Fig. 2. Spectra of GB and NOA with response to P, M, and ${\gamma }_{\mathrm{m}}$.

a Magnetic field dependence of the diagonal parts of effective dielectric tensor (${\epsilon }_{xx}$ and ${\epsilon }_{yy}$) at 4 K in the magnetic field (H_dc|| [110]). Symmetric part of effective dielectric spectra (${\epsilon }_{xy}^{\mathrm{S}}$, see Eq. (1)) representing the optical rotation of GB under b time reversal and c space inversion. Antisymmetric part of effective dielectric spectra (${\epsilon }_{xy}^{\mathrm{A}}$) representing the optical rotation of NOA under d time reversal and e space inversion. The magnetically-induced chirality γ_m = ±, and equivalently the sign of P, are denoted. f Magnetic field dependence of the peak magnitude of Im[${\epsilon }_{xy}^{\mathrm{A}}$] (red) and Im[${\epsilon }_{xy}^{\mathrm{S}}$] (blue) and the magnetization M (black line) of CuFe_1-xGa_xO₂ (x = 0.035) (right axis)²⁹. The filled and open circles denote the peak magnitude for (γ_m = +, +P) and (γ_m = −, −P) states, respectively. (See Supplementary Note 2 for details of spectra).