Nanoscale Lattice Fluctuations in Cuprates and Manganites

{Local lattice displacements giving a nanoscale inhomogeneous pattern due to mesoscopic phase separation in the correlated transition metal perovskites play a distinct role for high T c superconductivity (HTcS) in the copper oxides and for colossal magneto resistance (CMR) in manganese oxides. Experimentally the local structure physics of these correlated oxides owes a lot to the extended X-ray absorption fine structure (EXAFS) using polarized synchrotron radiation sources, a local and fast experimental probe that has revealed several key structural aspects. Here we have briefly reviewed some of our studies on the local displacements in the electronically active Cu-O lattice in the copper oxide superconductors and the Mn-O lattice of the manganese oxide CMR and charge ordered systems, exploiting the EXAFS technique. In the copper oxides the determination of polaronic distortions by polarized Cu-K-edge EXAFS has revealed superlattice of distorted stripes intercalated with undistorted stripes with the chemical potential tuned near a shape resonance for the interband scattering in a system with two electronic components that can amplify the critical temperature. On the other hand, the Mn K-edge EXAFS has been applied to underline the importance of the local Mn-O displacements to characterize various phases in the perovskite manganese oxides.}