Resonant x-ray diffraction of the magnetoresistant perovskite Pr_0.6Ca_0.4MnO₃

We report a resonant x-ray-diffraction study of the magnetoresistant perovskite Pr_0.6Ca_0.4MnO₃. We discuss the spectra measured above and below the semiconductor-insulator transition temperature with the aid of a detailed formal analysis of the energy and polarization dependences of the structure factors and ab initio calculations of the spectra. In the low-temperature insulating phase, we find that inequivalent Mn atoms order in a CE-type pattern and that the crystallographic structure of La_0.5Ca_0.5MnO₃ [Radaelli et al., Phys. Rev. B 55, 3015 (1997)] can also describe this system in detail. Instead, the alternative structure proposed for the so-called Zener-polaron model [Daoud-Aladine et al., Phys. Rev. Lett. 89, 097205 (2002)] is ruled out by crystallographic and spectroscopic evidence. Our analysis supports a model involving orbital ordering. However, we confirm that there is no direct evidence of charge disproportionation in the Mn K-edge resonant spectra. Therefore, we consider a CE-type model in which there are two Mn sublattices, each with partial e_g occupancy. One sublattice consists of Mn atoms with the 3x²-r² or 3y²-r² orbitals partially occupied in an alternating pattern, the other sublattice with the x²-y² orbital partially occupied.