Magnetic transitions in two novel mixed-valence iron(II)–iron(III) metal formate frameworks: Two sublattice model

We study the two-sublattice model in the mean field theory by expanding the Gibbs free energy in terms of the magnetizations M1 (Mup) and M2 (Mdown) with the quadratic coupling M12M22 (quadrupolar interactions) for the order–disorder transition in the two mixed-valence iron (II)-iron (III) metal formate frameworks, C2H5NH3FeIIFeIIIHCOO6 and C2H52NH2FeIIFeIIIHCOO6. Expressions derived from the Gibbs free energy for the temperature dependence of the magnetizations M1 and M2, are fitted to the observed data (H=100Oe) from the literature for the two mixed-valence iron (II) – iron (III) system. The inverse susceptibilities (χ1-1 and χ2-1) are predicted as a function of temperature (H=100Oe) from the two-sublattice model. Additionally, the field dependence of the total magnetization (M=M1+M2) is analyzed using the literature data for the compounds studied. We find that the two-sublattice model with the quadrupolar interactions, is satisfactory to describe the order–disorder transition in the two mixed-valence iron (II) – iron (III) metal formate frameworks as studied here. It indicates that the two-sublattice model can also be applied to some other multiferroic mixed materials.