Structural origin of dipole x-ray resonant scattering in the low-temperature phase of Nd_0.5Sr_0.5MnO₃

We have investigated the low-temperature phase of a Nd_0.5Sr_0.5MnO₃ single crystal by x-ray resonant scattering at the Mn K edge of the (3 0 0), (0 3 0), and (0 5∕2 0) reflections. Strong resonances were observed for the σ–σ^′ channel in the (3 0 0) and (0 3 0) reflections and for the σ–π^′ channel in the (0 5∕2 0) reflection. These resonances show a π periodicity on the azimuthal angle, having the intensity at the minimum position almost zero. The intensity dependence on the photon energy, azimuthal angle and polarization has been analyzed using a semi-empirical structural model. Contrary to previous claims of charge (Mn³⁺-Mn⁴⁺) and orbital ordering in this compound, our results show that the dipole resonant superlattice reflections can be explained by the presence of two types of Mn sites with different local geometric structures. One of the Mn sites is surrounded by a tetragonal-distorted oxygen octahedron, whereas the other site has a nearly regular octahedral environment. This model also shows that no real space-charge ordering is needed to explain the experimental data. Intermediate-valence states according to a fractional charge segregation Mn^+3.42-Mn^+3.58 were deduced.