Figure 2. THz Faraday and Kerr rotation spectra of the magnetic TI film.

(a) Transmittance (left ordinate) spectra of the magnetic TI film at various temperatures and optical conductance (right ordinate) σ_xx spectrum at T=4.3 K. The transmittance close to unity was observed, indicating the negligible carrier absorptions due to fine-tuning of the Fermi level within the magnetic mass-gap of the surface state. The low-lying optical phonon mode is discerned as a tiny dip around 7 meV and also as the peak of optical conductance spectrum. (b,c) Complex Faraday (b) and Kerr (c) rotation spectra at 1.5 K (see the main text and Methods for definition). The real parts (θ_F and θ_K) represent the rotation angle of light polarization. The imaginary parts (η_F and η_K) represent the ellipticity, which is negligibly small as expected. Rotation angles at ω=0 evaluated from the d.c. transport data (Fig. 1c) are also plotted on the left ordinates. (d) Temperature dependence of the Faraday (red) and Kerr (blue) rotation spectra with the evaluated ω=0 values on the ordinates. The error bars in b–d are evaluated by s.e.m. of several runs of measurement.