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Micro-Raman spectroscopy has been used to study lattice dynamics associatedwith the ferroelectric domains of a BiFeO$_3$ single crystal at lowtemperature. The phonon assignment shows a large frequency splitting betweenthe transverse and longitudinal components of the A$_1$ phonon mode related tothe Bi-O bonds in contrast with thin films where the splitting is negligible.Applying an external electric field induces frequency shifts of the low energymodes related to the Bi-O bonds. These softenings are due to a tensile stressvia the piezoelectric effect. We give estimates of the phonon deformationpotentials.

Electric field effect on BiFeO$_3$ single crystal investigated by Raman spectroscopy