Macroscopic Symmetry Research Articles

Symmetry‐sensitive plasmonic enhancement of nonlinear optical intensity in nano‐micro hierarchical structures on silver

We created nano‐micro hierarchical surface structures on Ag and measured their optical second harmonic generation (SHG) response. We found that the hierarchical surface structures can significantly modify the optical nonlinearity of the metal surfaces. The macroscopic symmetries of surface's shape influenced SHG. In addition, the observed SHG on Ag showed the contribution by the surface plasmon excitation. We also observed unique anisotropic enhancement of SHG in metal. We attribute our observations to both symmetry and surface plasmons on nano‐micro hierarchical structures. Copyright © 2016 John Wiley & Sons, Ltd.

Smectic-like bâtonnets in nematic/twist-bend nematic biphasic samples

ABSTRACTWe have studied a mixture of the twist-bend nemogenic dimer CB7CB with rod-like nematic molecules, which exhibits nematic (N) and twist-bend nematic (NTB) phases and a very large biphasic coexistence range. At the N-NTB transition, we observe the nucleation of highly anisometric NTB droplets which are very similar to the classic smectic A (SmA) bâtonnets. These observations confirm the recently proposed close analogy between the NTB and SmA phases, on the basis of their identical macroscopic symmetry. As for their smectic analogues, the NTB bâtonnets are fluid in two dimensions; they easily merge when brought into contact and they are solid-like in that they did not flow along their optic axis. The observed fluidity and low viscosity show that the NTB phase is indeed a nematic phase, i.e. an anisotropic fluid, rather than a soft crystal or glassy state. Unlike their smectic analogues, the NTB bâtonnets have almost perfect symmetry of revolution and the axis of the NTB helix is uniformly aligned parallel to the long axis of the bâtonnet. The large aspect ratio of the bâtonnets, typically ≈ 10–30, indicates a very strong anisotropy of the N-NTB interfacial energy, W2/W0 ≈ 200–2000, and suggests that the anchoring energy differs from the usual Rapini–Papoular form.

Theory of antiferroelectric phase transitions

At variance with structural ferroic phase transitions which give rise to macroscopic tensors coupled to macroscopic fields, criteria defining antiferroelectric (AFE) phase transitions are still under discussion due to the absence of specific symmetry properties characterizing their existence. They are recognized by the proximity of a ferroelectric (FE) phase induced under applied electric field, with a double hysteresis loop relating the induced polarization to the electric field and a typical anomaly of the dielectric permittivity. Here, we show that there exist indeed symmetry criteria defining AFE transitions. They relate the local symmetry of the polar crystallographic sites emerging at an AFE phase transition with the macroscopic symmetry of the AFE phase. The dielectric properties of AFE transitions are deduced from a Landau theoretical model in which ferroelectric and ferrielectric phases are shown to stabilize as the result of specific symmetry-allowed couplings of the AFE order- parameter with the field-induced polarization.

Superdipole glass ground state of relaxor ferroelectrics

ABSTRACTQuenched random fields (RFs) are well-known to be a basic driving force of the peculiar behavior of relaxor ferroelectrics such as PbMg1/3Nb2/3O3 (PMN), SrxBa1-xNb2O6 (SBN), and BaTi1-xZrxO3 (BTZ), hence, giving rise to strong frequency dispersion of the dielectric response, an apparent lack of macroscopic symmetry breaking at low temperatures, and the formation of polar nanoregions (PNRs) thus creating random ‘domain states’. A fundamental completion of relaxor physics toward a superdipolar cluster glass ground state of the randomly interacting PNRs appears necessary as evidenced by dynamic criticality and non-ergodic aging and rejuvenation processes.

Symmetry Guide to Ferroaxial Transitions.

The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO_{2}, LuFe_{2}O_{4}, and URu_{2}Si_{2}.

Optical second harmonic generation from nanostructure-covered micro-cubes on nickel

In this study, we aimed to create the nano-micro hierarchical surface structures on Ni and analyze their optical second harmonic generation (SHG) response. The hierarchical surface structures were found to significantly modify the optical nonlinearity of the metal surface. The macroscopic symmetry of the surface’s shape influenced SHG, and the excitation of surface plasmon (SP) enhanced SHG. On the other hand, the nanostructures on the micro-cubes had an additional effect on the generated SHG. The mechanism of anisotropic SHG enhancement by the nano-micro structures has been investigated.

Symmetry breaking in hexagonal and cubic polymorphs of BaTiO3

BaTiO3 appears in cubic and hexagonal variants, both of which are centrosymmetric. Samples of cubic BaTiO3 are known to exhibit breaking of the centric symmetry locally and globally. It has been proposed that the local symmetry breaking originates in polar regions, the precursors of the ferroelectric phase. Origins of the macroscopic symmetry breaking, which are not well understood, have been previously tentatively correlated with inhomogeneities in the samples, such as strain gradients that may align or redistribute objects such as charged point defects or polar regions making material macroscopically polar. No such data are available for BaTiO3 with hexagonal symmetry. We compare dielectric, elastic, and pyroelectric properties of the two materials in polycrystalline form. In contrast to cubic BaTiO3, hexagonal BaTiO3 does not exhibit macroscopic pyroelectric response at room temperature. This is consistent with apparent absence of polar regions in the hexagonal material, and the fact that in hexagonal BaTiO3, strain rather than polarization is the order parameter for the phase transition into ferroelectric-ferroelastic phase. The thermally stimulated currents measured in hexagonal and cubic BaTiO3, however, show that both materials exhibit noncentric macroscopic symmetry. This result supports the idea that extrinsic factors, such as strain gradients, which are apparently common for both materials, may break the macroscopic symmetry, which may then lead to alignment and redistribution of polar regions or charged defects.

Propagation characteristics of SH waves in a functionally graded piezomagnetic layer on PMN-0.29PT single crystal substrate

The shear horizontal waves in a functionally graded piezomagnetic (FGPM) layer bonded on 0.71Pb(Mg1/3Nb2/3)O3–0.29PbTiO3 (PMN–0.29PT) single crystal substrate is investigated in this paper. The material parameters of the FGPM layer vary in the same exponential function along the thickness direction. The PMN–0.29PT single crystal under consideration is poled along the [011]c direction so that the macroscopic symmetry is orthonormal mm2. The dispersion equations are derived for the magnetically open and closed boundary conditions on the surface of FGPM layer. The dispersive behaviours are graphically illustrated and analyzed. The results show that the cut orientation of the PMN–0.29PT single crystal as well as the magnetic boundary conditions and gradient coefficient of FGMP layer have significant influences on the dispersion behaviours.

Phase transitions, domain structure, and pseudosymmetry in La- and Ti-doped BiFeO3

The phase transitions and domain structure of the promising PbO-free solid solution series, (0.95-x)BiFeO3-xLaFeO3-0.05La2/3TiO3, were investigated. X ray diffraction (XRD) revealed a transition from a ferroelectric R3c to a PbZrO3-like (Pbam) antiferroelectric (AFE) structure at x = 0.15 followed by a transition to a paraelectric (PE, Pnma) phase at x > 0.30. The ferroelastic/ferroelectric twin domain width decreased to 10–20 nm with increasing x as the AFE phase boundary was approached but coherent antiphase tilted domains were an order of magnitude greater. This domain structure suggested the local symmetry (20 nm) is lower than the average structure (R3c, a−a−a−) of the tilted regions. The PE phase (x = 0.35) exhibited a dominant a−a−c+ tilt system with Pnma symmetry but diffuse reflections at ∼1/4{ooe} positions suggest that short range antipolar order is residual in the PE phase. The complex domain structure and phase assemblage of this system challenge the conventional interpretation of phase transitions based on macroscopic symmetry. Instead, it supports the notion that frustration driven by chemical distributions at the nanometric level influences the local or pseudo-symmetry as well as the domain structure, with XRD giving only the average macroscopic structure.

Tuning and Freezing Disorder in Photonic Crystals using Percolation Lithography.

Although common in biological systems, synthetic self-assembly routes to complex 3D photonic structures with tailored degrees of disorder remain elusive. Here we show how liquids can be used to finely control disorder in porous 3D photonic crystals, leading to complex and hierarchical geometries. In these optofluidic crystals, dynamically tunable disorder is superimposed onto the periodic optical structure through partial wetting or evaporation. In both cases, macroscopic symmetry breaking is driven by subtle sub-wavelength variations in the pore geometry. These variations direct site-selective infiltration of liquids through capillary interactions. Incorporating cross-linkable resins into our liquids, we developed methods to freeze in place the filling patterns at arbitrary degrees of partial wetting and intermediate stages of drying. These percolation lithography techniques produced permanent photonic structures with adjustable disorder. By coupling strong changes in optical properties to subtle differences in fluid behavior, optofluidic crystals may also prove useful in rapid analysis of liquids.

Macroscopic time-reversal symmetry breaking at a nonequilibrium phase transition.

We study the entropy production in a globally coupled Brownian particles system that undergoes an order-disorder phase transition. Entropy production is a characteristic feature of nonequilibrium dynamics with broken detailed balance. We find that the entropy production rate is subextensive in the disordered phase and extensive in the ordered phase. It is found that the entropy production rate per particle vanishes in the disordered phase and becomes positive in the ordered phase following critical scaling laws. We derive the scaling relations for associated critical exponents. The disordered phase exemplifies a case where the entropy production is subextensive with the broken detailed balance.

Elastic wave scattering in random anisotropic solids

Abstract A general ultrasonic scattering model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is developed allowing the texture and grain orientation frames to be independent and the wave propagation direction arbitrary in those frames. Numerical examples are given for an approximate texture model exhibiting triclinic macroscopic symmetry for triclinic crystallites. The scattering coefficients are obtained from integrands of the attenuation coefficients recently derived elsewhere in the Born approximation for the same problem. The results obtained are reducible to the known scattering/backscattering coefficients for a macroscopically isotropic medium in the limit of negligible macroscopic anisotropy. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and ellipsoidal shaped grains. As in the macroscopically isotropic case, the scattering coefficients are factorized into an elastic factor dependent on the preferred crystallographic orientation of the grains and a frequency dependent geometric factor affected by grain size and shape. A general reciprocity relationship for the scattering coefficients is obtained and discussed. Simulation results are presented to shed light on the effect of texture, grain shape and nondimensional frequency on ultrasonic scattering. An approximation of the quasilongitudinal wave polarization, that neglects the deviation of the polarization vector from the propagation direction, on the backscattering coefficient is investigated and the error of the approximation is estimated.

Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries

A general ultrasonic attenuation model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is described with proper accounting for the anisotropic Green’s function for the reference medium. The texture and the ellipsoidal grain frames in the model are independent and the wave propagation direction is arbitrary. The attenuation coefficients are obtained in the Born approximation accompanied by the Rayleigh and stochastic asymptotes. The scattering model displays statistical anisotropy due to two independent factors: (1) shape of the oriented grains and (2) preferred crystallographic orientation of the grains leading to macroscopic anisotropy of the homogenized reference medium. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and elongated-shaped grains. It predicts the strength of ultrasonic scattering and its dependence on frequency and propagation direction as a function of grain shape, grain crystallographic symmetry and macroscopic texture parameters and provides the texture-induced dependence of macroscopic ultrasonic velocity on propagation angle. It considers proper wave polarizations due to macroscopic anisotropy and scattering-induced transformations of waves with different polarizations. Competing effects of grain shape and texture on the attenuation are observed. In contrast to the macroscopically isotropic case, where in the stochastic regime the attenuation is highest in the direction of the longest ellipsoidal axis of the grain, the wave attenuation in the elongation direction may be suppressed or amplified by the texture with different effects on the quasilongitudinal and quasitransverse waves. The frequency behavior is also interestingly affected by texture: a hump in the total attenuation coefficient is found for the fast quasitransverse wave which is purely the result of macroscopic anisotropy and the existence of two quasitransverse waves; this hump is not observed in the macroscopically isotropic case. Striking differences of the texture effect on the directional dependences of the attenuation coefficients are found at low versus high frequencies.

An Evolutionary Algorithm for the Texture Analysis of Cubic System Materials Derived by the Maximum Entropy Principle

Based on the principle of maximum entropy method (MEM) for quantitative texture analysis, the differential evolution (DE) algorithm was effectively introduced. Using a DE-optimized algorithm with a faster but more stable convergence rate of iteration reliable complete orientation distributions (C-ODF) have been obtained for deep-drawn IF steel sheets and the recrystallized aluminum foils after cold-rolling, which are designated as showing a macroscopic cubic-orthogonal symmetry. With special reference to the data processing, no more other assumptions are required for DE-optimized MEM except that the system entropy approach the maximum.

Breaking of macroscopic centric symmetry in paraelectric phases of ferroelectric materials andimplications for flexoelectricity.

A centrosymmetric stress cannot induce a polar response in centric materials; piezoelectricity is, for example, possible only in non-centrosymmetric structures. An exception is metamaterials with shape asymmetry, which may be polarized by stress even when the material is centric. In this case the mechanism is flexoelectricity, which relates polarization to a strain gradient. The flexoelectric response scales inversely with size, thus a large effect is expected in nanoscale materials. Recent experiments in polycrystalline, centrosymmetric perovskites (for example, (Ba,Sr)TiO3) have indicated values of flexoelectric coefficients that are orders of magnitude higher than theoretically predicted, promising practical applications based on bulk materials. We show that materials with unexpectedly large flexoelectric response exhibit breaking of the macroscopic centric symmetry through inhomogeneity induced by the high-temperature processing. The emerging electro-mechanical coupling is significant and may help to resolve the controversy surrounding the large apparent flexoelectric coefficients in this class of materials.

Effect of an inhomogeneous initial stress on Love wave propagation in 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 single crystal layered structure poled along [011

The propagation behavior of Love wave in 0.67Pb(Mg1/3Nb2/3)O–0.33PbTiO3 (PMN–0.33PT) single crystal layered structure with the inhomogeneous initial stress varying along thickness is studied in this paper. The interface between PMN–PT layer and elastic substrate is perfectly bonded. The surface of the layered system is free of traction and electrically shorted or open. PMN–0.33PT single crystal is considered [011]c polarized, and has macroscopic symmetry of orthogonal mm2. The Frobenius method is employed to solve governing equation with variable coefficient. The analytical dispersion equations are derived for different boundary conditions. The numerical results show that the Frobenius method can provide a good asymptotic approximation when the retained number of items in Frobenius series is sufficient. It is found that the inhomogeneous initial stress has strong effect on the dispersion characteristics comparing with constant initial stress, whereas has less effect on the cut-off frequency for the first two modes of Love wave. The gradient coefficients of inhomogeneous initial stress can obviously affect the phase velocity and corresponding electromechanical coupling factor, and can also change the distributions of mechanical displacement, electrical potential and stress. The obtained results can provide a predictable and theoretical basis for design and manufacture of high performance surface acoustic wave devices.

Nuclear Enhanced MEM Used to Analyze Local Distortions in Lead Chalcogenides

We introduce a novel method for reconstructing nuclear density distributions (NDDs): Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron data. The method was conceived to analyse local distortions in the thermoelectric lead chalcogenides, PbX (X = S, Se, Te). Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as waste heat recovery. The extraordinary thermoelectric performance of binary lead chalcogenides has caused huge research activity, but the mechanisms governing their unexpected low thermal conductivity still remain a controversial topic. It has been proposed to result from giant anharmonic phonon scattering or from local fluctuating dipoles on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason PbX was until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we investigate PbX using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method (MEM) and NEXMEM. In addition NEXMEM has been validated by testing against simulated powder diffraction data of PbTe with known displacements of Pb. The increased resolution of NEXMEM proved essential for resolving Pb-displacement of 0.2 Å in simulated data. The figure below shows Pb in the (100) plane for MEM, NEXMEM and the actual NDD of the test structure. Our findings outline the extent of disorder in lead chalcogenides, promoting our understanding of this class of high-performance thermoelectric materials. Furthermore we introduce NEXMEM which can be used for widespread characterization of subtle atomic features in crystals with unusual properties.

Characterization of Local Distortions in Thermoelectric Lead Chalcogenides

Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as efficient waste heat recovery. The extraordinary thermoelectric performance of binary lead chalcogenides has caused huge research activity, but the mechanisms governing their unexpected low thermal conductivity still remain a controversial topic. It has been proposed to result from giant anharmonic phonon scattering or from local fluctuating dipoles on the Pb site, emerging with temperature on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason lead chalcogenides were until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we probe the peculiar structural features in PbX (X = S, Se, Te) using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method. Distorted atoms are detected and quantified by refinement of anharmonic probability density functions. The charge density analysis is complemented by nuclear density distributions (NDDs) reconstructed from neutron diffraction data and by a novel method: Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron diffraction data. The increased atomic resolution introduced by NEXMEM proved essential for resolving atomic distortions, see figure below showing Pb in the (100) plane. Our findings outline the extent of disorder and anharmonicity in binary lead chalcogenides, promoting our fundamental understanding of this class of high-performance thermoelectric materials. The applied approach can be used in general, opening up for widespread characterization of subtle features in crystals with unusual properties.

Constraints on Jones transmission matrices from time-reversal invariance and discrete spatial symmetries

Optical spectroscopies are most often used to probe dynamical correlations in materials, but they are also a probe of symmetry. Polarization anisotropies are of course sensitive to structural anisotropies, but have been much less used as a probe of more exotic symmetry breakings in ordered states. In this paper a Jones transfer matrix formalism is discussed to infer the existence of exotic broken symmetry states of matter from their electrodynamic response for a full complement of possible broken symmetries including reflection, rotation, rotation-reflection, inversion, and time-reversal. A specific condition to distinguish the case of macroscopic time-reversal symmetry breaking is particularly important as in a dynamical experiment like optics, one must distinguish $reciprocity$ from time-reversal symmetry as dissipation violates strict time-reversal symmetry of an experiment. Different forms of reciprocity can be distinguished, but only one is a sufficient (but not necessary) condition for macroscopic time-reversal symmetry breaking. I show the constraints that a Jones matrix develops under the presence or absence of such symmetries. These constraints typically appear in the form of an algebra relating matrix elements or overall constraints (transposition, unitarity, hermiticity, normality, etc.) on the form of the Jones matrix. I work out a number of examples including the trivial case of a ferromagnet, and the less trivial cases of magnetoelectrics and vector and scalar spin "chiral" states. I show that the formalism can be used to demonstrate that Kerr rotation must be absent in time-reversal symmetric chiral materials. The formalism here is discussed with an eye towards its use in time-domain THz spectroscopy in transmission, but with small modifications it is more generally applicable.

Determination of full set material constants of [011]c poled 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 single crystal from one sample.

0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 single crystals poled along [011]c have macroscopic orthorhombic mm2 symmetry. There are total 17 independent material coefficients for this symmetry so that the determination of self-consistent full matrix data is extremely difficult because many samples are needed and there is a large property variation from sample to sample. To overcome this self-consistency difficulty, we have developed a combined ultrasonic pulse-echo and impedance spectroscopy method, which can extract all coefficients from only one small sample. This method is especially useful for piezoelectric materials whose properties are strongly dependent on geometry and for crystals with only limited size available.