Polarons and polaron correlations in 40\% doped bilayer manganite.

Among the compounds exhibiting colossal magnetoresistance, the bilayer manganites, La$_{2-2x}$Sr$_{1+2x}$Mn$_2$O$_7$, where $x$ is the hole doping in the MnO$_2$ layers, are advantageous to study because the reduced dimensionality strongly enhances the spin and charge fluctuations. For the intermediate doping regime ($32\%\le x \le42\%$), the magnetoresistance is strongly enhanced near the combined metal-insulator and ferromagnetic transition. Here, we report on our detailed x-ray scattering investigation of the diffuse scattering associated with lattice distortions around localized charges (polarons) as well as short-ranged polaron correlations present in the paramagnetic phase of the $x=40\%$ doped compound, both collapsing at $T_{\mathrm{C}}=112$~K. We have studied in detail the temperature dependence to high temperatures ($T = 50$~K - 500~K) and are able to directly extract a polaron activation energy from the data.