Orbital and charge ordering in La_{1-cursive greek chi}Sr_{1+cursive greek chi}MnO₄ (0.4 ≤ cursive greek chi ≤ 0.5)

Hole concentration dependence of charge order (CO) and orbital order (OO) in layered perovskite compounds La_{1-cursive Greek chi}Sr_{1+cursive Greek chi}MnO₄ has been studied by means of the resonant X-ray scattering technique. Both CO and OO are observed below 210K in the compounds having the hole concentration cursive Greek chi between 0.5 and 0.48, but neither is observed for cursive Greek chi ≤ 0.46. The transition temperatures are nearly independent of cursive Greek chi between 0.5 and 0.48. Correlation lengths ξ's for both orders obtained from analyses of superlattice peak profiles are finite at any temperature. Moreover, in contrast to the cubic perovskite, ξ for OO is larger than that for CO, ξ for OO is as short as that for CO at the critical concentration of cursive Greek chi = 0.48. These results suggest that OO is prerequisite to the forming of CO in this system.