Lattice-form dependent charge- and orbital- ordered states in perovskite-related mangananites

Charge and orbital order in half-doped manganites has been extensively studied since the magnetic-field induced melting of charge and orbital order (CO-OO) results in colossal magnetoresistance phenomena. However, there remain two points to be clarified, concerning the CO-OO states. First issue is the degree of charge disproportionation (CD); Full CD between Mn$^{3+}$ and Mn$^{4+}$ ions has been widely believed while charge density wave ordering with less distinct CD has also been recently proposed. Another issue is the orbital shape (OS) at Mn$^{3+}$ ion in the CO-OO phase. The reason why the OSs of (La,Ca)MnO$_3$ ((3y$^2$-r$^2$)/(3$x^2$-r$^2$)) and (La,Sr)$_2$MnO$_4$ ((y$^2$-z$^2$)/(z$^2$-x$^2$)) are different is not clarified. In our study, we tried to clarify the CDs and OSs in (Eu,Ca)$_2$MnO$_4$ and (Pr,Sr,Ca)$_3$Mn$_2$O$_7$ by means of x-ray crystal structural analyses and well established methods of bond valence sum and Kanamori diagram, and to compare with those of (Pr,Ca)MnO$_3$. We found that the CD of all the samples is much smaller than unity. In addition, the CDs and OSs are systematically dependent on the dimension of MnO$_6$ network. From simple consideration, we concluded that apical oxygens play an important role.