Quantitative analysis of the diffuse scattering from a bilayer manganite

Magnetoresistance in manganese oxides is strongly enhanced by the presence of Jahn-Teller polarons and short range correlations between them. While previous investigations have shown the existence of both local lattice distortions and short-range order, a detailed quantitative description of the local structure, how it evolves as a function of temperature and doping, and how it affects the physical properties is still lacking. Here we present a detailed analysis of the diffuse scattering measured over a large range of temperatures from a bilayer manganite exhibiting colossal magnetoresistance. Focusing on the diffuse scattering around a single Bragg Peak and utilizing a point-defect approximation, we are able to derive a complete picture of the detailed temperature dependence of the Jahn-Teller distorted MnO$_6$ octahedra. These results further serve as a first test of the formalism for the quantitative analysis of the diffuse scattering over a large volume of reciprocal space, including both diffuse scattering from local defects close to Bragg Peaks, as well diffuse scattering due to short-range correlations.