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Temperature-Dependent Infrared Reflectivity Studies of Multiferroic TbMnO_{3}: Evidence for Spin-Phonon Coupling

We have measured near normal incidence far infrared (FIR) reflectivity spectra of a single crystal of TbMnO3 from 10K to 300K in the spectral range of 50 cm$^{-1}$ to 700 cm$^{-1}$. Fifteen transverse optic (TO) and longitudinal optic (LO) modes are identified in the imaginary part of the dielectric function $ε_2$($ω$) and energy loss function Im(-1/$ε$($ω$)), respectively. Some of the observed phonon modes show anomalous softening below the magnetic transition temperature T$_N$ (~ 46K). We attribute this anomalous softening to the spin-phonon coupling caused by phonon modulation of the super-exchange integral between the Mn$^{3+}$ spins. The effective charge of oxygen (Z$_O$) calculated using the measured LO-TO splitting increases below T$_N$.