Modeling hyperfine parameters observed from the charge-ordered to valence-mixed state of NdBaFe₂O₅

Orbital populations of the minority-spin Fe ²⁺ electron in NdBaFe₂O₅ are extracted from electric and magnetic hyperfine parameters of ⁵⁷Fe Mössbauer spectra across the temperature interval where charge ordering of the valence state 2.5+ of iron occurs. The previously used approach that assigns the minority-spin population to a single lowest-energy d orbital is expanded to three orbitals by setting up a system of equations in terms of the Fe²⁺/Fe³⁺ balance from isomer shift, a point-charge model for the valence and ligand contributions to the electric-field gradient, a point-dipole model for the dipolar contribution and an iterative scheme for small orbital contributions to the internal magnetic field. This allows us to model the hyperfine fields (electric and magnetic) in the intermediate temperature range of partial charge ordering between T_V=210K and T_p=285K, for which the one-orbital model was insufficient.