Raman spectroscopy of the charge- and orbital-ordered state in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$

Polarized Raman spectra from microcrystals of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ were studied as a function of temperature, excitation photon energy, and scattering configuration. At temperatures below the transition from ferromagnetic metallic phase to antiferromagnetic insulating charge- and orbital-ordered (COO) phase, several lines appear in Raman spectra excited with photon energies $ħ{\omega }_L<2.5\mathrm{}\hspace{0.5em}\mathrm{eV}.$ We argue that their appearance signals ordering and freezing of the Jahn-Teller distortions at this transition temperature into a superstructure with a doubled elementary cell. We suggest a simplified structural model based on an analysis of the normal phonon modes in the COO phase, neglecting the octahedral tilts and containing ordered ${\mathrm{Mn}}^{4+}{\mathrm{O}}_6$ (undistorted) and ${\mathrm{Mn}}^{3+}{\mathrm{O}}_6$ (Jahn-Teller distorted) octahedra. The symmetries of the experimentally observed Raman lines are determined by comparing their relative intensities to those predicted by the polarization selection rules for a finely twinned quasicubic crystal. The most intensive Raman lines are assigned to definite normal modes in close comparison with corresponding modes in COO layered manganites and undoped $R{\mathrm{MnO}}_3$ $(R=\mathrm{La},$ Y).