NdBaFe2O5+w and steric effect of Nd on valence mixing and ordering of Fe

NdBaFe₂O₅ above and below Verwey transition is studied by synchrotron X-ray powder diffraction and Mössbauer spectroscopy and compared with GdBaFe₂O₅ that adopts a higher-symmetry charge-ordered structure typical of the Sm-Ho variants of the title phase. Differences are investigated by Mössbauer spectroscopy accounting for iron valence states at their local magnetic and ionic environments. In the charge-ordered state, the orientation of the electric-field gradient (EFG) versus the internal magnetic field (B) agrees with experiment only when contribution from charges of the ordered d_xz orbitals of Fe²⁺ is included, proving thus the orbital ordering. The EFG magnitude indicates that only some 60% of the orbital order occurring in the Sm-Ho variants is achieved in NdBaFe₂O₅. The consequent diminishing of the orbit contribution (of opposite sign) to the field B at the Fe²⁺ nucleus explains why B is larger than for the Sm-Ho variants. The decreased orbital ordering in NdBaFe₂O₅ causes a corresponding decrease in charge ordering, which is achieved by decreasing both the amount of the charge-ordered iron states in the sample and their fractional valence separation as seen by the Mössbauer isomer shift. The charge ordering in NdBaFe₂O_5+w is more easily suppressed by the oxygen nonstoichiometry (w) than in the Sm-Ho variants. Also the valence mixing into Fe^2.5+ is destabilized by the large size of Nd. The orientation of the EFG around this valence-mixed iron can only be accounted for when the valence-mixing electron is included in the electrostatic ligand field. This proves that the valence mixing occurs between the two iron atoms facing each other across the structural plane of the rare-earth atoms.