Faraday Angle Research Articles

Faraday rotation and transmittance as markers of topological phase transitions in 2D materials

We analyze the magneto-optical conductivity (and related magnitudes like transmittance and Faraday rotation of the irradiated polarized light) of some elemental two-dimensional Dirac materials of group IV (graphene analogues, buckled honeycomb lattices, like silicene, germanene, stannane, etc.), group V (phosphorene), and zincblende heterostructures (like HgTe/CdTe quantum wells) near the Dirac and gamma points, under out-of-plane magnetic and electric fields, to characterize topological-band insulator phase transitions and their critical points. We provide plots of the Faraday angle and transmittance as a function of the polarized light frequency, for different external electric and magnetic fields, chemical potential, HgTe layer thickness and temperature, to tune the material magneto-optical properties. We have shown that absortance/transmittance acquires extremal values at the critical point, where the Faraday angle changes sign, thus providing fine markers of the topological phase transition. In the case of non-topological materials as phosphorene, a minimum of the transmittance is also observed due to the energy gap closing by an external electric field.

Magneto-optical epitaxial bismuth-substituted yttrium iron garnet thin films on a diamagnetic substrate for low temperature applications

The uprising interest in the integration of the magneto-optical iron garnets into the field of quantum information processing imposes requirements for the damping parameter and optical properties at low temperatures. Typically, high quality iron garnet films are mostly grown epitaxially on the paramagnetic substrates that have rare-earth elements in its composition, which leads to an increase of their magnetic damping at temperatures below 100 K. Here, we epitaxially grew magneto-optical ferromagnetic garnet films on a diamagnetic yttrium scandium gallium garnet substrate to demonstrate narrow ferromagnetic resonance (FMR) linewidth at temperature range from 300 K to 4 K. The maximum Faraday angle measured at wavelength of 660 nm is ΘF = 0.34 ⋅103 deg/cm at 65 K. The FMR linewidth of the iron garnet film gets slightly larger as temperature decreases, but still remains at a level of 35 Oe at 4 GHz even at 4 K. The investigated iron garnet thin films grown on diamagnetic substrates can be successfully implemented in low-temperature technological applications that require low damping and high magneto-optical response.

Faraday angle prediction based on 1-D CNN on the J-TEXT tokamak

The Faraday angle is an indispensable physical parameter to evaluate and reconstruct the current density profile which is imperative for advanced tokamak operation and physics study. The POLARIS system has been implemented on J-TEXT since 2012 for the measurement of the Faraday angle and this system occasionally encounters operational failures that result in the inability to provide measurements. So a deep learning model is trained to predict the Faraday angle when the POLARIS is unable to provide the measurement. The model is primarily based on a 1-D convolutional neural network (CNN) and is equipped with multiple convolutional paths that can accommodate various lengths of diagnostic data. The data of 100 shots are used to train the 1-D CNN model, and 30 shots are used to optimize the hyperparameters and select the model which performs best during the training process. The results on a test set of 30 shots show that the model obtains a satisfactory fitting effect.

Theoretical investigations on Kerr and Faraday rotations in topological multi-Weyl Semimetals

Motivated by the recent proposal of giant Kerr rotation in WSMs, we investigate the Kerr and Faraday rotations in time-reversal broken multi-Weyl semimetals (mWSMs) in the absence of an external magnetic field. Using the framework of Kubo response theory, we find that both the longitudinal and transverse components of the optical conductivity in mWSMs are modified by the topological charge (nn). Engendered by the optical Hall conductivity, we show in the thin film limit that, while the giant Kerr rotation and corresponding ellipticity are independent of nn, the Faraday rotation and its ellipticity angle scale as nn and n^2n2, respectively. In contrast, the polarization rotation in semi-infinite mWSMs is dominated by the axion field showing nn dependence. In particular, the magnitude of Kerr (Faraday) angle decreases (increases) with increasing nn in Faraday geometry, whereas in Voigt geometry, it depicts different nn-dependencies in different frequency regimes. The obtained results on the behavior of polarization rotations in mWSMs could be used in experiments as a probe to distinguish single, double, and triple WSMs, as well as discriminate the surfaces of mWSMs with and without hosting Fermi arcs.

Theoretical studies of magneto-optical Kerr and Faraday effects in two-dimensional second-order topological insulators

Optical approaches are useful for studying the electronic and spin structure of materials. Here, based on the tight-binding model and linear response theory, we investigate the magneto-optical Kerr and Faraday effects in two-dimensional second-order topological insulators (SOTI) with external magnetization. We find that orbital-dependent Zeeman term induces band crossings for SOTI phase, which are absent for trivial phase. In the weak-magnetization regime, these crossings give rise to giant jumps (peaks) of Kerr and Faraday angles (ellipticity) for SOTI phase. In the strong-magnetization regime, we find that two nearly flat bands are formed at the high-symmetry point of Brillouin zone of SOTI phase. These flat bands give rise to two successive giant jumps (peaks) of Kerr and Faraday angles (ellipticity). These phenomena provide new possibilities to characterize and detect the two-dimensional SOTI phase.

Magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulators

Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes. Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulator MnBi2Te4. We find that by breaking the combined mirror symmetries with either perpendicular electric field or external magnetic moment, Kerr and Faraday effects occur. Under perpendicular electric field, antiferromagnetic topological insulators (AFMTI) show sharp peaks at the interband transition threshold, whereas trivial insulators show small adjacent positive and negative peaks. Gate voltage and Fermi energy can be tuned to reveal the differences between AFMTI and trivial insulators. We find that AFMTI with large antiferromagnetic order can be proposed as a pure magneto-optical rotator due to sizable Kerr (Faraday) angles and vanishing ellipticity. Under external magnetic moment, AFMTI and trivial insulators are significantly different in the magnitude of Kerr and Faraday angles and ellipticity. For the qualitative behaviors, AFMTI shows distinct features of Kerr and Faraday angles when the spin configurations of the system change. These phenomena provide new possibilities to optically detect and manipulate the layered topological antiferromagnets.

Faraday Angle and Accuracy Measurement of Magneto-Optic Current Transmission Based on New Telluride Glass

Two robust temperature-insensitive magneto-optical current sensor prototypes, based on double polarimetric processing schemes and single light way methods, were constructed using light reflection and light transition, respectively. A diamagnetism TeO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -PbO-ZnO-BaF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> bulk glass was fabricated as a sensing head which, with/without a silver layer, acts as a mirror sputtered by RF sputtering. The Verdet constant of the TPZBF glass was measured using the self-made optical bench. The current sensors were evaluated under various currents and different temperatures. Results indicated that the constructed low-cost current sensor prototypes are accurate and stable for current sensing applications.

Validation of theory-based integrated modeling and new insights for a high-performance steady-state scenario with only RF heating on EAST

Theory-based integrated modeling is validated against high-performance steady-state core plasmas on EAST in the high poloidal beta (β p) regime with only RF heating. Reasonably good agreement between the modeling results and experimental measurements is obtained not only for the temperature profiles but also for the 11-chord line-integrated densities and Faraday angles for the first time. This validation effort demonstrates that the safety factor profiles can be non-reversed in high β p experiments on EAST. The inaccessibility for LH waves observed in conventional ray-tracing simulations for some high β p experiments is effectively mitigated by including the modeling of wave propagation in the scrape-off layer. The observed confinement improvement with density increasing (Gong et al 2019 Nucl. Fusion 59 086030) can be attributed to the reduction of turbulent transport by the collisional stabilization in trapped electron modes, rather than by the Shafranov shift stabilization effect which was proposed to be the major cause of confinement enhancement in previous literature. Based on the successful validation and newly gained physical insights, predictive modeling is performed for core plasma considering the future upgrade capacity of LH wave system and shows that the high-performance steady-state H-mode scenario on EAST can be extended to the regime with q 95 to be ITER relevant.

Tunable and enhanced Faraday rotation induced by the epsilon-near-zero response of a Weyl semimetal

In this paper, we theoretically study the Faraday (FR) rotation effect excited by a transverse-magnetic (TM)-polarized wave passing through a bulk Weyl semimetal (WSM). Results show that the FR angle maintains a large value $(\ensuremath{\sim}\text{--}{21}^{\ensuremath{\circ}})$ with high transmission $(|{t}_{pp}|\ensuremath{\sim}87%)$, which is caused by the close transmission coefficient of $|{t}_{ps}|$ $|{t}_{ps}|$ and $|{t}_{pp}|$. What is more important, the FR angle can be further enhanced at the epsilon-near-zero (ENZ) frequency, where a maximum FR rotation angle (absolute value) of 45\ifmmode^\circ\else\textdegree\fi{} has been obtained due to the sharp decreases of $|{t}_{pp}|$. Remarkably, the ENZ frequency of the WSM can be regulated by varying the Fermi energy and tilt degree, resulting in the tunable and enhanced FR angle at the different ENZ frequencies. Particularly, it is demonstrated that the incident angle should be declined with the increase of WSM thickness for enhancing the FR angle at the ENZ frequency. We also examine the effect of Weyl node separation on the FR angle. Our studies provide a simple and effective method to enhance and control the FR effect with a WSM or other topological semimetals.

Giant THz Faraday rotation with stacked magnetized graphene

It has been recently discovered that strong magnetoplasmonic effects exist on graphene and may open a new avenue for many novel THz non-reciprocal devices. The magnetoplasmonic response of two-dimensional graphene strongly depends on the electromagnetic properties of the surrounding medium. We develop a modified transmission line analog formulation to investigate the Faraday and Kerr rotation associated with multi-sheet magnetized graphene embedded in the layered medium. The formulation utilizes a junction transformer to model anisotropic conductive sheets at the interfaces and is highly numerically efficient and stable. It is also demonstrated for the first time that a multiple heterojunctions conjugated photonic crystal with graphene embedded at the interfaces will significantly enhance the magneto-optical effect of the system. 15.3° Faraday angle under 0.25 T low static bias magnetic field is achieved at 15 THz with a high transmittance, which enables the design of accessible high-performance non-reciprocal devices in the high THz frequency regime. The proposed formulation and design principle may lay the foundation for future THz graphene-based plasmonic devices.

Ambipolar magneto-optical response of ultralow carrier density topological insulators

We have investigated the THz range magneto-optical response of ultralow carrier density films of Sb$_2$Te$_3$ using time-domain THz polarimetry. Undoped Sb$_2$Te$_3$ has a chemical potential that lies inside the bulk valence band. Thus its topological response is masked by bulk carriers. However, with appropriate buffer layer engineering and chemical doping, Sb$_2$Te$_3$ thin films can be grown with extremely low electron or hole densities. The ultralow carrier density samples show unusual optical properties and quantized response in the presence of magnetic fields. Consistent with the expectations for Dirac fermions, a quantized Hall response is seen even in samples where the zero field conductivity falls below detectable levels. The discontinuity in the Faraday angle with small changes in the filling fraction across zero is manifestation of the parity anomaly in 2D Dirac systems with broken time reversal symmetry.

Preparation and orientation mechanism analysis of (BiTm)&lt;sub&gt;3&lt;/sub&gt;(GaFe)&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt; magneto-optical single crystal film with out-of-plane orientation

Liquid-phase epitaxy (LPE) is one of the best techniques for the preparation of single crystal garnet films. However, the specific Faraday rotation angle of Yttrium iron garnet (YIG) is small, and its easy magnetization axis is parallel to the film surface. The YIG requires a large external saturation field, which cannot meet the development needs of magneto-optical devices. It is found that Bi-substituted YIG(Bi:YIG) film has a larger specific Faraday angle. By adjusting the easy magnetization axis of Bi: YIG perpendicular to the film surface, the saturation magnetization of Bi: YIG can be reduced, so that it can work under a small external magnetic field. This meets the development needs of miniaturization and energy saving of magneto-optical device. The saturation magnetization of garnet film can be effectively reduced by substituting Ga&lt;sup&gt;3+&lt;/sup&gt; for YIG crystal, mainly for Fe&lt;sup&gt;3+&lt;/sup&gt; at the 24d position of its tetrahedron. And the lattice constants of Gd&lt;sub&gt;3&lt;/sub&gt;Ga&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt; (GGG) and YIG are 1.2383 nm and 1.2376 nm, respectively. However, the radius of Bi&lt;sup&gt;3+&lt;/sup&gt; (10.8 nm) is larger than that of Y&lt;sup&gt;3+&lt;/sup&gt; (9.0 nm), the lattice mismatch of garnet film increases with the incorporation of Bi&lt;sup&gt;3+&lt;/sup&gt;. In order to neutralize the lattice expansion caused by Bi&lt;sup&gt;3+&lt;/sup&gt;, Tm&lt;sup&gt;3+&lt;/sup&gt; (8.69 nm) with a radius smaller than that of Y&lt;sup&gt;3+&lt;/sup&gt; (9.0 nm) is selected. Based on the theoretical analysis of the magnetocrystalline anisotropy of garnet film, (BiTm)&lt;sub&gt;3&lt;/sub&gt;(GaFe)&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt; mono-crystalline films with different growth temperatures and different thickness values are grown by LPE on GGG (111) substrates. The experimental results show that when the thickness of epitaxial film is greater than 1 μm, the influence of shape anisotropy on magnetocrystalline anisotropy can be ignored. With the increase of growth temperature, the substitution number of Bi&lt;sup&gt;3+&lt;/sup&gt; ions decreases gradually, the lattice constant of epitaxial film decreases gradually, and the lattice mismatch first decreases and then increases. Then, the state of compressive stress gradually changes into that of tensile stress. Compared with growth-induced anisotropy, the stress-induced anisotropy is dominant in the change of magnetocrystalline anisotropy. The Verdet constant of (BiTm)&lt;sub&gt;3&lt;/sub&gt;(GaFe)&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt; film is 11.8 × 10&lt;sup&gt;4&lt;/sup&gt; rad/Tm@1064 nm. The results show that the prepared (BiTm)&lt;sub&gt;3&lt;/sub&gt;(GaFe)&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt; mono-crystalline films have great development potential in magneto-optical devices.

Влияние ионного облучения на магнитные свойства пленок CoPt

The possibility of using He+ ion implantation with an energy of 20 keV for modifying the domain structure and magnetic properties of CoPt films formed by electron beam evaporation with different compositions - Co0.45Pt0.55 and Co0.35Pt0.65 - has been investigated. For the irradiated CoPt samples of both compositions, a decrease in the coercivity (narrowing of the hysteresis loop on the magnetic field dependences of the Faraday angle and magnetization) with an increase in the He+ ion fluence from 2×1014 to 4×1014 cm−2 was found. In this case, the remanent magnetization of the Co0.35Pt0.65 films coincides with the value of saturation magnetization, while for Co0.45Pt0.55, a decrease in the remanent magnetization is observed. Magnetic force microscopy has shown that for the Co0.45Pt0.55 alloy, with an increase in the ion fluence up to 3 × 1014 cm−2, the largest number of isolated circular domains (skyrmions) is formed, while for He+ irradiation with a fluence of 4×1014 cm−2 for Co0.35Pt0.65, in addition to isolated circular domains, 360-degree domain walls (1D skyrmions) are observed. At the same time, the study of CoPt films by the Mandelstam-Brillouin spectroscopy method revealed an increase in the shift between the Stokes and anti-Stokes components of the spectrum and thus a significant increase of the Dzyaloshinsky-Moriya interaction for the irradiated samples. Simulation using the SRIM software showed that the applied ion irradiation causes the asymmetric mixing of Co and Pt atoms and thus, this may underlie the mechanism of the of the ion irradiation on magnetic properties and domain structure in CoPt films.

Linear dichroism infrared resonance in overdoped, underdoped, and optimally doped cuprate superconductors

By measuring the polarization changes in THz, infrared, and visible radiation over an extended energy range (3-2330 meV), we observe symmetry-breaking in cuprate high temperature superconductors over wide energy, doping, and temperature ranges. We measure the polarization rotation and ellipticity of transmitted radiation though thin films as the sample is rotated. We observe a two-fold rotational symmetry in the Faraday angle, which is associated with linear dichroism (LD) and occurs when electromagnetic radiation polarized along one direction is absorbed more strongly than radiation polarized in the perpendicular direction. Such polarization anisotropies can be generally associated with symmetry breakings. We measure the amplitude of the LD signal and study its temperature, energy, and doping dependence. The LD signal shows a resonant behavior with a peak in the few hundred meV range, which is coincident with the mid-infrared optical feature that has been associated with the formation of the pseudogap state. The strongest LD signal is found in under-doped films, although it is also observed in optimally- and over-doped samples. The LD signal is consistent with nematic charge ordering as well as novel magnetoelectric effects.

Optimization of the POlarimeter-INTerferometer diagnostics system on EAST

A double-pass, radial-view, 11-chord POlarimeter-INTerferometer (POINT) system has been routinely operated on the Experimental Advanced Superconducting Tokamak (EAST) to provide electron density and current density information for physics research. Stray light occurs due to spurious reflections from optical elements, including lenses, waveplates, windows, and even detectors, along the optical path and can seriously deteriorate the accuracy of the Faraday rotation measurements. As a result of stray light contamination, periodic oscillations can be observed in the Faraday rotation data during the density ramp-up phase. Aiming to realize real-time current profile feedback control using Faraday effect measurements, the contamination from stray light must be removed. Some optimization methods have been explored to decrease the error induced by stray light. The results show that the Faraday angle oscillation during the density ramp-up phase is reduced from 3̂–5̂ to 0.5̂–1̂ (double-pass). Measurement of the noncollinearity error is also performed for the POINT system on EAST. This optimization allows for more accurate current profile measurements for physics research.

Micromagnetic and Magnetooptical Properties of Ferromagnetic/Heavy Metal Thin Film Structures

The magnetic properties of CoPt, CoPd, and FePd thin films with different contents of a ferromagnetic material fabricated by electron beam evaporation have been compared. The micromagnetic structure investigations have shown a decrease in the magnetic domain size with an increase in the Co content in the CoPt and CoPd films, which has been attributed to the presence of two magnetic phases in the films. The magnetooptical studies have shown anomalously large Faraday angles and the absence of Kerr effect in the CoPt films, which make them attractive for application in optics. In the FePd films, the minimum coercivity values have been obtained from the magnetic-field dependences of the magnetization, which has also been related to the magnetic structure features.

Determination of Faraday angle under conditions of multiple-beam interference by using transmission and reflection spectra in non-polarized light

The work is aimed at reliably determining the Faraday angle under conditions of multiple-beam interference. In our experiments we investigated the influence of the magnetic field oriented along the direction of light propagation on the transmission and reflection spectra of coherent samples. The experiments were performed using the free plane-parallel n-InAs plate and n-GaAs/Al structures. The transmission and reflection spectra were registered in non-polarized light. It has been ascertained that changes in these spectra under the action of the magnetic field are caused by Faraday rotation and can be modeled by the spectral dependence of the rotation angle. We provide theoretical calculations and an algorithm to process the experimental spectra and determine their uncertainties. The offered method allows the determining of the spectral dependences of Faraday rotation angle as well as effective masses of electrons in the studied semiconductors.

Compact four-port circulator based on 2D photonic crystals with a 90° rotation of the light wave for photonic integrated circuits applications

A four-port optical circulator based on two-dimensional square lattice photonic crystals is reported. It is simple besides the brief framework. The crystalline geometrical structure of the circulator makes 90° non-reciprocal transmissions of electromagnetic waves with low insertion loss and high levels of isolation by the diligence of magneto-optic crystals. The structure is novel because it uses a resonant cavity with a simple design. Also, in comparison to prior models, the proposed four-port circulator utilizes a two-dimensional square lattice crystal structure with a cylindrical ferrite section of the π/4 Faraday angle. The finite element method is used for this anisotropic medium to get the tensor elements in this simulation. The importance of the gyromagnetic properties of ferrite crystals for the non-reciprocal transmission is investigated. Furthermore, the corresponding S-parameters for this circulator are analyzed and reported. Due to the compact size and ease of fabrication, this device can be realized for applications such as splitting and isolation in photonic integrated circuits.

Study on lattice constant and magnetic properties of bismuth substituted YIG polycrystal thin film on different substrates prepared by rf magnetron sputtering

In this study, we investigated the magnetic and magneto-optical properties of Bi1.5Y1.5Fe5O12 (Bi:YIG) films prepared on quartz and silicon substrates, respectively, by radio frequency magnetron sputtering and disposed by microwave annealing. The results indicated that the lattice constant and magnetic properties were significantly different on different substrates. First, the lattice constant of film on quartz substrate was found to be 9% greater than that on silicon substrate because of larger residual stress. Second, the grain size of film on silicon substrate was smaller than that on quartz substrate at same annealing temperature, which led to its magnetization being 70% smaller than that on quartz substrate and coercive force was 50% less. Finally, the transmittance of the Bi:YIG film and pure YIG was studied and the Faraday angle of Bi1.5Y1.5Fe5O12 film on quartz substrate was found to be − 8°/µm at λ = 544 nm and − 1.8°/µm at λ = 677 nm.

Микромагнитные и магнитооптические свойства пленочных структур вида ферромагнетик/тяжелый металл

The paper presents a comparative analysis of the magnetic properties of thin films of CoPt, CoPd, FePd alloys. The films were fabricated by electron-beam evaporation, with the variation of a ferromagnetic material content. Studies of the micromagnetic structure showed a decrease in the size of magnetic domains with an increase of the Co content in CoPt and CoPd films, which is associated with the presence of two magnetic phases in the films. Magneto-optical studies have shown abnormally high Faraday angles and the absence of the Kerr effect for CoPt films, which makes them attractive for practical applications in optics. The minimum coercive field values in magnetic field dependences of magnetization, as compared with other films, were obtained for FePd films, which is also associated with the peculiarities of the magnetic structure.