Electrodynamics of a multiferroic perovskite manganite in terahertz frequency range*

There is a growing interest for the study of the magnetoelectric effect, as stimulated by the observation of a magnetic control of the ferroelectric polarization in perovskite manganites. Recently, a broad peak structure was observed in TbMnO$_3$ and GdMnO$_3$ in terahertz (THz) frequency range [1]. The spin-wave excitation driven by ac electric field, which is referred to as electromagnon, was proposed as an origin of this structure. However, detailed characteristics, especially, the role of the rare-earth ion and the relationship between the complex dielectric constant $\tilde\epsilon$ in THz and low ($\sim$kHz) frequency range were not clarified yet. Here we used the THz time-domain spectroscopy to directly extract $\tilde\epsilon(\omega)$ (1.2-- 4.5 meV) of a multiferroic perovskite manganite and discuss the origin of the ferroelectricity, as manifested by a gigantic response of the low-frequency $\tilde\epsilon(\omega)$ with temperature and magnetic fields. [1] A. Pimenov {\it et al.}, Nat. Phys. {\bf 2}, 97 (2006).