Spatial Distribution Of Polarization Research Articles

Electrostatic coupling and interface intermixing in ferroelectric superlattices

A thermodynamic model is developed to study electrostatic coupling and interface intermixing in superlattices comprising alternate layers of ferroelectrics and paraelectrics. Interface intermixing leads to inhomogeneous internal electric field and polarization in superlattices. The spatial distribution of polarization extends into the layer over a distance governed by its correlation length. Periodic modulation of the internal electric field and polarization in superlattices are correlated. Interface intermixing enhances the depolarization field of superlattices; however, it has a negligible effect on polarization and transition temperature. The internal electric field, originating from the electrostatic coupling between ferroelectric layers, plays a dominant role in determining the properties of superlattices.

Complete polarization and phase control for focus-shaping in high-NA microscopy

We show that, in order to attain complete polarization control across a beam, two spatially resolved variable retardations need to be introduced to the light beam. The orientation of the fast axes of the retarders must be linearly independent on the Poincaré sphere if a fixed starting polarization state is used, and one of the retardations requires a range of 2π. We also present an experimental system capable of implementing this concept using two passes on spatial light modulators (SLMs). A third SLM pass can be added to control the absolute phase of the beam. Control of the spatial polarization and phase distribution of a beam has applications in high-NA microscopy, where these properties can be used to shape the focal field in three dimensions. We present some examples of such fields, both theoretically calculated using McCutchen's method and experimentally observed.

Recent Applications of Landau-Ginzburg Theory to Ferroelectric Superlattices: A Review

This article briefly reviews recent developments of Landau-Ginzburg theory to ferroelectric phase transitions in superlattices. An overview of the contributions of Landau-type theory to study ferroelectric superlattices is given. Recent findings from first-principles calculations and experiments on intermixing, local polarization coupling and polar discontinuity at interfaces that are not address in these contributions are highlighted. This is followed by a review of recent developments of Landau-Ginzburg theory that addresses these emergent phenomena at interfaces, which is the focus of this review article. The Landau-Ginzburg approach to ferroelectric superlattices with spatial distribution of polarization is outlined. It describes the formation of intermixed layer with properties different from those of both layers. These intermixed layers are mutually coupled through the local polarization at interfaces. Polarization continuity or continuity at interfaces is determined by the nature of the intermixed layer formed at the interface region. Recent results obtained in investigating superlattices comprised primarily of ferroelectric and paraelectric materials are discussed. The results include modulated polarizations, phase transitions, dielectric susceptibilities and switching behaviors.

Electronic structure and transport on the surface of topological insulator attached to an electromagnetic superlattice

We study the electronic structure and transport for Dirac electron on the surface of a three-dimensional (3D) topological insulator attached to an electromagnetic superlattice. It is found that, by means of the transfer-matrix method, the number of electronic tunneling channels for magnetic barriers in antiparallel alignment is larger than that in parallel alignment, which stems to the energy band structures. Interestingly, a remarkable semiconducting transport behavior appears in this system with a strong magnetic barrier due to low energy band nearly paralleling to the Fermi level. Consequently, there is only small incident angle transport in the higher energy region when the system is modulated mainly by the higher electric barriers. We further find that the spatial distribution of the spin polarization oscillates periodically in the incoming region, but it is almost in-plane with a fixed direction in the transmitting region. The results may provide a further understanding of the nature of 3D TI surface states, and may be useful in the design of topological insulator-based electronic devices such as collimating electron beam. (C) 2012 Elsevier B.V. All rights reserved.

Spatial distribution of spin polarization in a channel on the surface of a topological insulator

We study the spatial distribution of electron spin polarization for a gate-controlled T-shaped channel on the surface of a three-dimensional topological insulator (3D TI). We demonstrate that an energy gap depending on channel geometry parameters is definitely opened due to the spatial confinement. Spin surface locking in momentum space for a uniform wide channel with Hamiltonian linearity in the wavevector is still kept, but it is broken with Hamiltonian nonlinearity in the wavevector, like that for two-dimensional surface states widely studied in the literature. However, the spin surface locking for a T-shaped channel is broken even with Hamiltonian linearity in the wavevector. Interestingly, the magnitude and direction of the in-plane spin polarization are spatially dependent in all regions due to the breaking of translational symmetry of the T-shaped channel system. These interesting findings for an electrically controlled nanostructure based on the 3D TI surface may be testable with the present experimental technique, and may provide further understanding the nature of 3D TI surface states.

POLAR STRUCTURES OF PbMg1/3Nb2/3O3-PbTiO3 RELAXORS: PIEZORESPONSE FORCE MICROSCOPY APPROACH

Relaxor ferroelectrics are one of the mysterious objects of the solid-state physics studied over 50 years. The physical properties of relaxors were mainly assessed by scattering and dielectric methods and revealed the importance of polarization correlations with the short-range order, so-called polarization nanoscale regions. This paper review recent progress achieved by using piezoresponse force microscopy (PFM) to analyze the spatial distribution of polarization and its evolution with time, temperature, and electric field for the most popular relaxor family: solid solutions between PbMg1/3Nb2/3O3 and PbTiO3 . The PFM technique has proved to be a powerful tool for the investigation of local properties of relaxors where optical techniques obviously fail because of their lack of resolution. The PFM study of relaxors clearly helps to understand the mechanism of polarization distribution and illustrates the importance of mesoscopic polarization patterns that were until now overlooked by major theories of the relaxor state.

Sound velocity variation as function of polarization state in Lead Zirconate Titanate (PZT) Ceramics

There are several ultrasonic techniques to measure the sound velocity, for example, the pulse-echo method. In such method, the size of transducer used to measure the sound velocity must be in the same order of the sample size. If not, the incompatibility of sizes becomes an error source of the sound velocity measurement. In this work, the Laser Induced Pressure Pulse (LIPP) method is used as ultrasonic method. This method has been very useful for studying the spatial distribution of charges and polarization in dielectrics. We take advantage of the fact that the method allows the sound velocity measurement, to study its variation as function of polarization state in (PZT) ceramics. In a sample with a known thickness e, the sound velocity ν is deduced from the measurement of the transit time T.The sound velocity depends on the elastic constants which in turn they depend on poling conditions. Thus, the variation of the sound velocity is related to the direction and the amplitude of the polarization.

Spatially resolved hard X-ray polarization in solar flares: effects of Compton scattering and bremsstrahlung

This paper aims to study the polarization of hard X-ray (HXR) sources in the solar atmosphere, including Compton backscattering of photons in the photosphere (the albedo effect) and the spatial distribution of polarization across the source. HXR photon polarization and spectra produced via electron-ion bremsstrahlung are calculated from electron distributions typical for solar flares. Compton scattering and photoelectric absorption are then modelled using Monte Carlo simulations of photon transport in the photosphere. Polarization maps across HXR sources (primary and albedo components) for each of the modelled electron distributions are calculated at various source locations from the solar centre to the limb. We show that Compton scattering produces a distinct polarization variation across the albedo patch at peak albedo energies of 20-50 keV for all anisotropies modelled. The results show that there are distinct spatial polarization changes in both the radial and perpendicular to radial directions across the extent of the HXR source at a given disk location. In the radial direction, the polarization magnitude and direction at specific positions along the HXR source will either increase or decrease with increased photon distribution directivity towards the photosphere. We also show how high electron cutoff energies influence the direction of polarization at above ~100 keV. Spatially resolved HXR polarization measurements can provide important information about the directivity and energetics of the electron distribution. Our results indicate the preferred angular resolution of polarization measurements required to distinguish between the scattered and primary components. We also show how spatially resolved polarization measurements could be used to probe the emission pattern of an HXR source, using both the magnitude and the direction of polarization.

Spin polarization and charge transmission for a waveguide on surface of topological insulator

We study the spatial distribution of spin polarization and charge transmission for a T-shaped waveguide formed by gate electrodes on the surface of three-dimensional (3D) topological insulator (TI). We demonstrate that an energy gap depending on waveguide geometry parameters is opened and the spin surface-locking is broken by the electrical confinement on the surface of 3D TI. Using continuous condition for the wavefunctions at boundaries between different regions to determine the scattering coefficients, we find that the waveguide can provide an in-plane spin-polarized electron output. This interesting finding may be useful in further understanding surface states of 3D TI.

Publisher’s Note: Spectral and spatial distribution of polarization at the LaAlO3/SrTiO3interface [Phys. Rev. B83, 155405 (2011)

Publisher’s Note: Spectral and spatial distribution of polarization at the LaAlO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>/SrTiO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>interface [Phys. Rev. B<b>83</b>, 155405 (2011)

Spatial gradient of dynamic nuclear spin polarization induced by breakdown of the quantum Hall effect

We studied spatial distribution of dynamic nuclear polarization (DNP) in a Hall-bar device in a breakdown regime of the quantum Hall effect (QHE). We detected nuclear magnetic resonance (NMR) signals from the polarized nuclear spins by measuring the Hall voltage $V_{xy}$ using three pairs of voltage probes attached to the conducting channel of the Hall bar. We find that the amplitude of the NMR signal depends on the position of the Hall voltage probes and that the largest NMR signal is obtained from the pair of probes farthest from the electron-injecting electrode. Combined with results on pump-and-probe measurements, we conclude that the DNP induced by QHE breakdown develops along the electron-drift direction.

Influence of Natural Aging on the Polarization Profile in PZT-Based Ceramics

In the present work the polarization state of PZT-based ceramics was studied by the thermal square wave method at single frequency. Spatial polarization distributions across the thickness are studied for piezoceramic samples processed with different metallization routes (standard industrial and microwave). It is shown that in the course of natural aging the uniform polarization distribution transforms into a nonuniform one.

Metrology of degree of coherence of circularly polarized optical waves

AbstractThe use of the method of field polarization modulation for defining the degree of coherence of circularly polarized waves is offered. The role of the reference circularly polarized wave in transforming the spatial distribution of polarization into the depth of visibility modulation of the resulting distribution, which can be metrologically estimated and analyzed, is demonstrated.

Measuring the spatial polarization distribution of multimode beams emerging from passive step-index large-mode-area fibers

We measure the polarization state of each guided transversal mode propagating in step-index large-mode-area fibers (V≈4) using a correlation-filter based measurement technique in combination with a Stokes parameter measurement. The entire emerging beam, expressed in terms of a phase-dependent superposition of linearly polarized modes, demonstrates spatially varying polarization properties. By knowing the information about modal amplitudes and phase differences, full information about the optical field is available.

Phase field simulations of low-dimensional ferroelectrics

This paper reviews the previous work on phase field simulations of low-dimensional ferroelectrics of two-dimensional epitaxial ferroelectric islands, thin films, and nanoparticles. The simulations are conducted in real space with exact boundary conditions of a low-dimensional ferroelectric, but consuming a much longer simulation time in comparison with that conducted in Fourier space. For ferroelectric islands and thin films, the simulations exhibit spatial polarization distributions with different types of domain walls and find two critical thicknesses, at which the simulated material changes from a multidomain state to a single-domain state and from ferroelectric phase to paraelectric phase, respectively. The remanent polarization and the coercive field of the simulated ferroelectric films both decrease with decreasing film thickness. The simulations exhibit vortex patterns of polarizations, which have purely toroidal moments of polarizations and macroscopically negligible averaged polarizations, in stress-free nanoparticles when long-range electrostatic interactions are fully taken into account. However, a single-domain structure without any toroidal moment of polarizations is formed in small nanoparticles with strong long-range elastic interactions.

Spatial Modulation of Spin Polarization within a Single Co Island

When electrons are confined to nanostructures, quantum interference takes place due to their wave-particle duality. Using spin-polarized scanning tunneling microscopy, we studied the influence of quantum interference of electrons on the spatial distribution of the spin polarization within a single magnetic nanostructure. We find changes in both the magnitude and sign of the spin polarization on a subnanometer scale. We compare our experimental results with ab initio calculations of the spin-resolved local density of states (LDOS). We find that the modulation of the spin-polarization at a given energy can be ascribed to the different magnitudes of spatially modulated majority states and non-modulated minority states contributing to the total LDOS.

On polarization metrology (estimation) of the degree of coherence of optical waves

A new approach is proposed for estimating the degree of coherence of optical waves. The possibility of transformation of the spatial polarization distribution in the measured spatial intensity distribution for determining the degree of correlation of superposing waves, linearly polarized in the plane of incidence, is shown.

A Comparison of Three Techniques for Solving the Fredholm Integral Equation of the Laser Intensity Modulation Method (LIMM)

The Laser Intensity Modulation Method (LIMM) is widely used for the determination of the spatial distribution of polarization in polar ceramics and polymers, and space charge in non-polar polymers. The analysis of experimental data requires a solution of a Fredholm integral equation of the 1st kind. This is an ill-posed problem that has multiple and very different solutions. A number of methods have been used to solve this problem. In this paper, a comparison is made among three different techniques: the Scale Transformation Method, the Polynomial Regularization L-Curve Method and the Monte Carlo Method. The accuracy and ease of use of the three techniques are compared using both simulated and experimental data.

Enhancement of the electromechanical response in ferroelectric ceramics by design

It is demonstrated based on continuum mechanics modeling and simulation that it is possible to obtain polycrystalline ceramic ferroelectric (FE) materials which beggar single crystals in electromechanical properties. The local inhomogeneities at the FE domain-scale level due to spontaneous polarization and the underlying anisotropy are taken into consideration in the framework of mathematical homogenization of physical properties in FE materials. The intrinsic randomness of the spatial distribution of polarization is shown to be judiciously employed for the design of better polycrystalline FEs. The noncollinear rotation of the net polarization vectors embedded in crystallites of the ceramic FEs is demonstrated to play the key role in the enhancement of physical properties.

Phase‐Field Method of Phase Transitions/Domain Structures in Ferroelectric Thin Films: A Review

This article briefly reviews recent applications of phase‐field method to ferroelectric phase transitions and domain structures in thin films. It starts with a brief introduction to the thermodynamics of coupled electromechanical systems and the Landau description of ferroelectric transitions in homogeneous ferroelectric single crystals. The thermodynamic potentials of a homogeneous crystal under different mechanical boundary conditions are presented, including the thin‐film boundary conditions. The phase‐field approach to inhomogeneous systems containing domain structures is then outlined. It describes a domain structure using the spatial distribution of spontaneous polarization. The evolution of a domain structure towards equilibrium is driven by the reduction in the total‐free energy of an inhomogeneous domain structure including the chemical driving force, domain wall energy, electrostatic energy as well as elastic energy. A number of examples are discussed, including phase transitions and domain stability in ferroelectric thin films and superlattices. It is demonstrated that using a set of independently measured thermodynamic parameters for the corresponding bulk single crystals, the phase‐field approach is able to quantitatively predict not only the strain effect on phase transition temperatures but also the correct ferroelectric domain structures for a given strain and temperature.