Visualization of charge ordering in a half-doped manganite by an electrostatic potential analysis

We have experimentally investigated the charge density distribution and the electrostatic potential for a charge-ordering doped manganite, Nd1/2 Sr1/2 MnO3. In the charge-ordered state, we observed a zigzag pattern of the charge density within the (010) plane. Judging from the MnO6 distortion, we ascribed the pattern to the bonding electron in the px(y) - d x2 - y2 hybridized state, not to the so-called d3 x2 - r2/d3 y2 - r2 orbital ordering. We further calculated the electrostatic potential U(r) from the charge density and the atomic positions, which clearly indicates the checkerboard-type charge disproportionation within the (010) plane.