Polar phonons and spin excitations coupling in multiferroic ${\text{BiFeO}}_3$ crystals

Raman scattering measurements on ${\text{BiFeO}}_3$ single crystals show an important coupling between the magnetic order and lattice vibrations. The temperature evolution of phonons shows that the lowest energy $E$ and $A_1$ phonon modes are coupled to the spin order up to the Néel temperature. Furthermore, low temperature anomalies associated with the spin reorientation are observed simultaneously in both the $E$ phonon and the magnon. These results suggest that magnetostriction plays an important role in ${\text{BiFeO}}_3$.

Figure 1

(Color online) (a) Structure of the pseudocubic ${\text{BiFeO}}_3$ unit cell showing parallel and crossed polarizations geometries in the (010) plane; (b) parallel polarization Raman showing the spectra of the ${\psi }_2$, ${\varphi }_3$, and ${\psi }_4$ magnons; (c) crossed polarization measurements showing the ${\psi }_3$ magnon; (d) the lowest phonon mode at $75{\text{cm}}^{-1}$ measured under crossed polarization.

Figure 2

(Color online) (a) Cycloidal order showing $\varphi$ modes (orange ellipses) corresponding to vibrations along the tangent vector which belongs to the $xy$ plane and is perpendicular to each spin and $\psi$ modes (red ellipses) corresponding to ellipses elongated along $y$; the dashed ellipses correspond to the projection of the vibration modes in the $\left(xy\right)$ plane (b) Temperature evolution of the frequency of ${\psi }_2$ (square), ${\varphi }_3$ (circle), ${\psi }_3$ (triangle), and ${\psi }_4$ (star) magnon modes. Normalized intensity to the maximum intensity versus temperature for the (c) ${\psi }_2$, (d) ${\varphi }_3$, (e) ${\psi }_3$, and (f) ${\psi }_4$ modes. The arrows show the anomalies discussed in the text.

Figure 3

Temperature dependence of (a) the frequency and (b) the normalized intensity to the maximum intensity of the lowest phonon mode (diamond). The temperature evolution of the typical phonon mode at $353{\text{cm}}^{-1}$ (triangle) is also plotted.

Figure 4

High temperature dependence from 300 to 1000 K of the frequencies of the ${\psi }_2$ magnon (square) and the lowest $E$ (diamond) and $A_1$ mode (open star) normalized to their respective values at 10 K. The solid line is given by the ${\left(1-\frac{T}{T^{\ast }}\right)}^{\alpha }$ power law. The dashed line is a guide for the eyes. The short dashed line indicates the location of $T_N$ for our samples. The inset shows the $E$ and $A_1$ zone-center vibrational normal modes.