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The orbital shapes and charge disproportionations at nominal Mn$^{3+}$ andMn$^{4+}$ sites for the charge- and orbital-ordered phases have been studied onhalf-doped manganites Pr(Sr$_{0.1}$Ca$_{0.9}$)$_2$Mn$_2$O$_7$ andEu$_{0.5}$Ca$_{1.5}$MnO$_4$ with double-layer and single-layer Mn-O networks,respectively, by means of x-ray structural analyses, in comparison withPr$_{0.5}$Ca$_{0.5}$MnO$_3$ with the pseudo cubic network. In a single-layerEu$_{0.5}$Ca$_{1.5}$MnO$_4$ system, the ($y^2-z^2$)/($z^2-x^2$)-type orbitalshape is observed, while the ($3y^2-r^2$)/($3x^2-r^2$)-type orbital shape in apseudo cubic Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ system. In a double-layerPr(Sr$_{0.1}$Ca$_{0.9}$)$_2$Mn$_2$O$_7$ system, the orbital shape is found toundergo a large change upon thermally induced rotation of orbital stripe.Furthermore, clear charge disproportionation is observed for the pseudo cubicand double-layer systems, while not in the single-layer system. These resultsindicate that the orbital shape and charge disproportionation are sensitive tothe dimension of Mn-O network.

Lattice-form dependent orbital shape and charge disproportionation in charge- and orbital-ordered manganites