Fig. 1. Gyrotropic birefringence (GB) and natural optical activity (NOA) on electromagnon in helimagnet CuFe_1-xGa_xO₂ (x = 0.035).

a The ferroelectric polarization P parallel or antiparallel to the magnetization M induces the GB. The GB response can be viewed as the rotation of eigen polarization (green arrows). The reversal of either P or M reverses the sign of the rotation of eigen polarization. The nonreciprocal optical rotation of GB is represented by the symmetric off-diagonal elements in the effective dielectric tensor. b Schematics of the optical rotation by NOA. The chiral media show the optical rotation owing to the circular birefringence/dichroism, whose sign depends on the sign of chirality${\gamma }_{\mathrm{m}}$. The antisymmetric parts of the effective dielectric tensor represent the NOA. c Magnetic phase diagram of CuFe_1-xGa_xO₂ (x = 0.035) in the external magnetic field H_dc||[110]||${\mathbf{q}}_{\mathrm{m}}$²⁹. d The schematics of terahertz time-domain polarimetry and of conical screw spin structure in the magnetic field H_dc||[110]. The sign of chirality (${\gamma }_{\mathrm{m}}$) is rigidly connected to that of P as ${\gamma }_{\mathrm{m}}=\mathrm{sgn}\left(\mathbf{P}\right)$²⁹. e Imaginary parts of ${\epsilon }_{xx}$ and ${\epsilon }_{yy}$ in the magnetic field (5 T) at 4 K. f Rotation angle θ and ellipticity η for the incident light with E^ω||[110]. The sample thickness is 1 mm.