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The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e\(^{2}\)/2E\(_{0}\)hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.
The orthorhombic rare-earth manganite compounds \(R\)MnO\(_3\) show a global magnetic order for \(T\) < \(T\)\(_N\), and several representatives are multiferroic with a cycloidal spin ground state order for \(T\) < \(T\)\(_c\)\(_y\)\(_c\)\(_l\) < \(T\)\(_N\) \(\approx\) 40 K. We deduce from the temperature dependence of spin–phonon coupling in Raman spectroscopy for a series of \(R\)MnO\(_3\) compounds that their spin order locally persists up to about twice \(T\)\(_N\). Along the same line, our observation of the persistence of the electromagnon in GdMnO\(_3\) up to \(T\) \(\approx\) 100 K is attributed to a local cycloidal spin order for \(T\) > \(T\)\(_c\)\(_y\)\(_c\)\(_l\), in contrast to the hitherto assumed incommensurate sinusoidal phase in the intermediate temperature range. The development of the magnetization pattern can be described in terms of an order–disorder transition at \(T\)\(_c\)\(_y\)\(_c\)\(_l\) within a pseudospin model of localized spin cycloids with opposite chirality.