Lattice displacements above $T_C$ in the layered manganite ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_2{\mathrm{O}}_7$

Neutron-diffraction data presented in this paper demonstrate the relevance of lattice displacement above $T_C,$ in our understanding of the evolution of the crystal structure with temperature in the layered colossal magnetoresistance manganite ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_2{\mathrm{O}}_7.$ The anomalous temperature behavior of thermal diffuse scattering in ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_2{\mathrm{O}}_7$ strongly suggests that it arises from lattice displacements and correlates directly with anomalies in the displacement parameters of the O and Mn atoms and the Mn-O bond lengths. From our measurements, the insulator-metal transition can be described as a transition from a high-temperature state with disordered Mn-O bond lengths to a low-temperature state with a more uniform distribution on Mn-O bonds. These observations are in agreement with polaronic charge transport above $T_C$ in the perovskite manganites; as electron hopping is responsible for bond disorder above $T_C,$ below the transition where $e_g$ carriers are delocalized, any lattice displacements are uniformly averaged.