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Raman study of the phonon symmetries in BiFeO$_3$ single crystals

In bismuth ferrite (BiFeO3), antiferromagnetic and ferroelectric order coexist at room temperature, making it of particular interest for studying magnetoelectric coupling. The mutual control of magnetic and electric properties is very useful for a wide variety of applications. This has led to an enormous amount of research into the properties of BiFeO$_3$. Nonetheless, one of the most fundamental aspects of this material, namely the symmetries of the lattice vibrations, remains controversial.We present a comprehensive Raman study of BiFeO$_3$ single crystals with the approach of monitoring the Raman spectra while rotating the polarization direction of the excitation laser. Our method results in unambiguous assignment of the phonon symmetries and explains the origin of the controversy in the literature. Furthermore, it provides access to the Raman tensor elements enabling direct comparison with theoretical calculations. Hence, this allows the study of symmetry breaking and coupling mechanisms in a wide range of complex materials and may lead to a noninvasive, all-optical method to determine the orientation and magnitude of the ferroelectric polarization.