tetragonal (point groups: C_4v, D₄, D_4h, D_2d) symmetry sites is presented. The spin-orbit (λ) and the spin-spin (p) coupling contributions up to the fourth-order perturbation theory are taken into account within the ⁵D approximation. The package enables efficient numerical calculations of the Zeeman electronic (Ze) parameters and the zero-field splitting (ZFS) parameters for the S = 2 3d⁴ and 3d⁶ ions. The following terms are included: λ and λ² for the Ze parameters, λ², λ³, λ⁴, ρ, p² and λ²ρ for the second-rank ZFS ones, and λ⁴, ρ² and λ²ρ for the fourth-rank ZFS ones. The program is applicable to all possible energy level schemes with a ground orbital singlet arising from the ⁵D multiplet due to orthorhombic or tetragonal symmetry crystal fields. The input parameters are λ, ρ, the energy levels Δ_j (j = 1, 2, 3, 4) and the mixing coefficient s, which can be obtained from other spectroscopic data. The ZFS parameters output in the extended Stevens notation B^q_k and b^q_k, as well as the conventional notation (D, E; a, F, K), is provided. Copyright © 1996 Elsevier Science Ltd.