Electromagnons in the multiferroic state of perovskite manganites with symmetric exchange striction

We have investigated electrically active magnetic excitations (electromagnons) in perovskite manganites with the $E$-type (up-up-down-down) spin structure by terahertz spectroscopy. ${\text{Eu}}_{1-x}{\text{Y}}_x{\text{MnO}}_3$ $\left(0.1\le x\le 1\right)$ and ${\text{Y}}_{1-y}{\text{Lu}}_y{\text{MnO}}_3$ $\left(0\le y\le 1\right)$ without magnetic $f$ moments, which host collinear sinusoidal, $A$-type, cycloidal, and $E$-type spin orders, are used to examine the systematics of possible electromagnons. Three-peak structures (2.8, 4.3, and 5.6 meV) of magnetic origin show up in the $E$-type phase with little composition $\left(y\right)$ dependence of frequencies, making a contrast with the electromagnons observed in the cycloidal-spin $\left(x\le 0.8\right)$ phases. One of these electromagnon is ascribed to the zone-edge magnon mode based on the calculated magnon dispersions.

Figure 1

(Color online) (a) The phase diagram of ${\text{Eu}}_{1-x}{\text{Y}}_x{\text{MnO}}_3$ $\left(0.1\le x\le 1\right)$ and ${\text{Y}}_{1-y}{\text{Lu}}_y{\text{MnO}}_3$ $\left(0\le y\le 1\right)$ reproduced from Refs. 8, 25, 26. The $\text{Im}\left[ϵ\mu \right]$ spectra for (b) $A$-type, (c) $ab$-cycloidal, and (d) $E$-type spin phase with the schematic spin structures.

Figure 2

(Color online) (a) Temperature dependence of $\text{Im}\left[ϵ\mu \right]$ spectra for ${\text{LuMnO}}_3$. (b) $\text{Im}\left[ϵ\mu \right]$ spectra of the $E$-type phase at 4 K for ${\text{Y}}_{1-y}{\text{Lu}}_y{\text{MnO}}_3$ ($y=0.25$, 0.5, 0.75, and 1) with vertical offset for clarity. Peak positions are indicated by the vertical dotted lines.

Figure 3

(Color online) Temperature dependence of spectral weight ($\Delta N_{\text{eff}}$; see text for definition) of the electromagnon (or electric dipole active magnetic excitation); (a) $A$-type $\left(x=0.2\right)$, $ab$-cycloidal $\left(x=0.6\right)$ for ${\text{Eu}}_{1-x}{\text{Y}}_x{\text{MnO}}_3$, and (b) $E$-type spin phase, $y=0.25$, 0.5, 0.75, and 1 for ${\text{Y}}_{1-y}{\text{Lu}}_y{\text{MnO}}_3$.

Figure 4

(Color online) (a) The composition ($x$ and $y$) dependence of frequencies of EM for the cycloidal and $E$-type spin phases (or of AFMR for $A$-type spin phase). The energies of EM obtained by calculation are also included. The schematic spin configuration of the $E$-type state and zone-edge magnon in (b) $ab$ plane and (c) $bc$ plane. The magnetic parameters $J_1$, $J_2$, and $J_c$, and unit-cell length along $a$, $b$, and $c$ axes are displayed. (d) The magnon dispersions calculated for the $E$-type $\left(\theta =0\right)$ and cycloidal phase $\left(\theta =\pi /4\right)$ in the case of the $A$-site ionic radius of $1.05\text{Å}$ (see text). The Brillouin zone along $q_b$ is a half of that for the chemical lattice [see Fig. 4b], and hence the zone-edge mode is folded into $q_b=0$. The EM is indicated by an open circle (red online) at 2.8 meV. (e) Tilting angle $\theta$ dependence of the normalized absorption intensity by SES and IDM mechanisms.