Resonant x-ray scattering (RXS) at the Mn $K$ edge has been used to characterize the low temperature ordered phase of ${\mathrm{Bi}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$. Strong resonances were observed for the (030), (050), $(05∕20)$, $(07∕20)$, $\left(4\frac{1}{2}0\right)$, and $\left(3\frac{1}{2}0\right)$ reflections as the photon energy is tuned through the Mn $K$ edge. The reported azimuthal and polarization dependence of the resonant intensities indicates that the low temperature phase is described as a checkerboard ordering of two types of Mn sites with different local geometrical structures. One of the sites is anisotropic, a tetragonal distorted oxygen octahedron and the other one is isotropic, a nearly undistorted oxygen octahedron. The distinction of these two Mn sites is accompanied by a displacement of the Mn atoms transverse to the $b$ axis. We conclude that this checkerboard-ordered pattern is a common ground state in half-doped manganites. Intermediate valence states according to fractional charge segregation were deduced for the two nonequivalent Mn atoms, far from the localized ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Mn}}^{4+}$ ionic species. Hence, the experimental data discard the ionic model of charge and orbital ordering of localized $3d$ (or $3d$-like) states at the Mn site (or the $\mathrm{Mn}{\mathrm{O}}_6$ cluster). We suggest a description of the RXS in terms of band structure effects and lattice dynamics.

• Received 31 May 2005

DOI:https://doi.org/10.1103/PhysRevB.73.205107