Raman spectroscopy of the charge-orbital ordering in layered manganites

The lattice and electronic response in the course of concomitant charge and orbital-ordering transition has been investigated for single crystals of layered manganites, single-layered ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_4,$ and bilayered ${\mathrm{LaSr}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7,$ by Raman-scattering spectroscopy. In the charge-orbital-ordered state $(T<\mathrm{}217\mathrm{}$ K for ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_4$ and $\sim 100\hspace{0.5em}\mathrm{K}<T<\mathrm{}210\mathrm{}$ K for ${\mathrm{LaSr}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7),$ four phonon modes are activated in the ${\mathrm{MnO}}_2$ plane, indicating the existence of both Jahn-Teller type and breathing mode type lattice distortions. The diffuse scattering response with $B_{1g}$ symmetry is suppressed in the charge-orbital-ordered state, both for ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_4$ and ${\mathrm{LaSr}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7,$ signaling that the fluctuation caused by the dynamical charge-orbital correlation is suppressed in the charge-orbital-ordered state. These features reveal the unique nature of the charge-orbital-ordering transition realized by the complex interplay of charge and orbital degrees of freedom.