Infrared phonon dynamics of a multiferroic Bi Fe O 3 single crystal

We discuss the infrared reflectivity measurement on a $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ single crystal between $5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and room temperature. The nine predicted $ab$-plane $E$ phonon modes are fully and unambiguously determined. The frequencies of the four ${A}_{1}$ $c$-axis phonons are found. These results settle issues between theory and data on ceramics. Our findings show that the softening of the lowest frequency $E$ mode is responsible for the temperature dependence of the dielectric constant, indicating that the ferroelectric transition in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ is soft-mode driven.