Macroscopic Symmetry Research Articles

A New Mechanism of the Incommensurate Phase Transition

A new mechanism of incommensurate (INC) phase transition will be mentioned. The INC phase may be stabilized by freezing of a soft mode on the [k, k, 0] or [k, k, 1/2] branch induced by the parabolic splitting of the doubly degenerate modes at the Brillouin zone boundary (1/2, 1/2, 0) or (1/2, 1/2, 1/2). A simple model theory of the incommensurate phase transition of this type is proposed, which easily reproduces a special feature for the INC phase that the macroscopic symmetry changes at the INC phase transition.

Closed-circuit domain quadruplets in BaTiO3nanorods embedded in a SrTiO3film

Cylindrical BaTiO${}_{3}$ nanorods embedded in $\ensuremath{\langle}100\ensuremath{\rangle}$-oriented SrTiO${}_{3}$ epitaxial film in a brushlike configuration are investigated in the framework of the Ginzburg-Landau-Devonshire model. It is shown that strain compatibility at BaTiO${}_{3}$/SrTiO${}_{3}$ interfaces keeps BaTiO${}_{3}$ nanorods in the rhombohedral phase even at room temperature. Depolarization field at the BaTiO${}_{3}$/SrTiO${}_{3}$ interfaces is reduced by an emission of the 109${}^{\ensuremath{\circ}}$ or 71${}^{\ensuremath{\circ}}$ domain boundaries. In case of 10--80-nm diameter nanorods, the ferroelectric domains are found to form a quadruplet with a robust flux-closure arrangement of the in-plane components of the spontaneous polarization. The out-of-plane components of the polarization are either balanced or oriented up or down along the nanorod axis. Switching of the out-of-plane polarization with coercive field of about $5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ V/m occurs as a collapse of a 71${}^{\ensuremath{\circ}}$ cylindrical domain boundary formed at the curved circumference surface of the nanorod. The remnant domain quadruplet configuration is chiral, with the ${C}_{4}$ macroscopic symmetry. More complex stable domain configurations with coexisting clockwise and anticlockwise quadruplets contain interesting arrangement of strongly curved 71${}^{\ensuremath{\circ}}$ boundaries.

Direct Evidence for Local Symmetry Breaking during a Strain Glass Transition

Strain glass transition is a unique nanoscale displacive transition with local symmetry breaking while maintaining the macroscopic symmetry or average structure unchanged. It usually occurs in the "nonmartensitic" composition range of a martensitic system. So far, only indirect evidence exists for such a transition, essentially from macroscopic measurements and low-resolution transmission electron microscopy observations, and there is a lack of direct evidence for the speculated local symmetry breaking and the sluggish nature of the glass transition. In this Letter we report in situ high-resolution transmission electron microscopy observations on a Ti50(Pd41Cr9) strain glass alloy and direct evidence for these key issues. Our results show that at temperatures well above the strain glass transition temperature (Tg), the lattice is essentially an undistorted B2 structure. With approaching Tg, the local symmetry breaking gradually occurs with the formation and growth of nanomartensite clusters with a combined stacking period of three and four plane intervals, but the average structure measured by x-ray diffraction remains B2. These nanomartensite clusters become finally frozen below Tg. Our results provide not only a microscopic basis for the macroscopic properties of strain glass, but also new insights into a range of possible applications of this unique class of materials.

Controlling a whispering-gallery-doublet-mode avoided frequency crossing: Strong coupling between photon bosonic and spin degrees of freedom

A combination of electron spin interactions in a magnetic field allows us to control the resonance frequencies of a high-Q whispering-gallery (WG) cavity mode doublet, resulting in precise measurements of an avoided crossing between the two modes comprising the doublet. We show that the resonant photons effectively behave as spin-$\frac{1}{2}$ particles and that the physical origins of the doublet phenomenon arise from an energy splitting between the states of photon spin angular momentum. The exclusive role of the photon spin in splitting the mode frequency is emphasized, and we demonstrate that the gyrotropic and anisotropic properties of the crystalline media supporting the WG mode lead to strong coupling between the bosonic and the spin degrees of freedom of cavity photons. Despite the demonstrated similarities to Jaynes-Cummings-type systems, the mode doublet system exhibits a significant difference due to its linearity. Unlike traditional experiments dealing with interactions between fields and matter, here the crystalline medium plays a role of macroscopic symmetry breaking, assisting in the strong coupling between these photon degrees of freedom. Such a regime is demonstrated experimentally with a method to effectively control the photon spin state. Our experiments demonstrate controllable time-reversal symmetry breaking in a high-$Q$ cavity.

Primary and secondary pyroelectric coefficients of rhombohedral and tetragonal single-domain relaxor-PbTiO3 single crystals

The primary and secondary pyroelectric coefficients were determined for binary (1-x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN-PT) and ternary Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PIN-PMN-PT) relaxor-PT single crystals. The secondary pyroelectric coefficients were calculated from the thermodynamic inter-relationship between the piezoelectric, elastic, and thermal expansion coefficients. Poling along [111] and [001] directions resulted in single-domain state of “1R” and “1T” and a macroscopic symmetry of 3m and 4mm for rhombohedral (x = 0.28) and tetragonal (x = 0.42) crystals, respectively, enabling relatively large values of pyroelectric coefficients p ≥ 5.7 × 10−4 C/m2 K. The calculated results show that the secondary pyroelectric coefficients are in the range of (−0.62 ∼ −1.06) × 10−4 C/m2 K for rhombohedral crystals and (0.70 ∼ 1.14) × 10−4 C/m2 K for tetragonal crystals, significantly lower than that of primary pyroelectric coefficients, which is important for thermal directional and imaging applications. In contrast, high d15 piezoelectric coefficients (>2000 pC/N), together with zero pyroelectric coefficients in thickness shear crystals, also makes them promising candidates for piezoelectric sensors where thermal noise is undesirable.

Liquid crystals of the twenty-first century – nematic phase of bent-core molecules

Bent-core (BC) materials that form nematic liquid crystals (BC nematics (BCNs)) are known only since 2000, but since then they have been intensively studied. In this review we give a comprehensive summary of the main research directions and results. After discussing representative examples of molecules making BCNs, we review theoretical predictions and experimental findings about macroscopic symmetries, such as chirality of achiral and chiral molecules, tetrahedratic symmetry and phase biaxiality versus uniaxiality. Then we describe the properties of smectic nano clusters often observed in BCNs, and discuss rheological properties that reveal unusually large viscosities and small twist and bend elastic constants. Finally, we focus on the electric properties of BCNs, such as dielectric and ferroelectric properties, electroconvection (EC) and electromechanical effects.

Spinodal decomposition and the emergence of dissipative transient periodic spatio-temporal patterns in acentrosomal microtubule multitudes of different morphology

We have studied a spontaneous self-organization dynamics in a closed, dissipative (in terms of guansine 5'-triphosphate energy dissipation), reaction-diffusion system of acentrosomal microtubules (those nucleated and organized in the absence of a microtubule-organizing centre) multitude constituted of straight and curved acentrosomal microtubules, in highly crowded conditions, in vitro. Our data give experimental evidence that cross-diffusion in conjunction with excluded volume is the underlying mechanism on basis of which acentrosomal microtubule multitudes of different morphologies (straight and curved) undergo a spatial-temporal demix. Demix is constituted of a bifurcation process, manifested as a slow isothermal spinodal decomposition, and a dissipative process of transient periodic spatio-temporal pattern formation. While spinodal decomposition is an energy independent process, transient periodic spatio-temporal pattern formation is accompanied by energy dissipative process. Accordingly, we have determined that the critical threshold for slow, isothermal spinodal decomposition is 1.0 ± 0.05 mg/ml of microtubule protein concentration. We also found that periodic spacing of transient periodic spatio-temporal patterns was, in the overall, increasing versus time. For illustration, we found that a periodic spacing of the same pattern was 0.375 ± 0.036 mm, at 36 °C, at 155th min, while it was 0.540 ± 0.041 mm at 31 °C, and at 275th min after microtubule assembly started. The lifetime of transient periodic spatio-temporal patterns spans from half an hour to two hours approximately. The emergence of conditions of macroscopic symmetry breaking (that occur due to cross-diffusion in conjunction with excluded volume) may have more general but critical importance in morphological pattern development in complex, dissipative, but open cellular systems.

A New Type of Incommensurate Phase Transition Caused by Parabolic Splitting of Degenerate Modes

On the basis of the model of the minimal lattice with orthogonal partial translation (MOPT) lattice, it is shown that, around a special point at the Brillouin zone boundary, a saddlelike dispersion relation appears and the parabolic splitting of degenerate modes takes place. A new type of incommensurate phase is stabilized by the freezing of the soft mode belonging to the lower branch induced by the parabolic splitting. A simple model theory of the incommensurate phase transition of this type is proposed, which easily reproduces one of the most remarkable features showing that the macroscopic symmetry changes in the incommensurate phase transition.

Investigation of odd-order nonlinear susceptibilities in atomic vapors

We theoretically deduce the macroscopic symmetry constraints for arbitrary odd-order nonlinear susceptibilities in homogeneous media including atomic vapors for the first time. After theoretically calculating the expressions using a semiclassical method, we demonstrate that the expressions for third- and fifth-order nonlinear susceptibilities for undressed and dressed four- and six-wave mixing (FWM and SWM) in atomic vapors satisfy the macroscopic symmetry constraints. We experimentally demonstrate consistence between the macroscopic symmetry constraints and the semiclassical expressions for atomic vapors by observing polarization control of FWM and SWM processes. The experimental results are in reasonable agreement with our theoretical calculations.

Complete set of elastic, dielectric, and piezoelectric constants of [011]C poled rhombohedral Pb(In0.5Nb0.5)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3:Mn single crystals.

Mn modified rhombohedral Pb(In0.5Nb0.5)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT:Mn) single crystals poled along [011]C crystallographic direction exhibit a "2R" engineered domain configuration, with macroscopic mm2 symmetry. The complete sets of material constants were determined using combined resonance and ultrasonic methods, and compared to [001]C poled PIN-PMN-PT:Mn crystals. The thickness shear piezoelectric coefficient d15 and electromechanical coupling factor k15 were found to be on the order of ∼3000 pC/N and 0.92, respectively, with longitudinal piezoelectric coefficient d33 and coupling factor k33 being on the order of ∼1050 pC/N and 0.90. Of particular importance is that PIN-PMN-PT:Mn single crystals exhibited high mechanical quality factor Q33 ∼ 1000, comparable to "hard" PZT8 ceramics, which can also be confirmed by the low extrinsic contribution, being ≤2% from the Rayleigh analysis.

Crystal structure, differential scanning calorimetric, infrared spectroscopy and theoretical studies of C(NH2)2(NH)*CH2[dbnd]CHCOOH noncentrosymmetric crystal

The X-ray and vibrational spectroscopic analysis of a new molecular complex of guanidine and acrylic acid are reported. The crystal of C(NH2)2(NH)*CH2CHCOOH belongs to Pna21 space group of orthorhombic system with Z=4, a=9.9242(34)Å, b, c=8.3951(14)Å. In the crystal structure the macroscopic symmetry center is absent.The differential scanning calorimetric (DSC) experiment of powder sample indicates on continuous phase transition at 235.8K.The room temperature infrared spectrum of guanidine*acrylic acid powder sample has been measured. The spectrum is discussed on the basis of crystallographic data. The IR spectra for the powder sample were also measured at low temperatures (12–300K). The temperature relationships of band position for obtained spectra are analyzed.Additionally, the results of theoretical calculation of vibrational spectra, equilibrium structure, HOMO, LUMO and first order hyperpolarizability are presented.

Photoacoustic Monitoring of the Macroscopic Orientational Order in Disperse Red 1 Azo-Dye-Based Dissolutions

The polarized pulsed-laser photoacoustic (PLPA) methodology was implemented to characterize the macroscopic molecular orientational order as a function of the applied electric field in an azo-dye-based dissolution. It is shown in this work that photoacoustic signals are highly sensitive to the material anisotropy when PLPA analyses are performed. In particular, the macroscopic molecular symmetries and structural organization of rod-like azo-dyes (Disperse Red 1: DR1) prepared in heavily loaded toluene dissolutions, have been studied. Experiments evidence unambiguous information concerning the molecular organization detected via simultaneous optical transmission and PLPA measurements. Indeed, in the electrically poled stage, it is shown that the Fourier, correlation, and root-mean-square analyses performed on the PLPA signals, as functions of the incident linear polarization of the laser source (orthogonal states $$P_\mathrm{in}$$ and $$S_\mathrm{in}$$ , respectively), reveal the main optical axis, symmetry, and structure of the aligned compounds in the liquid phase. An important advantage of the PLPA method is that it can be implemented with poor or null optical transmission anisotropic materials.

Symmetry of piezoelectric (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3(x=0.31) single crystal at different length scales in the morphotropic phase boundary region

We use probes of three different length scales to examine symmetry of ($1\ensuremath{-}x$)Pb(Mg${}_{1/3}$Nb${}_{2/3}$)O${}_{3}$-$x$PbTiO${}_{3}$ (PMN-$x$PT) single crystals in the morphotropic phase boundary (MPB) region at composition $x$ $=$ 0.31 (PMN-31$%$ PT). On the macroscopic scale, x-ray diffraction (XRD) shows a mixture of strong and weak diffraction peaks of different widths. The closest match to XRD peak data is made with monoclinic $Pm$ (M${}_{\mathrm{C}}$) symmetry. On the local scale of a few nanometers, convergent beam electron diffraction (CBED) studies, with a 1.6-nm electron probe, reveal no obvious symmetry. These CBED experimental patterns can be approximately matched with simulations based on monoclinic symmetry, which suggests locally distorted monoclinic structure. A monoclinic $Cm$ (M${}_{\mathrm{A}}$ or M${}_{\mathrm{B}}$)-like symmetry could also be obtained from certain regions of the crystal by using a larger electron probe size of several tens of nanometers in diameter. Thus the monoclinic symmetry of single crystal PMN-31$%$PT is developed only in parts of the crystal by averaging over locally distorted structure on the scale of few tens of nanometers. The macroscopic symmetry observed by XRD is a result of averaging from the local structure in PMN-31$%$PT single crystal. The lack of local symmetry at a few nanometers scale suggests that the polarization switching results from a change in local displacements, which are not restricted to specific symmetry planes or directions.

Anomalous Electro-Optic Effect in Polar Liquid Films

We present an anomalous electro-optic effect in polar liquid films: liquids, usually considered to be isotropic, possess the linear electro-optic effect that occurs only in materials lacking inversion symmetry. Due to the observed large effect in the low-frequency range and slow response speed, this strange effect was thought to come from the field-induced orientation of large mass. Therefore, we brought forward a physical model that contributed to the interpretation of this phenomenon: field-induced pre-oriented, short-range orderly dipole clusters in liquid films break the macroscopic symmetry and results in this asymmetric effect. Finally, combined with spectral analysis, the formation of clusters induced by an electric pulse was proved.

The magnetoelectric effect due to local noncentrosymmetry

Magnetoelectrics often possess ions located in noncentrosymmetric surroundings. Based on this fact we suggest a microscopic model of magnetoelectric interaction and show that the spin–orbit coupling leads to spin-dependent electric dipole moments of the electron orbitals of these ions, which results in non-vanishing polarization for certain spin configurations. The approach accounts for the macroscopic symmetry of the unit cell and is valid for both commensurate and complex incommensurate magnetic structures. The model is illustrated by the examples of MnWO4, MnPS3 and LiNiPO4. Application to other magnetoelectrics is discussed.

Control of Cross-Sections and Optical Nonlinearity of Pt Nanowires and the Roughness Effect

In this paper we review our fabrication of Pt nanowire arrays on MgO(110) faceted templates by a shadow deposition method and our control of their cross-sectional shapes by adjusting the deposition directions of platinum. We obtained nanowire arrays with Cs and C2v macroscopic symmetries. These macroscopic symmetries influence optical second harmonic generation (SHG) susceptibility elements of the nanowire arrays sensitively. On the other hand, the roughness of the nanowires had an effect on the rotational SHG patterns as a function of the sample rotation angle around the surface normal. We tried to explain the pattern change by a second-order perturbation scheme with respect to the roughness amplitude.

RANDOM FIELDS IN RELAXOR FERROELECTRICS — A JUBILEE REVIEW

Substitutional charge disorder as in PbMg1/3Nb2/3O3 , structural cation vacancies as in Sr x Ba 1-x Nb 2 O 6 and isovalent substitution of off-centered cations as in BaTi 1-x Sn x O 3 and BaTi 1-x Zr x O 3 give rise to quenched electric random-fields (RF s ), which we proposed to be at the origin of the peculiar behavior of relaxor ferroelectrics 20 years ago. These are, e.g. a strong frequency dispersion of the dielectric response and an apparent lack of macroscopic symmetry breaking in the low temperature phase. Both are related to mesoscopic RF-driven phase transitions, which give rise to irregularly shaped quasi-stable polar nanoregions below the characteristic temperature T*, but above the global transition temperature Tc. Their co-existence with the paraelectric parent phase can be modeled by time-dependent field equations under the control of quenched RF s and stress-free strain (in the case of order parameter dimension n ≥ 2). Transitions into global polar order at Tc may occur in uniaxial relaxors as observed on the uniaxial relaxor ferroelectric Sr0.8Ba0.2Nb2O6 and come close to RF Ising model criticality. Re-entrant relaxor transitions as observed in solid solutions of Ba2Pr0.6Nd0.4(FeNb4)O15 are proposed to evidence the coexistence of distinct normal and relaxor ferroelectric phases within the framework of percolation theory.

Theoretical investigation of magnetoelectric effects in Ba2CoGe2O7

A joint theoretical approach, combining macroscopic symmetry analysis with microscopic methods (density functional theory and model cluster Hamiltonian), is employed to shed light on magnetoelectricity in Ba2CoGe2O7. We show that the recently reported experimental trend of polarization guided by magnetic field can be predicted on the basis of phenomenological Landau theory. From the microscopic side, Ba2CoGe2O7 emerges as a prototype of a class of magnetoelectrics, where the cross coupling between magnetic and dipolar degrees of freedom needs, as main ingredients, the on-site spin-orbit coupling and the spin-dependent O p - Co d hybridization, along with structural constraints related to the noncentrosymmetric structural symmetry and the peculiar configuration of CoO4 tetrahedrons.

X-ray photon correlation spectroscopy of structural fluctuations in relaxor ferroelectrics PZN-9%PT

We have performed an x-ray photon correlation spectroscopy measurement of 91%Pb(Zn1/3Nb2/3)O3-9%PbTiO3 and found a slow structural fluctuation in time near TC. The slow fluctuation consists of long-term and short-term fluctuations. We have derived the short-term fluctuation from the intensity fluctuations and found out the relaxation time to be an order of 10 s. It is suggested that the slow fluctuation is owing to the competition between macroscopic tetragonal symmetry and the microscopic orthorhombic symmetry. The competition should be a main reason for the low-frequency dielectric permittivity.

Investigation of the nonlinear optical properties of metamaterials by second harmonic generation

Nonlinear optical spectroscopy is applied to two types of metamaterials: (i) variations of split-ring resonators fabricated as periodic two-dimensional arrays of gold on SiO2, and (ii) gratings of periodically spaced straight wires of gold on multiferroic hexagonal single crystals from the RMnO3 family. Optical second harmonic generation (SHG) on samples of type (i) is used to characterize the nonlinear response of metamaterials in dependence of the photon energy and the size, shape, and symmetry of the nanoscopic building blocks constituting the metamaterials. We find a complex dependence of the SHG spectra on the design parameters that requires an in-depth theoretical analysis. SHG is applied to samples of type (ii) to enhance the nonlinear optical performance of functional materials by writing a metamaterial acting as optical catalyst on top. We observe an enhancement of the SHG signal induced by the ferroelectric order of the RMnO3 crystals, yet with pronounced variations between samples. Measurements of both types, (i) and (ii), show that a comprehensive understanding of the nonlinear optical properties of metamaterials requires one to go beyond a macroscopic symmetry treatment. In fact, structural inhomogeneities on the level of the nanoscopic building blocks have a major impact.