image: Valence mixing and charge ordering are two separate cooperative phenomena

Mixed-valence image exhibits a robust Verwey-type transition. The trend in the volume change suggests a first-order transition up to the nonstoichiometry level of about image. 57Fe Mössbauer spectroscopy, differential scanning calorimetry and synchrotron X-ray powder diffraction are used to study the valence mixing and charge ordering in image as a function of the nonstoichiometry parameter w. 151Eu Mössbauer spectroscopy is used as a selective probe into the ferromagnetic valence-mixing coupling along c above the Verwey transition, and reveals that increasing w destroys this coupling in favor of a G-type magnetic order in parallel with the progressive removal of the valence-mixed iron states accounted for by 57Fe Mössbauer spectroscopy. This removal proceeds according to a probability scheme of mixing between ferromagnetically coupled divalent and trivalent neighbor iron atoms along c across the R layer. In contrast, the concentration decrease of the orbital- and charge-ordered states in image is found to be a linear function of w. Valence mixing and charge ordering are therefore two separate cooperative phenomena. The enthalpy of the Verwey-type transition between these two cooperative systems is a linear function of w, which suggests that it originates from the latent heat of freezing into the long-range ordered orbital- and charge-ordered state. The enthalpy becomes zero at the nonstoichiometry level of about image.