Electrically driven spin excitation in the ferroelectric magnet ${\text{DyMnO}}_3$

Temperature (5–250 K) and magnetic-field (0–70 kOe) variations of the low-energy (1–10 meV) electrodynamics of spin excitations have been investigated for a complete set of light-polarization configurations for a ferroelectric magnet ${\text{DyMnO}}_3$ by using terahertz time-domain spectroscopy. We identify the pronounced absorption continuum (1–8 meV) with a peak feature around 2 meV, which is electric-dipole active only for the light $E$ vector along the $a$ axis. This absorption band grows in intensity with lowering temperature from the spin-collinear paraelectric phase above the ferroelectric transition but is independent of the orientation of spiral spin plane ($bc$ or $ab$), as shown on the original $P_{\text{s}}$ (ferroelectric polarization) $\parallel c$ phase as well as the magnetic-field induced $P_{\text{s}}\parallel a$ phase. The possible origin of this electric-dipole active band is argued in terms of the large fluctuations of spins and spin current.

Figure 1

(Color online) Schematic illustration of the experimental setup for terahertz time-domain spectroscopy in a transmission geometry.

Figure 2

(Color online) Low-energy electrodynamics of a complete set of available configurations of single crystals of ${\text{DyMnO}}_3$ measured around 10 K in zero magnetic field. Upper and lower panels show the real and imaginary parts of $ϵ\mu$ spectrum (closed circles) when $E^{\omega }$ and $H^{\omega }$ were set parallel to the crystallographic axes of $ac$, $ab$, and $bc$ surface crystal plates. The solid lines in (a) and (b) are results of a least-squares fit to reproduce low-lying and high-lying peak structures by assuming two Lorentz oscillators for $ϵ$. On the contrary, $ϵ\mu$ spectra in (d), (e), and (f) can be reproduced by two Lorentz oscillators for $ϵ$ and $\mu$ as indicated by solid lines.

Figure 3

(Color online) Temperature dependence of the real (upper panels) and imaginary (lower panels) parts of the selected $ϵ\mu$ spectra (closed circles) of ${\text{DyMnO}}_3$ for (a) $E^{\omega }\parallel a$, (b) $H^{\omega }\parallel a$, and (c) $H^{\omega }\parallel c$. Note that the scale of the vertical axis is different in respective figures. The $\text{Im}\left[ϵ\mu \right]$ spectra shown in (b) and (c) are vertically offset for clarity. We also plot the extracted $\text{Im}\left[ϵ\right]$ and $\text{Im}\left[\mu \right]$ spectra [at (b) 5 and (c) 4.2 K] indicated by dotted and gray lines, respectively, by assuming that $\text{Im}\left[ϵ\mu \right]$ spectrum can be represented by two Lorentz oscillators for $ϵ$ and $\mu$ (solid lines). The $\text{Im}\left[\mu \right]$ spectrum is multiplied by 5. On the contrary, $ϵ\mu$ spectra for $E^{\omega }\parallel a$ [(a)] can be fitted by two Lorentz oscillators.

Figure 4

(Color online) Temperature $\left(T\right)$ dependence of the integrated spectral weight per Mn-site, $N_{\text{eff}}$, as defined by Eq. (1) in the text of the $ac$ surface crystal plate of ${\text{DyMnO}}_3$ for (a) $H^{\omega }\parallel a$ and (b) $E^{\omega }\parallel a$. The upper panel of (a) shows the phase diagram with variation of $T$. PE and PM stand for paraelectric and paramagnetic, respectively. We also show the schematic illustrations of the $bc$ spiral and collinear spin states induced by $T$. Néel temperature $T_{\text{N}}^{\text{Mn}}$ (39 K) and ferroelectric transition temperature $T_{\text{c}}$ (19 K) are indicated by vertical solid lines in (a) and (b). The data measured at 75 and 249 K were also plotted at the 50 K position in (b) with square and triangle symbols, respectively. The horizontal dashed line in (a) represents the estimated contribution of the optical-phonon absorption at 5 K.

Figure 5

(Color online) Magnetic-field $\left(H\right)$ dependence of the real (upper panels) and imaginary (lower panels) parts of the selected $ϵ\mu$ spectra (closed circles) of the $ac$ surface crystal plate of ${\text{DyMnO}}_3$ at 7 K when (a) $E^{\omega }$ or (b) $H^{\omega }$ was set parallel to the $a$ axis. The ferroelectric polarization flop occurs at 20 kOe for $H\parallel b$. Note that $\text{Im}\left[ϵ\mu \right]$ spectra in (b) are vertically offset for clarity and that the scale of the vertical axis is different in (a) and (b).

Figure 6

(Color online) Magnetic-field $\left(H\right)$ dependence of the integrated spectral weight per Mn-site, $N_{\text{eff}}$, as defined by Eq. (1) in the text of the $ac$ surface crystal plate of ${\text{DyMnO}}_3$ for (a) $H^{\omega }\parallel a$ and (b) $E^{\omega }\parallel a$, measured at 7 K. The upper panel of (a) shows the phase diagram with variation of $H$. We also show the schematic illustrations of the $bc$ and $ab$ spiral spin planes induced by $H$. $H$ of 20 kOe at which the ferroelectric polarization flop occurs at 7 K, is indicated by the vertical solid line in (a) and (b). The difference of $N_{\text{eff}}$ at 7 K with [in (a) and (b)] and without $H$ (in Fig. 4), arises from the difference of the integrated energy range (see text).

Figure 7

(Color online) (a) Sample geometry with the complex Fresnel transmission coefficients from vacuum to the sample $t_{\text{v}\to \text{s}}$ and from the sample to vacuum $t_{\text{s}\to \text{v}}$. The complex transmission coefficient $t$ was obtained by Eq. (B1). $d$ and $\tilde{n}$ are the thickness and the complex refractive index of the sample, respectively. (b) Typical example of the measured terahertz wave form in time-domain with and without the sample ($ac$ surface crystal plate of ${\text{DyMnO}}_3$) measured at 5.2 K in zero magnetic field. $E^{\omega }$ and $H^{\omega }$ were set parallel to the $c$ and $a$ axes, respectively. The amplitude of the transmitted terahertz wave form with the sample was vertically offset for clarity. (c) Power transmission spectrum of ${\text{DyMnO}}_3$.

Figure 8

(Color online) (a) Validity of using Eqs. (B2a, B2b) instead of Eqs. (B3a, B3b). The $\text{Im}\left[ϵ\mu \right]$ spectra of ${\text{DyMnO}}_3$ for $E^{\omega }\parallel c$ and $H^{\omega }\parallel a$ at 5.2 K was almost unchanged even if we used Eqs. (B3a, B3b). The fixed parameters of $\text{Re}\left[\mu \right]$ and $\text{Im}\left[\mu \right]$ are described in the right-hand side of the figure, which were confirmed to be reasonable by assuming that $ϵ$ can be represented by a single Lorentz oscillator [see (b)]. (b) The estimated $\text{Im}\left[\mu \right]$ spectrum (closed circles) by assuming that $ϵ$ can be represented by a single Lorentz oscillator. We also plot the $\text{Im}\left[\mu \right]$ spectrum (a solid line) as extracted from Eq. (B1) combined with Eqs. (B2a, B2b).