Magnetostructural correlations for Fe2+ ions at orthorhombic sites in FeCl2·4H2O and FeF2·4H2O crystals modeled by microscopic spin Hamiltonian approach

Abstract

The microscopic spin Hamiltonian (MSH) theory developed up to the fourth-order perturbation theory for 3d4 and 3d6 ions with spin S=2 within the 5D approximation is employed to predict the zero field splitting (ZFS) parameters and the Zeeman electronic (Ze) ones. The SH parameters, measurable by electron magnetic resonance (EMR), are expressed in terms of the microscopic parameters, i.e. the spin–orbit (λ), spin–spin (ρ) coupling constants, and the crystal-field (ligands-field) energy levels (∆i) within the 5D multiplet. The energies, ∆i, are indirectly related with structural data, thus enabling investigation of magnetostructural correlations. As a case study Fe2+ (3d6; S=2) ions at orthorhombic sites in FeCl2·4H2O and FeF2·4H2O crystals are considered. Calculations of the ZFS and Ze parameters are carried out for wide ranges of values of the microscopic parameters using the package MSH/VBA. Dependence of the theoretically determined ZFS parameters bkq (in the Stevens notation) and the Zeeman factors gi on λ, ρ, and ∆i is examined and suitable graphs are presented. The absolute value of dominant ZFS parameter |b20| is predicted to be in the range from nearly 8.5 to 1.4 cm−1. Matching the theoretical SH parameters and the experimental ones enables determination of the suitable values of λ, ρ, and ∆i. The fourth-rank ZFS parameters and the ρ(spin–spin)-related contributions, considered for the first time here, are found important. The MSH predictions may be verified and fine-tuned by high-magnetic field and high-frequency EMR measurements. The method employed here and the present results may be also useful for other structurally related systems.