Origin of Electromagnon Excitations in Multiferroic $R{\mathrm{MnO}}_3$

Electromagnon excitations in multiferroic orthorhombic $R{\mathrm{MnO}}_3$ are shown to result from the Heisenberg coupling between spins despite the fact that the static polarization arises from the much weaker Dzyaloshinskii-Moriya exchange interaction. We present a model incorporating the structural characteristics of this family of manganites that is confirmed by far infrared transmission data as a function of temperature and magnetic field and inelastic neutron scattering results. A deep connection is found between the magnetoelectric dynamics of the spiral phase and the static magnetoelectric coupling in the collinear $E$ phase of this family of manganites.

Figure 1

(a) Zero field absorption spectra in ${\mathrm{TbMnO}}_3$. Main features of the spectra correspond to 2 electromagnon peaks at 25 and $60{\mathrm{cm}}^{-1}$ that activate below $T_{\mathrm{FE}}$ and the lowest infrared active phonon just below $120{\mathrm{cm}}^{-1}$. Additionally, a broad absorption below the phonon persists well above $T_N$. (b) Magnetic field dependence ($\mathbf{H}\parallel b$) of the low temperature spectra. The frequencies of the electromagnons shift in the high field phase, and their intensities increase. (c) Absorption spectrum for the expected polarization of the KBN electromagnon. The new absorption line around $21{\mathrm{cm}}^{-1}$ in the high field phase is magnetic dipole active given that the expected contribution to $\epsilon$ [shown in (d)] is larger than found in the static measurements [18].

Figure 2

One $ab$ layer of the Pbnm unit cell of $R{\mathrm{MnO}}_3$ consisting of 4 Mn ions (blue circles) and 4 oxygen ions (pink circles). The displacements of the oxygen ions from the midpoints of the straight lines (dashed lines) connecting neighboring Mn ions are $\delta r_{1+b,2+a}=(\delta x;\delta y;\delta z)$, $\delta r_{1,2}=(-\delta x;-\delta y;-\delta z)$, $\delta r_{1,2+a}=(-\delta x;\delta y;\delta z)$, and $\delta r_{1+b,2}=(\delta x;-\delta y;-\delta z)$. The labels of the Mn ions in the next layer (with $z=c/2$) are given in parentheses. The displacements of the oxygen ions in the next layer have opposite $\delta z$.

Figure 3

(a) The typical magnon spectrum for a circular $bc$ spiral along $\mathbf{k}=(0,k_b,0)$, where $k_b$ is measured in units of $\frac{2\pi }{b}$. The empty and solid circles mark the position of, respectively, the KBN electromagnon and the electromagnon excited through the rotationally invariant coupling equation (3). (b) Corresponding dielectric susceptibility for the (arbitrarily broadened) single-magnon peak (solid line) and the bimagnon spectrum (histogram).