We introduce an equivalent-circuit element based on the theory of interface pinning in random systems, to analyze the contribution of domain wall motion below the coercive field to the impedance of a ferroelectric, as a function of amplitude $E_0$ and frequency $f$ of an applied ac electric field. We investigate capacitor stacks, containing ferroelectric 0.5(Ba$_{0.7}$Ca$_{0.3}$)TiO$_{3}$--0.5Ba(Zr$_{0.2}$Ti$_{0.8}$)O$_{3}$ (BCZT) thin films, epitaxially grown by pulsed laser deposition on Nb-doped SrTiO$_3$ single crystal substrates and covered with Au electrodes. Impedance spectra from $f=10$\,Hz to 1\,MHz were collected at different $E_0$. Deconvolution of the spectra is achieved by fitting the measured impedance with an equivalent-circuit model of the capacitor stacks, and we extract the domain-wall-motion induced amplitude- and frequency-dependent dielectric response of the BCZT films from the obtained fit parameters. From an extended Rayleigh analysis, we quantify the coupling strength between dielectric nonlinearity and dielectric dispersion in the BCZT films and identify different domain-wall-motion regimes. Finally, we construct a schematic diagram of the different domain-wall-motion regimes and discuss the corresponding domain-wall dynamics.
The behavior of antiferromagnetic domain wall (ADW) against the background of a periodic ferroelectric domain structure has been investigated. It has been shown that the structure and the energy of ADW change due to the interaction with a ferroelectric domain structure. The ferroelectric domain boundaries play the role of pins for magnetic spins, the spin density changes in the vicinity of ferroelectric walls. The ADW energy becomes a periodical function on a coordinate which is the position of ADW relative to the ferroelectric domain structure. It has been shown that the energy of the magneti…
Ferroelectric-like hysteresis loops of CaCu3Ti4O12 (CCTO) ceramic have been observed. We found that this unusual feature does not arise from the displacement of the Ti ions in the TiO6 octahedron, but apparently comes from the charges at the grain boundaries which consist of a CuO layer. The relaxation time of 2.9 milliseconds by the charges from the grain boundary, nearly corresponding to the inverse P - V sampling frequency of 1kHz, has been found in the impedance spectrum. According to the micro-Raman mapping, the CuO layer is found in the grain boundary and is perfectly distinguished from …
Motion of ferroelectric domain walls greatly contributes to the macroscopic dielectric and piezoelectric response of ferroelectric materials. The domain wall motion through the ferroelectric material is however hindered by pinning on crystal defects which substantially reduces these contributions. Here, using thermodynamic models based on the Landau-Ginzburg-Devonshire theory, we find a relation between microscopic reversible motion of non-ferroelastic 180-degree domain walls interacting with a periodic array of pinning centers and the nonlinear macroscopic permittivity. We show, that the reve…
Structural, impedance, ferroelectric and magnetic properties were examined in multiferroic Bi_{2}Fe_{4(1-x)}Co_{4x}O_{9} (0$\leq$x$\leq$0.02) ceramics synthesized via solid-state reaction method. X-ray diffraction analysis and Rietveld refinement showed secondary phase formation (for x$\geq$0.01) which was subsequently confirmed from room temperature Raman spectroscopy study. The frequency dependence of impedance and electric modulus of the material showed the presence of non-Debye type relaxation in all the samples. The values of the activation energies calculated from imaginary impedance and…
An impedance spectroscopy (IS) is a versatile tool to study the effect of grains (bulk), grain boundaries and electrode-electrolyte interface on dielectric and electrical properties of electro-ceramics. This study only focuses the high frequency (1 kHz to 10 MHz) probe of bulk ferroelectric capacitance near ferroelectric phase transition temperature (FPTT). The PZTFW single phase and PZTFW-CFO composites, respectively, have been investigated to understand the microstructure-property relation. Keeping in mind the complex microstructure of both systems, low frequency ( less than 1 kHZ ) impedanc…
An evidence that the dielectric ageing in the polydomain Pb(Zr0.45Ti0.55)O3 thin films is controlled by progressive pinning of 180 domain walls is presented. To provide such a conclusion, we use a general method, which is based on the study of the time evolution of the nonlinear, but anhysteretic, dielectric response of the ferroelectric to a weak electric field. A thermodynamic model of the ferroelectric system where the dielectric response is controlled by bending movements of pinned 180 domain walls is developed. Within this model, the nonlinear permittivity of the ferroelectric is expresse…
Field-induced domain wall dynamics in ferroelectric materials underpins multiple applications ranging from actuators to information technology devices and necessitates a quantitative description of the associated mechanisms including giant electromechanical couplings, controlled non-linearities, or low coercive voltages. While the advances in dynamic Piezoresponse Force Microscopy measurements over the last two decades have rendered visualization of polarization dynamics relatively straightforward, the associated insights into the local mechanisms have been elusive. Here we explore the domain …
We report on antiferroelectriclike double polarization hysteresis loops in multiferroic HoMnO3 thin films below the ferroelectric Curie temperature. This intriguing phenomenon is attributed to the domain pinning by defect dipoles which were introduced unintentionally during film growth process. Electron paramagnetic resonance suggests the existence of Fe1+ defects in thin films and first principles calculations reveal that the defect dipoles would be composed of oxygen vacancy and Fe1+ defect. We discuss migration of charged point defects during film growth process and formation of defect dipo…
We investigate theoretically the polarization switching kinetics in ferroelectric thin films. In such substances, the domain walls are pinned by (usually dipole) defects, which are present also in ordered samples as technologically unavoidable impurities. This random interaction with dipole pinning centers results, in particular, in exponentially broad distribution of switching times. Under supposition of low pinning centers concentration, we derive the distribution function of switching times showing that it is not simply Lorentzian (as it was first suggested by Tagantsev et al [\prb, {\bf 66…
Microwave measurements have recently been successfully applied to measure ferroelectric materials on the nanoscale, including detection of polarization switching and ferroelectric domain walls. Here we discuss the question whether scanning probe microscopy (SPM) operating at microwave frequency can identify the changes associated with the soft phonon dynamics in a ferroic. The analytical expressions for the electric potential, complex impedance and dielectric losses are derived and analyzed, since these physical quantities are linked to experimentally-measurable properties of the ferroic. As a…
Domain-Wall-Mediated Ultralow-Barrier Sliding and Pinning in Ferroelectric Moiré Superlattices Revealed by Machine Learning
National Center for Nanoscience and Technology, Chinese Academy of Sciences（中国科学院国家纳米科学中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Songshan Lake Materials Laboratory（松山湖材料实验室）
We use atomistic simulations to study the interactions between two-dimensional domain walls and Sr inclusions in the prototypical ferroelectric BaTiO$_3$. Based on nudged elastic band calculations we predict that the energy barrier for domain wall movement increases in the vicinity of small planar Sr inclusions which may act as pinning centers. We link this observation to the local increase in polarization by larger oxygen off-centering and validate our predictions by molecular dynamics simulations of field-driven domain walls at finite temperatures.
Electric-polarization reversibility in nano-ferroelectric structures renders them as a convenient platform for exploring phase transitions and developing energy-efficient switching devices. However, the fundamental question of how ferroic domains switch, i.e. how the polarization changes from one state to another, is yet to be answered fully. There are contradicting models and a wide body of accumulated data which disagree as to whether the switching requires domain nucleation. Moreover, ferroelectric domains switch under electric fields that are supposedly too weak to form nucleation sites, i…
We report on the electric field response of 180 degree nanodomain walls in BaTiO$_3$ using in situ electrical biasing in transmission electron microscopy (TEM). The sample is biased on a micro-device designed for reliable testing whose key attributes are confirmed by finite element calculations. The presence of weakly charged zig-zag domain walls at room temperature is attributed to the geometric confinement of the device. The motion of the domain walls under the applied electric field allows to extract local P-E loops where distinct domain wall pinning in deep and random energy potential prof…
Surface Acoustic Wave (SAW) resonances were imaged within a closed domain in the ferroelectric LiTaO$_3$ via scanning Microwave Impedance Microscopy (MIM). The MIM probe is used for both SAW generation and measurement, allowing contact-less measurement within a mesoscopic structure. Measurements taken over a range of microwave frequencies are consistent with a constant acoustic velocity, demonstrating the acoustic nature of the measurement.
We investigate magnetic domain wall (MDW) dynamics induced by applied electric fields in ferromagnetic-ferroelectric thin-film heterostructures. In contrast to conventional driving mechanisms where MDW motion is induced directly by magnetic fields or electric currents, MDW motion arises here as a result of strong pinning of MDWs onto ferroelectric domain walls (FDWs) via local strain coupling. By performing extensive micromagnetic simulations, we find several dynamical regimes, including instabilities such as spin wave emission and complex transformations of the MDW structure. In all cases, th…
Ferroelectric domain structure evolution induced by an external electric field was investigated by means of nematic liquid crystal (NLC) method in two strontium-barium niobate single crystals of nominal composition: Sr_{0.70}Ba_{0.30}Nb_{2}O_{6} (SBN:70 - relaxor) and Sr_{0.26}Ba_{0.74}Nb_{2}O_{6} (SBN:26 - ferroelectric). Our results provide evidence that the broad phase transition and frequency dispersion that are exhibited in SBN:70 crystal have a strong link to the configuration of ferroelectric microdomains. The large leakage current revealed in SBN:26 may compensate internal charges acti…
Shear-Mode Raman Imaging of Ferroelectric Switching in Multilayer 3$R$-MoS$_2$
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理实验室和物理系）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（物质材料研究机构电子光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料研究机构材料纳米构造研究中心）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）
The elastic response of BaTiO$_3$ single crystals during electric field cycling at room temperature has been studied using in-situ Resonant Ultrasound Spectroscopy (RUS), which allows monitoring of both the elastic and anelastic changes caused by ferroelectric polarization switching. We find that the first ferroelectric switching of a virgin single crystal is dominated by ferroelastic 90° switching. In subsequent ferroelectric switching, ferroelastic switching is reduced by domain pinning and by the predominance of 180° ferroelectric domains, as confirmed by polarized light microscopy. RUS und…
We report the nanoscale electrical imaging results in hexagonal $Lu_{0.6}Sc_{0.4}FeO_3$ single crystals using conductive atomic force microscopy (C-AFM) and scanning microwave impedance microscopy (MIM). While the dc and ac response of the ferroelectric domains can be explained by the surface band bending, the drastic enhancement of domain wall (DW) ac conductivity is clearly dominated by the dielectric loss due to DW vibration rather than mobile-carrier conduction. Our work provides a unified physical picture to describe the local conductivity of ferroelectric domains and domain walls, which …
The antiferromagnetic domain structure of a multiferroic has been investigated in the presence of a ferroelectric domain structure. It has been demonstrated that an inhomogeneous magnetoelectric (flexomagnetoelectric) interaction leads to pinning of antiferromagnetic domain walls at the walls of the ferroelectric domains and to a change in the structure of antiferromagnetic domain walls.
We simulate from first-principles the energetic, structural, and electronic properties of ferroelectric domains in ultrathin capacitors made of a few unit cells of BaTiO$_3$ between two metallic SrRuO$_3$ electrodes in short circuit. The domains are stabilized down to two unit cells, adopting the form of a domain of closure, common in ferromagnets but only recently detected experimentally in ferroelectric thin films. The domains are closed by the in-plane relaxation of the atoms in the first SrO layer of the electrode, that behaves more like SrO in highly polarizable SrTiO$_3$ than in metallic…
We have investigated the crystal structure and the ferroelectric properties of BaTiO3 thin films with YBa2Cu3O7-d as the bottom and Au as the top electrode. Epitaxial heterostructures of YBa2Cu3O7-d and BaTiO3 were prepared by dc and rf sputtering, respectively. The crystal structure of the films was characterised by x-ray diffraction. The ferroelectric behaviour of the BaTiO3 films was confirmed by hysteresis loop measurements using a Sawyer Tower circuit. We obtain a coercive field of 30 kV/cm and a remanent polarisation of 1.25 \muC/cm. At sub-switching fields the capacitance of the films o…
The role of elastic defects on the kinetics of 180-degree uncharged ferroelectric domain wall motion is explored using continuum time-dependent LGD equation with elastic dipole coupling. In one dimensional case, ripples, steps and oscillations of the domain wall velocity appear due to the wall-defect interactions. While the defects do not affect the limiting-wall velocity vs. field dependence, they result in the minimal threshold field required to activate the wall motions. The analytical expressions for the threshold field are derived and the latter is shown to be much smaller than the thermo…
Ferroelectric materials are spontaneous symmetry breaking systems characterized by ordered electric polarizations. Similar to its ferromagnetic counterpart, a ferroelectric domain wall can be regarded as a soft interface separating two different ferroelectric domains. Here we show that two bound state excitations of electric polarization (polar wave), or the vibration and breathing modes, can be hosted and propagate within the ferroelectric domain wall. Specially, the vibration polar wave has zero frequency gap, thus is constricted deeply inside ferroelectric domain wall, and can propagate eve…
Ferroelectric domain switching in c-axis-oriented epitaxial Pb(Zr0.2Ti0.8)O3 thin films was studied using different field geometries and compared to numerical simulations and theoretical predictions. With carbon nanotubes as electrodes, continuous nanodomains as small as 9 nm in radius in a 270 nm thick film could be switched, remaining stable for over 20 months. Defect pinning of domain walls appears to play a key role in stabilizing such domains, below the predicted thermodynamic size limit.
The effective piezoelectric coefficients of twin walls in tetragonal ferroelectric are calculated in the framework of decoupling approximation and Landau-Ginzburg-Devonshire theory allowing for polarization gradient terms, electrostriction and flexoelectric coupling. Using an example of piezoelectric response of a1-a2 twins to a homogeneous electric field, we show that the response is almost independent on the flexoelectric coupling, but is very sensitive to the values of polarization gradient coefficients. This behavior originates from the strong coupling between local dielectric susceptibili…
We investigated domain kinetics by measuring the polarization switching behaviors of polycrystalline Pb(Zr,Ti)O$_{3}$ films, which are widely used in ferroelectric memory devices. Their switching behaviors at various electric fields and temperatures could be explained by assuming the Lorentzian distribution of domain switching times. We viewed the switching process under an electric field as a motion of the ferroelectric domain through a random medium, and we showed that the local field variation due to dipole defects at domain pinning sites could explain the intriguing distribution.
Microstrctural, vibrational, ferroelectric and dielectric properties investigation reveals non-stoichiometric chemical ordered regions (CORs) and relaxor like dielectric characteristics in lead magnesium niobate (PMN) ceramics uniaxially hot pressed (HP) at 800 oC to 1200 oC. Occurance of (1/2 1/2 1/2) superlattice reflections along <111> in <110> zone axis SAED pattern as well as the presence of bright nano-meter regions in corresponding dark-field images in 800 oC hot pressed PMN demonstrates formation of the CORs as soon as perovskite phase is formed during calcination and remains unaffecte…
Using Landau-Ginzburg-Devonshire approach, we predict the intrinsic instability of the ferroelectric-ferroelastic domain walls in the multiferroic BiFeO3 emerging from the interplay between the gradient terms of the antiferrodistortive and ferroelectric order parameters at the walls. These instabilities are the interface analogue of the structural instabilities in the vicinity of phase coexistence in the bulk; and so they do not steam from incomplete polarization screening in thin films or its spatial confinement, electrostrictive or flexoelectric coupling. The effect of BiFeO3 material parame…
We present measurements of the microwave complex surface impedance at 47.7 GHz in YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) films deposited by pulsed laser deposition with the explicit goal to introduce BaZrO$_3$ (BZO) nanoinclusions. Composite targets obtained by addition of BZO powder in molar percents ranging from 2.5 to 7 mol.% have been prepared and characterized. Measurements of the microwave surface impedance indicate a broadened transition in zero field, however compensated by a very large pinning frequency, indicating that while intergrain properties are still to be optimized the effect of nanome…
Using the model system of ferroelectric domain walls, we explore the effects of long-range dipolar interactions and periodic ordering on the behavior of pinned elastic interfaces. In piezoresponse force microscopy studies of the characteristic roughening of intrinsic 71° stripe domains in BiFeO$_3$ thin films, we find unexpectedly high values of the roughness exponent ζ = 0.74 $\pm$ 0.10, significantly different from those obtained for artificially written domain walls in this and other ferroelectric materials. The large value of the exponent suggests that a random field-dominated pinning, com…
We have investigated non-equilibrium properties of proper uniaxial Sn$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ ferroelectrics with the Type II incommensurate phase above Lifshitz point $x_{\rm LP} \sim 0.28$. We measured dielectric susceptibility with cooling and heating rate ranging 0.002-0.1~K/min, and high-resolution ultrasound experiments and hypersound Brillouin scattering. For samples with $x \geqslant 0.28$ clear anomalies were observed at incommensurate second order transition ($T_i$) and at first order lock-in transition ($T_c$) in the regime of very slow cooling rate, whereas the intermediate I…
The interaction of electric field with charged domain walls in ferroelectrics is theoretically addressed. A general expression for the force acting per unit area of a charged domain wall carrying free charge is derived. It is shown that, in proper ferroelectrics, the free charge carried by the wall is dependent on the size of the adjacent domains. As a result, it was found that the mobility of such domain wall (with respect to the applied field) is sensitive to the parameters of the domain pattern containing this wall. The problem of the force acting on a planar charged 180-degree domain wall …
In this work structural refinement, complex impedance spectroscopy, and Raman spectroscopy have been investigated on Na$_{0.5}$(Bi$_{1-x}$Dy$_x$)$_{0.5}$TiO$_3$ (xDyNBT) ceramic systems. The pure NBT, 2DyNBT and 5DyNBT compounds crystallize in a rhombohedral structure while the 15DyNBT composition crystallizes in an orthorhombic Pnma structure. We reported that dysprosium addition affects the phase transition temperatures as well as the dielectric losses. The electrical transport at high temperatures was investigated using the CIS over a wide frequency range. The studied samples showed a non-D…
We investigate ferroelectric- and resistive switching behavior in 18-nm-thick epitaxial BaTiO$_3$ (BTO) films in a model electrolyte-ferroelectric-semiconductor (EFS) configuration. The system is explored for its potential as a ferroelectric microelectrode in bioelectronics. The BTO films are grown by pulsed laser deposition (PLD) on semiconducting Nb-doped (0.5 wt\%) SrTiO$_{3}$ (Nb:STO) single crystal substrates. The ferroelectric properties of the bare BTO films are demonstrated by piezoresponse force microscopy (PFM) measurements. Cyclic voltammetry (CV) measurements in EFS configuration, …
Ba1-xMgx(Ti0.9Zr0.1)O3(x= 0.01 and 0.02) ceramics were prepared using the conventional solid state reaction. Rietveld refinement performed on X-ray diffraction patterns indicates that the samples are tetragonal crystal structure with P4mm space group. By increasing Mg content from 1 to 2% the unit cell volume decreased. Likewise, the grains size is greatly reduced from 10 to 4 micrometer. The temperature dependence of dielectric constants at different frequencies exhibited typical relaxor ferroelectric characteristic, with sensitive dependence in frequency and temperature for ac conductivity. …
Engineering Grain Boundary Commensurability for Ferroelectric Stabilization in Hafnia-Based Films
Rice University（莱斯大学）；Rice Advanced Materials Institute, Rice University（莱斯大学先进材料研究所）；University of Pennsylvania（宾夕法尼亚大学）；Texas A&M University（德克萨斯农工大学）；University of California, Berkeley（加州大学伯克利分校）；Advanced Photon Source, Argonne National Laboratory（阿贡国家实验室先进光子源）；Smalley-Curl Institute, Rice University（莱斯大学斯马利-柯尔研究所）
Oxygen-vacancies-related dielectric relaxation and scaling behaviors of Bi0.9La0.1Fe0.98Mg0.02O3 (BLFM) thin film have been investigated by temperature-dependent impedance spectroscopy from 40 oC up to 200 oC. We found that hopping electrons and single-charged oxygen vacancies (VO.) coexist in the BLFM thin film and make contribution to dielectric response of grain and grain boundary respectively. The activation energy for VO. is shown to be 0.94 eV in the whole temperature range investigated, whereas the distinct activation energies for electrons are 0.136 eV below 110oC and 0.239 eV above 11…
Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of novel metamaterials. Here we demonstrate a room-temperature ferroelectric semiconductor that is assembled using mono- or few- layer MoS2. These van der Waals heterostructures feature broken inversion symmetry, which, together with the asymmetry of atomic arrangement at the interface of two 2D crystals, enables ferroelectric domains with alternating out-of-plane polarisation arranged into a twist-controlled network. The latter can be moved by applying out-of-plane electrical fields, as visualized…
Effect of thermal annealing on dielectric and ferroelectric properties of aerosol-deposited $0.65\text{Pb}(\text{Mg}_{1/3}\text{Nb}_{2/3})\text{O}_{3}-0.35\text{PbTiO}_{3}$ thick films
Using piezoresponse force microscopy on epitaxial ferroelectric thin films, we have measured the evolution of domain wall roughening as a result of heat-quench cycles up to 735C, with the effective roughness exponent ζ changing from 0.25 to 0.5. We discuss two possible mechanisms for the observed ζ increase: a quench from a thermal 1-dimensional configuration, and from a locally-equilibrated pinned configuration with a crossover from a 2- to 1-dimensional regime. We find that the post-quench spatial structure of the metastable states, qualitatively consistent with the existence of a growing dy…
It is known that the permittivity of the ferroelectric films is affected by several phenomena, which deteriorate the material quality (e.g. the redistribution of the crystal lattice defects, appearance of the electrode-adjacent non-ferroelectric layers or the spontaneous polarization screening due to a free charge injection across the electrode-adjacent layer, etc.). It is also known that the permittivity of ferroelectric polydomain films is controlled by the sum of two contributions: the crystal lattice (intrinsic) contribution and the domain wall movement (extrinsic) contribution. It is the …
Spintronic devices currently rely on magnetic switching or controlled motion of domain walls by an external magnetic field or spin-polarized current. Achieving the same degree of magnetic controllability using an electric field has potential advantages including enhanced functionality and low power consumption. Here, we report on an approach to electrically control local magnetic properties, including the writing and erasure of regular ferromagnetic domain patterns and the motion of magnetic domain walls, in multiferroic CoFe-BaTiO3 heterostructures. Our method is based on recurrent strain tra…
Dielectric response e*(f,T) and polar phonon spectra of coarse grain (grain size ~ 4 mkm) and fine grain (grain size ~ 150 nm) ceramics of PbMg_(1/3)Nb_(2/3)O3-35%PbTiO3 were investigated at temperatures 10 - 900 K. e*(f,T) in coarse-grain ceramics exhibits relaxor behavior at high temperatures and a sharp anomaly at the ferroelectric phase transition. The fine-grain ceramics exhibit mainly relaxor ferroelectric behavior with a smaller dielectric constant. The difference is explained by different relaxational dynamics of polar nanoclusters, which appear to be more stabilized at high temperatur…
We propose a self-consistent theoretical approach capable to describe the peculiarities of the anisotropic nanodomain formation induced by a charged AFM probe on non-polar cuts of ferroelectrics. The proposed semi-phenomenological approach accounts for the difference of the threshold fields required for the domain wall motion along non-polar X- and Y - cuts, and polar Z - cut of LiNbO3. The effect steams from the fact, that the minimal distance between the equilibrium atomic positions of domain wall and the profile of lattice pinning barrier appeared different for different directions due to t…
