Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnO3

We report a resonant x-ray-diffraction study of the magnetoresistant perovskite ${\mathrm{Pr}}_{0.6}{\mathrm{Ca}}_{0.4}{\mathrm{MnO}}_3.$ 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 ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ [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 ${3x}^2-r^2$ or ${3y}^2-r^2$ orbitals partially occupied in an alternating pattern, the other sublattice with the $x^2-y^2$ orbital partially occupied.