Atomistic molecular dynamic simulations of multiferroics

Ferroelectricity in Ultrathin Halide Perovskites

Ferroelectricity has recently been demonstrated in germanium-based halide perovskites. We use first-principles-based simulations to study 4-18 nm CsGeBr3 films and develop a theory for ferroelectric ultrathin films. The theory introduces (i) a local order parameter, which identifies phase transitions into both monodomain and polydomain phases, and (ii) a dipole pattern classifier, which allows efficient and reliable identification of dipole patterns. Application of the theory to both halides CsGeBr3 and CsGeI3 and oxide BiFeO3 ultrathin ferroelectrics reveals two distinct scenarios. First, the films transition into a monodomain phase below the critical value of the residual depolarizing field. Above this critical value, the second scenario occurs, and the film undergoes a transition into a nanodomain phase. The two scenarios exhibit opposite responses of Curie temperature to thickness reduction. Application of a dipole pattern classifier reveals rich nanodomain phases in halide films: nanostripes, labyrinths, zig-zags, pillars, and lego domains.

Unusual magnetic interaction in CrTe: insights from machine-learning and empirical models

Chromium telluride (CrTe) has received much attention due to its small magnetic anisotropy, which hosts the potential for complex magnetic structures. However, its magnetic properties have been relatively unexplored with numerical simulations, as the magnetic interactions inside are quite unusual. In this study, we employ both a machine-learning model and an empirical model to investigate the magnetic phase transitions of bulk and monolayer CrTe, revealing the existence of unusual magnetic interaction, which can be captured by the machine-learning model but not the simple empirical model. Furthermore, our results also demonstrate that magnetic moments further apart exhibit stronger interactions than those in closer proximity, deviating from typical behavior.

Electrostatics and domains in ferroelectric superlattices

The electrostatics arising in ferroelectric/dielectric two-dimensional heterostructures and superlattices is revisited within a Kittel model in order to define and complete a clear paradigmatic reference for domain formation. The screening of the depolarizing field in isolated ferroelectric or polar thin films via the formation of 180° domains is well understood, where the width of the domains w grows as the square-root of the film thickness d, following Kittel's Law for thick enough films (w ≪ d). For thinner films, a minimum is reached for w before diverging to a monodomain. Although this behaviour is known to be qualitatively unaltered when the dielectric environment of the film is modified, we consider the quantitative changes in that behaviour induced on the ferroelectric film by different dielectric settings: as deposited on a dielectric substrate, sandwiched between dielectrics, and in a superlattice of alternating ferroelectric/dielectric films. The model assumes infinitely thin domain walls, and therefore is not expected to be reliable for film thickness in the nanometre scale. The polarization field P(r) does vary in space, deviating from ±P _S , following the depolarizing field in linear response, but the model does not include a polarization-gradient term as would appear in a Ginzburg-Landau free energy. The model is, however, worth characterizing, both as paradigmatic reference, and as applicable to not-so-thin films. The correct renormalization of parameters is obtained for the thick-film square-root behaviour in the mentioned settings, and the sub-Kittel regime is fully characterized. New results are presented alongside well-known ones for a comprehensive description. Among the former, a natural separation between strong and weak ferroelectric coupling in superlattices is found, which depends exclusively on the dielectric anisotropy of the ferroelectric layer.

The Experimentalist's Guide to the Cycloid, or Noncollinear Antiferromagnetism in Epitaxial BiFeO3

Bismuth ferrite (BiFeO₃ ) is one of the most widely studied multiferroics. The coexistence of ferroelectricity and antiferromagnetism in this compound has driven an intense search for electric-field control of the magnetic order. Such efforts require a complete understanding of the various exchange interactions that underpin the magnetic behavior. An important characteristic of BiFeO₃ is its noncollinear magnetic order; namely, a long-period incommensurate spin cycloid. Here, the progress in understanding this fascinating aspect of BiFeO₃ is reviewed, with a focus on epitaxial films. The advances made in developing the theory used to capture the complexities of the cycloid are first chronicled, followed by a description of the various experimental techniques employed to probe the magnetic order. To help the reader fully grasp the nuances associated with thin films, a detailed description of the spin cycloid in the bulk is provided. The effects of various perturbations on the cycloid are then described: magnetic and electric fields, doping, epitaxial strain, finite size effects, and temperature. To conclude, an outlook on possible device applications exploiting noncollinear magnetism in BiFeO₃ films is presented. It is hoped that this work will act as a comprehensive experimentalist's guide to the spin cycloid in BiFeO₃ thin films.

Spin dynamics, antiferrodistortion and magnetoelectric interaction in multiferroics. The case of BiFeO3

We present a theoretical study of the spin dynamics in perovskite-like multiferroics with homogeneous magnetic order in the presence of external magnetic and electric fields. A particular example of such material is BeFeO3 in which the spin cycloid can be suppressed by application of external magnetic field, doping or by epitaxial strain. Understanding the effect of the external electric field on the spin-wave spectrum of these systems is required for devices based on spin wave interference and other innovative advances of magnonics and spintronics. Thus, we propose a model for BiFeO3 in which the thermodynamic potential is expressed in terms of polarization \boldsymbol{P}, antiferrodistortion \boldsymbol{\Omega}, antiferromagnetic moment \boldsymbol{L} and magnetization \boldsymbol{M}. Based on this model, we derive the corresponding equations of motion and demonstrate the existence of electromagnons, that is, magnons that can be excited by electric fields. These excitations are closely related to the magnetoelectric effect and the dynamics of the antiferrodistortion \boldsymbol{\Omega}. Specifically, the influence of the external electric field on the magnon spectra is due to reorientation of both polarization \boldsymbol{P} and antiferrodistortion \boldsymbol{\Omega} under the influence of the electric field and is linked to emergence of a field-induced anisotropy.

Lattice and spin dynamics in multiferroic BiFeO3 and RMnO3

The multiferroic materials BiFeO₃ and RMnO₃ exhibit coexisting magnetic order and ferroelectricity, and provide exciting platforms for new physics and potentially novel devices, where intriguing interplay between phonons and magnons exists. In this review, we paint a complete picture of bulk BiFeO₃ together with orthorhombic and hexagonal RMnO₃ (R includes rare-earth elements and yttrium) by summarizing the dynamics of spin and lattice and their magnetoelectric coupling, as well as the methods of controlling these characteristics under non-equilibrium conditions, from experimental and simulation perspectives.

Novel Dynamical Magnetoelectric Effects in Multiferroic BiFeO_{3}

An atomistic effective Hamiltonian scheme is employed within molecular dynamics simulations to investigate how the electrical polarization and magnetization of the multiferroic BiFeO_{3} respond to time-dependent ac magnetic fields of various frequencies, as well as to reveal the frequency dependency of the dynamical (quadratic) magnetoelectric coefficient. We found the occurrence of vibrations having phonon frequencies in both the time dependency of the electrical polarization and magnetization (for any applied ac frequency), therefore making such vibrations of electromagnonic nature, when the homogeneous strain of the system is frozen (case 1). Moreover, the quadratic magnetoelectric coupling constant is monotonic and almost dispersionless in the sub-THz range in this case 1. In contrast, when the homogeneous strain can fully relax (case 2), two additional low-frequency and strain-mediated oscillations emerge in the time-dependent behavior of the polarization and magnetization, which result in resonances in the quadratic magnetoelectric coefficient. Such additional oscillations consist of a mixing between acoustic phonons, optical phonons, and magnons, and reflect the existence of a new quasiparticle that can be coined an "electroacoustic magnon." This latter finding can prompt experimentalists to shape their samples to take advantage of, and tune, the magnetostrictive-induced mechanical resonance frequency, in order to achieve large dynamical magnetoelectric couplings.

Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.

Learning through ferroelectric domain dynamics in solid-state synapses

In the brain, learning is achieved through the ability of synapses to reconfigure the strength by which they connect neurons (synaptic plasticity). In promising solid-state synapses called memristors, conductance can be finely tuned by voltage pulses and set to evolve according to a biological learning rule called spike-timing-dependent plasticity (STDP). Future neuromorphic architectures will comprise billions of such nanosynapses, which require a clear understanding of the physical mechanisms responsible for plasticity. Here we report on synapses based on ferroelectric tunnel junctions and show that STDP can be harnessed from inhomogeneous polarization switching. Through combined scanning probe imaging, electrical transport and atomic-scale molecular dynamics, we demonstrate that conductance variations can be modelled by the nucleation-dominated reversal of domains. Based on this physical model, our simulations show that arrays of ferroelectric nanosynapses can autonomously learn to recognize patterns in a predictable way, opening the path towards unsupervised learning in spiking neural networks.

Subterahertz dielectric relaxation in lead-free Ba(Zr,Ti)O3 relaxor ferroelectrics

Relaxors are complex materials with unusual properties that have been puzzling the scientific community since their discovery. The main characteristic of relaxors, that is, their dielectric relaxation, remains unclear and is still under debate. The difficulty to conduct measurements at frequencies ranging from ≃1 GHz to ≃1 THz and the challenge of developing models to capture their complex dynamical responses are among the reasons for such a situation. Here, we report first-principles-based molecular dynamic simulations of lead-free Ba(Zr0.5Ti0.5)O3, which allows us to obtain its subterahertz dynamics. This approach reproduces the striking characteristics of relaxors including the dielectric relaxation, the constant-loss behaviour, the diffuse maximum in the temperature dependence of susceptibility, the substantial widening of dielectric spectrum on cooling and the resulting Vogel-Fulcher law. The simulations further relate such features to the decomposed dielectric responses, each associated with its own polarization mechanism, therefore, enhancing the current understanding of relaxor behaviour.

Driving Spin Excitations by Hydrostatic Pressure in BiFeO(3)

Optical spectroscopy has been combined with computational and theoretical techniques to show how the spin dynamics in the model multiferroic BiFeO(3) responds to the application of hydrostatic pressure and its corresponding series of structural phase transitions from R3c to the Pnma phases. As pressure increases, multiple spin excitations associated with noncollinear cycloidal magnetism collapse into two excitations, which show jump discontinuities at some of the ensuing crystal phase transitions. The effective Hamiltonian approach provides information on the electrical polarization and structural changes of the oxygen octahedra through the successive structural phases. The extracted parameters are then used in a Ginzburg-Landau model to reproduce the evolution with pressure of the spin wave excitations observed at low energy, and we demonstrate that the structural phases and the magnetic anisotropy drive and control the spin excitations.

Structure and spin dynamics of multiferroic BiFeO3

Multiferroic materials have attracted much interest due to the unusual coexistence of ferroelectric and (anti-)ferromagnetic ground states in a single compound. They offer an exciting platform for new physics and potentially novel devices. BiFeO3 is one of the most celebrated multiferroic materials and has highly desirable properties. It is the only known room-temperature multiferroic with TC ≈ 1100 K and TN ≈ 650 K, and exhibits one of the largest spontaneous electric polarisations, P ≈ 80 µC cm(-2). At the same time, it has a magnetic cycloid structure with an extremely long period of 620 Å, which arises from competition between the usual symmetric exchange interaction and the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. There is also an intriguing interplay between the DM interaction and single ion anisotropy K. In this review, we have attempted to paint a complete picture of bulk BiFeO3 by summarising the structural and dynamic properties of both the spin and lattice parts and their magneto-electric coupling.

The role of mechanical boundary conditions in the soft mode dynamics of PbTiO3

The role of different mechanical boundary conditions in the soft mode dynamics of ferroelectric PbTiO3 is systematically investigated using first-principles-based simulations and analytical model. The change in the soft mode dynamics due to hydrostatic pressure, uniaxial and biaxial stresses and biaxial strains is studied in a wide temperature range. Our computations predict: (i) the existence of Curie-Weiss laws that relate the soft mode frequency to the stress or strain; (ii) a non-trivial temperature evolution of the associated Curie-Weiss constants; (iii) a qualitative difference between the soft mode response to stresses/strains and hydrostatic pressure. The latter finding implies that the Curie-Weiss pressure law commonly used for residual stress estimation may not apply for the cases of uniaxial and biaxial stresses and strains. On the other hand, our systematic study offers a way to eliminate this difficulty through the establishment of Curie-Weiss stress and strain laws. Implications of our predictions for some available experimental data are discussed.

Ultrafast switching of the electric polarization and magnetic chirality in BiFeO3 by an electric field

Using a first-principles-based effective Hamiltonian within molecular dynamics simulations, we discover that applying an electric field that is opposite to the initial direction of the polarization results in a switching of both the polarization and the magnetic chirality vector of multiferroic BiFeO3 at an ultrafast pace (namely, of the order of picoseconds). We discuss the origin of such a double ultrafast switching, which is found to involve original intermediate magnetic states and may hold promise for designing various devices.

Crafting the magnonic and spintronic response of BiFeO3 films by epitaxial strain

Multiferroics are compounds that show ferroelectricity and magnetism. BiFeO3, by far the most studied, has outstanding ferroelectric properties, a cycloidal magnetic order in the bulk, and many unexpected virtues such as conductive domain walls or a low bandgap of interest for photovoltaics. Although this flurry of properties makes BiFeO3 a paradigmatic multifunctional material, most are related to its ferroelectric character, and its other ferroic property--antiferromagnetism--has not been investigated extensively, especially in thin films. Here we bring insight into the rich spin physics of BiFeO3 in a detailed study of the static and dynamic magnetic response of strain-engineered films. Using Mössbauer and Raman spectroscopies combined with Landau-Ginzburg theory and effective Hamiltonian calculations, we show that the bulk-like cycloidal spin modulation that exists at low compressive strain is driven towards pseudo-collinear antiferromagnetism at high strain, both tensile and compressive. For moderate tensile strain we also predict and observe indications of a new cycloid. Accordingly, we find that the magnonic response is entirely modified, with low-energy magnon modes being suppressed as strain increases. Finally, we reveal that strain progressively drives the average spin angle from in-plane to out-of-plane, a property we use to tune the exchange bias and giant-magnetoresistive response of spin valves.