Resonant x-ray scattering of the Bi$_{1-x}$Sr$_{x}$MnO$_{3}$ (x$\le $0.5) charge-ordered phases

Charge-orbital ordering (CO-OO) in Bi$_{1-x}$Sr$_{x}$MnO$_{3}$ (x=0.3, 0.5) have been studied by resonant x-ray scattering (RXS) at the Mn K edge. Strong resonances were observed at the Mn K-edge for weak superstructure (h00), (0k0) and forbidden (h/200), (0k/20) reflections with h, k odd within the \textit{ab} plane (\textit{Ibmm} setting) in both single crystals. Additional (hk0) and (hk/20) with k odd have also been studied. The azimuth angle and polarization dependence of the resonant intensity for this set of reflections point out to a structural transition at the T$_{COO}$ that stabilizes an checkerboard ordering of two non-equivalent Mn atoms with different local geometrical structures and a very small charge segregation for both x=0.5 and x=0.3 compounds. We can conclude that A$_{1-x}$B$_{x}$MnO$_{3}$ tends to order in a checkerboard pattern independently of the nature of the A and B atoms and for x even far from 0.5. Furthermore, the electronic states of the two non-equivalent Mn atoms are far from the ionic (+3 and +4) species.