IR phonons induced by the helical magnetic order in multiferroic TbMn$_2$O$_5$

The interplay between magnetic order and the lattice in multiferroic crystals has produced such interesting phenomena as polarization reversal and change of dielectric properties with magnetic fields \footnote{Hur, N et al. Nature \textbf{429} (2004) 392.}. Ferroelectricity in the multiferroic materials REMn$_{2}$O$_{5}$ (RE = rare earth) is thought to originate from a helical antiferromagnetic order. In order to study this possiblity we have made an infrared study of TbMn$_{2}$O$_{5}$. We find that several IR phonons show correlations with the distinct magnetic and dielectric phase transitions. Of special interest is the phonon spectrum for light polarization along the b axis where a mode at $\sim$ 706 cm$^{-1}$ exists only in the commensurate magnetic phase with \textbf{k} = (1/2,0,1/4) in the temperature range of 24-33 K. Possible scenarios for this phonon are: (1) the appearance of zone-folded modes; (2) the activation of previously silent modes due to the reduction of crystal symmetry. These scenarios are discussed in terms of the spin-lattice coupling in this class of materials.