Electric Polarization Vector Research Articles

The Discovery of Polarized Water Vapor Megamaser Emission in a Molecular Accretion Disk

For the first time in an extragalactic source, we detect linearly polarized H2O maser emission associated with the molecular accretion disk of NGC 1068. The position angles of the electric polarization vectors are perpendicular to the axes of filamentary structures in the molecular accretion disk. The inferred magnetic field threading the molecular disk must lie within ∼35° of the sky plane. The orientation of the magnetic fields relative to the disk plane implies that the maser region is unstable to hydromagnetically powered outflow; we speculate that the maser region may be the source of the larger-scale molecular outflow found in Atacama Large Millimeter/submillimeter Array studies. The new very long baseline interferometry observations also reveal a compact radio continuum source, NGC 1068*, aligned with the near-systemic maser spots. The molecular accretion disk must be viewed nearly edge on, and the revised central mass is M = (16.6 ± 0.1) × 106 M ☉.

Determination of the internal structural heterogeneity of natural diamond: Methodological aspects of using confocal Raman spectroscopy with polarization analysis

Aim. To describe a technique for studying the internal structural heterogeneity of natural diamond crystals, based on confocal Raman spectroscopy with polarization analysis, including angular resolution, at high spectral (0.5–0.6 cm–1) and spatial (1 μm) resolution. Results. The parameters of the F2g vibrational mode in diamond (position, width, intensity, shape, including the Gaussian and Lorentzian contributions to the broadening) are determined by the superposition influence of a number of factors, including the type and content of structural stresses, deformations, various types of defects, as well as orientation of crystallographic axes of the crystal relative to the directions of incident and scattered rays and the directions of their electric polarization vectors. The proposed analytical technique includes: (1) analysis of the crystallographic orientation of the sample in the spectrometer coordinate system and possible misorientations of its fragments with an error of ≈8–15°; (2) visualization of the distribution of structural stresses, deformations, twins, impurity defects and their associates based on sample surface mapping by spectral parameters of the F2g vibration mode; (3) obtaining statistical characteristics of the internal structural heterogeneity of the samples based on diagrams of spectral parameter frequency with a statistically significant number (≈103): unimodality (uni-, bimodal distributions) and distribution dispersion (from ≈0.1 to ≈0.6 cm–1 for width and from ≈0.04 to ≈0.6 cm–1 for line position). The procedure was tested using two synthetic CVD diamond single crystals doped with nitrogen and boron. The possibility of typification of natural samples by statistical characteristics of internal heterogeneity is considered using the example of samples from kimberlite pipes of Yakutia and placers of the Western Cis-Urals. Conclusions. A method for determining the internal structural heterogeneity of natural diamond crystals based on confocal Raman spectroscopy with polarization analysis is proposed. The possibility of using statistical characteristics of heterogeneity as a typomorphic feature of the original diamond source is demonstrated. The proposed diagrams are promising for sample comparison and typification.

Rayleigh wave propagation in centrosymmetric materials with micro-stiffness, flexoelectric and micro-inertia effects

A theoretical investigation of Rayleigh waves propagation in polarized media has been carried out using a reformulated flexoelectric theory for isotropic dielectrics with micro-inertia effect. Within this non-classical theory, the internal energy density is the functional of the strain tensor, dilatation gradient, deviatoric part of stretch gradient and rotation gradient tensors, polarization vector, and polarization gradient. The obtained system of governing equations additionally contains three material length-scale parameters to account the micro-stiffness effect, one material constant to capture the micro-inertia effect, two flexoelectric constants to describe the flexoelectric effect and three length scale parameters related to the polarization gradient. To solve the coupled governing equations, the method of Lamé-type potentials for mechanical displacement and electric polarization vectors is used. The influences of various factors such as micro-stiffness, flexoelectricity, electric quadrupoles and micro-inertia effects on the phase velocity of the Rayleigh waves in a homogeneous isotropic half-space are studied. It is found that above effects become significant with the increase of the wavenumber. This study can be important for the investigation of high frequency surface acoustic waves in dielectric materials.

Modelling coupled electro-mechanical phenomena in elastic dielectrics using local conformal symmetry

The local scaling symmetry of the Lagrange density is exploited to investigate the myriad electro-mechanical coupling effects observed in the elastic dielectrics. In contrast to most known flexoelectricity theories, this approach has also explicated on the geometric underpinnings of the induced polarization and electric potential. Due to the inhomogeneous scaling of the metric, the invariance of the Lagrange density will be lost. To restore the gauge invariance of the Lagrange density, we introduce the notion of minimal replacement, viz., define a gauge covariant operator in place of the ordinary partial derivative. Minimal replacement introduces gauge compensating one form field. We relate the exact part of the gauge compensating one form field with electric potential. However, the gauge compensating one form field's anti-exact part is correlated with the electric polarization vector. We constructed different components of the gauge invariant energy density using the geometric objects like scale invariant gauge curvature. We appropriately contracted the skew symmetric gauge curvature tensor with the metric to construct the scale invariant energy associated with the gauge field. Finally, we derive the governing coupled equations employing Hamilton's principle. In order to assess how the theory performs, we carry out a few numerical simulations and validation. Model prediction of the pressurized flexoelectric disk with a central hole shows good agreement with the analytical solution. We also investigated flexoelectric cantilever beam subjected to a point load and different earthing conditions. Explorations of this kind of coupling may have notable implications in many industrial and laboratory applications.

Enhancement of optical properties of two-dimensional Bi2Te2Se by biaxial strain based on first-principles

The study of two-dimensional flexible materials in mechanic and optics has gained significant attention. By applying strain to modify the internal structure of materials, researchers can investigate the resulting mechanical and optical changes, offering exciting opportunities for further exploration in this field. The electronic structure, mechanical properties, and optical properties of the two-dimensional trigonal system Bi2Te2Se under biaxial strain regulation were investigated by using the first-principles plane pseudopotential plane wave method based on density generalized function theory. The analysis reveals that the energy bandwidth of Bi2Te2Se decreases with increasing strain until the band gap reaches 0 at 9% strain, causing the system to shift from a semiconductor to a conductor. The electronic density of states is primarily determined by the 6p orbitals of Bi and 5p orbitals of Te. With regards to its mechanical properties, Bi2Te2Se satisfies the mechanical stability criterion under different strains. As the strain increases from 0% to 6%, the material becomes increasingly brittle, with its interior transitioning from metallic to covalent bonds. However, the material toughness begins to improve from 6% to 9%, with the interior transitioning from covalent to metallic bonding. The performance improvement of Bi2Te2Se varies depending on the two electric field polarization vectors along [1 0 0] and [0 0 1] directions under strain. The material shows distinct application prospects in terms of absorption coefficient, reflectivity, refractive index, and lossiness under two directions. This paper provides a theoretical reference for the future mechanical and optical applications of Bi2Te2Se.

Nonlinear Optical and Magnetic Properties of FeII-SCN-HgII Isomers: Centrosymmetric Layers and Chiral Networks

Research on isomers is highly desirable due to their prospective role in better understanding of physicochemical properties of similar systems and further development of multifunctional molecular materials. Iron(II) and tetra(thiocyanato)mercury(II) ions self-assembled in the presence of 2-acetylpyridine (2-acpy) excess to form two {[Fe(2-acpy)][Hg(μ-SCN)4]}n isomers: two-dimensional (2D) centrosymmetric layers with folded ring structural motifs (1) and three-dimensional (3D) chiral networks with right- or left-handed {···Fe-NCS-Hg-SCN···}∞ helixes (2). New methods of designing and synthesizing functional thiocyanate-bridged materials have been proposed. In addition, the similarity between 1 and 2 allowed for the description of subtle changes in IR and UV-visible spectra. Moreover, 2 shows spontaneous resolution, and it crystallizes in the noncentrosymmetric space group P21, leading to the occurrence of nonlinear optical activity in circular dichroism studies and second harmonic generation (SHG). At room temperature, the SH susceptibility for powder sample 2 reached 6.0 × 10-11 esu. Ab initio calculations indicated the electric polarization vector and the crystallographic twofold screw axis pass through the aromatic ring. Magnetic studies for 1 and 2 revealed high-spin iron(II) with zero-field splitting at low temperatures. Analysis of magnetic data gave |D| = 37.45 cm-1, |E/D| = 5.59 cm-1, and ⟨g⟩ = 2.15 for 1, |D| = 36.78 cm-1, |E/D| = 4.92 cm-1, and ⟨g⟩ = 2.18 for 2, and information about the orientation of magnetic anisotropy vectors for both compounds.

Origin of circular dichroism in resonant elastic x-ray scattering from magnetic and polar chiral structures

Circular dichroism in resonant elastic x-ray scattering (CD-REXS) has recently been observed in chiral structures composed of multiferroic materials as well as magnetic moments or electric polarization vectors. In order to comprehensively understand the experimental results of these previous studies, we present here in detail the analytical formulation of CD-REXS for one-dimensional helices composed of magnetic moments and electric polarization vectors, respectively. In particular, by comparing CD-REXS for a proper-screw-shaped Bloch-type helix and cycloid-shaped N\'eel-type helix, we found that CD-REXS for both magnetic and polar helices can discriminate between both types of helices. We also found that the x-ray polarization factor depending on the scattering geometry is a significant factor in determining the characteristics of CD-REXS for chiral structures. The results obtained from the detailed formulas can be intuitively understood using the concept of mirror reflection. In particular, in this way it can be understood that Bloch- and N\'eel-type helices correspond to truly chiral and achiral structures, respectively, and why CD-REXS is able to distinguish between these two types of helices.

High temperature phase transitions in NaNbO3 epitaxial films grown under tensile lattice strain

We have investigated high temperature phase transitions in NaNbO3 thin films epitaxially grown under tensile lattice strain on (110) DyScO3 substrates using metal-organic vapor phase epitaxy. At room temperature, a very regular stripe domain pattern consisting of the monoclinic a1a2 ferroelectric phase was observed. Temperature-dependent studies of the refractive index and the optical bandgap as well as in situ high-resolution x-ray diffraction measurements prove a ferroelectric–ferroelectric phase transition in the range between 250 and 300 °C. The experimental results strongly suggest that the high-temperature phase exhibits a distorted orthorhombic a1/a2 crystal symmetry, with the electric polarization vector lying exclusively in the plane. A second phase transition was observed at about 500 °C, which presumably signifies the transition to the paraelectric phase. Both phase transitions show a pronounced temperature-dependent hysteresis, indicating first-order phase transitions.

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO3/SrTiO3 superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.

Synthetic Aperture Radar 3-D Polarimetry

An synthetic aperture radar (SAR) 3-D polarimetry method using a radially polarized antenna is described. A 3-D target scattering model is developed based on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times3$ </tex-math></inline-formula> polarimetric scattering matrix, allowing a target to be characterized by its interaction with 3-D electric field polarization vectors. The difficulties in measuring the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times3$ </tex-math></inline-formula> scattering matrix for a target are discussed, mainly that its measurement requires the target to be interrogated from multiple and specific incidence angles. The advantages of a radially polarized antenna for 3-D polarimetry are discussed, resulting from the diversity afforded in the polarization of the radiated electric field. An image reconstruction algorithm is then developed to enable 3-D polarimetry imaging to be performed from SAR measurements made with a radially polarized antenna, by which a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times3$ </tex-math></inline-formula> scattering matrix can be generated for every image voxel. Subsequently, a radially polarized antenna was fabricated and used to image two separate samples. The first target contained complex surface curvature and was used to demonstrate the efficacy of this technique for use on general targets. The second sample contained many small targets with different orientations (in 3-D) and was used to evaluate and demonstrate the accuracy of this method for performing 3-D orientation estimation.

Low magnetic-field induced high temperature dynamic magnetoelectric coupling performances in Z-type Sr3Co2Fe24O41

Magnetic-field induced dynamic magnetoelectric coupling effects and polarization performance of Z-type Sr3Co2Fe24O41 (SCFO) ceramic has been investigated. Results found that SCFO’s transverse tapered magnetic structure can induce electric polarization, and its electric polarization direction will not change under external magnetic effects. First-order dynamic magnetoelectric coupling coefficient (α) and second-order dynamic magnetoelectric coupling coefficient (β) of SCFO exhibited strong response main in magnetic structural phase transition region. The magnetoelectric structural phase transition position appeared in low magnetic field, and the magnetic moment vector and its corresponding electric polarization vector of SCFO exhibited the most unstable state near its equilibrium position, which is beneficial for inducing strong dynamic magnetoelectric coupling response. When the applied magnetic fields to SCFO increased, the magnetic moment stability near the equilibrium position increased, and the dynamic magnetoelectric coupling response decreased. Results showed that the dynamic magnetoelectric coupling response of SCFO can bear T 1 = 370 K high temperature. The dynamic magnetoelectric coupling response induced by low magnetic fields in SCFO contributes to its actual application in next generation magnetoelectric information storage devices.

Polarization vector formalism of plasma weak turbulence

This paper formulates the plasma weak turbulent theory based on the unit electric field polarization vector. This concept is not intrinsically new, and partial formulations of weak turbulence processes based on the polarization vector approach are found in the literature. However, the present paper applies such a method uniformly to all the relevant processes for the first time, thus unifying the existing formalisms. The present result potentially provides many advantages including the fact that it facilitates the complex manipulations of various tensor coupling coefficients that dictate the wave–wave and nonlinear wave–particle interactions. To demonstrate its validity, the limit of unmagnetized plasmas is considered, and it is shown that the known results are recovered. The present formalism can be extended to more complex situations including magnetized plasmas, which is a subject of future work.

Compact explicit matrix representations of the flexoelectric tensor and a graphic method for identifying all of its rotation and reflection symmetries

Flexoelectricity is an electromechanical phenomenon produced in a dielectric material, with or without centrosymmetric microstructure, undergoing a non-uniform strain. It is characterized by the fourth-order flexoelectric tensor, which links the electric polarization vector with the gradient of the second-order strain tensor. Our previous work [H. Le Quang and Q.-C. He, Proc. R. Soc. A 467, 2369 (2011)] solved the fundamental theoretical problem of determining the number and types of all rotational symmetries that the flexoelectric tensor can exhibit. In the present study, compact explicit matrix representations of the flexoelectric tensor are provided so as to facilitate the use of it with any possible rotational symmetry. The number and types of all reflection symmetries that the flexoelectric tensor can have are also determined. To identify the rotational symmetry and reflection symmetry of a given flexoelectric tensor, a simple and efficient graphic method based on the concept of pole figures is presented and illustrated.

ПЕРЕМАГНИЧИВАНИЕ И НЕОДНОРОДНЫЙ МАГНИТОЭЛЕКТРИЧЕСКИЙ ЭФФЕКТ В НАНОРАЗМЕРНОЙ ДВУХСЛОЙНОЙ ФЕРРОМАГНИТНОЙ ПЛЕНКЕ С КОМБИНИРОВАННОЙ ОДНООСНОЙ И КУБИЧЕСКОЙ АНИЗОТРОПИЕЙ В СЛОЯХ

A numerical study of the magnetization reversal of a two-layer exchange-coupled ferromagnetic plate of finite dimensions, which has a combined uniaxial anisotropy (of the "easy axis" type for the upper layer and «easy plane» for the lower one) and cubic anisotropy with orientation [111]. It is shown that, in the presence of cubic anisotropy, the ground state of magnetization turns out to be uniform in the plane of the film. However, there is discontinuity at the interface between the film layers. This inhomogeneity can lead to the appearance of electric polarization due to the magnetoelectric effect. The electric polarization vector in this case lies in the plane of the film. Its modulus increases with increasing cubic anisotropy. In addition, with an increase in cubic anisotropy, a hysteresis of electrical polarization is observed.

Large linear magnetoelectric effect induced by an external magnetic field in the collinear antiferromagnet DyCrO4

A microscopic theory of the interaction of Cr spins with electric and magnetic fields in ${\mathrm{DyCrO}}_{4}$ is described. The derived effective energy operator allows calculating the electric polarization vector using information about the magnetic structure. The calculated linear electric polarization in electric and magnetic fields at $Hl3\phantom{\rule{4.pt}{0ex}}\text{T}$ is consistent with the available experimental data. The electric field is induced by an odd crystalline field on chromium ions and the charge transfer process from the nearest oxygen ions. The enhancement of the magnetic field is associated with magnetic susceptibility, mainly due to dysprosium ions.

Resonant light absorption and plasmon tunability of lateral triangular Au nanoprisms array

Optical characteristics and electric field distribution of triangular Au nanoprism in a unit and units array under polarized light irradiation were systematically studied by numerical simulation with finite difference time domain method. It is found that the plasmonic properties of the triangular nanoprism are dominated by the electric polarization rather than the wave propagation. The triangular nanoprism presents similar optical response with a strong dipole band under different wave propagations if the electric polarization vectors are parallel to the triangular cross section. The lateral triangular Au nanoprisms array possesses a large tunability of the plasmonic properties contributed from the combined influence of inter-particle distance, particles size, polarization angle and even environmental medium. From the plasmon band shift versus the refractive index, ultra-high local surface plasmon resonance sensitivity (509.96 nm/RIU, figure of merit=5.55) is reached at ∼850nm, making this array promising for biochemical sensing applications.

Electric polarization in two-layer bounded ferromagnetic film

A numerical study of the ground state of a two-layer ferromagnetic bounded film is carried out. The film layers have uniaxial anisotropy easy-plane and easy-axis. All calculations were carried out for films with parameters of ferrites-garnets – Materials that admit a magnetoelectric effect. The ground state was calculated using a three-dimensional micromagnet modeling package OOMMF for rectangular films of different sizes. It was shown that in a film, along with a homogeneous ground state, the vortex distribution of the magnetization is realized. For the vortex distribution, the electric polarization is calculated. It was found that the component of the electric polarization vector of the film perpendicular to the film plane is nonzero. This is due to the presence of the vortex core. The change in the electric polarization due to magnetic reversal of the film by an external magnetic field is studied. It is shown that as the field increases, the polarization modulus also increases to certain field values, and then decreases to zero. As the transverse dimensions of the film decrease, the magnitude of the maximum of the electric polarization increases.

Local atomic geometry and Ti 1s near-edge spectra in PbTiO3 and SrTiO3.

We study Ti 1s near-edge spectroscopy in PbTiO3 at various temperatures above and below its tetragonal-to-cubic phase transition, and in SrTiO3 at room temperature. Ab initio molecular dynamics (AIMD) runs on 80-atom supercells are used to determine the average internal coordinates and their fluctuations. We determine that one vector local order parameter is the dominant contributor to changes in spectral features: the displacement of the Ti ion with respect to its axial O neighbors in each Cartesian direction, as these displacements enhance the cross section for transitions to Eg-derived core-hole exciton levels. Using periodic five-atom structures whose relative Ti-O displacements match the root-mean-square values from the AIMD simulations, and core-hole Bethe-Salpeter equation (BSE) calculations, we quantitatively predict the respective Ti 1s near-edge spectra. Properly accounting for atomic fluctuations greatly improves the agreement between theoretical and experimental spectra. The evolution of relative strengths of spectral features vs temperature and electric field polarization vector are captured in considerable detail. This work shows that local structure can be characterized from first-principles sufficiently well to aid both the prediction and the interpretation of near-edge spectra.

A finite strain modeling for electro-viscoelastic materials

Of interest in this work is the multi-physics modeling of electrically sensitive materials known to have viscoelastic properties. We show how the current state of the art in the modeling of electro-mechanics in deformable media can easily be integrated within the unified framework of continuum thermodynamics, this latter being crucial in setting the convenient forms for the constitutive laws and evolution equations. The formulation is developed within the finite strain range and we adopt the nowadays well-accepted multiplicative decomposition of the deformation gradient into elastically relaxing and viscous parts giving rise to an intermediate configuration on which the electric field vectors can eventually be transported. The paper discusses in depth such a formulation. Among others, it is implicitly found that the electric displacement and polarization vectors can be split into equilibrium and non-equilibrium parts. A model example is proposed for the purpose of demonstration to study some phenomena qualitatively. The paper presents also the numerical design of a simplified version within the context of the finite element method to illustrate the effectiveness of the proposed framework for structural simulations.

Thermodynamics of polarized relativistic matter

We give the free energy of equilibrium relativistic matter subject to external gravitational and electromagnetic fields, to one-derivative order in the gradients of the external fields. The free energy allows for a straightforward derivation of bound currents and bound momenta in equilibrium. At leading order, the energy-momentum tensor admits a simple expression in terms of the polarization tensor. Beyond the leading order, electric and magnetic polarization vectors are intrinsically ambiguous. The physical effects of polarization, such as the correlation between the magneto-vortically induced surface charge and the electro-vortically induced surface current, are not ambiguous.