Angular dispersion of oblique phonon modes in ${\mathrm{BiFeO}}_3$ from micro-Raman scattering

The angular dispersion of oblique phonon modes in a multiferroic ${\mathrm{BiFeO}}_3$ has been obtained from a micro-Raman spectroscopic investigation of a coarse grain ceramic sample. Continuity of the measured angular dispersion curves allows conclusive identification of all pure zone-center polar modes. The method employed here to reconstruct the anisotropic crystal property from a large set of independent local measurements on a macroscopically isotropic ceramic sample profits from the considerable dispersion of the oblique modes in ferroelectric perovskites and it can be in principle conveniently applied to any other optically uniaxial ferroelectric material.

Figure 1

Angular phonon dispersion curves of BiFeO${}_3$. Continuous lines are evaluated by diagonalization of the matrix defined in Eq. (1) with TO and LO frequencies (a) taken from DFT data of Ref.23 and (b) adjusted to present Raman data (as explained in the text). Full lines stand for dispersive oblique modes, dashed lines for the purely transverse $E$(TO) branches. Open circles are values of the fitted DHO frequencies from individual Raman spectra as a function of the angle $\varphi$ determined from Eq. (2). Full and open triangles stand for the Raman frequencies from Fig. 1. of Refs. 9 and,10 respectively (1 cm${}^{-1}=29.979$ 245 8 GHz).

Figure 2

Raman spectra from selected grains of the investigated BiFeO${}_3$ ceramics. Top and bottom spectra correspond to grains with their optical axes almost parallel and almost perpendicular to the incident laser beam, respectively. Point symbols indicate positions of the TO and LO frequencies of the pure $A_1$ and $E$ modes.