Motion and teleportation of polar bubbles in low-dimensional ferroelectrics

Electric bubbles are sub-10nm spherical vortices of electric dipoles that can spontaneously form in ultra-thin ferroelectrics. While the static properties of electric bubbles are well established, little to nothing is known about the dynamics of these particle-like structures. Here, we reveal pathways to realizing both the spontaneous and controlled dynamics of electric bubbles in ultra-thin Pb(Zr0.4Ti0.6)O3 films. In low screening conditions, we find that electric bubbles exhibit thermally-driven chaotic motion giving rise to a liquid-like state. In the high screening regime, we show that bubbles remain static but can be continuously displaced by a local electric field. Additionally, we predict and experimentally demonstrate the possibility of bubble teleportation - a process wherein a bubble is transferred to a new location via a single electric field pulse of a PFM tip. Finally, we attribute the discovered phenomena to the hierarchical structure of the energy landscape.

Tuning the Multiferroic Properties of BiFeO_{3} under Uniaxial Strain

More than twenty years ago, multiferroic compounds combining in particular magnetism and ferroelectricity were rediscovered. Since then, BiFeO_{3} has emerged as the most outstanding multiferroic by combining at room temperature almost all the fundamental or applicative properties that may be desired: electroactive spin wave excitations called electromagnons, conductive domain walls, or a low band gap of interest for magnonic devices. All these properties have so far only been discontinuously strain engineered in thin films according to the lattice parameter imposed by the substrate. Here we explore the ferroelectricity and the dynamic magnetic response of BiFeO_{3} bulk under continuously tunable uniaxial strain. Using elasto-Raman spectroscopy, we show that the ferroelectric soft mode is strongly enhanced under tensile strain and driven by the volume preserving deformation at low strain. The magnonic response is entirely modified with low energy magnon modes being suppressed for tensile strain above pointing out a transition from a cycloid to an homogeneous magnetic state. Effective Hamiltonian calculations show that the ferroelectric and the antiferrodistortive modes compete in the tensile regime. In addition, the homogeneous antiferromagnetic state becomes more stable compared to the cycloidal state above a +2% tensile strain close to the experimental value. Finally, we reveal the ferroelectric and magnetic orders of BiFeO_{3} under uniaxial strain and how the tensile strain allows us to unlock and to modify in a differentiated way the polarization and the magnetic structure.

Realistic Spin Model for Multiferroic NiI_{2}

A realistic first-principle-based spin Hamiltonian is constructed for the type-II multiferroic NiI_{2}, using a symmetry-adapted cluster expansion method. Besides single ion anisotropy and isotropic Heisenberg terms, this model further includes the Kitaev interaction and a biquadratic term, and can well reproduce striking features of the experimental helical ground state, that are, e.g., a proper screw state, canting of rotation plane, propagation direction, and period. Using this model to build a phase diagram, it is demonstrated that, (i) the in-plane propagation direction of ⟨11[over ¯]0⟩ is determined by the Kitaev interaction, instead of the long-believed exchange frustrations and (ii) the canting of rotation plane is also dominantly determined by Kitaev interaction, rather than interlayer couplings. Furthermore, additional Monte Carlo simulations reveal three equivalent domains and different topological defects. Since the ferroelectricity is induced by spins in type-II multiferroics, our work also implies that Kitaev interaction is closely related to the multiferroicity of NiI_{2}.

Magnetization Compensation Temperature and Frustration-Induced Topological Defects in Ferrimagnetic Antiperovskite Mn_{4}N

First-principles-based simulations are conducted to investigate magnetic properties and topological spin textures in the antiperovskite Mn_{4}N ferrimagnet. A magnetization compensation temperature, resulting from a competition between different Mn sublattices, is found in this system, when under thermal equilibrium. Striking metastable topological states are also discovered, including nanometric hedgehog-antihedgehog pairs that originate from frustrated exchange interactions rather than the usual Dzyaloshinskii-Moriya interaction.

Ultrafast Neuromorphic Dynamics Using Hidden Phases in the Prototype of Relaxor Ferroelectrics

Materials possessing multiple states are promising to emulate synaptic and neuronic behaviors. Their operation frequency, typically in or below the GHz range, however, limits the speed of neuromorphic computing. Ultrafast THz electric field excitation has been employed to induce nonequilibrium states of matter, called hidden phases in oxides. One may wonder if there are systems for which THz pulses can generate neuronic and synaptic behavior, via the creation of hidden phases. Using atomistic simulations, we discover that relaxor ferroelectrics can emulate all the key neuronic and memristive synaptic features. Their occurrence originates from the activation of many hidden phases of polarization order, resulting from the response of nanoregions to THz pulses. Such phases further possess different dielectric constants, which is also promising for memcapacitor devices.

Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics

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.

Magnetic-Domain-Wall-Induced Electrical Polarization in Rare-Earth Iron Garnet Systems: A First-Principles Study

First-principles methods are employed to understand the existence of magnetic-domain-wall-induced electric polarization observed in rare-earth iron garnets. In contrast with previous beliefs, it is found that the occurrence of such polarization neither requires the local magnetic moments of the rare-earth ions nor noncollinear magnetism. It can rather be understood as originating from a magnetoelectric effect arising from ferromagnetic interactions between octahedral and tetrahedral Fe ions at the domain walls, and the mechanism behind is found to be a symmetric exchange-striction mechanism.

Electric-Field Switching of Magnetic Topological Charge in Type-I Multiferroics

Applying electric field to control magnetic properties is a very efficient way for spintronics devices. However, the control of magnetic characteristics by electric fields is not straightforward, due to the time-reversal symmetry of magnetism versus spatial inversion symmetry of electricity. Such fundamental difficulty makes it challenging to modify the topology of magnetic skyrmionic states with electric field. Here, we propose a novel mechanism that realizes the electric-field (E) switching of magnetic topological charge (Q) in a controllable and reversible fashion, through the mediation of electric polarization (P) and Dzyaloshinskii-Moriya interaction (D). Such a mechanism is coined here EPDQ. Its validity is demonstrated in a multiferroic VOI_{2} monolayer, which is predicted to host magnetic bimerons. The change in magnetic anisotropy is found to play a crucial role in realizing the EPDQ process and its microscopic origin is discussed. Our study thus provides a new approach toward the highly desired electric-field control of magnetism.

Linear Versus Nonlinear Electro-Optic Effects in Materials

Two schemes are proposed to compute the nonlinear electro-optic (EO) tensor for the first time. In the first scheme, we compute the linear EO tensor of the structure under a finite electric field, while we compute the refractive index of the structure under a finite electric field in the second scheme. Such schemes are applied to Pb(Zr,Ti)O_{3} and BaTiO_{3} ferroelectric oxides. It is found to reproduce a recently observed feature, namely, why Pb(Zr_{0.52}Ti_{0.48})O_{3} adopts a mostly linear EO response while BaTiO_{3} exhibits a strongly nonlinear conversion between electric and optical properties. Furthermore, the atomistic insight provided by the proposed ab initio scheme reveals the origin of such qualitatively different responses, in terms of the field-induced behavior of the frequencies of some phonon modes and of some force constants.

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2

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 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-principles-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 3d transition metal compounds.

Designing Multifunctionality via Assembling Dissimilar Materials: Epitaxial AlN/ScN Superlattices

First-principles calculations are performed to investigate the effect of epitaxial strain on energetic, structural, electrical, electronic, and optical properties of 1×1 AlN/ScN superlattices. This system is predicted to adopt four different strain regions exhibiting different properties, including optimization of various physical responses such as piezoelectricity, electro-optic and elasto-optic coefficients, and elasticity. Varying the strain between these four different regions also allows the creation of an electrical polarization in a nominally paraelectric material, as a result of a softening of the lowest optical mode, and even the control of its magnitude up to a giant value. Furthermore, it results in an electronic band gap that cannot only change its nature (direct vs indirect), but also cover a wide range of the electromagnetic spectrum from the blue, through the violet and near ultraviolet, to the middle ultraviolet. These findings thus point out the potential of assembling two different materials inside the same heterostructure to design multifunctionality and striking phenomena.

Electric-Field Control of Magnetization, Jahn-Teller Distortion, and Orbital Ordering in Ferroelectric Ferromagnets

Controlling the direction of the magnetization by an electric field in multiferroics that are both ferroelectric and strongly ferromagnetic will open the door to the design of the next generation of spintronics and memory devices. Using first-principles simulations, we report that the discovery that the PbTiO_{3}/LaTiO_{3} (PTO/LTO) superlattice possesses such highly desired control, as evidenced by the electric-field-induced rotation of 90° and even a possible full reversal of its magnetization in some cases. Moreover, such systems also exhibit Jahn-Teller distortions, as well as orbital orderings, that are switchable by the electric field, therefore making PTO/LTO of importance for the tuning of electronic properties too. The origin for such striking electric-field controls of magnetization, Jahn-Teller deformations, and orbital orderings resides in the existence of three different types of energetic coupling: one coupling polarization with antiphase and in-phase oxygen octahedral tiltings, a second one coupling polarization with antiphase oxygen octahedra tilting and Jahn-Teller distortions, and finally a biquadratic coupling between antiphase oxygen octahedral tilting and magnetization.

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.

Cooperative Couplings between Octahedral Rotations and Ferroelectricity in Perovskites and Related Materials

The structure of ABO_{3} perovskites is dominated by two types of unstable modes, namely, the oxygen octahedral rotation (AFD) and ferroelectric (FE) mode. It is generally believed that such AFD and FE modes tend to compete and suppress each other. Here we use first-principles methods to show that a dual nature of the FE-AFD coupling, which turns from competitive to cooperative as the AFD mode strengthens, occurs in numerous perovskite oxides. We provide a unified model of such a dual interaction by introducing novel high-order coupling terms and explain the atomistic origin of the resulting new form of ferroelectricity in terms of universal steric mechanisms. We also predict that such a novel form of ferroelectricity leads to atypical behaviors, such as an enhancement of all the three Cartesian components of the electric polarization under hydrostatic pressure and compressive epitaxial strain.

Photostriction and elasto-optic response in multiferroics and ferroelectrics from first principles

The present work reviews a series of recent first-principles studies devoted to the description of the interaction of light and strain in ferroelectric and multiferroic materials. Specifically, the modelling schemes used in these works to describe the so-called photostriction and elasto-optic effects are presented, in addition to the results and analysis provided by these ab initio calculations. In particular, the large importance of the piezoelectric effect in the polar direction in the photostriction of ferroelectric materials is stressed. Similarly, the occurrence of low-symmetry phases in lead titanate thin films under tensile strain is demonstrated to result in large elasto-optic constants. In addition, first-principle calculations allow to gain microscopic knowledge of subtle effects, for instance in the case of photostriction, where the deformation potential effect in directions perpendicular to the polar axis is shown to be almost as significant as the piezoelectric effect. As a result, the numerical methods presented here could propel the design of efficient opto-mechanical devices.

Emergent Berezinskii-Kosterlitz-Thouless Phase in Low-Dimensional Ferroelectrics

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 BaTiO_{3} 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.

Toy model for uncommon spin-orbit-driven spin-torque terms

A toy model combining the angular magneto electric (AME) coupling Hamitonian (Mondal et al 2015 Phys. Rev. B 92 100402) with long-range magnetic dipolar interactions is used to investigate spin-torque phenomena in a magnetic spin valve. It is found that such model (1) gives rise to spin-torque expressions that are analogous in form to those of the common spin-transfer torques; but also (2) predicts additional spin-torque terms, which are generated by an electrical current oriented along unconventional, in-plane directions. The magnitude of the AME induced terms is estimated and the conditions under which they may contribute significantly are explored.

Microscopic origins of the large piezoelectricity of leadfree (Ba,Ca)(Zr,Ti)O3

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_0.2Ti_0.8)O₃-x(Ba_0.7Ca_0.3)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.

Photostrictive Two-Dimensional Materials in the Monochalcogenide Family

Photostriction is predicted for group-IV monochalcogenide monolayers, two-dimensional ferroelectrics with rectangular unit cells (the lattice vector a_{1} is larger than a_{2}) and an intrinsic dipole moment parallel to a_{1}. Photostriction is found to be related to the structural change induced by a screened electric polarization (i.e., a converse piezoelectric effect) in photoexcited electronic states with either p_{x} or p_{y} (in-plane) orbital symmetry that leads to a compression of a_{1} and a comparatively smaller increase of a_{2} for a reduced unit cell area. The structural change documented here is 10 times larger than that observed in BiFeO_{3}, making monochalcogenide monolayers an ultimate platform for this effect. This structural modification should be observable under experimentally feasible densities of photexcited carriers on samples that have been grown already, having a potential usefulness for light-induced, remote mechano-optoelectronic applications.

Designing lead-free antiferroelectrics for energy storage

Dielectric capacitors, although presenting faster charging/discharging rates and better stability compared with supercapacitors or batteries, are limited in applications due to their low energy density. Antiferroelectric (AFE) compounds, however, show great promise due to their atypical polarization-versus-electric field curves. Here we report our first-principles-based theoretical predictions that Bi_1-xR_xFeO₃ systems (R being a lanthanide, Nd in this work) can potentially allow high energy densities (100-150 J cm^-3) and efficiencies (80-88%) for electric fields that may be within the range of feasibility upon experimental advances (2-3 MV cm^-1). In addition, a simple model is derived to describe the energy density and efficiency of a general AFE material, providing a framework to assess the effect on the storage properties of variations in doping, electric field magnitude and direction, epitaxial strain, temperature and so on, which can facilitate future search of AFE materials for energy storage.

Fluctuations and Topological Defects in Proper Ferroelectric Crystals

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.

Structural Phase Transition and Material Properties of Few-Layer Monochalcogenides

GeSe and SnSe monochalcogenide monolayers and bilayers undergo a two-dimensional phase transition from a rectangular unit cell to a square unit cell at a critical temperature T_{c} well below the melting point. Its consequences on material properties are studied within the framework of Car-Parrinello molecular dynamics and density-functional theory. No in-gap states develop as the structural transition takes place, so that these phase-change materials remain semiconducting below and above T_{c}. As the in-plane lattice transforms from a rectangle into a square at T_{c}, the electronic, spin, optical, and piezoelectric properties dramatically depart from earlier predictions. Indeed, the Y and X points in the Brillouin zone become effectively equivalent at T_{c}, leading to a symmetric electronic structure. The spin polarization at the conduction valley edge vanishes, and the hole conductivity must display an anomalous thermal increase at T_{c}. The linear optical absorption band edge must change its polarization as well, making this structural and electronic evolution verifiable by optical means. Much excitement is drawn by theoretical predictions of giant piezoelectricity and ferroelectricity in these materials, and we estimate a pyroelectric response of about 3×10^{-12}  C/K m here. These results uncover the fundamental role of temperature as a control knob for the physical properties of few-layer group-IV monochalcogenides.

Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations

The radio-frequency dielectric response of the lead-free Ba(Zr_{0.5}Ti_{0.5})O_{3} relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors.

Photostriction in Ferroelectrics from Density Functional Theory

An ab initio procedure allowing the computation of the deformation of ferroelectric-based materials under light is presented. This numerical scheme consists in structurally relaxing the system under the constraint of a fixed n_{e} concentration of electrons photoexcited into a specific conduction band edge state from a chosen valence band state, via the use of a constrained density functional theory method. The resulting change in lattice constant along a selected crystallographic direction is then calculated for a reasonable estimate of n_{e}. This method is applied to bulk multiferroic BiFeO_{3} and predicts a photostriction effect of the same order of magnitude than the ones recently observed. A strong dependence of photostrictive response on both the reached conduction state and the crystallographic direction (along which this effect is determined) is also revealed. Furthermore, analysis of the results demonstrates that the photostriction mechanism mostly originates from the screening of the spontaneous polarization by the photoexcited electrons in combination with the inverse piezoelectric effect.

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.

Topological Point Defects in Relaxor Ferroelectrics

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(Zr_{0.5}Ti_{0.5})O_{3} (BZT) and Pb(Sc_{0.5}Nb_{0.5})O_{3} (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.

Frustration and Self-Ordering of Topological Defects in Ferroelectrics

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.

Large elasto-optic effect and reversible electrochromism in multiferroic BiFeO3

The control of optical fields is usually achieved through the electro-optic or acousto-optic effect in single-crystal ferroelectric or polar compounds such as LiNbO₃ or quartz. In recent years, tremendous progress has been made in ferroelectric oxide thin film technology—a field which is now a strong driving force in areas such as electronics, spintronics and photovoltaics. Here, we apply epitaxial strain engineering to tune the optical response of BiFeO₃ thin films, and find a very large variation of the optical index with strain, corresponding to an effective elasto-optic coefficient larger than that of quartz. We observe a concomitant strain-driven variation in light absorption—reminiscent of piezochromism—which we show can be manipulated by an electric field. This constitutes an electrochromic effect that is reversible, remanent and not driven by defects. These findings broaden the potential of multiferroics towards photonics and thin film acousto-optic devices, and suggest exciting device opportunities arising from the coupling of ferroic, piezoelectric and optical responses.

Modern technology such as electronics and photovoltaics requires careful control of optical responses of electronic properties. Here, Sando et al. demonstrate a large variation of optical index and light absorption in multiferroic material BiFeO₃ thin films, tunable by in-film strain or electric field.

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.

Large Elasto-Optic Effect in Epitaxial PbTiO(3) Films

First-principles calculations are performed to investigate the elasto-optic properties of four different structural phases in (001) epitaxial PbTiO(3) films under tensile strain: a tetragonal (T) phase and an orthorhombic (O) phase, which are the ground states for small and large strain, respectively, and two low-symmetry, monoclinic phases of Cm and Pm symmetries that have low total energy in the intermediate strain range. It is found that the refractive indices of the T and O phases respond differently to epitaxial strain, evidenced by a change of sign of their effective elasto-optic coefficients, and as a result of presently discovered correlations between refractive index, axial ratio, and magnitude of the ferroelectric polarization. The difference in refractive indices between T and O and the existence of such correlations naturally lead to large elasto-optic coefficients in the Cm and Pm states in the intermediate strain range, because Cm structurally bridges the T and O phases (via polarization rotation and a rapid change of its axial ratio) and Pm adopts a similar axial ratio and polarization magnitude to Cm. The present results therefore broaden the palette of functionalities of ferroelectric materials, and suggest new routes to generate systems with unprecedentedly large elasto-optic conversion.

Predicted energetics and properties of rare-earth ferrites films grown on cubic (111)- and hexagonal (0001)-oriented substrates

First-principles calculations are performed to compare the energetics of several phases, including hexagonal polar P6(3)cm and perovskite non-polar Pbnm-like states, of epitaxial RFeO3 films (with R  =  Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Lu) grown on different cubic (1 1 1)- and hexagonal (0 0 0 1)-oriented substrates. The P63cm phase is found to be the ground state for large enough in-plane lattice parameters in all investigated RFeO3 films, and its polarization is tunable by the amount of epitaxial strain. Series of available substrates allowing the growth of hexagonal polar RFeO3 films, as well as other phenomena of fundamental and technological importance (e.g. different ground states and coexistence between several phases) are also predicted.

First-principles-based effective Hamiltonian simulations of bulks and films made of lead-free Ba(Zr,Ti)O3 relaxor ferroelectrics

A review of the recent development and application of a first-principles-derived effective Hamiltonian technique to the study of lead-free Ba(Zr,Ti)O3 (BZT) relaxor ferroelectrics is provided. In addition to the computation and analysis of macroscopic properties (such as different types of dielectric responses and electric polarization) and their connections to previous published works, particular emphasis is given to microscopic insights arising from this atomistic technique. These include (i) the numerically-found determination of the physical origin of the relaxor behavior in BZT; and (ii) the prediction of polar nanoregions and the evolution of their morphology as a response to temperature, electric fields and epitaxial misfit strain. Other striking phenomena that were predicted in BZT compounds, such as Fano resonance and field-driven percolation, are also documented and discussed. Finally, a brief perspective of possible remaining computational studies to be conducted in relaxor ferroelectrics, in order to further understand them, is attempted.

Predicted pressure-induced spin and electronic transition in double perovskite R2CoMnO6 (R = rare-earth ion)

Specific first-principles calculations are performed to predict structural, magnetic and electronic properties of seven double perovskite R2CoMnO6 materials, with R being a rare-earth ion, under hydrostatic pressure. All these compounds are found to undergo a first-order transition from a high spin (HS) to low spin (LS) state at a critical pressure (whose value is dependent on the R ion). Such transition not only results in a significant volume collapse but also yields a dramatic change in electronic structure. More precisely, the HS-to-LS transition is accompanied by a transition from an insulator to a half-metallic state in the R2CoMnO6 compounds having the largest rare-earth ionic radius (i.e., Nd, Sm, Gd and Tb) while it induces a change from an insulator to a semiconductor having a narrow band gap for the smallest rare-earth ions (i.e., R = Dy, Ho and Er). Experiments are called for to confirm these predictions.

Electronic properties of electrical vortices in ferroelectric nanocomposites from large-scale ab initio computations

An original ab initio procedure is developed and applied to a ferroelectric nanocomposite, in order to reveal the effect of electrical vortices on electronic properties. Such procedure involves the combination of two large-scale numerical schemes, namely, the effective Hamiltonian (to incorporate ionic degrees of freedom) and the linear-scaling three-dimensional fragment method (to treat electronic degrees of freedom). The use of such procedure sheds some light into the origin of the recently observed current that is activated at rather low voltages in systems possessing electrical vortices. It also reveals a novel electronic phenomena that is a systematic control of the type of the band-alignment (i.e., type I versus type II) within the same material via the temperature-driven annihilation/formation of electrical topological defects.

Predicting a ferrimagnetic phase of Zn(2)FeOsO(6) with strong magnetoelectric coupling

Multiferroic materials, in which ferroelectric and magnetic ordering coexist, are of practical interest for the development of novel memory devices that allow for electrical writing and nondestructive magnetic readout operation. The great challenge is to create room temperature multiferroic materials with strongly coupled ferroelectric and ferromagnetic (or ferrimagnetic) orderings. BiFeO_{3} is the most heavily investigated single-phase multiferroic to date due to the coexistence of its magnetic order and ferroelectric order at room temperature. However, there is no net magnetic moment in the cycloidal (antiferromagneticlike) magnetic state of bulk BiFeO_{3}, which severely limits its realistic applications in electric field controlled memory devices. Here, we predict that LiNbO_{3}-type Zn_{2}FeOsO_{6} is a new multiferroic with properties superior to BiFeO_{3}. First, there are strong ferroelectricity and strong ferrimagnetism at room temperature in Zn_{2}FeOsO_{6}. Second, the easy plane of the spontaneous magnetization can be switched by an external electric field, evidencing the strong magnetoelectric coupling existing in this system. Our results suggest that ferrimagnetic 3d-5d LiNbO_{3}-type material may therefore be used to achieve voltage control of magnetism in future memory devices.

Revisiting galvanomagnetic effects in conducting ferromagnets

The recently proposed coupling between the angular momentum density and magnetic moments is shown to provide a straightforward alternative explanation for galvanomagnetic effects, i.e. for both anisotropic magnetoresistance (AMR) and planar Hall effect (PHE). Such coupling naturally reproduces the general formula associated with AMR and PHE and allows for the occurrence of so-called 'negative AMR'. This coupling also provides a unifying link between AMR, PHE and the anomalous Hall effect (AHE) since this same coupling was previously found to give rise to AHE (Bellaiche et al 2013 Phys. Rev. B 88 161102).

Prediction of novel interface-driven spintronic effects

The recently proposed coupling between the angular momentum density and magnetic moment (Raeliarijaona et al 2013 Phys. Rev. Lett. 110 137205) is shown here to result in the prediction of (i) novel spin currents generated by an electrical current and (ii) new electrical currents induced by a spin current in systems possessing specific interfaces between two different materials. Some of these spin (electrical) currents can be reversed near the interface by reversing the applied electrical (spin) current. Similarities and differences between these novel spintronic effects and the well-known spin Hall and inverse spin Hall effects are also discussed.

Strain engineering of perovskite thin films using a single substrate

Combining temperature-dependent x-ray diffraction, Raman spectroscopy and first-principles-based effective Hamiltonian calculations, we show that varying the thickness of (Ba0.8Sr0.2)TiO3 (BST) thin films deposited on the same single substrate (namely, MgO) enables us to change not only the magnitude but also the sign of the misfit strain. Such previously overlooked control of the strain allows several properties of these films (e.g. Curie temperature, symmetry of ferroelectric phases, dielectric response) to be tuned and even optimized. Surprisingly, such desired control of the strain (and of the resulting properties) originates from an effect that is commonly believed to be detrimental to functionalities of films, namely the existence of misfit dislocations. The present study therefore provides a novel route to strain engineering, as well as leading us to revisit common beliefs.

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.

The stabilization of a single domain in free-standing ferroelectric nanocrystals

High resolution electron microscopy, electron diffraction and electron holography were used to study individual free-standing ∼ 30 nm barium titanate nanocrystals. Large unidirectional variations in the tetragonal distortion were mapped across the smaller nanocrystals, peaking to anomalously large values of up to 4% at the centers of the nanocrystals. This indicated that the nanocrystals consist of highly strained single ferroelectric domains. Simulations using an effective Hamiltonian for modeling a nanocrystal under a small depolarizing field and negative pressure qualitatively confirm this picture. These simulations, along with the development of a phenomenological model, show that the tetragonal distortion variation is a combined effect of: (i) electrostrictive coupling between the spontaneous polarization and strain inside the nanocrystal, and (ii) a surface-induced effective stress existing inside the nanodot. As a result, a 'strain skin layer', having a smaller tetragonal distortion relative to the core of the nanocrystal, is created.

Quantum anomalous Hall effect in graphene proximity coupled to an antiferromagnetic insulator

We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.

Control of ferroelectricity and magnetism in multi-ferroic BiFeO3 by epitaxial strain

Recently, strain engineering has been shown to be a powerful and flexible means of tailoring the properties of ABO3 perovskite thin films. The effect of epitaxial strain on the structure of the perovskite unit cell can induce a host of interesting effects, these arising from either polar cation shifts or rotation of the oxygen octahedra, or both. In the multi-ferroic perovskite bismuth ferrite (BiFeO3-BFO), both degrees of freedom exist, and thus a complex behaviour may be expected as one plays with epitaxial strain. In this paper, we review our results on the role of strain on the ferroic transition temperatures and ferroic order parameters. We find that, while the Néel temperature is almost unchanged by strain, the ferroelectric Curie temperature strongly decreases as strain increases in both the tensile and compressive ranges. Also unexpected is the very weak influence of strain on the ferroelectric polarization value. Using effective Hamiltonian calculations, we show that these peculiar behaviours arise from the competition between antiferrodistortive and polar instabilities. Finally, we present results on the magnetic order: while the cycloidal spin modulation present in the bulk survives in weakly strained films, it is destroyed at large strain and replaced by pseudo-collinear antiferromagnetic ordering. We discuss the origin of this effect and give perspectives for devices based on strain-engineered BiFeO3.

Prediction of a novel magnetoelectric switching mechanism in multiferroics

We report a first-principles study of the recently predicted Pmc21 phase of the multiferroic BiFeO3 material, revealing a novel magnetoelectric effect that makes it possible to control magnetism with an electric field. The effect can be viewed as a two-step process: Switching the polarization first results in the change of the sense of the rotation of the oxygen octahedra, which in turn induces the switching of the secondary magnetic order parameter. The first step is governed by an original trilinear-coupling energy between polarization, octahedral tilting, and an antiferroelectric distortion. The second step is controlled by another trilinear coupling, this one involving the predominant and secondary magnetic orders as well as the oxygen octahedral tilting. In contrast with other trilinear-coupling effects in the literature, the present ones occur in a simple ABO3 perovskite and involve a large polarization.

Effects of a rotating electric field on the properties of epitaxial (001) Pb(Zr,Ti)O3 ultrathin film: a first-principles-based study

Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions and subjected to an electric field rotating in the (1¯10) plane are investigated via the use of an effective Hamiltonian, for different magnitudes of this field. Varying the direction and magnitude of the electric field leads to specific reorganization of dipoles into original configuration states, whose microstructures and macroscopic properties are revealed. In particular, a novel (direction of the electric field-versus-magnitude of the electric field) phase diagram is reported here. The field-induced correlation between the polar distortions and the oxygen octahedral tilting is also discussed.

Properties of epitaxial films made of relaxor ferroelectrics

Finite-temperature properties of epitaxial films made of Ba(Zr,Ti)O3 relaxor ferroelectrics are determined as a function of misfit strain, via the use of a first-principles-based effective Hamiltonian. These films are macroscopically paraelectric at any temperature, for any strain ranging between ≃-3% and ≃+3%. However, original temperature-versus-misfit strain phase diagrams are obtained for the Burns temperature (Tb) and for the critical temperatures (Tm,z and Tm,IP) at which the out-of-plane and in-plane dielectric response peak, respectively, which allow the identification of three different regions. These latter differ from their evolution of Tb, Tm,z, and/or Tm,IP with strain, which are the fingerprints of a remarkable strain-induced microscopic change: each of these regions is associated with its own characteristic behavior of polar nanoregions at low temperature, such as strain-induced rotation or strain-driven elongation of their dipoles or even increase in the average size of the polar nanoregions when the strength of the strain grows.

Effect of chemical and hydrostatic pressures on structural and magnetic properties of rare-earth orthoferrites: a first-principles study

The dependence of structural and magnetic properties of rare-earth orthoferrites (in their Pbnm ground state) on the rare-earth ionic radius is systematically investigated from first principles. The effects of this 'chemical pressure' on lattice constants, Fe-O bond lengths, Fe-O-Fe bond angles and Fe-O bond length splittings are all well reproduced by these ab initio calculations. The simulations also offer novel predictions (on tiltings of FeO6 octahedra, cation antipolar displacements and weak magnetization) to be experimentally checked. In particular, the weak ferromagnetic moment of rare-earth orthoferrites is predicted to be a linear function of the rare-earth ionic radius. Finally, the effects of applying hydrostatic pressure on structural and magnetic behavior of SmFeO3 is also studied. It is found that, unlike previously assumed, hydrostatic pressure typically generates changes in physical properties that are quantitatively and even qualitatively different from those associated with the chemical pressure.

Effect of chemical pressure, misfit strain and hydrostatic pressure on structural and magnetic behaviors of rare-earth orthochromates

First-principles calculations are performed to investigate structural and magnetic behaviors of rare-earth orthochromates as a function of 'chemical' pressure (that is, the rare-earth ionic radius), epitaxial misfit strain and hydrostatic pressure. From a structural point of view, (i) 'chemical' pressure significantly modifies antipolar displacements, Cr-O-Cr bond angles and the resulting oxygen octahedral tiltings; (ii) hydrostatic pressure mostly changes Cr-O bond lengths; and (iii) misfit strain affects all these quantities. The correlations between magnetic properties (Néel temperature and weak ferromagnetic moments) and unit cell volume are similar when varying the misfit strain or hydrostatic pressure, but differ from those associated with the 'chemical' pressure. Origins of such effects are also discussed.