Temperature-dependent Raman spectroscopy of multiferroic TbMn$_2$O$_5$

Multiferroic materials that display coupling between order parameters, \textit{e.g.}, magnetic and dielectric, stimulate fundamental interest and provide the potential for applications in novel multifunctional devices. The multiferroic manganite TbMn$_2$O$_5$ exhibits non-collinear magnetic order and a strong magnetoelectric coupling effect. The recent observation\footnote{R. Vald\'{e}s Aguilar \textit{et al.}, Phys. Rev. B \textbf{74}, 184404 (2006).} of infrared (IR) phonon modes correlated with magnetic and dielectric phase transitions suggests a complementary Raman study may provide important information regarding the nature of coupling in these systems. We present Raman measurements of single-crystal TbMn$_2$O$_5$ in a collinear backscattering configuration as a function of temperature ($4-300\,$K) and polarization along various crystallographic axes. Additionally, we compare the temperature dependence of Raman active phonons with the activation of an IR forbidden mode in the low-temperature ferroelectric state.