Many technological applications are based on electric or magnetic order of materials, for instance magnetic memory. Multiferroics are materials which exhibit electric and magnetic order simultaneously. Due to the coupling of electric and magnetic eff
ects, these materials show a strong potential to control electricity and magnetism and, more generally, the properties and propagation of light. One of the most fascinating and counter-intuitive recent results in multiferroics is directional anisotropy, the asymmetry of light propagation with respect to the direction of propagation. The absorption in the material can be different for forward and backward propagation of light, which in extreme case may lead to complete suppression of absorption in one direction. Another remarkable effect in multiferroics is directional birefringence, i.e. different velocities of light for different directions of propagation. In this paper, we demonstrate giant directional birefringence in a multiferroic samarium ferroborate. The effect is easily observed for linear polarization of light in the range of millimeter-wavelengths, and survives down to very low frequencies. The dispersion and absorption close to the electromagnon resonance can be controlled and fully suppressed in one direction. Therefore, samarium ferroborate is a universal tool for optical control: with a magnetic field as an external parameter it allows switching between two functionalities: polarization rotation and directional anisotropy.
The terahertz (THz) frequency range (0.1-10 THz) fills the gap between the microwave and optical parts of the electromagnetic spectrum. Recent progress in the generation and detection of the THz radiation has made it a powerful tool for fundamental r
esearch and resulted in a number of applications. However, some important components necessary to effectively manipulate THz radiation are still missing. In particular, active polarization and phase control over a broad THz band would have major applications in science and technology. It would, e.g., enable high-speed modulation for wireless communications and real-time chiral structure spectroscopy of proteins and DNA. In physics, this technology can be also used to precisely measure very weak Faraday and Kerr effects, as required, for instance, to probe the electrodynamics of topological insulators. Phase control of THz radiation has been demonstrated using various approaches. They depend either on the physical dimensions of the phase plate (and hence provide a fixed phase shift) or on a mechanically controlled time delay between optical pulses (and hence prevent fast modulation). Here, we present data that demonstrate the room temperature giant Faraday effect in HgTe can be electrically tuned over a wide frequency range (0.1-1 THz). The principle of operation is based on the field effect in a thin HgTe semimetal film. These findings together with the low scattering rate in HgTe open a new approach for high-speed amplitude and phase modulation in the THz frequency range.
Using THz spectroscopy in external magnetic fields we investigate the low-temperature charge dynamics of strained HgTe, a three dimensional topological insulator. From the Faraday rotation angle and ellipticity a complete characterization of the char
ge carriers is obtained, including the 2D density, the scattering rate and the Fermi velocity. The obtained value of the Fermi velocity provides further evidence for the Dirac character of the carriers in the sample. In resonator experiments, we observe quantum Hall oscillations at THz frequencies. The 2D density estimated from the period of these oscillations agrees well with direct transport experiments on the topological surface state. Our findings open new avenues for the studies of the finite-frequency quantum Hall effect in topological insulators.
The behavior of the low-frequency electromagnon in multiferroic DyMnO3 has been investigated in external magnetic fields and in a magnetically ordered state. Significant softening of the electromagnon frequency is observed for external magnetic field
s parallel to the a-axis (BIIa), revealing a number of similarities to a classical soft mode behavior known for ferroelectric phase transitions. The softening of the electromagnon yields an increase of the static dielectric permittivity which follows a similar dependence as predicted by the Lyddane-Sachs-Teller relation. Within the geometry BIIb the increase of the electromagnon intensity does not correspond to the softening of the eigenfrequency. In this case the increase of the static dielectric permittivity seem to be governed by the motion of the domain walls.
Terahertz electromagnetic excitations in the multiferroic TbMnO3 at the field-induced magnetic transition are investigated for different orientations of the magnetic cycloid. In addition to the electromagnon along the a-axis, the detailed polarizatio
n analysis of the experimental spectra suggests the existence of an electro-active excitation for ac electric fields along the crystallographic c-axis. This excitation is possibly the electro-active eigenmode of the spin cycloid in TbMnO3, which has been predicted within the inverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling.
Magnetic and magnetoelectric excitations in the multiferroic TbMnO_3 have been investigated at terahertz frequencies. Using different experimental geometries we can clearly separate the electro-active excitations (electromagnons) from the magneto-act
ive modes, i.e. antiferromagnetic resonances (AFMR). Two AFMR resonances were found to coincide with electromagnons. This indicates that both excitations belong to the same mode and the electromagnons can be excited by magnetic ac-field as well. In external magnetic fields and at low temperatures distinct fine structure of the electromagnons appears. In spite of the 90^o rotation of the magnetic structure, the electromagnons are observable for electric ac-fields parallel to the a-axis only. Contrary to simple expectations, the response along the c-axis remains purely magnetic in nature.
