Possible Observation of Cycloidal Electromagnons in ${\mathrm{BiFeO}}_3$

We unravel the magnon spectra of ${\mathrm{BiFeO}}_3$ by means of low-energy inelastic light scattering. We show the existence of two species of magnons corresponding to spin wave excitations in and out of the cycloidal plane. These excitations might be interpreted as electromagnon modes. The present observations present an unique opportunity to study the competition between ferroelectric and magnetic orders.

Figure 1

(a) Structure of the pseudocubic ${\mathrm{BiFeO}}_3$ unit cell. Only the Bi atoms are displayed for more clarity. The spontaneous polarization $P$ is along the [111] direction, and the spiral magnet propagation defined by the wave vector $q$ is along the [$10\overline{1}$] direction. (b) These two directions define the ($\overline{1}2\overline{1}$) cycloidal plane where the spin rotation occurs. (c) Parallel ($\parallel$) and crossed polarizations ($\perp$) are in the (010) plane and can be defined with respect to the $q$ wave vector. However, the exact direction of the [$10\overline{1}$] axis in the (010) plane is not directly accessible, and thus the direction of the electrical fields in the parallel polarizations configuration is either perpendicular or parallel to the wave vector $q$.

Figure 2

Raman spectra of spin excitations in ${\mathrm{BiFeO}}_3$ in sample $A$. The equally and nonequally spaced modes at low frequencies correspond, respectively, to $\Psi$ and $\Phi$ cycloidal modes selected using parallel ($\parallel$) and crossed ($\perp$) polarizations as defined in Fig. 1. The inset shows the superposition of the $\Psi$ and $\Phi$ cycloidal modes measured under the same experimental conditions on sample $B$. The $\Psi$ series is shifted to higher energy in comparison with the $\Phi$ one. We can see that the ${\Psi }_0$ and ${\Phi }_1$ mode energies are distinct.

Figure 3

$\Phi$ (squares) and $\Psi$ (circles) mode frequencies of sample $A$ as a function of the mode index $n$. The sample $B$ modes are included in the error bars. The energies of the $\Phi$ and $\Psi$ series fit quite well with the calculated cyclon [$E_c(n)$] and extra-cyclon [$E_{\mathrm{exc}}(n)$] energy levels by taking a cyclon energy of ${ϵ}_c(q)=7.5\pm 0.2{\mathrm{cm}}^{-1}$.

Figure 4

(a) Normalized Raman intensity of $\Phi$ (squares) and $\Psi$ (circles) magnon modes (sample $A$) by the most intense peak (${\Psi }_3$) as a function of the mode index. (b) Temperature dependence of the four magnon energies (${\Psi }_2$, ${\Phi }_2$, ${\Phi }_4$, and ${\Psi }_4$) and of one typical optical phonon mode. The decreasing slope of the magnon wave number presents a anomaly around 140 K. (c) Normalized intensity of the magnon and phonon excitation. The magnon intensity exhibits a maximum at 140 K unlike the phonon mode.