Incommensurate Phase Research Articles

Dielectric Relaxation in a Nanosize Ferroelectric with an Incommensurate Phase Rb2ZnCl4

Dielectric Relaxation in a Nanosize Ferroelectric with an Incommensurate Phase Rb2ZnCl4

Harmonic Analysis of the Polarization Reversal of the Rb2ZnCl4 Crystal in the Incommensurate Phase

The polarization reversal of Rb2ZnCl4 crystals in the incommensurate phase near a ferroelectric phase transition (PT) under the action of harmonic electric field has been studied using harmonic analysis. During polarization reversal of a test sample under the action of harmonic electric field, a PT induced by the electric field from the incommensurate phase to the ferroelectric phase and a PT from the field-induced ferroelectric phase back to the incommensurate phase occur. The study of the active and reactive contributions to the amplitudes of current density harmonics made it possible to determine the current values of harmonic electric field intensity at which the corresponding PTs occur.

The size effects on phase transitions in ferroics

The features of phase transitions temperature behavior in nanosized ferroics are discussed in the framework of phenomenological theories. It is shown that in the case of second-order transitions to both the commensurate and incommensurate phases, the critical temperature can shift significantly depending on the characteristic dimensions of the sample and the properties of the surface. In materials with the first-order phase transition, size effects have a significant influence on the nucleation process, leading to the transition temperature shift or even the phase transition type change have been determined.

Dielectric Relaxation in a Nanosize Ferroelectric with an Incommensurate Phase Rb2ZnCl4

The dielectric properties of a composite obtained by embedding a ferroelectric salt Rb2ZnCl4 into a porous glass matrix with an average size of through pores of about 46 nm have been studied within the temperature range of 100–350 K at frequencies of 5–500 kHz. An increase in the dielectric permittivity dispersion depth Δε upon sample cooling, due to an increase in the concentration of “relaxers” and an increase in their dipole moment, was found. An analysis of the dielectric response features showed that a domain structure is formed in the ferroelectric phase of Rb2ZnCl4 particles, the mobility of which in the vicinity of the freezing temperature Tf obeys the empirical Vogel–Fulcher relation

Phase transitions and magnetoelectricity in Fe implanted TlInS2 and TlGaSe2 ferroelectric crystals

The dielectric constant measurements of Fe implanted TlInS2 and TlGaSe2 crystals without and under application of constant magnetic field have been performed. It has been observed that the implantation of the crystals with Fe ions caused the formation of ferromagnetic layer in the irradiated region, which leads to considerable shifts of the successive incommensurate and commensurate phase transitions to high temperatures in the heating regime. Remarkable shifts of the phase transition temperatures back to the low temperature region on heating of the samples were observed on applying the magnetic field perpendicularly to the implanted surface. None changes of the phase transition temperature points on measurements of the samples have been observed in cooling regime. The obtained results are interpreted as magnetodielectric effects that resulted from magnetoelectric coupling between ferromagnetic and ferroelectric constituents of the composite structure.

Nanoscale Size Effects on Push-Pull Fe-O Hybridization through the Multiferroic Transition of Perovskite ϵ-Fe2O3.

Multiferroics have tremendous potential to revolutionize logic and memory devices through new functionalities and energy efficiencies. To reach their optimal capabilities will require better understanding and enhancement of the ferroic orders and couplings. Herein, we use ϵ-Fe2O3 as a model system with a simplifying single magnetic ion. Using 15, 20, and 30 nm nanoparticles, we identify that a modified and size-dependent Fe-O hybridization changes the spin-orbit coupling and strengthens it via longer octahedra chains. Fe-O hybridization is modified through the incommensurate phase, with a unique two-step rearrangement of the electronic environment through this transition with attraction and then repulsion of electrons around tetrahedral Fe. Interestingly, size effects disappear in the high-temperature phase where the strongest Fe-O hybridization occurs. By manipulating this hybridization, we tune and control the multiferroic properties.

Reduced crystal symmetry as the origin of the ferroelectric polarization within the commensurate magnetic phase of TbMn2O5

Reduced crystal symmetry as the origin of the ferroelectric polarization within the commensurate magnetic phase of TbMn₂O₅

Selective Electron-Phonon Coupling in Dimerized 1T-TaS2 Revealed by Resonance Raman Spectroscopy.

The layered transition-metal dichalcogenide material 1T-TaS2 possesses successive phase transitions upon cooling, resulting in strong electron-electron correlation effects and the formation of charge density waves (CDWs). Recently, a dimerized double-layer stacking configuration was shown to form a Peierls-like instability in the electronic structure. To date, no direct evidence for this double-layer stacking configuration using optical techniques has been reported, in particular through Raman spectroscopy. Here, we employ a multiple excitation and polarized Raman spectroscopy to resolve the behavior of phonons and electron-phonon interactions in the commensurate CDW lattice phase of dimerized 1T-TaS2. We observe a distinct behavior from what is predicted for a single layer and probe a richer number of phonon modes that are compatible with the formation of double-layer units (layer dimerization). The multiple-excitation results show a selective coupling of each Raman-active phonon with specific electronic transitions hidden in the optical spectra of 1T-TaS2, suggesting that selectivity in the electron-phonon coupling must also play a role in the CDW order of 1T-TaS2.

Tunable antiferroelectric ceramic polarization via regulating incommensurate phase and domain features

Due to the high demand for dielectric materials with high energy density, the energy storage performance of antiferroelectric ceramic capacitors has always gained much attention. Polarization intensity is a key factor that is closely related to the energy storage density. However, thus far, there has been a lack of research studies or successful methods to effectively modulate polarization intensity. The behavior of the polarization process is complex and contains domain nucleation, growth, and flip-flapping. Based on this finding, the introduction of Nb5+ at the B-site was designed to influence the three stages of antiferroelectric polarization by regulating the balance between the ferroelectric and antiferroelectric phases, and eventually realized regulation of the saturation polarization intensity in the (Pb1-1.5xLax)(Zr0.5Sn0.43Ti0.07)O3 antiferroelectric ceramics. The saturation polarization intensity has increased from 25.56 to 42 μC/cm2 with Nb5+ content increases from 0 to 4 mol% and the hysteresis was kept low, Pb0.94La0.04(Zr0.65Sn0.35)0.975Nb0.02O3 is the optimal component with a high releasable energy density of 8.26 J/cm3 and an energy storage efficiency of 90.31%. This work provides an in-depth explanation of the microscopic mechanism of antiferroelectric ceramic polarization and presents a novel approach for the composition design of high-energy storage density antiferroelectric ceramics.

Vortex solitons in moiré optical lattices.

We show that optical moiré lattices enable the existence of vortex solitons of different types in self-focusing Kerr media. We address the properties of such states both in lattices having commensurate and incommensurate geometries (i.e., constructed with Pythagorean and non-Pythagorean twist angles, respectively), in the different regimes that occur below and above the localization-delocalization transition. We find that the threshold power required for the formation of vortex solitons strongly depends on the twist angle and, also, that the families of solitons exhibit intervals where their power is a nearly linear function of the propagation constant and they exhibit a strong stability. Also, in the incommensurate phase above the localization-delocalization transition, we found stable embedded vortex solitons whose propagation constants belong to the linear spectral domain of the system.

Commensurate and spiral magnetic order in the doped two-dimensional Hubbard model: Dynamical mean-field theory analysis

We develop a dynamical mean-field theory approach for the spiral magnetic order, changing to a local coordinate frame with preferable spin alignment along the $z$-axis, which can be considered with the impurity solvers treating the spin diagonal local Green's function. We furthermore solve the Bethe-Salpeter equations for nonuniform dynamic magnetic susceptibilities in the local coordinate frame. We apply this approach to describe the evolution of magnetic order with doping in the $t-t'$ Hubbard model with $t'=0.15$, which is appropriate for the description of the doped La$_2$CuO$_4$ high-temperature superconductor. We find that with doping the antiferromagnetic order changes to the $(Q,\pi)$ incommensurate one, and then to the paramagnetic phase. The spectral weight at the Fermi level is suppressed near half filling and continuously increases with doping. The dispersion of holes in the antiferromagnetic phase shows qualitative agreement with the results of the $t$-$J$ model consideration. In the incommensurate phase we find two branches of hole dispersions, one of which crosses the Fermi level. The resulting Fermi surface forms hole pockets. We also consider the dispersion of the magnetic excitations, obtained from the non-local dynamic magnetic susceptibilities. The transverse spin excitations are gapless, fulfilling the Goldstone theorem; in contrast to the mean-field approach the obtained magnetic state is found to be stable. The longitudinal excitations are characterized by a small gap, showing the rigidity of the spin excitations. For realistic hopping and interaction parameters we reproduce the experimentally measured spin-wave dispersion of La$_2$CuO$_4$.

Incommensurate charge density wave in multiband intermetallic systems exhibiting competing orders

The appearance of an incommensurate charge density wave vector $\textbf{Q} = (Q_x,Q_y)$ on multiband intermetallic systems presenting commensurate charge density wave (CDW) and superconductivity (SC) orders is investigated. We consider a two-band model in a square lattice, where the bands have distinct effective masses. The incommensurate CDW (inCDW) and CDW phases arise from an interband Coulomb repulsive interaction, while the SC emerges due to a local intraband attractive interaction. For simplicity, all the interactions, the order parameters and hybridization between bands are considered $\textbf{k}$-independent. The multiband systems that we are interested are intermetallic systems with a $d$-band coexisting with a large $c$-band, for which a mean-field approach has proved suitable. We obtain the eigenvalues and eigenvectors of the Hamiltonian numerically and minimize the free energy density with respect to the diverse parameters of the model by means of the Hellmann-Feynman theorem. We investigate the system in real as well as momentum space and we find an inCDW phase with wave vector $\textbf{Q} = (\pi, Q_y) = (Q_x, \pi)$. Our numerical results show that the arising of an inCDW state depends on parameters, such as the magnitude of the inCDW and CDW interactions, band filling, hybridization and the relative depth of the bands. In general, inCDW tends to emerge at low temperatures, away from half-filling. We also show that, whether the CDW ordering is commensurate or incommensurate, large values of the relative depth between bands may suppress it. We discuss how each parameter of the model affects the emergence of an inCDW phase.

New insights into suppression of intermediate incommensurate phase in lead zirconate stannate titanate antiferroelectric system

New insights into suppression of intermediate incommensurate phase in lead zirconate stannate titanate antiferroelectric system

Wetting transition in the transverse-field spin- 12 XY model with boundary fields

The wetting transition in the transverse-field spin-$\frac{1}{2}$ XY model with opposite boundary fields ${h}_{L}^{x}{h}_{R}^{x}<0$ is studied analytically and numerically. We find that the phase diagram is complex and that the wetting transition is of three types: first, second, and fourth order. The energy gap is obtained analytically, and the magnetization profile, correlation functions, and wetting layer thickness are obtained numerically. For $|{h}_{L}^{x}|,|{h}_{R}^{x}|<{h}_{w}$, a first-order phase transition occurs at ${h}_{L}^{x}=\ensuremath{-}{h}_{R}^{x}$, where ${h}_{w}$ is the continuous wetting transition point. For $|{h}_{R}^{x}|$ larger than ${h}_{w}$, the continuous wetting transition occurs at ${h}_{L}^{x}={h}_{w}$, and vice versa. For $g\ensuremath{\ne}1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, the wetting transition is second order, and commensurate and incommensurate phases occur for $g<1\ensuremath{-}{\ensuremath{\gamma}}^{2}$ and $g>1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, respectively. For $g=1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, the wetting transition is fourth order. For this fourth-order phase transition, the third derivative of the surface magnetization oscillates and diverges near the transition point. The correlation length exponent is $\ensuremath{\nu}=2$, and the dynamic exponent is $z=2$. Thus, this fourth-order transition belongs to a new universality class. The wetting behavior is induced by asymmetric boundary fields ${h}_{L}^{x}=\ensuremath{-}{h}_{R}^{x}$ and its finite-size scaling is discussed.

Anisotropic Melting of Frustrated Ising Antiferromagnets.

Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition T_{N}. In this Letter, we use large-scale MonteCarlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gaslike paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range T_{N}<T<T^{*}, whose width increases as magnetic frustrations grow. This intermediate phase is typically characterized by short-range correlations; however, the two-dimensional nature of the model allows for an additional exotic feature-formation of an incommensurate liquidlike phase with algebraically decaying spin correlations. The two-stage melting of magnetic order is generic and pertinent to many frustrated quasi-2D magnets with large (essentially classical) spins.

Topological properties in an Aubry–André–Harper model with p-wave superconducting pairing

Abstract We study the topological properties of the one-dimensional p-wave Aubry–André–Harper (AAH) model with periodic incommensurate potential and transition coupling. The calculation results show that due to co-influence of the incommensurate potential and modulation phase, three topological phases arise in different parameter regions: a topologically trivial phase, Su–Schrieffer–Heeger (SSH)-like topological phase, and Kitaev-like topological superconducting phase with Majorana zero modes. By evaluating the Andreev reflection conductance, we see that in the Kitaev-like phase, the quantized conductance plateau comes into being at the zero-bias limit, due to the occurrence of resonant Andreev reflection. In addition, when the disorder effect is incorporated, the SSH-like topology is modified sensitively and the degenerate topological states split, whereas the Kitaev-like topological phase is robust to weak disorder. Finally, we find that disorder can induce topological phase transition, i.e. from the topologically trivial phase to the topological phase. Based on these results, we believe that our findings have significance for studying the topological phase transition in a one-dimensional topological superconducting system. Also, it provides a feasible scheme for clarifying different topological phases.

Nonreciprocity of Optical Absorption in the Magnetoelectric Antiferromagnet CuB2O4

The change in the absorption spectra due to reversal of the direction of light propagation (nonreciprocity of absorption) is a consequence of a simultaneous violation of both time-reversal and spatial-inversion symmetries. Here, we report on a high-resolution spectroscopic study of absorption nonreciprocity in the noncentrosymmetric multiferroic CuB2O4 below the antiferromagnetic transition temperature TN = 21 K in the commensurate phase in magnetic fields up to 0.5 T. The study was performed in a broad spectral region covering several exciton transitions, which all are followed by an anomalously rich structure due to the multiple exciton-magnon-phonon satellites. Two components were resolved for the spectral line near 1.4 eV corresponding to the exciton transition between the ground and the first excited state. A quantitative theory of the optical absorption and nonreciprocity at this line was developed. The theory takes into account the interference between the electric and magnetic dipole contributions to the absorption and gives an adequate explanation of the relevant effects.

Quantum tricriticality of incommensurate phase induced by quantum strings in frustrated Ising magnetism

Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as “quantum strings”. Here we study an extended transverse field Ising model on a triangular lattice. Using large-scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensurate ordering wave vector and the density of quantum strings, which is reminiscent of hole density in under-doped cuprate superconductors. When introducing the next-nearest-neighbor interaction, we observe a quantum tricritical point out of the incommensurate phase. After carefully analyzing the ground state energies within different string topological sectors, we conclude that this tricriticality is non-trivially caused by effective long-range inter-string interactions with two competing terms following different decaying behaviors.

Vacancy-induced supersolidity of the second He4 layer on a biphenylene carbon sheet

We have performed path-integral Monte Carlo calculations to investigate various quantum phases of $^{4}\mathrm{He}$ layers adsorbed on a biphenylene sheet, a recently synthesized two-dimensional network of carbon atoms. Three different commensurate solid phases are identified in the first $^{4}\mathrm{He}$ layer, which is found to be completed to a ${\mathrm{C}}_{2/2}$ commensurate solid at an areal density of 0.119 ${\AA{}}^{\ensuremath{-}2}$. We have also found that the commensurate structure of the completed first layer allows second-layer $^{4}\mathrm{He}$ atoms to constitute a stable commensurate ${\mathrm{C}}_{2/3}$ structure at a total helium coverage of 0.199 ${\AA{}}^{\ensuremath{-}2}$. Furthermore, this second-layer commensurate structure is observed to be stable even with the formation of vacancies that are mobile to instigate the superfluid response at low temperatures. This unequivocally shows that vacancy-induced supersolidity can be realized in the second $^{4}\mathrm{He}$ layer on biphenylene.

High-pressure structural transition and magnetic phase diagram of CuB2O4

Noncentrosymmetric $\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{O}}_{4}$ is a prototypical system with interacting spin sublattices of different dimensionality, exhibiting diverse magnetic structures and magnetic phase transitions. Here we report pressure-induced structural evolution of $\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{O}}_{4}$ and its effect on the magnetic phase diagram. Powder x-ray diffraction (XRD), Raman scattering, and infrared phonon measurements have been performed under high pressure at room temperature. Although XRD shows lattice stability up to $\ensuremath{\sim}25\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, Raman and IR phonon measurements reveal structural anomaly near 3 GPa, followed by a structural phase transition at $\ensuremath{\sim}12\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. Pressure evolution of the zero-phonon lines in the low-temperature optical absorption studies helps identifying the symmetry change of the Cu sites modifying the crystal-field energy levels at the structural transition. High-pressure magnetization measurements have been performed with magnetic field applied perpendicular to the tetragonal $c$ axis. With increasing pressure the saturation magnetization of the commensurate weak ferromagnetic phase increases with systematic reduction of its turnup critical field. Pressure-induced systematic suppression of the dc susceptibility in this phase is attributed to the reduced critical field, indicating pressure-driven enhanced stability of the weak ferromagnetic phase at high pressure. Whereas, below 10 K the critical field of the incommensurate-commensurate transition increases with pressure, indicating enhanced stability of the incommensurate helical order at high pressure.