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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.
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.