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In bismuth ferrite (BiFeO3), antiferromagnetic and ferroelectric ordercoexist at room temperature, making it of particular interest for studyingmagnetoelectric coupling. The mutual control of magnetic and electricproperties is very useful for a wide variety of applications. This has led toan enormous amount of research into the properties of BiFeO$_3$. Nonetheless,one of the most fundamental aspects of this material, namely the symmetries ofthe lattice vibrations, remains controversial.We present a comprehensive Ramanstudy of BiFeO$_3$ single crystals with the approach of monitoring the Ramanspectra while rotating the polarization direction of the excitation laser. Ourmethod results in unambiguous assignment of the phonon symmetries and explainsthe origin of the controversy in the literature. Furthermore, it providesaccess to the Raman tensor elements enabling direct comparison with theoreticalcalculations. Hence, this allows the study of symmetry breaking and couplingmechanisms in a wide range of complex materials and may lead to a noninvasive,all-optical method to determine the orientation and magnitude of theferroelectric polarization.

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