Electromagnons in the Spin Collinear State of a Triangular Lattice Antiferromagnet

Terahertz time-domain spectroscopy was performed to directly probe the low-energy (1–5 meV) electrodynamics of triangular lattice antiferromagnets ${\mathrm{CuFe}}_{1-x}{\mathrm{Ga}}_x{\mathrm{O}}_2$ ($x=0.00$, 0.01, and 0.035). We discovered an electromagnon (electric-field-active magnon) excitation at 2.3 meV in the paraelectric $\uparrow \uparrow \downarrow \downarrow$ collinear magnetic phase, while this electromagnon vanishes in the ferroelectric helimagnetic phase. Anticorrelation with noncollinear magnetism excludes the exchange-striction mechanism as the origin of dynamical magnetoelectric coupling, and hence evidences the observation of a spin-orbit coupling mediated electromagnon in the present compound.

Figure 1

(a) Crystal structure and (b) $x\mathrm{\text{−}}T$ magnetic phase diagram at $H=0$ for ${\mathrm{CuFe}}_{1-x}{\mathrm{Ga}}_x{\mathrm{O}}_2$. (c) $H\mathrm{\text{−}}T$ magnetic phase diagram for the $x=0.01$ specimen with static $H\parallel c$. Circles and squares are the data points obtained from the measurements of magnetization with $T$- and $H$-increasing runs, respectively. Open (closed) symbols represent the data points determined in this work (the previous work by Terada et al. [22]). Panels (d) and (e) indicate magnetic structures of the NC (FE) and CM4 phase, respectively. Dashed square in (e) represents the magnetic unit cell in the CM4 phase. The directions of magnetic $q$ vector and electric polarization $P$ are also indicated.

Figure 2

Real and imaginary parts of $ϵ\mu$ spectra ($\mathrm{Re}[ϵ\mu ]$ and $\mathrm{Im}[ϵ\mu ]$) for the $x=0.01$ specimen measured at 4.4 K with various light-polarization configurations.

Figure 3

(a)–(c) Absorption coefficient $\alpha$, real and imaginary part of $ϵ$ and $\mu$ spectra for the $x=0.01$ specimen at 4.4 K with $E^{\omega }\parallel [110]$ and $H^{\omega }\parallel [1\overline{1}0]$. Solid lines in (b) and (c) represent the fits with the sum of Lorentzian functions. (d) Spin structure of the CM4 magnetic ground state. Panels (e) and (f) indicate the possible excitation modes corresponding to the observed genuine magnon (AFMR) and electromagnon (EM), respectively. In (f), $S_1$ and $S_3$ rotate to the opposite direction of $S_2$ and $S_4$ within a plane perpendicular to $\overrightarrow{q}$. (g) Spin-wave (magnon) dispersion of ${\mathrm{CuFeO}}_2$ along the $(h,h,0)$ direction as suggested in Ref. 30.

Figure 4

$T$ dependence of $\mathrm{Im}[ϵ\mu ]$ spectra measured with $E^{\omega }\parallel [110]$ and $H^{\omega }\parallel [1\overline{1}0]$ for (a) $x=0.00$, (b) $x=0.01$, and (c) $x=0.035$ specimens, respectively. (d) $\mathrm{Im}[ϵ]$ spectra for the $x=0.01$ specimen measured at 6 K with $E^{\omega }\parallel [110]$ and $H^{\omega }\parallel [001]$ in various magnitudes of static $H$ ($H^{\mathrm{dc}}$) applied along the [001] direction. $H$ dependence of observed EM peak positions (circle), as well as the development of resonance modes previously reported by the ESR study for the $x=0.00$ specimen [32] (square), are plotted in (e).