Charge and Lattice Dynamics of Ordered State in   La$_{1/2}$Ca$_{1/2}$MnO$_3$: Infrared Reflection Spectroscopy Study
  We report an infrared reflection spectroscopy study of La$_{1/2}$Ca$_{1/2}$MnO$_3$ over a broad frequency range and temperature interval which covers the transitions from the high temperature paramagnetic to ferromagnetic and, upon further cooling, to antiferromagnetic phase. The structural phase transition, accompanied by a ferromagnetic ordering at T$_C$=234 K, leads to enrichment of the phonon spectrum. A charge ordered antiferromagnetic insulating ground state develops below the N\'eel transition temperature T$_N$=163 K. This is evidenced by the formation of charge density waves and opening of a gap with the magnitude of 2$\Delta_0$ = (320 $\pm$ 15) cm$^{-1}$ in the excitation spectrum. Several of the infrared active phonons are found to exhibit anomalous frequency softening. The experimental data suggest coexistence of ferromagnetic and antiferromangetic phases at low temperatures. 
A.P. Litvinchuk, M.N. Iliev, M. Pissas, and C.W. Chu