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=e2/2hc (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.

In contrast to well studied multiferroic manganites with a spiral structure, the electric polarization in multiferroic borates is induced within collinear antiferromagnetic structure and can easily be switched by small static fields. Because of specific symmetry conditions, static and dynamic properties in borates are directly connected, which leads to giant magnetoelectric and magnetodielectric effects. Here we prove experimentally that the giant magnetodielectric effect in samarium ferroborate SmFe3(BO3)4 is of intrinsic origin and is caused by an unusually large electromagnon situated in the microwave range. This electromagnon reveals strong optical activity exceeding 120 degrees of polarization rotation in a millimeter thick sample

Using electron-spin-resonance (ESR) technique we investigate the magnetic structure of CuCrO2, quasi-two-dimensional antiferromagnet with weakly distorted triangular lattice. Resonance frequencies and the excitation conditions in CuCrO2 at low temperatures are well described in the frame of cycloidal spin structure, defined by two susceptibilities parallel and perpendicular to the spin plane (χ ⊥ and χ ) and by a biaxial crystal-field anisotropy. In agreement with the calculations, the character of the eigenmodes changes drastically at the spin-flop transition. The splitting of the observed modes can be well attributed to the resonances from different domains. The domain structure in CuCrO2 can be controlled by annealing of the sample in magnetic field.

The universal value of Faraday rotation angle close to the fine structure constant (α ≈ 1/137) is experimentally observed in thin HgTe quantum wells with thickness on the border between trivial insulating and the topologically non-trivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the hole-like carriers extracted from the analysis of the transmission data shows theoretically predicted universal value of σxy = e 2 /h consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electron-like part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model. PACS numbers:The strong spin-orbit coupling and an inverted band structure in mercury telluride makes this material to a nearly universal tool to probe novel physical effects with the film thickness being a tuning parameter [1,2]. If the thickness of HgTe wells is below critical, d < d c ≈ 6.3 nm, the sequence of the conduction and valence bands is conventional and a trivial insulating state is realized. For thicker films and in the bulk mercury telluride the inversion of valence and conduction bands leads to topologically non-trivial surface states [3,4]. This state is characterised by the locking of the electron spin and the electron momentum and they are topologically protected against non-magnetic impurity scattering.If the thickness of HgTe well is equal to critical, the gap between valence and conduction bands disappears and a two-dimensional (2D) electron gas is formed with Dirac cone dispersion [1,2]. Close to the center of the Dirac cone the electron spin is not a good quantum number, but has to be replaced by pseudo-spin or helicity [3,5]. Due to the particle-hole symmetry of these states, the quantum Hall effect becomes shifted by a half-integer and takes the form σ xy = γ(n+1/2)e 2 /h. In well-investigated case of graphene [6,7] the states are fourfold degenerate, i.e. γ = 4, as two Dirac cones are present in the Brillouin zone which are both doubly spin-degenerate.Magneto-optics in the terahertz range has been proven to be an effective tool to investigate two-dimensional conducting states in several quantum systems, like graphene [8-10], Bi 2 Se 3 [11][12][13][14], and HgTe [15][16][17][18][19][20][21][22]. Magneto-optical spectroscopy has the advantages of being contact-free and of directly accessing the effective mass m c via the cyclotron resonance Ω c = eB/m c . Here B is the external magnetic field.In the dynamical regime the unusual character of the quantum Hall effect in systems with Dirac cones can be shown [23][24][25][26] to lead to a universal values of the Faraday and Kerr rotation with θ F = α ∼ 1/137 and θ K = π/2, respectively. Such predictions have been recently confirmed experimentally in graphene [9], where the Faraday angle is additio...

Electric manipulation of magnetic properties is a key problem of materials research. To fulfil the requirements of modern electronics, these processes must be shifted to high frequencies. In multiferroic materials this may be achieved by electric and magnetic control of their fundamental excitations. Here we identify magnetic vibrations in multiferroic iron-borates which are simultaneously sensitive to external electric and magnetic fields. Nearly 100 % modulation of the terahertz radiation in an external field is demonstrated for SmFe3(BO3)4. High sensitivity can be explained by a modification of the spin orientation which controls the excitation conditions in multiferroic borates. These experiments demonstrate the possibility to alter terahertz magnetic properties of materials independently by external electric and magnetic fields.