Optimal T-C in layered manganites: Different roles of coherent and incoherent lattice distortions

Neutron powder diffraction experiments on layered manganites La2-2xSr1+2xMn 2O7 (0.32 less than or equal to x less than or equal to 0.40) show that coh erent lattice anomalies observed at the Curie temperature (lattice paramete rs, Mn-O bond lengths) reverse sign at x approximate to 0.36, coinciding wi th the maximum T-C approximate to 131 K. Remarkably, the anomalies are comp letely suppressed at this crossover composition. Incoherent distortions, as measured by anisotropic Debye-Waller factors, undergo an abrupt decrease b elow T-C. The magnitude of this anomaly changes very little with x and does not display any sign reversal for x approximate to 0.36.