Infrared study of the phonon modes in PrMnO$_3$ and CaMnO$_3$

The infrared (IR) reflectivity spectra of orthorhombic manganese perovskites PrMnO$_3$ and CaMnO$_3$ are studied in the frequency range of optical phonon modes at temperatures varying from 300 to 4 K. The IR phonon spectra of these two materials are analyzed by a fitting procedure based on a Lorentz model, and assigned to definite vibrational modes of $Pnma$ structures by comparison with the results of lattice dynamical calculations. The calculations have been performed in the framework of a shell model using short range Born-Mayer-Buckingham and long range Coulomb potentials, whose parameters have been optimized in order that the calculated Raman and IR active phonon frequencies, and lattice parameters match with their experimental values. We find a close correspondence between the values of the IR phonon frequencies of PrMnO$_3$ and CaMnO$_3$, which shows that the substitution of the Pr$^{3+}$ ions with Ca$^{2+}$ results in a reduction of the frequency of medium- and high-energy IR phonons, and an increase of the frequency of those of low-energy. Nevertheless, the experimentally obtained IR phonon amplitudes of the two materials appear to be unrelated. A comparative study of the vibrational patterns of these modes reveals that most of them correspond to complex atomic vibrations significantly different from PrMnO$_3$ to CaMnO$_3$ which cannot be assigned only to a given type of vibration (external, bending, or stretching modes). In particular, these results confirm that the structure of CaMnO$_3$ is quite far from the ideal (cubic) perovskite structure.