Possible presence of a charge-orbital density wave in layered manganites Nd_1-xCa_1+xMnO₄

We have studied the structural modifications related to the charge-orbital ordering for single-layered manganites Nd_1-xCa_1+xMnO₄ with both commensurate and incommensurate doping levels (0.55≦x≦0.75). High-resolution electron microscopy (HREM) revealed transverse and sinusoidal structural modulations with a doping-level-dependent period of d_s=a/(1-x) in the charge-orbital ordered phases. We discuss the possibility of an orbital-density wave as well as a charge-density wave based on the HREM observation of the single-layered manganites.