An analytical theory is developed for predicting the nonlinear susceptibility of ionic polarization to continuous electromagnetic waves in both bulk and strained thin film ferroelectrics. Using a perturbation method for solving the nonlinear equation of motion for ionic polarization within the framework of Landau-Ginzburg-Devonshire theory, the full second-order nonlinear susceptibility tensor is derived as a function of frequency, temperature, and strain. The theory predicts the coexistence of a significantly enhanced second-order dielectric susceptibility and a relatively low dielectric loss in BaTiO3 films with a strain-stabilized monoclinic ferroelectric phase and in a strained SrTiO3 film near its temperature-driven second-order ferroelectric-to-paraelectric phase transition. This work establishes a theoretical framework for predicting and exploiting nonlinear interactions between THz waves and ferroelectric materials, and more generally, suggests exciting opportunities to strain-engineer nonlinear dynamical properties of ferroelectrics beyond the static and quasi-static limits.
Inspired by recent advancement of low-power ferroelectic-gated memories and transistors, we propose a design of ferroelectic-gated nanoplasmonic devices based on graphene sheets clamped in ferroelectric crystals. We show that the two-dimensional plasmons in graphene strongly couple with the phonon-polaritons in ferroelectrics at terahertz frequencies, leading to characteristic modal wavelength of the order of 100--200 nm at only 3--4 THz. By patterning the ferroelectrics into different domains, one can produce compact on-chip plasmonic waveguides, which exhibit negligible crosstalk even at 50 …
We observe a terahertz radiation from a hydrogen-bonded organic molecular ferroelectric 5,6-dichloro-2-methylbenzimidazole excited by a femtosecond laser pulse at room temperature. The emitted terahertz wave consists of three oscillatory components, the frequencies of which agree with those of Raman- and infrared-active phonon modes. This suggests that the terahertz radiation is attributed to polarization modulations by infrared-active phonons excited via the impulsive stimulated Raman scattering processes. By taking into account the Raman polarizability tensor and dipole-moment for each phono…
We report on the emission of terahertz radiation by irradiation of femtosecond laser pulses in non-centrosymmetric paraelectric and ferroelectric phases of Co$_3$B$_7$O$_{13}$I boracite. The Generation of the terahertz waves in both phases is caused by optical rectification via a second-order nonlinear optical effect. In the ferroelectric phase, we successfully visualized ferroelectric domains by analyzing the polarization state of the terahertz wave radiated from the crystal. In a large area of the crystal ($\sim$ 500 $\times$ 500 $μ$m$^2$), the observed polarization vector of the radiated te…
We demonstrate a new method to detect ferroelectric domains in inside and surface regions of organic ferroelectrics by mapping out two orthogonally polarized terahertz waves radiated from the crystal upon the irradiation of near-infrared femtosecond laser pulses. We used polarization dependence of the effective depths radiating the terahertz waves, which originate from the optical anisotropy in the terahertz frequency region. This allows us to distinguish ferroelectric domains in the inside and surface regions of the crystals. We applied this method to a room-temperature organic supramolecular…
We investigate oscillation dynamics of a periodic structure of the $180^\circ$ domain walls in nanometricaly thin substrate-deposited ferroelectric films and superlattices. We calculate dynamic permittivity of such structures and reveal a collective resonance mode, which in the typical ferroelectric compounds, PbTiO3/SrTiO3, lies in the sub- and low THz frequency range of 0.3-3THz. We propose the reflection-absorbtion spectroscopy experiments to observe this mode.
The symmetry breaking induced by the ferroelectric transition often triggers the emergence of topological electronic states such as Weyl fermions in ferroelectric-like metals/semimetals. Such strong coupling between the lattice deformation and electronic states is therefore essentially important for the control of novel topological phases. Here, we study the terahertz lattice and charge dynamics in ferroelectric semiconductor SnxPb1-xTe thin films hosting versatile topological phases by means of the terahertz time-domain spectroscopy. With lowering the temperature, the resonant frequency of tr…
Far-infrared and terahertz spectroscopy of ferroelectric soft and central modes in thin films on substrates is reviewed. In addition to classical displacive proper ferroelectrics, also incipient and relaxor ferroelectrics and multiferroics are discussed. Special attention is paid to differences between the soft-mode behavior in thin films and bulk materials (ceramics and single crystals) and their influence on the low-frequency permittivity. Particularly the effects of the thin film strains and depolarizing electric fields of the probing waves on the grain boundaries are emphasized. The soft-m…
Recent experiments have demonstrated that light can induce a transition from the quantum paraelectric to the ferroelectric phase of SrTiO$_3$. Here, we investigate this terahertz field-induced ferroelectric phase transition by solving the time-dependent lattice Schrödinger equation based on first-principles calculations. We find that ferroelectricity originates from a light-induced mixing between ground and first excited lattice states in the quantum paraelectric phase. In agreement with the experimental findings, our study shows that the non-oscillatory second harmonic generation signal can b…
Intense, few-cycle pulses in the terahertz frequency range have strong potential for schemes of control over vibrational modes in solid-state materials in the electronic ground-state. Here we report an experiment using single cycle terahertz pulses to directly excite lattice vibrations in the ferroelectric material $\mathrm{Sn_2P_2S_6}$ and ultrafast x-ray diffraction to quantify the resulting structural dynamics. A model of a damped harmonic oscillator driven by the transient electric field of the terahertz pulses describes well the movement of the Sn$^{2+}$ ion along the ferroelectric soft m…
Terahertz radiation by optical rectification has been observed at room temperature in a hydrogen-bonded organic molecular ferroelectric crystal, 2-phenyl malondialdehyde (PhMDA). The radiated electromagnetic wave consisted of a single-cycle terahertz pulse with a temporal width of $\sim$ 0.5 ps. The terahertz radiation amplitude divided by the sample thickness in PhMDA was nearly equivalent to that in a typical terahertz wave emitter ZnTe. This is attributable to a long coherence length in the range of 130 $\sim$ 800 $μ$m for the terahertz radiation from PhMDA. We also discussed the possibilit…
Ferroelectric and multiferroic materials form an important class of functional materials. Over the last twenty years, first-principles-based effective Hamiltonian approaches have been successfully developed to simulate these materials. In recent years, effective Hamiltonian approaches were further combined with molecular dynamics methods to investigate terahertz dynamical properties of various perovskites. With this combination, a variety of ferroelectric and multiferroic materials, including BaTiO_{3}, Ba(Sr,Ti)O_{3}, Pb(Zr,Ti)O_{3}, BiFeO_{3}, and SrTiO_{3} bulks and films have been simulate…
The polarization and the susceptibility of a ferroelectric multilayer with a non-ferroelectric slab are investigated within the framework of transverse Ising model with a four-spin interaction term. The effect of the thickness and the position of the non-ferroelectric slab are investigated in this paper. We find that the increase of the thickness of the non-ferroelectric will decrease the polarization and the susceptibility of the film. If the position of the non-ferroelcetric slab shifts from the center of the film to the surface, the number of the peaks of the susceptibility will change. And…
We detected broadband coherent terahertz (THz) emission from multiferroic BiFeO3 after illuminating a high-quality bulk single ferroelectric domain crystal with a ~100 fs optical pulse. The dependence of the emitted THz waveform on the energy and polarization of the optical pulse is consistent with the optical rectification mechanism of THz emission. The THz emission provides a sensitive probe of the electric polarization state of BiFeO3, enabling applications in ferroelectric memories and ferroelectric domain imaging. We also report room-temperature THz optical constants of BiFeO3.
The dynamical processes associated with electric field manipulation of the polarization in a ferroelectric remain largely unknown but fundamentally determine the speed and functionality of ferroelectric materials and devices. Here we apply sub-picosecond duration, single-cycle terahertz pulses as an ultrafast electric field bias to prototypical BaTiO$_3$ ferroelectric thin films with the atomic-scale response probed by femtosecond x-ray scattering techniques. We show that electric fields applied perpendicular to the ferroelectric polarization drive large amplitude displacements of the titanium…
We calculate the pyrocoefficient, static dielectric susceptibility profiles and its thickness dependence of ferroelectric thin films. Also, the temperature dependences of above quantities have been calculated. For the calculations we use Landau phenomenological theory, leading to Lame equations. These equations subject to boundary conditions with different extrapolation length on the surfaces have been solved numerically. The divergency of pyroelectric coefficient and static dielectric susceptibility in the vicinity of thickness induced ferroelectric phase transition (i.e. at $l\approx l_c$ or…
Long-range effects on the pyroelectric coefficient and susceptibility of a ferroelectric bilayer with a ferroelectric interfacial coupling are investigated by use of the transverse Ising model within the framework of mean-field theory. The effects of the interfacial coupling and the transverse field on the pyroelectric coefficient and susceptibility of the bilayer are investigated by taking into account the long-range interaction. It is found that the pyroelectric coefficient and susceptibility increase with the decrease of the magnitude of the long-range interaction and the interfacial coupli…
Flexoelectric effect impact on the generalized susceptibility and soft phonons dispersion was not studied in the long-range ordered phases of ferroics. The gap in the knowledge motivated us to establish the impact of the flexocoupling on the correlation function of the long-range order parameter fluctuations in ferroelectric phase of ferroics with local disordering sources. Within Landau-Ginzburg-Devonshire approach we obtained analytical expressions for the generalized susceptibility and phonon dispersion relations in the ferroelectric phase. Unexpectedly, the joint action of static and dynam…
Remarkably high values of polarization as well as a significant magnetic susceptibility have been observed in multiferroic Bismuth Ferrite (BFO) in the form of nanorods protruding out. These were developed on porous Anodised Alumina (AAO) templates using wet chemical technique. Diameters of nanorods are in the range of 20-100 nm. The high values of polarization and magnetic susceptibility are attributed to the BFO nanorod structures giving rise to the directionality. There is no leakage current in P-E loop examined at various frequencies. Magnetocapacitance measurements reflect a significant e…
Terahertz Control of Optical Second-Harmonic Generation in Displacive Ferroelectrics: Electronic Bloch-State Reconstruction
School of Information Science and Technology, University of Science and Technology of China（中国科学技术大学信息科学与技术学院）；Guilin Julian Technology Co., Ltd.（桂林朱利安科技有限公司）；School of Electronic Engineering and Automation, Guilin University of Electronic Technology（桂林电子科技大学电子工程与自动化学院）；School of Chemistry and Chemical Engineering, Shaanxi University of Science and Technology（陕西科技大学化学与化工学院）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）
Ferroelectrics usually adopt a multi-domain state with domain walls separating domains with polarization axes oriented differently. It has long been recognized that domain walls can dramatically impact the properties of ferroelectric materials. The enhancement of low-field susceptibility/permittivity under subswitching conditions is usually attributed to the reversible domain wall vibration. Recent experiments highlight the stationary domain wall contribution to the dielectric susceptibility irrespective of any lateral displacements or deformations of the wall. We study the effects of domain w…
We propose that concurrently magnetic and ferroelectric, i.e. multiferroic, compounds endowed with electrically-active magnetic excitations (electromagnons) provide a key to produce large directional dichroism for long wavelengths of light. By exploiting the control of ferroelectric polarization and magnetization in a multiferroic oxide Ba$_2$CoGe$_2$O$_7$, we demonstrate the realization of such a directional light-switch function at terahertz frequecies in resonance with the electromagnon absorption. Our results imply that this hidden potential is present in a broad variety of multiferroics.
Terahertz (THz) radiation has been observed from multiferroic BiFeO$_3$ thin films via ultrafast modulation of spontaneous polarization upon carrier excitation with illumination of femtosecond laser pulses. The radiated THz pulses from BiFeO$_3$ thin films were clarified to directly reflect the spontaneous polarization state, giving rise to a memory effect in a unique style and enabling THz radiation even at zero-bias electric field. On the basis of our findings, we demonstrate potential approaches to ferroelectric nonvolatile random access memory with nondestructive readability and ferroelect…
Using effective-field theory with correlations, we investigate the effects of interfacial pseudo-spin coupling fluctuations on the susceptibility and polarization of ferroelectric superlattices within the framework of transverse Ising model. It is found that the interfacial coupling fluctuations increase the susceptibility in the low temperature region. For a strong interfacial coupling, the phase transition temperature decreases with the strength of fluctuations of the interfacial coupling. The dependence of the susceptibility on the superlattice period of $BaTiO_{3}/SrTiO_{3}$ are plotted fo…
Anomalously large dielectric aging is found in the high-susceptibility plateau ferroelectric regime of ~95% deuterated potassium dihydrogen phosphate (DKDP). Much less aging is found in non-deuterated KDP. Optical images of the DKDP domain structure show no dramatic change during aging. Small changes in electric field restore the pre-aged susceptibility, but the previous aging almost recovers after returning to the aging field. Susceptibility vs. field can show memory of at least two prior aging fields. Rectifying non-linear susceptibility develops for fields slightly above or below a prior ag…
In the paper we present analytical calculations of the profiles and average values correlation radius of polarization fluctuations and generalized susceptibility in thin ferroelectric films of thickness L with in-plane (a-films) and out-of-plane (c-films) polarization orientation. The contribution of polarization gradient, surface energy and depolarization field (if any) were taken into account. For the second order ferroelectrics the correlation radius and generalized susceptibility diverge at the film critical thickness Lcr as anticipated. In the case of a-films where depolarization field is…
We theoretically explore mechanisms that can potentially give rise to the steady-state and transient negative capacitance in a uniaxial ferroelectric film stabilized by a dielectric layer. The analytical expressions for the steady-state capacitance of a single-domain and poly-domain states are derived within Landau-Ginzburg-Devonshire approach and used to study the state stability vs. the domain splitting as a function of dielectric layer thickness. Analytical expressions for the critical thickness of the dielectric layer, polarization amplitude, equilibrium domain period and susceptibility ar…
Coherent seeding and control of dynamical ferroelectricity by phonon anharmonicity
Peking University（北京大学）；Beihang University（北京航空航天大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家研究中心）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
Entanglement of two different quantum orders is of an interest of the modern condensed matter physics. One of the examples is the dynamical multiferroicity, where fluctuations of electric dipoles lead to magnetization. We investigate this effect at finite temperature and demonstrate an elevated magnetic response of a ferroelectric near the ferroelectric quantum critical point (FE QCP). We calculate the magnetic susceptibility of a bulk sample on the paraelectric side of the FE QCP at finite temperature and find enhanced magnetic susceptibility near the FE QCP. We propose quantum paraelectric s…
The time dependent cluster approximation called the path probability method (PPM) is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KH2PO4-type hydrogen-bonded ferroelectrics in order to calculate the homogeneous dynamical susceptibility above and below the ferroelectric transition temperature. Above the transition temperature all the calculations are carried out analytically in the cactus approximation of the PPM. Below the transition temperature the dynamical susceptibility is also calculated accurately since the analytical solution of spontaneous polarization in t…
In the first part of this work we calculate the high frequency magnetoelectric susceptibility of a simultaneously ferroelectric and canted antiferromagnetic (also know as weak ferromagnetic) thin film with magnetostrictive magnetoelectric coupling. We show that a dynamic coupling exists between the ferroelectric and optic antiferromagnetic excitations. In the second part of the paper, we calculate using an effective medium method the susceptibility of a heterostructure comprising alternating thin films of such a material together with a ferromagnet. Dipolar magnetic fields serve to couple the …
We report a neutron scattering study of the ferroelectric phase transition in Sr$_{0.585}$Ce$_{0.025}$Ba$_{0.39}$Nb$_2$O$_6$ (SBN-61:Ce). We find no evidence for a soft transverse optic phonon. We do, however, observe anisotropic diffuse scattering. This scattering has inelastic and elastic contributions. In the paraelectric phase the susceptibility associated with the elastic diffuse scattering follows well the anomaly of the dielectric susceptibility of SBN-61:Ce. In the ferroelectric phase the lineshape of the elastic scattering is consistent with the form expected for the ferroelectric dom…
We compute from first principles the infrared dispersion of the nonlinear susceptibility $χ^{(2)}$ in zincblende semiconductors. At terahertz frequencies the nonlinear susceptibility depends not only on the purely electronic response $χ^{(2)}_{\infty}$, but also on three other parameters $C_1$, $C_2$ and $C_3$ describing the contributions from ionic motion. They relate to the TO Raman polarizability, the second-order displacement-induced dielectric polarization, and the third-order lattice potential. Contrary to previous theory, we find that mechanical anharmonicity ($C_3$) dominates over elec…
Recent spectroscopic studies at terahertz frequencies for a variety of multiferroics endowed with both ferroelectric and magnetic orders have revealed the possible emergence of a new collective excitation, frequently referred to as electromagnon. It is magnetic origin, but becomes active in response to the electric field component of light. Here we give an overview on our recent advance in the terahertz time-domain spectroscopy of electromagnons or electric-dipole active magnetic resonances, focused on perovskite manganites--$R$MnO$_3$ ($R$ denotes rare-earth ions). The respective electric and…
Ultrafast optical control of ferroelectricity using intense terahertz fields has attracted significant interest. Here we show that the nonlinear interactions between two optical phonons in SnTe, a two-dimensional in-plane ferroelectric material, enables a dynamical amplification of the electric polarization within subpicoseconds time domain. Our first principles time dependent simulations show that the infrared-active out-of-plane phonon mode, pumped to nonlinear regimes, spontaneously generates in-plane motions, leading to rectified oscillations in the in-plane electric polarization. We sugge…
The dynamic dielectric susceptibility and elastic compliance of the relaxor ferroelectric PLZT 9/65/35 have been measured under different cooling and heating protocols, in order to study aging and memory. The memory of multiple aging stages has been found (several dips in the susceptibility curves on heating), as in spin glass systems below the glass transition. Remarkably, in PLZT the memory is retained also above the freezing temperature deduced from the dynamic susceptibilities. The results are discussed in the light of the existing models of aging and memory in spin and dipolar glasses.
Coupling of Electronic Transitions to Ferroelectric Order in a 2D Semiconductor
Columbia University（哥伦比亚大学）；Graduate Center, City University of New York（纽约市立大学研究生中心）；Advanced Science Research Center, City University of New York（纽约市立大学先进科学研究中心）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Pennsylvania State University（宾夕法尼亚州立大学）
In this paper, we present a microscopic model for heterogeneous ferroelectric and an order parameter for relaxor phase. We write a Landau theory based on this model and its application to ferroelectric PbFe$_{1/2}$Ta$_{1/2}$O$_3$ (PFT) and antiferroelectric NaNbO$_3$:Gd. We later discuss the coupling between soft mode and domain walls, soft mode and quasi-local vibration and resulting susceptibility function.
The presence of a space charge region induces an internal electric field within the charged region that, in a ferroelectric material, would rotate the polarisations to align with the field. The strength of the induced field would therefore determine the domain patterns and polarisation switching properties of the material. Using a phase-field model, we investigate the effect of charged layers in fully and partially depleted BiFeO$_3$ thin films in the rhombohedral phase. While the domain pattern in a charge-free BiFeO$_3$ film consists of only two polarisation variants, we observe complex patt…
LiOsO3 is one of the first materials identified in a recent literature as a 'polar metal', a class of materials that are simultaneously noncentrosymmetric and metallic. In this work, the linear and nonlinear optical susceptibility of LiOsO3 is studied by means of ellipsometry and optical second harmonic generation (SHG). Strong optical birefringence is observed using spectroscopic ellipsometry. The nonlinear optical susceptibility extracted from SHG polarimetry reveals that the tensor components are of the same magnitude as in isostructural insulator LiNbO3, except the component along the pola…
A thermodynamic theory of ferroelectric thin film multilayers is developed. The free energy function is written down using a multilayer model in which c-domain layers of one ferroelectric material alternate with a-domain layers of a second ferroelectric material. We assume that the interfaces are perfectly sharp and that the polarization at these boundaries is zero. The renormalization of the free energy coefficients due to the stresses in the films and to the depolarizing field was taken into account, as well as the renormalization of the coefficients of the polarization gradients. The equili…
The dielectric permittivity e at frequencies from [10^(-1) -10^(-5)] Hz to 10^5 Hz is studied in perovskite (1-x)Pb(Mg1/3Nb2/3)O3 - xPbTiO3 relaxor ferroelectric ceramics of different compositions x = 0.35, 0.25 and 0, which exhibit, below the temperature of the diffuse epsilon'(T) maximum Tm, a tetragonal ferroelectric, a rhombohedral ferroelectric and a nonergodic relaxor phase, respectively. The universal relaxor dispersion previously observed at temperatures near and above Tm in the ceramics of x=0.25, is also found to exist in other compositions. This dispersion is described by the fracti…
Perovskite solid solutions PbHfO3-PbSnO3 offer valuable opportunities for studying the formation mechsnisms of incommensurate phases, owing to the presence of an intermediate (between cubic and incommensurate) phase, which is stabilized in PbHfO3 upon PbSnO3 admixture. Here, x-ray diffuse scattering signal is used to quantify the evolution of susceptibilities related to different modes of distortion (ferroelectric, incommensurate, antiferrodistortive) as a function of temperature and the results are critically compared to the predictions of a minimal symmetry-based Landau-like model with two c…
For the first time we proposed the model for the calculations of the relaxor ferroelectrics films properties in the framework of the random field theory. We took into account the misfit strain between film and substrate as well as surface piezoelectric effect that causes built-in electric field in the strained films. In the statistical theory framework we calculated random field distribution function with the electric dipoles and monopoles as the field sources. It was shown that with thickness decrease the mean field decreases, while the width of the distribution function increases. This leads…
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Stanford PULSE Institute, SLAC National Accelerator Laboratory（斯坦福PULSE研究所，SLAC国家加速器实验室）；Department of Chemistry, Massachusetts Institute of Technology（麻省理工学院化学系）；Elettra-Sincrotrone（埃莱特拉同步辐射中心）；Paul Scherrer Institut（保罗谢尔研究所）
In order to understand the physical hysteresis loops clearly, we constructed a novel model, which is combined with the electric field, the temperature, and the stress as one synthetically parameter. This model revealed the shape of hysteresis loop was determined by few variables in ferroelectric materials: the saturation of polarization, the coercive field, the electric susceptibility and the equivalent field. Comparison with experimental results revealed the model can retrace polarization versus electric field and temperature. As a applications of this model, the calculate formula of energy s…
We verify whether the previously developed model of a KD2PO4 crystal, with the shear strain eps6 taken into account, is able to describe the longitudinal electric field E3 influence on the KH2PO4 family ferroelectrics. Major effects of the strain eps6 are splitting of the Slater energies of the short-range correlations and the effective field created by piezoelectric coupling. Calculated TC-E3 phase diagrams, field dependences of polarization, susceptibility, and elastic constant of deuterated KD2PO4 and pure KH2PO4 well accord with the available experimental data. For a consistent description…
Electric dipoles of water molecules, enclosed singly in regularly spaced nanopores of a cordierite crystal, become ordered at low temperature due to their mutual interaction and show the frequency dependence of their dielectric susceptibility, typical for relaxor ferroelectrics, according to recent experimental data. The corresponding phase transition is accompanied by anomalies in thermodynamic quantities, such as heat capacity and dielectric susceptibility, which are calculated here using the Monte Carlo method, and their agreement the experimental data is discussed. Despite the increase in …
The calculation of the polarization in ferroelectric thin films is performed using an analytical solution of the Euler-Lagrange differential equation with boundary conditions with different extrapolation lengths of positive sign on the surfaces. The depolarization field effect is taken into account in the model for a short-circuited single domain film, that is a perfect insulator. It is shown that the calculation of the polarization and other properties profiles and average values can be reduced to the minimization of the free energy expressed as a power series of the average polarization with…
Large low-frequency noise is found in some perovskite relaxor ferreoelectrics when they are polarized, regardless of whether the polarization is accompanied by an applied electric field. The noise appears both in the ferroelectric and relaxor states, including in the nominally ergodic paraelectric state at temperatures above the susceptibility peak. Since it is present whenever the samples are microphonic due to piezoelectricity but not evident when they are not microphonic, it appears to be a response to mechanical strain changes. Dependence of the noise on sample thermal history indicates th…
