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It has been experimentally observed that changes in the nanopore structure have a great impact on the ferroelectric domain structure, and then, the ferroelectric polarization value of the film can be controlled to increase the response of the electrocaloric effect. This phenomenon has great application prospects in refrigeration applications. In this study, the evolution process of the domain structure of porous ferroelectric films of Pb0.7 Sr0.3TiO3 (PST) with different pore shapes was obtained through phase field simulation, and the influence of the pore shape on the performance of electrocaloric was predicted and analyzed. The results show that different shapes of pores can control the magnitude of the adiabatic temperature change. Among them, the anisometric ellipse shaped pore thin film can obtain a maximum adiabatic temperature change of 8 K, which is a significant improvement compared with traditional PST ceramics and PST non-porous films. This large adiabatic temperature change is due to the pore-induced domain switching. Therefore, controlling the pore shapes provides a new idea for optimizing the electrocaloric properties of porous ferroelectric thin films. [ABSTRACT FROM AUTHOR]

In this paper, the optical and static permittivities of CaCu3Ti4O12 supercells are calculated based on the Skanavi model by decomposing the electric field of molecules into the electric field of ions. The results show that the Skanavi model's theoretical predictions are significantly more accurate than those of the Clausius–Mossotti equation and Born model and are in good agreement with the experimental data. In addition, the absence of ferroelectricity in CaCu3Ti4O12 is also revealed by investigating the changes in the structural coefficients of the effective electric field caused by the displacement of Ti4+ along the z-axis. Finally, by analyzing the contribution of TiO6 octahedra or CuO4 planar squares to the static permittivity, the main polarization unit in the structure of CaCu3Ti4O12 has been discovered. This study not only makes up for the insufficient research on the polarization mechanism of CaCu3Ti4O12 but also provides a new tool to explore the polarization mechanism of other materials. [ABSTRACT FROM AUTHOR]

Ferroelectric topological structures have broad application prospects for high-density information storage for long-term data retention via topological protection. However, the high-density memory component might generate tremendous power consumption, causing the failure of ferroelectric devices due to the severe thermal effect. There remains an emergent issue on the synchronous achievement of high-density data storage with the decreasing influences of the thermal effects in ferroelectric topological domain structures. Here, we introduce dual-probe excitation to control the symmetry of the electric field and integrate the phase field simulation for modulating the flux-closure ferroelectric domain configuration to simultaneously improve the memory storage unit and thermal conductivity at the nanoscale in PbTiO3 thin film under a piezoresponse force microscopy experiment. It is found that the grown flux-closure polar state in both in-plane directions encourages us to enhance the storage density during dual-probe excitation in topological ferroelectric memory devices. Moreover, the increased number of flux-closure polar states and the decreased density of the domain walls can be obtained by using dual-probe excitation. Finally, we figured out that both the double-staircase-like and paddle-like domain configurations exhibit large storage units and effective thermal conductivity simultaneously under dual-probe excitation. Our study gives a guideline to synchronously improve storage performance and thermal conductivity through multiple-probe excitations in topological ferroelectric materials and devices. [ABSTRACT FROM AUTHOR]

The manipulation of low-energy matter properties such as superconductivity, ferromagnetism, and ferroelectricity via cavity quantum electrodynamics engineering has been suggested as a way to enhance these many-body collective phenomena. In this work, we investigate the effective interactions between low-energy matter excitations induced by the off-resonant coupling with cavity electromagnetic modes. We extend a previous work by going beyond the dipole approximation accounting for the full polarization and magnetization densities of matter. We further include the often neglected diamagnetic interaction and, for the cavity, we consider general linear absorbing media with possibly non-local and non-reciprocal response. We demonstrate that, even in this general scenario, the effective cavity-induced interactions between the matter degrees of freedom are of electrostatic and magnetostatic nature. This confirms the necessity of a multimode description for cavity engineering of matter systems where the low-energy assumption holds. Our findings provide a theoretical framework for studying the influence of general optical environments on extended low-energy matter excitations. [ABSTRACT FROM AUTHOR]

Two-dimensional ferroelectric materials are beneficial for power-efficient memory devices and transistor applications. Here, we predict out-of-plane ferroelectricity in a new family of buckled metal oxide (MO; M: Ge, Sn, Pb) monolayers with significant spontaneous polarization. Additionally, these monolayers have a narrow valence band, which is energetically separated from the rest of the low-lying valence bands. Such a unique band structure limits the long thermal tail of the hot carriers, mitigating subthreshold thermionic leakage and allowing field-effect transistors (FETs) to function beyond the bounds imposed on conventional FETs by thermodynamics. Our quantum transport simulations reveal that the FETs based on these MO monolayers exhibit a large ON/OFF ratio with an average subthreshold swing of less than 60 mV/decade at room temperature, even for short gate lengths. Our work motivates further exploration of the MO monolayers for developing advanced, high-performance memory and logic devices. [ABSTRACT FROM AUTHOR]

Despite the extensive research on HfO2-based thin films, the ferroelectric orthorhombic phase formation remains unclear. This work proposes a physical picture throughout the entire annealing process to describe the phase transition. Subsequently, the phase evolution at various doping and annealing temperatures is illustrated based on a kinetic model formalized from the classical nucleation theory. It is found that the formation of the ferroelectric orthorhombic phase depends not only on a modest doping concentration but also on the thermal activation of the t-to-o phase transition provided by a sufficient annealing temperature. In addition, phase transition rates correlated to the monoclinic phase formation are effectively suppressed by doping. The exploration of combined effects of annealing parameters indicates a more decisive role of the annealing temperature rather than the keeping time for induced ferroelectricity, and the doping impact becomes significant when a critical annealing temperature is reached. This work provides an understanding for exploring the kinetic effect on the phase transition in HfO2-based thin films, which helps improve ferroelectricity in doped HfO2 ferroelectric films. [ABSTRACT FROM AUTHOR]

Recent studies have shown that proximity effects are able to substantially modulate the superconducting properties of various quasi-two-dimensional layered materials such as FeSe, FeSeTe, NbSe2, and NbS2. Due to their high surface charge concentration and high dielectric constants, ferroelectric materials provide an interesting avenue for inducing proximity effects in layered superconductors. In this study, we explore the interactions between FeSeTe and the two-dimensional ferroelectrics CuInP2S6 and CuInP2Se6. We found that contrary to the normal behavior of FeSeTe, FeSeTe/CuInP2S6, and FeSeTe/CuInP2Se6 heterostructures display a peculiar two-step superconducting transition. Further testing revealed a hysteresis loop in the IV curves of these samples when measured below the critical temperature indicating the presence of disorder and domains within FeSeTe. We conclude that these domains are responsible for the two-step transition in FeSeTe and hypothesize that they are induced by the domain structure of the aforementioned ferroelectric materials. [ABSTRACT FROM AUTHOR]

Improving piezoelectric and ferroelectric responses of group III-nitrides is desired for their potential applications in the emerging microelectromechanical-based systems. One possible approach to realize the optimization and control of functionalities is to bring together compounds with different properties to form the ordered multilayer superlattices. In this work, we systematically investigate the phase stability, piezoelectricity, and ferroelectricity in a class of wurtzite-structure-derived nitride superlattices with a periodic alternation of chemically and/or structurally different layers. The structural heterogeneity and phase stability of the ordered wurtzite-structure-derived superlattices are intimately related to the ionic radii mismatch between the substitutional compounds and the parent nitrides. Moreover, the internal structural distortion of the nitride superlattices has a crucial impact on the ferroelectricity and piezoelectricity, namely, piezoelectric and ferroelectric responses become increasingly enhanced as the buckled atomic layers becomes flatter. This work offers fundamental physical insights into the structure–property relationships in nitride superlattices and may propose some material design strategies for achieving high-performance materials with desired responses. [ABSTRACT FROM AUTHOR]

Ferroelectric properties of hafnium-based thin films have gained significant interest, yet the fundamental mechanisms responsible for the emergence of the ferroelectric phase continue to be inadequately investigated. In contrast with polycrystalline films fabricated by atomic layer deposition or sputter methods, which possess uncertainty in polarization orientation, epitaxial ferroelectric HfO2-based materials are less investigated, especially for factors such as electric field and oxygen vacancy, which are proposed and examined for their potential impacts on phase stability. In this study, Y-doped hafnium oxide (HYO) ferroelectric epitaxial films were fabricated using pulsed laser deposition, with variations in oxygen pressure during the deposition process. Structural and electrical analyses of HYO epitaxial ferroelectric films prepared under differing oxygen pressures revealed a correlation between the ferroelectric properties of the films and the oxygen content. An optimal selection of oxygen pressure was found to be conducive to the formation of HYO epitaxial ferroelectric films, presenting a promising avenue for future ferroelectric memory applications. [ABSTRACT FROM AUTHOR]

Ferroelectric properties of hafnium-based thin films have gained significant interest, yet the fundamental mechanisms responsible for the emergence of the ferroelectric phase continue to be inadequately investigated. In contrast with polycrystalline films fabricated by atomic layer deposition or sputter methods, which possess uncertainty in polarization orientation, epitaxial ferroelectric HfO2-based materials are less investigated, especially for factors such as electric field and oxygen vacancy, which are proposed and examined for their potential impacts on phase stability. In this study, Y-doped hafnium oxide (HYO) ferroelectric epitaxial films were fabricated using pulsed laser deposition, with variations in oxygen pressure during the deposition process. Structural and electrical analyses of HYO epitaxial ferroelectric films prepared under differing oxygen pressures revealed a correlation between the ferroelectric properties of the films and the oxygen content. An optimal selection of oxygen pressure was found to be conducive to the formation of HYO epitaxial ferroelectric films, presenting a promising avenue for future ferroelectric memory applications. [ABSTRACT FROM AUTHOR]

Ferroelectric HfO2-based thin films have attracted much interest in the utilization of ferroelectricity at the nanoscale for next-generation electronic devices. However, the structural origin and stabilization mechanism of the ferroelectric phase are not understood because the film is typically nanocrystalline with active yet stochastic ferroelectric domains. Here, electron microscopy is used to map the in-plane domain network structures of epitaxially grown ferroelectric Y:HfO2 films in atomic resolution. The ferroelectricity is confirmed in free-standing Y:HfO2 films, allowing for investigating the structural origin for their ferroelectricity by 4D-STEM, high-resolution STEM, and iDPC-STEM. At the grain boundaries of -oriented Pca21 orthorhombic grains, a high-symmetry mixed-(R3m, Pnm21) phase is induced, exhibiting enhanced polarization due to in-plane compressive strain. Nanoscale Pca21 orthorhombic grains and their grain boundaries with mixed-(R3m, Pnm21) phases of higher symmetry cooperatively determine the ferroelectricity of the Y:HfO2 film. It is also found that such ferroelectric domain networks emerge when the film thickness is beyond a finite value. Furthermore, in-plane mapping of oxygen positions overlaid on ferroelectric domains discloses that polarization is suppressed at vertical domain walls, while it is active when domains are aligned horizontally with subangstrom domain walls. In addition, randomly distributed 180° charged domain walls are confined by spacer layers.

Ferroelectricity in hafnium zirconium oxide (Hf1 − xZrxO2) and the factors that impact it have been a popular research topic since its discovery in 2011. Although the general trends are known, the interactions between fabrication parameters and their effect on the ferroelectricity of Hf1 − xZrxO2 require further investigation. In this paper, we present a statistical study and a model that relates Zr concentration (x), film thickness (tf), and annealing temperature (Ta) with the remanent polarization (Pr) in tungsten (W)-capped Hf1 − xZrxO2. This work involved the fabrication and characterization of 36 samples containing multiple sets of metal-ferroelectric-metal capacitors while varying x (0.26, 0.48, and 0.57), tf (10 and 19 nm), and Ta (300, 400, 500, and 600 ° C). In addition to the well-understood effects of x and Ta on the ferroelectricity of Hf1 − xZrxO2, the statistical analysis showed that thicker Hf1 − xZrxO2 films or films with higher x require lower Ta to crystallize and demonstrated that there is no statistical difference between samples annealed to 500 and 600 ° C, thus suggesting that most films fully crystallize with Ta ∼ 500 ° C for 60 s. Our model explains 95% of the variability in the Pr data for the films fabricated, presents the estimates of the phase composition of the film, and provides a starting point for selecting fabrication parameters when a specific Pr is desired. [ABSTRACT FROM AUTHOR]

Ever since ferroelectricity was discovered in HfO 2 , the question of its origin remains controversial. Here, we probe this question using a combination of Landau theory of phase transitions and first-principles computations. In such an approach, the energy landscape associated with the phase transition between cubic and different experimentally demonstrated phases of HfO 2 (tetragonal, monoclinic, orthorhombic Pbca, orthorhombic Pnma, and orthorhombic Pca 2 1) is explored using density functional theory calculations. Computations revealed that stabilization of all but orthorhombic Pbca phase is driven by a single unstable zone-boundary antipolar mode X 2 −. When coupled with zone-center modes (Γ 1 + and Γ 3 +), it stabilizes the tetragonal phase. Coupling with four additional modes (Γ 5 + , X 3 − , X 5 − , X 5 +) results in the monoclinic phase, which is the ground state of the material. If, however, Γ 5 + mode is replaced with Γ 4 − mode, orthorhombic polar phase Pca 2 1 is stabilized. The application of this framework to examine the effect of electric field on the ferroelectric phase of hafnia reveals that the field of 5 MV/cm is capable of stabilizing ferroelectric phase over the monoclinic one at 0 K. [ABSTRACT FROM AUTHOR]

BaTiO3 has been investigated nearly several decades due to its excellent ferroelectric and dielectric properties. However, the property evolution of BaTiO3 with a particle size of sub-10 nm is still unclear because of the difficulty during the fabrication and characterization. Here, a series of BaTiO3 nanoparticles with the average particle sizes of 2.8, 4.5 and 8.1 nm are achieved, and their phase structure, ferroelectric and dielectric properties are skillfully characterized. With the particle size decreasing from 8.1 to 2.8 nm, the nanoparticles show a declining non-centrosymmetry, nonlinear response, ferroelectricity and dielectric constant. Nevertheless, the 2.8 nm BaTiO3 nanoparticles still possess observable second harmonic generation, ferroelectric polarization switching behavior and butterfly loop, showing weak but distinguishable ferroelectricity. This research depicts a detailed ferroelectric and dielectric property evolution in sub-10 nm BaTiO3 nanoparticles, which provides theoretical basis and promising candidate for the future ferroelectric applications. [ABSTRACT FROM AUTHOR]

Size-driven transition of aNote, that the phasesn antiferroelectric into a polar ferroelectric or ferrielectric state is a strongly debated issue from both experimental and theoretical perspectives. While critical thickness limits for such transitions have been explored, a bottom-up approach in the ultrathin limit considering few atomic layers could provide insight into the mechanism of stabilization of the polar phases over the antipolar phase seen in bulk PbZrO3. Here, we use first-principles density functional theory to predict the stability of polar phases in Pt/PbZrO3/Pt nanocapacitors. In a few atomic layer thick slabs of PbZrO3 sandwiched between Pt electrodes, we find that the polar phase originating from the well established R3c phase of bulk PbZrO3 is energetically favorable over the antipolar phase originating from the Pbam phase of bulk PbZrO3. The famous triple-well potential of antiferroelectric PbZrO3 is modified in the nanocapacitor limit in such a way as to swap the positions of the global and local minima, stabilizing the polar phase relative to the antipolar one. The size effect is decomposed into the contributions from dimensionality reduction, surface charge screening, and interfacial relaxation, which reveals that it is the creation of well-compensated interfaces that stabilizes the polar phases over the antipolar ones in nanoscale PbZrO3. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) van der Waals (vdW) materials offer vast potential for designing ferroelectrics with desired properties through simple layer stacking. Here, based on first principles, we demonstrate that the vdW layered crystals RuX2 (X = Cl, Br, and I) are a class of 2D multiferroic sliding ferroelectrics. The stacking of two magnetic RuX2 monolayers with the same orientation breaks the spatial inversion symmetry, resulting in a stable vertical polarization. In addition, the direction of polarization can be reversed through slight interlayer sliding, in which it only needs to overcome the small energy barrier of 7.16 meV. Among these layered crystals, the bilayer RuI2 not only possesses a remarkable sliding ferroelectricity of 0.49 pC/m but also exhibits stable long-range magnetic order due to its large magnetic anisotropy energy. When the RuI2 stack is increased to trilayers, the polarization significantly increases to 1.03 pC/m, which is much larger than that of its bilayer structure. Furthermore, the application of compressive strain results in a substantial increase in vertical polarization. This work provides an efficient method for designing 2D multiferroic sliding ferroelectric materials by stack engineering. [ABSTRACT FROM AUTHOR]

The study on altermagnet is receiving extensive research efforts due to its directional-dependent spin-polarized band structure. Here, we investigate the multifunctional properties of the Janus Cr2SeO monolayer system. The Cr2SeO monolayer exhibits an in-plane magnetic anisotropy energy of -0.28 meV/cell and a Neel temperature of around 280 K, which is further enhanced to 315 K under 1% uniaxial compressive strain. The Janus Cr2SeO exhibits spin band inversion with a large spin splitting of 0.38 eV at the Y and X high-symmetry points. Nonetheless, the valleys are degenerated due to the diagonal mirror symmetry. The uniaxial strain effectively breaks the diagonal mirror symmetry in the Janus Cr2SeO monolayer, and the strain-induced valley polarization of up to 90 meV is achieved. Furthermore, the uniaxial strain tunes the band gap between 0.30 eV to 0.76 eV. Moreover, Cr2SeO demonstrates ferroelectricity, with a total electric polarization of 5.34 pC/m, which increases to 5.52 pC/m under small uniaxial strain. Besides, we found a large vertical piezoelectric coefficient d31 of 1.18 pm/V. Our study suggests that the Janus Cr2SeO is a promising platform for Valleytronics and ferroelectric memory applications at room temperature. [ABSTRACT FROM AUTHOR]

The discovery of ferroelectric phases in HfO2 offers insights into ferroelectricity. Its unique fluorite structure and complex polarization switching pathways exhibit distinct characteristics, challenging conventional analysis methods. Combining group theory and first-principles calculations, we identify numerous unconventional electric polarization switching pathways in HfO2 with energy barriers of 0.32 to 0.57 eV as a function of the different shift in the suboxygen lattices. In total, we identify 47 switching pathways for the orthorhombic phase, corresponding to the left cosets of the Fm3m group with Pca21 group. Contrary to the conception that the tetracoordinated oxygen (OIV) layers are inactive, our result demonstrates that both the tricoordinated oxygen (OIII) and OIV can be displaced, leading to polarization switching along any axial direction. The multiple switching pathways in HfO2 result in both 180° polarization reversal and the formation of 90° domains observed experimentally. Calculations show that specific switching pathways depend on the orientation of the applied electric field relative to the HfO2 growth surface. This allows HfO2 to automatically adjust the in-plane polarization direction under an out-of-plane electric field, thereby maximizing the out-of-plane component and contributing to the wake-up process. These findings redefine the roles of OIII and OIV layers, clarify unconventional switching pathways, and enhance our understanding of electric field response mechanisms, wake-up, and fatigue in ferroelectrics. [ABSTRACT FROM AUTHOR]

Reversible ferroelectric domain wall movements beyond the 10 nm range associated with Rayleigh behavior are usually restricted to specific defect-engineered systems. Here, we demonstrate that such long-range movements naturally occur in the improper ferroelectric ErMnO3 during electric-field-cycling. We study the electric-field-driven motion of domain walls, showing that they readily return to their initial position after having traveled distances exceeding 250 nm. By applying switching spectroscopy band-excitation piezoresponse force microscopy, we track the domain wall movement with nanometric spatial precision and analyze the local switching behavior. Phase field simulations show that the reversible long-range motion is intrinsic to the hexagonal manganites, linking it to their improper ferroelectricity and topologically protected structural vortex lines, which serve as anchor point for the ferroelectric domain walls. Our results give new insight into the local dynamics of domain walls in improper ferroelectrics and demonstrate the possibility to reversibly displace domain walls over much larger distances than commonly expected for ferroelectric systems in their pristine state, ensuring predictable device behavior for applications such as tunable capacitors or sensors. The authors find the electric-field-driven motion of domain walls in the improper ferroelectric ErMnO3, showing that they readily return to their initial position after having travelled distances exceeding 250 nm. [ABSTRACT FROM AUTHOR]

Hexagonal boron nitride (hBN), a two-dimensional (2D) insulator, can act as a barrier layer to protect 2D materials and to bring out their intrinsic properties. Encapsulation of 2D materials with hBN sheets can improve the properties of 2D materials and allow the observation of unique physical phenomena. Here, we demonstrate the confined synthesis of 2D tin sulfide (SnS) and tin disulfide (SnS2) by the sulfurization of encapsulated Sn particles in the interlayer 2D space between large-area hBN sheets. First, we highlight the influence of the inert surface of hBN on the morphology of the deposited Sn. We found that using thin hBN as the bottom layer can prevent Sn agglomeration during encapsulation between hBN, making an ideal hBN/Sn/hBN structure for further sulfurization. Due to the high thermal stability, the hBN sheet can serve as a barrier layer, allowing Sn to be sulfurized without evaporation at high temperatures, resulting in the formation of 2D SnS and SnS2 between hBN sheets. Furthermore, the controlled synthesis of SnS and SnS2 can be achieved by encapsulating different amounts of Sn. This confined synthesis approach ensures clean interfaces and preserves the intrinsic properties of SnS and SnS2, while the hBN encapsulation provides long-term air stability. We further fabricated field-effect transistor (FET) devices of hBN-encapsulated SnS and SnS2, demonstrating semiconductor and ferroelectric properties. Our findings provide a strategy for the fabrication of hBN-protected air-sensitive 2D materials for applications in nanoelectronics and optoelectronics. [ABSTRACT FROM AUTHOR]

Doping is critical for inducing ferroelectricity in hafnia films, yet the underlying mechanisms remain debated. Here, through first-principles studies, we elucidate the pivotal role played by the complex phase transition mechanisms under carrier doping in understanding the origin of hafnia ferroelectricity. Specifically, electron doping orchestrates a metastable polar phase to stable antipolar phase transformation, driven by strong screening effects and weakened nonpolar covalent bonds, making n-type dopants rare. Conversely, weak screening effect and enhanced polar covalent bonding strengthen robust ferroelectricity, enabling significant ground-state phase transitions from the monoclinic to the polar orthorhombic phase and finally to the cubic phase under hole doping, a phenomenon prevalent in hafnia-based films doped with p-type dopants. Furthermore, this hole-enhanced polar distortion also results in an inverse size effect in hafnia ferroelectric films, unlike perovskite ferroelectrics. Our findings offer new insights into the preparation of robust hafnia-based ferroelectric films through doping or interface engineering. [ABSTRACT FROM AUTHOR]

The emerged wurtzite (wz) Al1−xBxN alloy has drawn increasing attention due to its superior ferroelectricity and excellent compatibility with microelectronics. We find that the stability and ferroelectric switching pathways of wz-Al1−xBxN alloys are affected by the orbital contribution, covalent bond strength, and elastic constant C14. As the concentration of B increases, the internal parameter u decreases while the elastic constant C14 increases, leading to an increase in spontaneous polarization and a decrease in the polarization switching barrier. The spontaneous polarization, polarization switching barrier, and band gap of wz-Al1−xBxN alloy can be further improved through the application of strain in a specific direction, resulting in a giant ferroelectricity. Additionally, the phase transformation of the wz-Al1−xBxN alloy induced by the increasing B composition can be regarded as a sequential process involving shrinkage, rotation, and deformation of tetrahedron. These findings give a deep understanding of the ferroelectric wz-Al1−xBxN alloy, and provide a guideline for designing a high-performance ferroelectric wz-Al1−xBxN alloy. [ABSTRACT FROM AUTHOR]

We report a general mechanism for building ferroelectricity in prevailing van der Waals (vdW) multilayers via interfacial engineering. Using sandwiched graphene/boron nitride (BN)/graphene multilayers as an exemplary system, we show that considerable electric polarization can arise at graphene/BN interfaces where charge redistribution enhances intralayer electric dipoles. Moreover, the electric polarization between BN layers is concertedly enhanced due to interlayer compression driven by an extraordinary cross-layer electrostatic attraction. Then, the interfacial polarization and enhanced interlayer polarization can serve as two elements for building robust ferroelectrics from vdW multilayers with cumulative, thickness-controllable polarization. We demonstrate this mechanism in generating an electric polarization of 1.0 pC/m in a nominally nonpolar BN monolayer sandwiched between graphene layers, and up to 4.2 pC/m in a sandwiched BN quadrilayer. These results underscore the previously unnoticed role of unavoidable hetero-interfaces in contributing to the observed ferroelectricity in diverse vdW devices. [ABSTRACT FROM AUTHOR]

Ferroelectric materials undergo a phenomenon called domain switching when subjected to electric fields exceeding a critical yielding value: an irreversible polarisation arises, that can be removed only by applying an appropriate electric field in the opposite sense. Under a cyclic electric field, this results in a hysteretic behaviour in the relation between the electric field and the polarisation. The hysteresis loop is a measure of the energy dissipated in the ferroelectric switching process. In this study, we introduce a rate-independent model of ferroelectricity, inspired by small-deformation elastoplasticity models. Analogously to the yielding surface in elastoplasticity, we define the switching surface, the boundary of the domain of the admissible states of the system. States in the interior of the domain are reversible, while states on the surface can be either reversible or irreversible, based on the relation between the electric field and the derivative of the yielding function with respect to the electric field. We solve a two-dimensional benchmark boundary-value problem by applying two numerical methods, Finite Differences and Finite Elements. Our results demonstrate the effectiveness of both methods in capturing the nonlinearities and reproducing the electrical hysteresis loops typical of ferroelectric materials. This work establishes a foundational framework for modelling rate-independent ferroelectricity and paves the way for future research on comprehensive elastoplastic-ferroelectric models for piezoelectric materials. [ABSTRACT FROM AUTHOR]