We report a neutron scattering study of a ferroelectric phase transition in Sr$_{0.61}$Ba$_{0.39}$Nb$_2$O$_6$ (SBN-61). The ferroelectric polarization is along the crystallographic $c$-axis but the transverse acoustic branch propagating along the $<$1, 1, 0$>$ direction does not show any anomaly associated with the this transition. We find no evidence for a soft transverse optic phonon. We do, however, observe elastic diffuse scattering. The intensity of this scattering increases as the sample is cooled from a temperature well above the phase transition. The susceptibility associated with this diffuse scattering follows well the anomaly of the dielectric permittivity of SBN-61. Below T$_\mathrm{c}$ the shape of this scattering is consistent with the scattering expected from ferroelectric domain walls. Our results suggest that despite apparent chemical disorder SBN-61 behaves as a classic order-disorder uniaxial ferroelectric with critical fluctuations in the range $<10^{-11}$ s.
Tetragonal ferroelectric/ferroelectric BaTiO3/PbTiO3 superlattice under uniaxial tensile stress along the c axis is investigated from first principles. We show that the calculated ideal tensile strength is 6.85 GPa and that the superlattice under the loading of uniaxial tensile stress becomes soft along the nonpolar axes. We also find that the appropriately applied uniaxial tensile stress can significantly enhance the piezoelectricity for the superlattice, with piezoelectric coefficient d33 increasing from the ground state value by a factor of about 8, reaching 678.42 pC/N. The underlying mech…
Discovery of topological polarization textures has put ferroelectrics at the frontier of topological matter science. High-symmetry ferroelectric oxide materials allowing for freedom of the polarization vector rotation offer a fertile ground for emergent topological polar formations, like vortices, skyrmions, merons, and Hopfions. It has been commonly accepted that uniaxial ferroelectrics do not belong in the topological universe because strong anisotropy imposes insurmountable energy barriers for topological excitations. Here we show that uniaxial ferroelectrics provide unique opportunity for …
For the first time in a bulk proper uniaxial ferroelectrics, double antiferroelectric-like hysteresis loops have been observed in the case of Sn$_2$P$_2$S$_6$ crystal. The quantum anharmonic oscillator model was proposed for description of such polarization switching process. This phenomenon is related to three-well local potential of spontaneous polarization fluctuations at peculiar negative ratio of coupling constants which correspond to inter-site interaction in given sublattice and interaction between two sublattices of Sn$_2$P$_2$S$_6$ modeled crystal structure. Obtained data can be used …
A phenomenological treatment of domain walls based on the Ginzburg-Landau-Devonshire theory is developed for uniaxial, trigonal ferroelectrics lithium niobate and lithium tantalate. The contributions to the domain wall energy from polarization and strain as a function of orientation are considered. Analytical expressions are developed which are analyzed numerically to determine the minimum polarization, strain, and energy configurations of domain walls. It is found that hexagonal y-walls are preferred over x-walls in both materials. This agrees well with experimental observation of domain geom…
The switching of electric polarization induced by electric fields -a fundamental functionality of ferroelectrics- is closely associated with the motions of the domain walls that separate regions with distinct polarization directions. Therefore, understanding domain-walls dynamics is of essential importance for advancing ferroelectric applications. In this Letter, we show that the topology of the multidomain structure can have an intrinsic impact on the degree of switchable polarization. Using a combination of polarization hysteresis measurements and piezoresponse force microscopy on a uniaxial…
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…
An exactly solvable lattice model with infinite-range potential is applied to uniaxial ferroelectrics. Asymptotically exact expression for free energy as a function of an order parameter at any temperatures is obtained. Effect of thermal expansion of lattice unit cell is taken into account. The free energy expansion in powers of order parameter in the vicinity of critical point is presented. Corrections to Landau expansion are obtained. In particular, it is shown that summand with external field contains a contribution of higher powers over order parameter. Keywords: Lattice model, Free energy…
We propose the Landau model for lock-in phase transitions in uniaxially modulated improper ferroelectric incommensurate-commensurate systems of class I. It includes Umklapp terms of third and fourth order and secondary order parameter representing the local polarization. The corresponding phase diagram has the structure of harmless staircase, with the allowed wave numbers obeying the Farey tree algorithm. Among the stable commensurate phases only those with periods equal to odd number of lattice constants have finite macroscopic polarizations. These results are in excellent agreement with expe…
Tris-sarcosine calcium chloride (TSCC) is a highly uniaxial ferroelectric with a Curie temperature of approximately 130K. By suppressing ferroelectricity with bromine substitution on the chlorine sites, pure single crystals were tuned through a ferroelectric quantum phase transition. The resulting quantum critical regime was investigated in detail - the first time for a uniaxial ferroelectric and for an organic ferroelectric - and was found to persist up to temperatures of at least 30K to 40K. The nature of long-range dipole interactions in uniaxial materials, which lead to non-analytical term…
Phase-field insight into the nature of topological polarization structures in uniaxial ferroelectrics
Institute of Materials Science, Technical University of Darmstadt（达姆施塔特工业大学材料科学研究所）；Institute of Physics, Czech Academy of Sciences（捷克科学院物理研究所）；Faculty of Mechatronics, Informatics and Interdisciplinary Studies, Technical University of Liberec（利贝雷茨工业大学机械、信息学及跨学科研究学院）
Correlated domain and crystallographic orientation mapping in uniaxial ferroelectric polycrystals by interferometric vector piezoresponse force microscopy
NTNU Norwegian University of Science and Technology（挪威科技大学）；Asylum Research an Oxford Instruments Company（阿苏姆研究（牛津仪器旗下公司））；University of Duisburg-Essen（杜伊斯堡-埃森大学）；Research Center Future Energy Materials and Systems, Research Alliance Ruhr（鲁尔研究联盟未来能源材料与系统研究中心）
The frequency dependence of the dielectric permitivity's maximum has been studied for poled and unpoled doped relaxor strontium barium niobate $Sr_{0.61}Ba_{0.39}Nb_{2}O_{6}:Cr^{3+}$ (SBN-61:Cr). In both cases the maximum found is broad and the frequency dispersion is strong. The present view of random fields compensation in the unpoled sample is not suitable for explaining this experimental result. We propose a new mechanism where the dispersion of quenched random electric fields, affecting the nanodomains, is minimized after poling. We test our proposal by numerical simulations on a random f…
Using Landau-Ginzburg-Devonshire theory we calculated numerically the static conductivity of both inclined and counter domain walls in the uniaxial ferroelectrics-semiconductors of n-type. We used the effective mass approximation for the electron and holes density of states, which is valid at arbitrary distance from the domain wall. Due to the electrons accumulation, the static conductivity drastically increases at the inclined head-to-head wall by 1 order of magnitude for small incline angles theta pi/40 by up 3 orders of magnitude for the counter domain wall (theta=pi/2). Two separate region…
We have modified Landau-Khalatnikov approach and shown that both the polar lattice and the screened charged defects determine the response of disordered ferroelectric-semiconductors. This system exhibits the spatially inhomogeneous switching under the external field while Landau-Khalatnikov model describes homogeneous switching with the sharp pyroelectric coefficient peak near the thermodynamic coercive field value. Our model gives more realistic pyroelectric hysteresis loop shape without any peaks near the coercive field and describes both qualitatively and quantitatively typical Pb(Zr,Ti)O_3…
We present a semi-empirical effective Hamiltonian to capture effects of disorder associated with Ba and Sr cations occupying $A$ sites in (Ba$_{x}$Sr$_{1-x}$)TiO$_3$ on its ferroelectric phase transition. Averaging between the parameters of first-principles effective Hamiltonians of end members BaTiO$_3$ and SrTiO$_3$, we include a term with an empirical parameter to capture the local polarization and strains arising from the difference between ionic radii of Ba and Sr. Using mixed-space molecular dynamics of the effective Hamiltonian, we determine $T$-dependent ferroelectric phase transitions…
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.
In the framework of the Landau-Ginzburg-Devonshire (LGD) approach we studied finite size effects of the phase diagram and domain structure evolution in spherical nanoparticles of uniaxial ferroelectric. The particle surface is covered by a layer of screening charge characterized by finite screening length. The phase diagram, calculated in coordinates "particle radius vs. screening length" has a wide region of versatile poly-domain structures separating single-domain ferroelectric and nonpolar paraelectric phases. Unexpectedly, we revealed a region of stable irregular labyrinthine domains in th…
The coupling of translational modes to the reorientational motion is an essential property of systems with internal orientational degrees of freedom. Due to their high complexity most of those systems (molecular crystals, glasses...) present a major puzzle for scientists. In this paper we analyze the Raman scattering of a relatively simple ferroelectric system, KTa(1-x)Nb(x)O(3), which may serve as a model for more complicated cases. We are showing that there is a strong coupling between translational and reorientational motion in the crystal. Our data suggest that this coupling is the main re…
Ferroelectric phase transition in the semiconductor Sn2P2S6 single crystal has been studied by means of neutron scattering in the pressure-temperature range adjacent to the anticipated tricritical Lifshitz point (p=0.18GPa, T=296K). The observations reveal a direct ferroelectric-paraelectric phase transition in the whole investigated pressure range (0.18 - 0.6GPa). These results are in a clear disagreement with phase diagrams assumed in numerous earlier works, according to which a hypothetical intermediate incommensurate phase extends over several or even tens of degrees in the 0.5GPa pressure…
For the first time we predict the conditions of superparaelectric phase appearance in the ensemble of non-interacting spherical ferroelectric nanoparticles. The superparaelectricity in nanoparticle was defined by analogy with superparamagnetism, obtained earlier in small nanoparticles made of paramagnetic material. Calculations of correlation radius, energetic barriers of polarization reorientation and polarization response to external electric field, were performed within Landau-Ginzburg phenomenological approach for perovskites Pb(Zr,Ti)O3, BiFeO3 and uniaxial ferroelectrics rochelle salt an…
The so-called interlayer-sliding ferroelectricity was recently proposed as an unconventional route to pursuit electric polarity in van der Waals multi-layers, which was already experimentally confirmed in WTe$_2$ bilayer even though it is metallic. Very recently, another van der Waals system, i.e., the ZrI$_2$ bilayer, was predicted to exhibit the interlayer-sliding ferroelectricity with both in-plane and out-of-plane polarizations [Phys. Rev. B \textbf{103}, 165420 (2021)]. Here the ZrI$_2$ bulk is studied, which owns two competitive phases ($α$ \textit{vs} $β$), both of which are derived fro…
For Sn$_2$P$_2$S$_6$ family of uniaxial ferroelectrics, the anharmonic quantum oscillators model, based on local three-well potential for spontaneous polarization fluctuations, has been used for a description of anharmonic properties, namely thermal expansion. The calculated pseudospin fluctuations spectra in ferroelectric phase demonstrate negative Grüneisen parameters for excitations that satisfy Curie-Weiss-like temperature and pressure dependencies in the vicinity of second order phase transition. Thermal expansion coefficient is calculated by evaluation of pseudospins entropy baric depend…
The ferroelectric trends of rutile (TiO$_2$) in bulk and at the (110) surface are investigated by means of ab initio density functional theory. We discuss the underlying mechanism of the incipient ferroelectric behavior of rutile in terms of Born effective charges, which we decompose in individual contributions by means of maximally localized Wannier functions. We show that a ferroelectric phase can be stabilized for a variety of different lattice distortions which all enlarge the shortest Ti-O distance, even if the longer apical Ti-O bond is simultaneously shortened. At the (110) surface, the…
Structural strain severely impacts material properties such as the linear and non-linear optical response. Moreover, strain plays a key role, e.g., in the physics of ferroelectrics and in particular of their domain walls. $μ$-Raman spectroscopy is a well-suited technique for the investigation of such strain effects, as it allows to measure the lattice dynamics locally. However, quantifying and reconstructing strain fields from Raman maps requires knowledge on the strain dependence of phonon frequencies. In this work, we have analyzed both theoretically and experimentally the phonon frequencies…
The barium sodium niobate (BNN) with tungsten-bronze structure is one of well-known optical crystals for electro-optic and nonlinear optic applications. This paper reviews the ferroelectric instability of BNN crystals. BNN is a uniaxial ferroelectric with a spontaneous polarization along the tetragonal $c$-axis. There is no report on the observation of an optical soft mode responsible for a ferroelectric phase transition. In the vicinity of the Curie temperature, $T_{\text{C}}=560$°C, an intense central peak (CP) related to the polarization fluctuations along the $c$-axis was observed by the b…
The domain structure of uniaxial ferroelectric lithium niobate single crystals is investigated using Raman spectroscopy mapping. The influence of doping with magnesium and poling at room temperature is studied by analysing frequency shifts at domain walls and their variations with dopant concentration and annealing conditions. It is shown that defects are stabilized at domain walls and that changes in the defect structures with Mg concentration can be probed by the shift of Raman modes. We show that the signatures of polar defects in the bulk and at the domain walls differ.
First-principles calculations of the epitaxial-strain phase diagram of perovskite SrCoO$_{3}$ are presented. Through combination of the large spin-phonon coupling with polarization-strain coupling and coupling of the band gap to the polar distortion, both tensile and compressive epitaxial strain are seen to drive the bulk ferromagnetic-metallic (FM-M) phase to antiferromagnetic-insulating-ferroelectric (AFM-I-FE) phases, the latter having unusually low elastic energy. At these coupled magnetic-ferroelectric metal-insulator phase boundaries, cross responses to applied electric and magnetic fiel…
The interaction between soft optic and acoustic phonons was investigated for Sn2P2(Se0.28S0.72)6 proper uniaxial ferroelectrics by Brillouin scattering and ultrasonic pulse-echo techniques. The elastic softening of hypersound velocity of transverse acoustic phonons and for both longitudinal and transverse ultrasound waves which propagate near direction of the modulation wave vector (in the incommensurate phase at x>xLP) was found at cooling to the Lifshitz point in the paraelectric phase. The strong increase of the ultrasound attenuation have also been observed. Such phenomena are related to t…
The behavior of PbTiO$_3$ under uniaxial strains and stresses is investigated from first-principles calculations within density functional theory. We show that irrespectively of the uniaxial mechanical constraint applied, the system keeps a purely ferroelectric ground-state, with the polarization aligned either along the constraint direction ($FE_z$ phase) or along one of the pseudo-cubic axis perpendicular to it ($FE_x$ phase). This contrasts with the cases of isotropic or biaxial mechanical constraints for which novel phases combining ferroelectic and antiferrodistortive motions have been pr…
Structural, electronic, ferroelectric, and optical properties of two-dimensional (2D) BiN monolayer material with phosphorene-like structure are studied in terms of the density functional theory and modern Berry phase ferroelectric method. Both phonon spectra and molecular dynamics simulations indicate that the BiN monolayer is a room-temperature stable 2D ferroelectric with polarization as large as 580 pC/m. Further studies show that the polarization in the BiN monolayer can be easily switched from [100] to [010] direction over the bridging saddle phase by applying a tensile [010] stress of 2…
Competing interactions and geometric frustration provide favourable conditions for exotic states of matter. Such competition often causes multiple phase transitions as a function of temperature and can lead to magnetic structures that break inversion symmetry, thereby inducing ferroelectricity [1-4]. Although this phenomenon is understood phenomenologically [3-4], it is of great interest to have a conceptually simpler system in which ferroelectricity appears coincident with a single magnetic phase transition. Here we report the first such direct transition from a paramagnetic and paraelectric …
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）
The local dynamics of the lead-free relaxor $0.964\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3-0.036\mathrm{BaTiO}_3$ (NBT-3.6BT) have been investigated by a combination of quasielastic neutron scattering (QENS) and ab initio molecular dynamics simulations. In a previous paper, we were able to show that the tetragonal platelets in the microstructure are crucial for understanding the dielectric properties of NBT-3.6BT [F. Pforr et al., Phys. Rev. B 94, 014105 (2016)]. To investigate their dynamics, ab initio molecular dynamics simulations were carried out using $\mathrm{Na}_{1/2}\mathrm{Bi}…
We have investigated non-equilibrium properties of proper uniaxial Sn$_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…
We employ a new method for studying compositionally disordered ferroelectric oxides. This method is based on the virtual crystal approximation (VCA), in which two or more component potentials are averaged into a composite atomic potential. In our method, we construct a virtual atom with the correctly averaged atomic size and atomic eigenvalues. We have used our new method to study the composition dependent phase transition in Pb(Zr_{1-x}Ti_x)O_3 lying between x=0.5 and x=0.4. We correctly predict the experimentally determined phase transition from the tetragonal phase to a low-temperature rhom…
For Sn$_2$P$_2$S$_6$ ferroelectrics the second order phase transitions line is observed until reaching the tricritical point at transition temperature lowering to 250 K by compression. Observed temperature-pressure phase diagram agrees with simulated diagram by MC calculations based on early founded by DFT study local potential for Sn$_2$P$_2$S$_6$ crystals. In addition to the tricritical point, the possibility of disordered and quadrupolar phases occurrence was shown. For mixed crystals with tin by lead substitution, the investigated ultrasound, hypersound and low frequency dielectric propert…
The nature of the "forbidden" local- and long-range polar order in nominally nonpolar paraelectric phases of ferroelectric materials has been an open question since the discovery of ferroelectricity in oxide perovskites (ABO3). A currently considered model suggests locally correlated displacements of B-site atoms along a subset of <111> cubic directions. Such offsite displacements have been confirmed experimentally, however, being essentially dynamic in nature they cannot account for the static nature of the symmetry-forbidden polarization implied by the macroscopic experiments. Here, in an at…
Phase engineering by strains in 2D semiconductors is of great importance for a variety of applications. Here, we present a study of strain induced ferroelectric (FE) transition on bismuth oxyselenide (Bi$_2$O$_2$Se) films, a high-performance (HP) semiconductor for next-generation electronics. Bi$_2$O$_2$Se is non-FE at ambient. Upon a loading force $\gtrsim 400$ nN, piezoelectric force responses exhibit butterfly loops on magnitude and 180$^\textrm{o}$ phase switching. By carefully ruling out extrinsic factors, these features are attributed to a transition to FE phase. The transition is furthe…
Using the Landau Ginzburg Devonshire theory and scalar approximation, we derived analytical expressions for the singular points (zeros, complex ranges) of the acoustic phonon mode (A mode) frequency in dependence on the wave vector k and examined the conditions of the soft A modes appearance in a ferroelectric depending on the magnitude of the flexoelectric coefficient f and temperature T. We predict that if the magnitude of the flexocoefficient f is equal to the temperature-dependent critical value fcr(T) at the temperature T=T_IC, the A mode frequency tends to zero at k=kr_0 and the spontane…
The stability of the disordered glassy phase in the relaxors PbMg1/3Nb2/3O3 and (PbMg1/3Nb2/3O3)0.88(PbTiO3)0.12, called PMN and PMN-PT, was investigated by preparing partially polarized samples and allowing them to age at zero field in the temperature range for which the phase is history-dependent. The PMN-PT polarization would spontaneously increase until long-range order formed, first appearing as giant polarization noise. Thus the thermodynamically stable phase in PMN-PT appears to be ferroelectric. In contrast, a PMN sample lacking the sharp first-order field-driven transition found in so…
Anomalous Transverse Response and Multi-Field Ferrialtermagnetic-Ferroelectric Valve with CrSb Flakes
Huazhong University of Science and Technology（华中科技大学）；Beijing Institute of Technology（北京理工大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）
研究提出铁磁反铁磁体概念，以 CrSb 薄片实现，集成铁电体和 Cu 间隔层设计出铁磁反铁磁-铁电阀，该阀有高自旋过滤率等特性，确立了铁磁反铁磁体在多场控制等自旋电子学和电子学方面的丰富平台地位。
Physical nature of "giant" magnetocaloric and electrocaloric effects, MCE and ECE, is explained in terms of the new fundamentals of phase transitions, ferromagnetism and ferroelectricity. It is the latent heat of structural (nucleation-and-growth) phase transitions from a normal crystal state to the orientation-disordered crystal (ODC) state where the constituent particles are engaged in thermal rotation. The ferromagnetism or ferroelectricity of the material provides the capability to trigger the structural phase transition by application, accordingly, of magnetic or electric field.
The effect of epitaxial strain on the phonon spectra, crystal structure, spontaneous polarization, dielectric, piezoelectric, and elastic properties of (001)-oriented ferroelectric (BaTiO$_3$)$_m$/(SrTiO$_3$)$_n$ superlattices ($m = n = {}$1-4) was studied using the first-principles density-functional theory. The ground state of free-standing superlattices is the monoclinic $Cm$ polar phase. Under the in-plane biaxial compressive strain, it transforms to tetragonal $P4mm$ polar phase, and under the in-plane biaxial tensile strain, it transforms to orthorhombic $Amm2$ polar phase. When changing…
The dipole ordering in Sn(Pb)$_2$P$_2$S(Se)$_6$ materials may be tuned by chemical substitution realizing a ferroelectric quantum phase transition and quantum glassy or relaxor type phenomena on different parts of the phase diagram. The introduction of Ge impurity increases the temperature of the phase transitions and initiates a more pronounced Ising type critical anomaly in Sn$_2$P$_2$S$_6$ crystal, does not shift the coordinate of the Lifshitz point $x_{\textrm {LP}}$ in Sn$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ mixed crystals, induces the appearance of a ferroelectric phase transition in quantum pa…
The deceptively simple inorganic salt ammonium sulfate undergoes a ferroelectric phase transition associated with a very large entropy change and both electrocaloric and barocaloric functionality. While the structural origins of the electrical polarisation are now well established, those of the entropy change have been controversial for over fifty years. This question is resolved here using a combination of DFT phonon calculations with inelastic neutron scattering under variable temperature and pressure, supported by complementary total and quasielastic neutron scattering experiments. A simple…
We have investigated the magnetic ground-state of the multiferroic relaxor ferroelectric \pfn with $μ$SR spectroscopy and neutron scattering. We find that a transition to a partially disordered phase occurs below T=20 K that coexists with long-range antiferromagnetic ordering. The disordered phase resembles a spin-glass. No clustering of magnetic ions could be evidenced by $μ$SR so that the coexistence appears homogeneous in the sample.
Using neutron diffraction, we have studied the magnetic field effect on charge structures in the charge-ordered multiferroic material LuFe$_2$O$_4$. An external magnetic field is able to change the magnitude and correlation lengths of the charge valence order even before the magnetic order sets in. This affects the dielectric and ferroelectric properties of the material and induces a giant magneto-electric effect. Our results suggest that the magneto-electric coupling in LuFe$_2$O$_4$ is likely due to magnetic field effect on local spins, in clear contrast to the case in most other known multi…
