Neutron inelastic scattering measurements of low-energy phonons in the multiferroic ${\mathrm{BiFeO}}_3$

We present neutron inelastic scattering measurements of the low-energy phonons in single crystal ${\mathrm{BiFeO}}_3$. The dispersions of the three acoustic phonon modes (LA along [100], ${\mathrm{TA}}_1$ along [010], and ${\mathrm{TA}}_2$ along $\left[1\overline{1}0\right])$ and two low-energy optic phonon modes (LO and ${\mathrm{TO}}_1)$ have been mapped out between $300$ and $700\mathrm{K}$. Elastic constants are extracted from the phonon measurements. The energy linewidths of both TA phonons at the zone boundary clearly broaden when the system is warmed toward the magnetic ordering temperature $T_N=640\mathrm{K}$. This suggests that the magnetic order and low-energy lattice dynamics in this multiferroic material are coupled.

Figure 1

The dynamic response function ${\chi }^{\prime \prime }(Q,\hslash \omega )$ of single crystal ${\mathrm{BiFeO}}_3$, at 300 K (top row), 500 K (middle row), and 700 K (bottom row). The intensities are shown in the $\left(HK0\right)$ plane, for $q$ along [100] (left column), $\left[1\overline{1}0\right]$ (middle column), and [010] (right column), respectively. The strong intensities visible near the top of each panel are spurious and occur when $\hslash \omega$ approaches $E_i$. These spurious intensities are temperature independent. They appear stronger at 300 K (top row) because the data have been divided by the Bose factor.

Figure 2

Phonon dispersions measured along various symmetry directions. The phonon energies are obtained from the fits described in the text. Lines are guides to the eye.

Figure 3

Energy cuts at $Q=(1.2,0.8,0)$ (top frame) and $Q=(1.5,0.5,0)$ (bottom frame). Plotted intensities correspond to ${\chi }^{\prime \prime }(Q,\hslash \omega )$ measured at 300 K (black circles), 500 K (blue triangles), and 700 K (red diamonds).

Figure 4

Energy widths $\left(2\Gamma \right)$ of acoustic phonons measured at different $Q$. The dashed line in the figure denotes the Nèel temperature $T_N$.