Observation of nonreciprocal directional dichroism via electromagnon resonance in a chiral-lattice helimagnet $\mathrm{B}{\mathrm{a}}_3\mathrm{NbF}{\mathrm{e}}_3\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_{14}$

Nonreciprocal directional dichroism (NDD) is investigated on a magnetic resonance with both electric and magnetic dipole activities, i.e., electromagnon, for a chiral-lattice helimagnet $\mathrm{B}{\mathrm{a}}_3\mathrm{NbF}{\mathrm{e}}_3\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_{14}$ by terahertz spectroscopy under the magnetic field. In the Voigt geometry, the electromagnon resonance causes the NDD in the helimagnetic phase in accord with the spin-driven ferroelectric polarization, whose polarity is uniquely selected owing to the structural chirality. In the Faraday geometry, all possible optical effects, including natural optical activity, magnetic optical activity and magnetochiral effect showing NDD, are separately evaluated by terahertz polarimetry technique. The NDD is manifested in the electromagnon resonance in the helimagnetic phase, while a formation of helimagnetic spin structure enhances the natural optical activity inherent to the structural chirality.

Figure 1

(a) Schematic of the spin structure of BNSFO in the screw-spin phase. (b) Schematic of the spin chain constituent of BNSFO [dotted square in Fig. 1] under a magnetic field perpendicular to [001]. The induced magnetization $\mathit{M}$ and orthogonal ferroelectric polarization $\mathit{P}$ are indicated. (c) Conical screw-spin chain under a magnetic field along the [001] axis. (d) Crystal structure of BNFSO. (e) Temperature dependence of the ferroelectric polarization along the [110] axis under the magnetic field parallel to $\left[1\overline{1}0\right]$ and with slight inclination with respect to $\left[1\overline{1}0\right]$. Inset shows the experimental geometry of the magnetic field and ferroelectric polarization. (f) Magnetic-field dependence of ferroelectric polarization with the same experimental configuration as with Fig. 1. As seen in (e) and (f) the sign of magnetic-field-induced $\mathit{P}$ is reversed between $\theta =-{10}^{\circ }$ and 10°, reflecting the helicity reversal of the induced cycloidal component.

Figure 2

(a) The experimental geometry of light polarization $\left({\mathit{E}}^{\omega }\perp \mathit{P}\right)$, ferroelectric polarization $\mathit{P}$, magnetization $\mathit{M}$, and spin structures for two different states in terms of the OME effect. (b) Complex refractive indices for different states in terms of the OME effect, as indicated by $+{\mathit{k}}^{\omega }$ and $-{\mathit{k}}^{\omega }$ [see text and Fig. 2 for definition] at 4 K under an external magnetic field (7 T). (c) Complex OME spectra $(\mathrm{\Delta }n$ and Δκ) derived from Fig. 2.

Figure 3

Temperature dependence of (a) extinction coefficient (κ) and (b) OME spectra (Δκ) at 7 T. (c) Temperature dependence of the peak magnitudes of OME effect (Δκ) and ordinary term of extinction coefficient $\left({\kappa }_{\mathrm{O}}\right)$. The intensity of ${\kappa }_{\mathrm{O}}$ is defined as $[\kappa (+{\mathit{k}}^{\omega })+\kappa (-{\mathit{k}}^{\omega })]/2$. (d) Magnetic-field dependence of extinction coefficient (κ) and OME spectra (Δκ) at 4 K. (e) Magnetic-field dependence of peak magnitudes of OME effect (Δκ) and ordinary term $\left({\kappa }_{\mathrm{O}}\right)$ at 4 K.

Figure 4

(a) The experimental geometry of light polarization $\left({\mathit{E}}^{\omega }\perp \mathit{P}\right)$, magnetization $\mathit{M}$, and spin structures for two different states in terms of the MCh effect; the helicity of the screw spins are the same, but their magnetizations are opposite. (b) Extinction coefficients for right- and left-circular polarizations under magnetic fields of +7 T and −7 T at 4K.

Figure 5

Complex refractive indices $(\mathrm{\Delta }n$ and Δκ) for independent optical activities (effect) derived from Fig. 4 with the use of Eq. (3). (a) Ordinary term $\left(N_{\mathrm{O}}=\mathrm{\Delta }{n}_{\mathrm{O}}+i\mathrm{\Delta }{\kappa }_{\mathrm{O}}\right)$, (b) magnetic optical activity $\left(N_{\mathrm{MOA}}=\mathrm{\Delta }{n}_{\mathrm{MOA}}+i\mathrm{\Delta }{\kappa }_{\mathrm{MOA}}\right)$, (c) MCh effect $\left(N_{\mathrm{MCh}}=\mathrm{\Delta }{n}_{\mathrm{MCh}}+i\mathrm{\Delta }{\kappa }_{\mathrm{MCh}}\right)$, and (d) natural optical activity $\left(N_{\mathrm{NOA}}=\mathrm{\Delta }{n}_{\mathrm{NOA}}+i\mathrm{\Delta }{\kappa }_{\mathrm{NOA}}\right)$ [see text and Eq. (2) and (3) for definition].

Figure 6

(a) Temperature dependences of the peak intensities for magnetic optical activity $(\mathrm{\Delta }{\kappa }_{\mathrm{MOA}}/\mathrm{\Delta }{\kappa }_{\mathrm{O}}$: MOA, circle), natural optical activity $(\mathrm{\Delta }{\kappa }_{\mathrm{NOA}}/\mathrm{\Delta }{\kappa }_{\mathrm{O}}$: NOA, triangle), and MCh effect $(\mathrm{\Delta }{\kappa }_{\mathrm{MCh}}/\mathrm{\Delta }{\kappa }_{\mathrm{O}}$: MCh, square) normalized by the ordinary term $\mathrm{\Delta }{\kappa }_{\mathrm{O}}$ at 7 T. Temperature dependences of (b) ordinary term, (c) magnetic optical activity, (d) MCh effect, and (e) natural optical activity at 7 T.