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

Abstract

A FORTRAN package based on the microscopic spin Hamiltonian expressions derived by computer algebra (ALTRAN) for the high spin ( S = 2) 3 d 4 and 3 d 6 ions with an orbital singlet ground state at orthorhombic (point groups: C 2 v , D 2, D 2 h ) and tetragonal (point groups: C 4 v , D 4, D 4 h , D 2 d) symmetry sites is presented. The spin—orbit (λ) and the spin—spin ( ρ) coupling contributions up to the fourth-order perturbation theory are taken into account within the 5 D approximation. The package enables efficient numerical calculations of the Zeeman electronic (Ze) parameters and the zero-field splitting (ZFS) parameters for the S = 2 3 d 4 and 3 d 6 ions. The following terms are included: λ and λ 2 for the Ze parameters, λ 2 , λ 3 λ 4 , ρ, ρ 2 and λ 2ρ for the second-rank ZFS ones, and λ 4 , ρ 2 and λ 2ρ for the fourth-rank ZFS ones. The program is applicable to all possible energy level schemes with a ground orbital singlet arising from the 5 D 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 k q and b k q , as well as the conventional notation ( D, E; a, F, K), is provided.