Rotation of orbital stripes and the consequent charge-polarized state in Pr(Sr$_{,}$Ca)$_{2}$Mn$_{2}$O$_{7}$

Nano-scale self-organization of electrons is ubiquitously observed in correlated-electron systems such as complex oxides of transition metals. The phenomenon of charge ordering (CO) or the formation of charge stripes, as observed for layered-structure cuprates and nickelates, is one such example. Among them, the CO in the manganites is closely tied to the orbital degree of freedom of $3d$ electrons, leading to the staggered orbital ordering (OO) or the formation of orbital stripes in the layered structure. Here, we present the phenomena of thermally-induced rotation of the orbital stripes by 90 degrees for bilayered manganite Pr(Sr$_{1-x}$Ca$_{x})_{2}$Mn$_{2}$O$_{7}$(x=0.9) with half hole-doping, i.e., a 1:1 ratio of Mn$^{3+}$/Mn$^{4+}$ [1]. The rotation of orbital stripes and the consequent CO coupled with the underlying lattice distortion were found to produce the charge-polarized state, as also evidenced by its activity of optical second harmonic generation. [1] Y. Tokunaga \textit{et al}., Nature Materials, doi:10.1038/nmat1773 (2006).