Versatile optical magnetoelectric effects by electromagnons in ${\mathrm{MnWO}}_4$ with canted spin-spiral plane

The optical magnetoelectric (OME) effect based on electromagnon resonance has been investigated in a multiferroic helimagnet ${\mathrm{MnWO}}_4$ with the canted spin-spiral plane by the terahertz spectroscopy. Versatile OME effects emerge from the canted spin-spiral state, including the magnetochiral effect as manifested by the nonreciprocal directional dichroism. In addition to the transverse fluctuation mode of the spin-driven ferroelectric polarization, the electromagnon with a character of the longitudinal amplitude mode was found to cause the OME effect characteristic of the canted spin-spiral plane.

Figure 1

(a) Schematics of the canted spin-spiral structure of ${\mathrm{MnWO}}_4$ (middle panel). The projections to the $ab$ plane turn into a proper screw component (upper panel) and to the $bc$ plane turn into the cycloidal spin components (lower panel). (b) The experimental geometry of light polarization ($E^{\omega }\parallel a, H^{\omega }\parallel b$), ferroelectric polarization ($P\parallel b$), and induced magnetization ($M\parallel a$) for the spin-spiral state in ${\mathrm{MnWO}}_4$. (c) Classification of the states in terms of the optical magnetoelectric (OME) effect given by the signs of $P$ and $M$ (see text). (d) Extinction coefficient $\kappa$ for the polarized light ($E^{\omega }\parallel a, H^{\omega }\parallel b$) at 4.4 K under the magnetic field (7 T). The signs of $P$ and $M$ for each spectrum are indicated. (e) Spectra of the OME effect ($\mathrm{\Delta }\kappa$) derived from the data in panel (d) (see text for definition).

Figure 2

(a) Magnetic phase diagram reproduced from Ref. [37] under a magnetic field along the $a$ axis. (b) Magnetic field dependence of the OME spectra ($\mathrm{\Delta }\kappa$) for $E^{\omega }\parallel a,H^{\omega }\parallel b$ at 4.5 K. (c) The magnetic field dependence (4.5 K) and (d) the temperature dependence (7 T) of $\kappa$. (e) The magnetic field dependence (4.5 K) and (f) the temperature dependence (7 T) of the OME spectra ($\mathrm{\Delta }\kappa$).

Figure 3

(a) Schematics of the polarization of light ($E^{\omega }\parallel b,H^{\omega }\parallel c$) and spin configurations. The helicities of spin orders with clockwise (left side) or counterclockwise (right side) are distinguished in term of the magnetochiral (MCh) effect (see text). (b) Spectra of $\kappa$ for $E^{\omega }\parallel b,H^{\omega }\parallel c$. The signs of $P$ and $M$ for each spectra are indicated. (c) Spectrum of the OME effect ($\mathrm{\Delta }\kappa$) derived from panel (b). The magnetic field dependence of (d) $\kappa$ and (e) the OME spectra ($\mathrm{\Delta }\kappa$) in the spin-spiral phase at 4.5 K.

Figure 4

(a) Schematics of geometry of the light polarization and the spin structure under the magnetic field along the $c$ axis. (b) Magnetic phase diagram of ${\mathrm{MnWO}}_4$ reproduced from Ref. [40] under the magnetic field ($H\parallel c$). (c) Absorption coefficient $\alpha$ for the distinct states in terms of the OME effect at 7 T (see text). (d) Spectrum of the OME effect (directional absorption difference, $\mathrm{\Delta }\alpha$) derived from (c). The temperature dependence of (e) $\alpha$ and (f) the OME spectra $\mathrm{\Delta }\alpha$ at 7 T.