Tools for magnetostructural correlations for the 3d8(3A2 state) ions at orthorhombic sites: Comparative study with applications to Ni2+ ions in Y2BaNiO5 and Nd2BaNiO5

Three approaches are employed to study magnetostructural correlations for the 3d8(3A2 state) ions at orthorhombic sites in crystals: (i) the higher-order perturbation theory (PT) of the microscopic spin Hamiltonian (MSH) parameters, (ii) the crystal field (CF) analysis (CFA) within all 3d8 states combined with the superposition model (SPM) calculations of CF parameters, and (iii) the second-order PT of MSH parameters. A comparative study is carried out to assess the merit of each modeling approach. These approaches enable predictions of the orthorhombic zero-field splitting parameters (ZFSPs) for the 3d8 ions at orthorhombic sites. Hence, correlation of the magnetic and spectroscopic properties with the structural ones may be considered. The approach (i) and (iii) take into account only the spin-orbit coupling (SOC) and a limited set of low lying states. Analysis of the expressions used in the approach (i) reveals discrepancies concerning: the sign of the SOC parameter, the cubic crystal field parameter Dq, the energy levels sequence, and numerical errors, which diminish its reliability. The distinction between the first- and second-kind orthorhombic symmetry is also elucidated. The approaches (i)-(iii) are applied for Ni2+ (S=1) ions in the Haldane gap systems Y2BaNiO5 and Nd2BaNiO5. The contributions to the ZFSPs due to the spin-spin and spin-other-orbit interactions considered using the approach (ii) are found nearly insignificant as compared with the dominant SOC ones. The results indicate that the approach (i)-corrected and (iii) may be employed only as an approximation. The approach (ii) together with the SPM/CFP modeling appear to be preferable and more reliable tools to study magnetostructural correlations and thus spectroscopic and magnetic properties of the 3d8(3A2 state) ions at orthorhombic sites in crystals.