Successive coupled charge, magnetic, and structural transitions in Ca$_{0.5}$Bi$_{0.5}$FeO$_{3}$

Stoichiometric Ca$_{0.5}$Bi$_{0.5}$FeO$_{3}$ containing high-valent Fe$^{3.5+}$ adopting the perovskite structure was prepared under a high oxygen pressure and shows two successive phase transitions on cooling at 240 K and 200 K. M{\"o}ssbauer spectroscopy and neutron powder diffraction data indicate that these transitions are associated with charge changes to relieve the instability of Fe$^{3.5+}$.The first transition is due to charge disproportionation of the iron centers while the second is due to intermetallic charge transfer between A-site Bi and B-site Fe. The transitions can be described as:\newline $(Ca^{2+}_{0.5}Bi^{3+}_{0.5})Fe^{3.5+}O_3 \rightarrow (Ca^{2+}_{0.5}Bi^{3+}_{0.5})(Fe^{(3.5-x)+}_{0.67}Fe^{(3.5+2x)+}_{0.33})O_3 \rightarrow \newline (Ca^{2+}_{0.5}Bi^{3+}_{0.25}Bi^{5+}_{0.25})Fe^{3+}O_3$ \newline In the intermediate temperature phase, one third of B-sites (Fe$^{(3.5+2x)+}$) do not contribute to the magnetic scattering while the remaining spins couple antiferromagnetically. The lowest temperature magnetic structure is simple G-type antiferromagnetic resulting from a structure containing only Fe$^{3+}$. Competing intermetallic and disproportionation charge instabilities result in a variety of electronic, magnetic, and structural ground states.