  We report x-ray scattering studies of short-range structural correlations and
diffuse scattering in Nd0.5Sr0.5MnO3. On cooling, this material undergoes a
series of transitions, first from a paramagnetic insulating (PI) to a
ferromagnetic metallic (FM) phase, and then to a charge-ordered (CO) insulating
state. Highly anisotropic structural correlations were found in both the PI and
FM states. The correlations increase with decreasing temperature, reaching a
maximum at the CO transition temperature. Below this temperature, they abruptly
collapsed. Single-polaron diffuse scattering was also observed in both the PI
and FM states suggesting that substantial local lattice distortions are present
in these phases. We argue that our measurements indicate that nanoscale regions
exhibiting layered orbital order exist in the paramagnetic and ferromagnetic
phases of Nd0.5Sr0.5MnO3.
