The orbital shapes and charge disproportionations at nominal Mn$^{ 3+}$ and Mn$^{ 4+}$ sites for the charge- and orbital-ordered phases have been studied on half-doped manganites Pr(Sr$_{ 0.1}$Ca$_{ 0.9}$)$_2$Mn$_2$O$_7$ and Eu$_{ 0.5}$Ca$_{ 1.5}$MnO$_4$ with double-layer and single-layer Mn-O networks, respectively, by means of x-ray structural analyses, in comparison with Pr$_{ 0.5}$Ca$_{ 0.5}$MnO$_3$ with the pseudo cubic network. In a single-layer Eu$_{ 0.5}$Ca$_{ 1.5}$MnO$_4$ system, the ($y^2-z^2$)/($z^2-x^2$)-type orbital shape is observed, while the ($3y^2-r^2$)/($3x^2-r^2$)-type orbital shape in a pseudo cubic Pr$_{ 0.5}$Ca$_{ 0.5}$MnO$_3$ system. In a double-layer Pr(Sr$_{ 0.1}$Ca$_{ 0.9}$)$_2$Mn$_2$O$_7$ system, the orbital shape is found to undergo a large change upon thermally induced rotation of orbital stripe. Furthermore, clear charge disproportionation is observed for the pseudo cubic and double-layer systems, while not in the single-layer system. These results indicate that the orbital shape and charge disproportionation are sensitive to the dimension of Mn-O network.
Categories: cond-mat.str-el