Optic phonon anomaly as a precursor to polaron formation in a layered CMR manganite.

We found evidence of a precursor effect to polaron formation in the bond stretching phonons in the bilayer CMR manganite La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ at 10K. Inelastic neutron scattering measurements of these phonons in the XX0 direction show that both the transverse and longitudinal branches broaden abruptly from X=0.15, where they are resolution limited, to X=0.25 where FWHM=13meV. They then narrow again on approach to the zone boundary (X=0.5). The shell model predicts a downward dispersion following the cosine function for the transverse branch and upward dispersion for the longitudinal branch, which is exactly what is observed in undoped cuprates. But in La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ both branches show a steep downward dispersion above x=0.15. The anomalous dispersion and broadening can be understood as a precursor effect to the CMR transition at 125K because they appear at the same wavevectors as the polaron peaks in the same compound observed above 125K near q=(0.27,0.27,0). This behavior is very unusual, because such precursor effects have previously been associated with phase transitions where charge order appears on cooling, not on heating as in CMR manganites.