Variation of charge/orbital ordering in layered manganitePr1−xCa1+xMnO4investigated by transmission electron microscopy

Structural features of the charge/orbital ordering $(\mathrm{C}\mathrm{O}∕\mathrm{O}\mathrm{O})$ in single-layered manganites ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_{1+x}\mathrm{Mn}{\mathrm{O}}_4$ $(0.3⩽x⩽0.65)$ have been investigated systematically by transmission electron microscopy. Analyses of electron-diffraction patterns as well as dark-field images have revealed that the $\mathrm{C}\mathrm{O}∕\mathrm{O}\mathrm{O}$ shows a striking asymmetric behavior as the hole doping $x$ deviates from $x=0.5$. The modulation wave number linearly decreases with increasing $x$ in the over-hole-doped $(x>0.5)$ crystals, while much less dependent on $x$ in the under-hole-doped $(x<0.5)$ crystals. A temperature-induced incommensurate-commensurate crossover is observed in $0.35<x<0.5$ and $x=0.65$. The correlation length of $\mathrm{C}\mathrm{O}∕\mathrm{O}\mathrm{O}$ in $x=0.3$ was proven to become shorter than that in $0.35⩽x⩽0.65$