Hole stripe and orbital fluctuating state in LaMnO$_{3+\delta}$ ($0.085\leq \delta\leq0.125$) unveiled by Raman spectroscopy

Giant softening by 30 cm$^{-1}$ of the 490- and 620-cm$^{-1}$ modes is observed by Raman scattering measurements below the Curie temperature of single crystalline LaMnO$_{3+\delta}$ ($0.085\leq \delta\leq0.125$). A pseudogap-like electronic continuum and a Fano antiresonance at 144 cm$^{-1}$ appear below the charge ordering temperature. This gives evidence for the presence of an orbital fluctuating state and the formation of a hole stripe, respectively. This is further corroborated by a unstructured broadening and shifting of multiphonon features with increasing doping $\delta$. Our study suggests the significance of double exchange mechanism in the charged ordered insulating state.