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Whilst often discussed as non-trivial phases of low-dimensional ferroelectrics, modulated polar phases such as the dipolar maze and the nano-bubble state have been appraised as essentially distinct. Here we emphasize their topological nature and show that these self-patterned polar states, but also additional mesophases such as the disconnected labyrinthine phase and the mixed bimeron-skyrmion phase, can be fathomed in their plurality through the unifying canvas of phase separation kinetics. Under compressive strain, varying the control parameter, i.e., the external electric field, conditions the nonequilibrium self-assembly of domains, and bridges nucleation and spinodal decomposition via the sequential onset of topological transitions. The evolutive topology of these polar textures is driven by the (re)combination of the elementary topological defects, merons and antimerons, into a plethora of composite topological defects such as the fourfold junctions, the bimeron and the target skyrmion. Moreover, we demonstrate that these manipulable defects are stable at room temperature and feature enhanced functionalities, appealing for devising future topological-based nanoelectronics., Understanding the processes underlying the self-assembly of polar textures is pivotal for the development of future technologies. Here, the authors reveal the dynamics of nonequilibrium phase transitions in low-dimensional ferroelectrics and emphasize their topological nature.

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.

An atomistic effective Hamiltonian is used to compute electrocaloric (EC) effects in rare-earth substituted BiFeO$_{3}$ multiferroics. A phenomenological model is then developed to interpret these computations, with this model indicating that the EC coefficient is the sum of two terms, that involve electric quantities (polarization, dielectric response), the antiferromagnetic order parameter, and the coupling between polarization and antiferromagnetic order. The first one depends on the polarization and dielectric susceptibility, has the analytical form previously demonstrated for ferroelectrics, and is thus enhanced at the ferroelectric Curie temperature. The second one explicitly involves the dielectric response, the magnetic order parameter and a specific magnetoelectric coupling, and generates a peak of the EC response at the N\'eel temperature. These atomistic results and phenomenological model may be put in use to optimize EC coefficients., Comment: 6 pages, 3 figures

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.

The Monte Carlo method is one of the first and most widely used algorithms in modern computational physics. In condensed matter physics, the particularly popular flavor of this technique is the Metropolis Monte Carlo scheme. While being incredibly robust and easy to implement, the Metropolis sampling is not well-suited for situations where energy and force evaluations are computationally demanding. In search for a more efficient technique, we here explore the performance of Hybrid Monte Carlo sampling, an algorithm widely used in quantum electrodynamics, as a structure prediction scheme for systems with long-range interactions. Our results show that the Hybrid Monte Carlo algorithm stands out as an excellent computational scheme that can not only significantly outperform the Metropolis sampling but also complement molecular dynamics in materials science applications, while allowing ultra-large-scale simulations of systems containing millions of particles. A hybrid Monte Carlo sampling algorithm is adopted to predict structures and properties in large-scale simulations with millions of particles. A team led by Laurent Bellaiche from the University of Arkansas perform hybrid Monte Carlo (HMC) sampling on effective Hamiltonian models of solid-state systems with long-range interactions, such as ferroelectric, relaxor and multiferroic materials at finite temperatures. They compare the results with those obtained by the Metropolis Monte Carlo (MMC) algorithm and thermalized molecular dynamics (MD). They find that the HMC scheme significantly outperforms MMC and MD for selected model cases. By implementing the HMC algorithm for GPU-oriented parallelization architectures, they can perform HMC simulations for a large scale material simulations with the particle number reaching 106. This algorithm may also be implemented for large-scale density functional theory calculations so that a more broad space of applications might open.

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...

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)O3ceramics 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.

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.

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.

An atomistic effective Hamiltonian is used to investigate electrocaloric (EC) effects of Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) relaxor ferroelectrics in its ergodic regime, and subject to electric fields applied along the pseudocubic [111] direction. Such Hamiltonian qualitatively reproduces (i) the electric field-versus-temperature phase diagram, including the existence of a critical point where first-order and second-order transitions meet each other; and (ii) a giant EC response near such critical point. It also reveals that such giant response around this critical point is microscopically induced by field-induced percolation of polar nanoregions. Moreover, it is also found that, for any temperature above the critical point, the EC coefficient-versus-electric field curve adopts a maximum (and thus larger electrocaloric response too), that can be well described by the general Landau-like model proposed in [Jiang et al, Phys. Rev. B 96, 014114 (2017)] and that is further correlated with specific microscopic features related to dipoles lying along different rhombohedral directions. Furthermore, for temperatures being at least 40 K higher than the critical temperature, the (electric field, temperature) line associated with this maximal EC coefficient is below both the Widom line and the line representing percolation of polar nanoregions., 6 pages, 5 figures

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.

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.

First-principles-based effective Hamiltonian simulations are used to reveal the hidden connection between topological defects (hedgehogs and antihedgehogs) and relaxor behavior. Such defects are discovered to predominantly lie at the border of polar nanoregions in both Ba(Zr0.5Ti0.5)O3 (BZT) and Pb(Sc0.5Nb0.5)O3 (PSN) systems, and the temperature dependency of their density allows us to distinguish between noncanonical (PSN) and canonical (BZT) relaxor behaviors (via the presence or absence of a crossing of a percolation threshold). This density also possesses an inflection point at precisely the temperature for which the dielectric response peaks. Moreover, hedgehogs and antihedgehogs are found to be mobile excitations, and the dynamical nature of their annihilation is demonstrated (using simple hydrodynamical arguments) to follows laws, such as those of Vogel-Fulcher and Arrhenius, that are characteristic of dipolar relaxation kinetics of relaxor ferroelectrics. © 2016 American Physical Society.

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.