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. 2020 Feb 14;11:909. doi: 10.1038/s41467-020-14690-6

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — a A schematic of our polarization-resolved measurement setup. WGP wire-grid polarizer. b Frequency dependence of the precision of the polarization rotation angle in this measurement evaluated by the standard deviation of the polarization rotation angle. The precision can be more improved with using a larger number (#) of data sets. For example, the precision for 20 data sets (#20) can be as small as several tens of μrad between 0.5 and 2.0 THz (See details in text and Methods). c, d The rotation-angle and ellipticity-angle spectra in Mn_3+xSn_1−x films (x = 0.02) with different film thicknesses at room temperature. The broken curves correspond to the data with a flipped sample for the opposite magnetization vector. e Filled circles are the averaged rotation angle as a function of the film thickness. The solid line is the calculation of Eq. (1) fixed the DC longitudinal and Hall conductivity for 200-nm-thick sample. f The real- and imaginary-part Hall conductivity spectra for Mn_3+xSn_1−x films. The solid curves show the low-frequency THz-TDS for x = 0.02 on a SiO₂ substrate and the open circles show the broadband spectrum for x = 0.08 on a Si substrate. g A schematic of interband transition across the type-II Weyl nodes. The error bars in f indicate the standard deviations for the statistical fluctuation after repeating the measurements.