Electromagnon resonance in a collinear spin state of the polar antiferromagnet ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$

Magnetic excitations are investigated for a hexagonal polar magnet $\mathrm{F}{\mathrm{e}}_2\mathrm{M}{\mathrm{o}}_3{\mathrm{O}}_8$ by terahertz spectroscopy. We observed magnon modes including an electric-field active magnon, electromagnon, in the collinear antiferromagnetic phase with spins parallel to the $c$ axis. We unravel the nature of these excitations by investigating the correlation between the evolution of the mode profile and the magnetic transition from antiferromagnetic to ferrimagnetic order induced by a magnetic field or Zn doping. We propose that the observed electromagnon mode involves the electric polarization oscillating within the $c$ plane induced by the collective precession of the spins through the same mechanism as producing the linear magnetoelectric effect.

Figure 1

(a) Crystal structure of $(\mathrm{Z}{\mathrm{n}}_y\mathrm{F}{\mathrm{e}}_{1-y}{)}_2\mathrm{M}{\mathrm{o}}_3{\mathrm{O}}_8$. (b) and (c) Magnetic-field $\left(H_{\mathrm{dc}}\right)$ vs temperature phase diagrams under $H_{\mathrm{dc}}\parallel c$ for $y=0$ and $y=0.125$, respectively, as reproduced from Ref. [36]. The magnetic structure of each phase is also shown. (d)–(i) Spectra of κ (imaginary part of the refractive index, i.e., extinction coefficient) for respective light polarizations at 4.5 K in a zero field (d)–(f) for $y=0$ and (g)–(i) for $y=0.125$.

Figure 2

(a)–(d) Temperature dependence of κ for $y=0$ in a zero field. Red (blue) curves are for EM (MM1) measured with different light polarizations. (e)–(h) Corresponding spectra of $y=0.125$ for MM2. Temperature dependence of spectral weight for (i) EM and MM1 and (j) MM2 in a zero field. Magnetization measured with ${\mu }_0{H}_{\mathrm{dc}}=0.1\mathrm{T}$ also is shown for comparison.

Figure 3

(a)–(c) κ spectra under various field magnitudes. Data are shifted vertically for clarity. Red (blue) curves are for the polarization $E^{\omega }\perp c$ and $H^{\omega }\parallel c$ ($H^{\omega }\perp c$ and $E^{\omega }\parallel c$). Blue curves in (b) are magnified by 2. (d)–(f) Evolution of excitation frequency with $H_{\mathrm{dc}}\parallel c$: red, blue, and green circles are for EM, MM1, and MM2, respectively. In (e), magnetization along the $c$ axis at 50 K is also shown for comparison.

Figure 4

(a) Schematic dynamical spin configurations with dynamical magnetization ($m_y\propto \delta S_{Ay}-\delta S_{By}$) and electric polarization ($p_y\propto \delta S_{Ay}{S}_{Bz}-S_{Az}\delta S_{By}$) oscillating on the $c$ plane for upper and bottom layers in a unit cell. (b)–(e) Corresponding spin configurations for the respective magnetic excitation modes.