Variation of charge-ordering transitions in $R_{1/3}{\mathrm{Sr}}_{2/3}{\mathrm{FeO}}_3\hspace{0.5em}(R=\mathrm{La},$ Pr, Nd, Sm, and Gd)

The change of the electronic and magnetic properties as well as the charge-ordering (CO) transition related with lattice dynamics has been systematically investigated for crystals of $R_{1/3}{\mathrm{Sr}}_{2/3}{\mathrm{FeO}}_3\hspace{0.5em}(R=\mathrm{La},$ Pr, Nd, Sm, and Gd) by transmission electron microscopy and measurements of transport, magnetic, and optical properties. In $R_{1/3}{\mathrm{Sr}}_{2/3}{\mathrm{FeO}}_3,$ the hybridization of O $2p$ and Fe $3d$ states, or the effective d electron hopping interaction, can be controlled to some extent by R-dependent lattice distortion. The ${\mathrm{La}}_{1/3}{\mathrm{Sr}}_{2/3}{\mathrm{FeO}}_3$ with least rhombohedral lattice distortion undergoes a CO phase transition with $T_{\mathrm{CO}}=198\mathrm{}\hspace{0.5em}\mathrm{K}$ accompanying charge disproportionation into nominally ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{5+}$ sites, as well as antiferromagnetic spin ordering. When the R-site ion is changed from $R=\mathrm{La}$ to smaller-size R ion towards $R=\mathrm{Gd},$ and hence the $p-d$ hybridization interaction is decreased, $T_{\mathrm{CO}}$ is decreased and finally the CO transition disappears for $R=\mathrm{Sm}$ and Gd. The optical conductivity spectra for the $R=\mathrm{La}$ – Nd compounds show a gap opening below $T_{\mathrm{CO}}$ and several activated phonon modes due to the periodic charge modulation. The spectral intensity of the new phonon modes shows a discontinuous increase at $T_{\mathrm{CO}}$ reflecting the first-order nature of the CO transition. In the cases of the $R=\mathrm{Sm}$ and Gd compounds with no CO transition, the gap feature is observed over a whole temperature region, while no phonon anomaly is discerned. These results imply that the strong $p-d$ hybridization as realized for $R=\mathrm{La},$ Pr, and Nd is necessary for stabilizing the specific valence-skipping charge-ordered state.