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Polar skyrmions are topologically stable, swirling polarization textures with particle-like characteristics, which hold promise for next-generation, nanoscale logic and memory. While understanding of how to create ordered polar skyrmion lattice structures and how such structure respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO3 films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics., Comment: 4 Figures

Nanoscale ferroelectric topologies such as vortices, anti-vortices, bubble patterns etc. are stabilized in thin films by a delicate balance of both mechanical and electrical boundary conditions. A systematic understanding of the phase stability of bubble domains, particularly when the above factors act simultaneously, remains elusive. Here we present first-principle-based simulations in combination with scanning probe microscopy of ultrathin epitaxial (001) PbZr0.4Ti0.6O3 heterostructures to address this gap. The simulations predict that as-grown labyrinthine domains will transform to bubbles under combinations of reduced film thickness, increased mechanical pressure and/or improved electrical screening. These topological transitions are explained by a common fundamental mechanism. Namely, we argue that, independently of the nature of the driving force, the evolution of the domain morphology allows the system to conserve its original residual depolarization field. Thereby, the latter remains pinned to a value determined by an external or built-in electric bias. To verify our predictions, we then exploit tomographic atomic force microscopy to achieve the concurrent effect of reducing film thickness and increased mechanical stimulus. The results provide a systematic understanding of phase stability and demonstrate controlled manipulation of nanoscale ferroelectric bubble domains.

This review summarizes recent works, all using a specific atomistic approach, that predict and explain the occurrence of key features for neuromorphic computing in three archetypical dipolar materials, when they are subject to THz excitations. The main ideas behind such atomistic approach are provided, and illustration of model relaxor ferroelectrics, antiferroelectrics, and normal ferroelectrics are given, highlighting the important potential of polar materials as candidates for neuromorphic computing. Some peculiar emphases are made in this Review, such as the connection between neuromorphic features and percolation theory, local minima in energy path, topological transitions and/or anharmonic oscillator model, depending on the material under investigation. By considering three different and main polar material families, this work provides a complete and innovative toolbox for designing polar-based neuromorphic systems.

Bubble-like domains, typically a precursor to the electrical skyrmions, arise in ultrathin complex oxide ferroelectric-dielectric-ferroelectric heterostructures epitaxially clamped with flat substrates. Here, it is reported that these specially ordered electric dipoles can also be retained in a freestanding state despite the presence of inhomogeneously distributed structural ripples. By probing local piezo and capacitive responses and using atomistic simulations, this study analyzes these ripples, sheds light on how the bubbles are stabilized in the modified electromechanical energy landscape, and discusses the difference in morphology between bubbles in freestanding and as-grown states. These results are anticipated to be the starting point of a new paradigm for the exploration of electric skyrmions with arbitrary boundaries and physically flexible topological orders in ferroelectric curvilinear space.

Utilization of van der Waals magnetic materials as the host of topologically protected skyrmionic and other complex spin textures has been drawing increasing attention. Here, using first-principles-based calculations, we predict a new stable magnetic ${\mathrm{CrGe}(\mathrm{Se},\mathrm{Te})}_{3}$ Janus monolayer with a strong Dzyaloshinskii-Moriya interaction (DMI), due to the breaking of inversion symmetry. Consequently, nanometric skyrmions (that carry a topological charge of $\ifmmode\pm\else\textpm\fi{}1$) and skyrmionium states (with a zero topological charge) can spontaneously form in the absence of magnetic field. We further unveil a subtle competition between DMI and frustration as key for stabilizing skyrmioniums.

Using an effective Hamiltonian scheme within classical Monte Carlo simulations, we numerically investigate the effect of epitaxial strain on various physical quantities of the promising lead-free $(1\ensuremath{-}x)\mathrm{Ba}({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}){\mathrm{O}}_{3}--x({\mathrm{Ba}}_{0.7}{\mathrm{Ca}}_{0.3}){\mathrm{TiO}}_{3}$ solid solutions for different compositions. It is found that some combinations of strain and concentration lead to physical responses that are not only broad with temperature around 300 K but also large, including dielectric and piezoelectric coefficients. The origins of these useful and striking features are revealed.

Effective Hamiltonian simulations are conducted to unveil the nature of the low-frequency polar modes in the prototype relaxor ferroelectric, $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$. Above the so-called ${T}^{*}$ temperature, only a single soft-mode exists, with its frequency increasing under heating. On the other hand, for temperatures lower than the freezing temperature, this single soft-mode splits into two modes, with one mode slightly changing its low resonant frequency while the other exhibiting a resonant frequency sharply increasing under cooling, in agreement with previous measurements. More importantly, we present evidences that these two modes can be regarded as Goldstone-like and Higgs-like modes, inherent to the Mexican-hat-form of the atomic displacement potential we also reveal here, therefore extending the types of systems exhibiting Higgs-boson characteristics to relaxor ferroelectrics.

An effective Hamiltonian scheme combined with a GPU implementation of the linear-scaling three-dimensional fragment (LS3DF) method is used to compute electronic properties of two topological object...

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold the promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl$_3$ and Na$_2$IrO$_3$, having an effective $S$=1/2 spin value. Here, via extensive first-principle-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe$_3$, that rather possess a $S$=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3$d$ transition metal compounds.

Topological magnetic states are promising for ultradense memory and logic devices. Recent progress in two-dimensional magnets encourages the idea to realize topological states, such as skyrmions and merons, in freestanding monolayers. However, monolayers such as ${\mathrm{CrI}}_{3}$ lack Dzyaloshinskii-Moriya interactions (DMIs) and thus do not naturally exhibit skyrmions/merons but rather a ferromagnetic state. Here we propose the fabrication of $\mathrm{Cr}{(\mathrm{I},X)}_{3}$ Janus monolayers, in which the Cr atoms are covalently bonded to the underlying I ions and top-layer Br or Cl atoms. By performing first-principles calculations and Monte Carlo simulations, we identify strong enough DMIs, which leads to not only helical cycloid phases, but also to topologically nontrivial states, such as the intrinsic domain wall skyrmions in $\mathrm{Cr}{(\mathrm{I},\mathrm{Br})}_{3}$ and the magnetic-field-induced bimerons in $\mathrm{Cr}{(\mathrm{I},\mathrm{Cl})}_{3}$. Microscopic origins of such spin textures are revealed as well.

The celebrated Berezinskii-Kosterlitz-Thouless (BKT) phase transition refers to a topological transition characterized, e.g., by the dissociation of vortex-antivortex pairs in two-dimensional (2D) systems. Such unusual phase has been reported in various types of materials, but never in the new class of systems made by one-unit-cell-thick (1UC) ferroelectrics (also coined as 2D ferroelectrics). Here, the use of a first-principles-based effective Hamiltonian method leads to the discovery of many fingerprints of a BKT phase existing in-between the ferroelectric and paraelectric states of 1UC tin tellurium being fully relaxed. Moreover, epitaxial strain is found to have dramatic consequences on the temperature range of such BKT phase for the 1UC SnTe. Consequently, our predictions extend the playground of BKT theory to a novel class of functional materials, and demonstrate that strain is an effective tool to alter BKT characteristics there.

Atomistic first-principles-based effective Hamiltonian simulations are conducted in some ferroelectric systems to predict the existence of a novel topological state. Such state is coined here as ``topological eclecton'' because it is made of a plethora of electrical topological defects, including (i) vortices and antivortices in different planes, (ii) hedgehogs and antihedgehogs, and (iii) a few skyrmions. Such state can be a ground state and readapt itself to form other striking topological states or phases when, e.g., heating the system or applying electric fields. In addition to its unique combined topological characteristics, it is also ferroelectric and chiral in nature.

We numerically investigate the phase diagram of the giant-piezoelectric (1−x) Ba(Zr0.2Ti0.8) O3−x (Ba0.7Ca0.3) TiO3 system, treating the ions either as classical objects (via classical Monte Carlo or CMC simulations) or quantum mechanically (via path-integral quantum Monte Carlo or PI-QMC simulations). It is found that PI-QMC not only provides a better agreement with available experimental data for the temperature-composition phase diagram, but also leads to the existence of an orthorhombic ground state in a narrow range of composition, unlike CMC that “only” yields ground states of rhombohedral or tetragonal symmetry. X-ray powder diffraction experiments are further conducted at 20 K. They confirm the occurrence of a quantum-fluctuation-induced orthorhombic state for some compositions and therefore validate the PI-QMC prediction. The role of quantum effects on the local structure, such as the annihilation of a homogeneous rhombohedral system in favor of an inhomogeneous mixing of orthorhombic and rhombohedral clusters, is also documented and discussed.

Distinct and novel features of nanometric electric topological defects, including dipole waves and dipole disclinations, are presently revealed in the PbTiO_{3} layers of PbTiO_{3}/SrTiO_{3} multilayer films by means of quantitative high-resolution scanning transmission electron microscopy. These original dipole configurations are confirmed and explained by atomistic simulations and have the potential to act as functional elements in future electronics.

In light of directives around the world to eliminate toxic materials in various technologies, finding lead-free materials with high piezoelectric responses constitutes an important current scientific goal. As such, the recent discovery of a large electromechanical conversion near room temperature in (1−x)Ba(Zr0.2Ti0.8)O3−x(Ba0.7Ca0.3)TiO3 compounds has directed attention to understanding its origin. Here, we report the development of a large-scale atomistic scheme providing a microscopic insight into this technologically promising material. We find that its high piezoelectricity originates from the existence of large fluctuations of polarization in the orthorhombic state arising from the combination of a flat free-energy landscape, a fragmented local structure, and the narrow temperature window around room temperature at which this orthorhombic phase is the equilibrium state. In addition to deepening the current knowledge on piezoelectricity, these findings have the potential to guide the design of other lead-free materials with large electromechanical responses., (Ba,Ca)(Zr,Ti)O3 ceramics have attracted interest as lead-free materials with large piezoelectric responses. Here, the authors use an atomistic model to show the electromechanical properties are due to a complex microstructure and polarization fluctuations in the narrowly stable orthorhombic phase.

International audience; Using first-principles-based simulations merging an effective Hamiltonian scheme with scaling, symmetry, and topological arguments, we find that an overlooked Berezinskii-Kosterlitz-Thouless (BKT) phase sustained by quasicontinuous symmetry emerges between the ferroelectric phase and the paraelectric one of BaTiO3 ultrathin film, being under tensile strain. Not only do these results provide an extension of BKT physics to the field of ferroelectrics, but they also unveil their nontrivial critical behavior in low dimensions.

Atomistic effective Hamiltonian simulations are used to investigate electrocaloric (EC) effects in the lead-free $\mathrm{Ba}({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}){\mathrm{O}}_{3}$ (BZT) relaxor ferroelectric. We find that the EC coefficient varies nonmonotonically with the field at any temperature, presenting a maximum that can be traced back to the behavior of BZT's polar nanoregions. We also introduce a simple Landau-based model that reproduces the EC behavior of BZT as a function of field and temperature, and which is directly applicable to other compounds. Finally, we confirm that, for low temperatures (i.e., in nonergodic conditions), the usual indirect approach to measure the EC response provides an estimate that differs quantitatively from a direct evaluation of the field-induced temperature change.

Observation of a new type of nanoscale ferroelectric domains, termed as “bubble domains”—laterally confined spheroids of sub-10 nm size with local dipoles self-aligned in a direction opposite to the macroscopic polarization of a surrounding ferroelectric matrix—is reported. The bubble domains appear in ultrathin epitaxial PbZr0.2Ti0.8O3/SrTiO3/PbZr0.2Ti0.8O3 ferroelectric sandwich structures due to the interplay between charge and lattice degrees of freedom. The existence of the bubble domains is revealed by high-resolution piezoresponse force microscopy (PFM), and is corroborated by aberration-corrected atomic-resolution scanning transmission electron microscopy mapping of the polarization displacements. An incommensurate phase and symmetry breaking is found within these domains resulting in local polarization rotation and hence impart a mixed Neel–Bloch-like character to the bubble domain walls. PFM hysteresis loops for the bubble domains reveal that they undergo an irreversible phase transition to cylindrical domains under the electric field, accompanied by a transient rise in the electromechanical response. The observations are in agreement with ab-initio-based calculations, which reveal a very narrow window of electrical and elastic parameters that allow the existence of bubble domains. The findings highlight the richness of polar topologies possible in ultrathin ferroelectric structures and bring forward the prospect of emergent functionalities due to topological transitions.

In light of directives around the world to eliminate toxic materials in various technologies, finding lead-free materials with high piezoelectric responses constitutes an important current scientific goal. As such, the recent discovery of a large electromechanical conversion near room temperature in (1-x)Ba(Zr

Homotopy theory and first-principles-based effective Hamiltonian simulations are combined to investigate the stability of topological defects in proper ferroelectric crystals. We show that, despite a nearly trivial topology of the order parameter space, these materials can exhibit stable topological point defects in their tetragonal polar phase and stable topological line defects in their orthorhombic polar phase. The stability of such defects originates from a novel mechanism of topological protection related to finite-temperature fluctuations of local dipoles.

A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.

We use a first-principles based approach to theoretically investigate the room-temperature phase diagram of $({\mathrm{BiFeO}}_{3}){}_{x}({\mathrm{BaTiO}}_{3}){}_{1\ensuremath{-}x}$ solid solutions. Using a modified effective Hamiltonian scheme, we show that random fields originating from off-valent substitutions decrease the ferroelectric transition temperature leading to a paraelectric ground state in the intermediate range of concentrations $x$. The predicted critical concentrations at which lattice distortions inherited from the ferroelectric phases of parent compounds vanish fall within the range of the experimental values. Furthermore, the obtained results give the necessary microscopical insight into the mechanism driving the pseudocubic phase formation.

Special quasirandom structures (SQS) are presently generated for disordered (A'1-x [Formula: see text] x )BX3 and A(B'1-x [Formula: see text] x )X3 perovskite solid solutions, with x = 1/2 as well as 1/3 and 2/3. These SQS configurations are obtained by imposing that the so-called Cowley parameters are as close to zero as possible for the three nearest neighboring shells. Moreover, these SQS configurations are slightly larger in size than those available in the literature for x = 1/2, mostly because of the current capabilities of atomistic techniques. They are used here within effective Hamiltonian schemes to predict various properties, which are then compared to those associated with large random supercells, in a variety of compounds, namely (Ba1-x Sr x )TiO3, Pb(Zr1-x Ti x )O3, Pb(Sc0.5Nb0.5)O3, Ba(Zr1-x Ti x )O3, Pb(Mg1/3Nb2/3)O3 and (Bi1-x Nd x )FeO3. It is found that these SQS configurations can reproduce many properties of large random supercells of most of these disordered perovskite alloys, below some finite material-dependent temperature. Examples of these properties are electrical polarization, anti-phase and in-phase octahedral tiltings, antipolar motions, antiferromagnetism, strain, piezoelectric coefficients, dielectric response, specific heat and even the formation of polar nanoregions (PNRs) in some relaxors. Some limitations of these SQS configurations are also pointed out and explained.