Bridging multiferroic phase transitions by epitaxial strain in BiFeO3

Insights into Strain Engineering: From Ferroelectrics to Related Functional Materials and Beyond

Ferroelectrics have become indispensable components in various application fields, including information processing, energy harvesting, and electromechanical conversion, owing to their unique ability to exhibit electrically or mechanically switchable polarization. The distinct polar noncentrosymmetric lattices of ferroelectrics make them highly responsive to specific crystal structures. Even slight changes in the lattice can alter the polarization configuration and response to external fields. In this regard, strain engineering has emerged as a prevalent regulation approach that not only offers a versatile platform for structural and performance optimization within ferroelectrics but also unlocks boundless potential in various functional materials. In this review, we systematically summarize the breakthroughs in ferroelectric-based functional materials achieved through strain engineering and progress in method development. We cover research activities ranging from fundamental attributes to wide-ranging applications and novel functionalities ranging from electromechanical transformation in sensors and actuators to tunable dielectric materials and information technologies, such as transistors and nonvolatile memories. Building upon these achievements, we also explore the endeavors to uncover the unprecedented properties through strain engineering in related chemical functionalities, such as ferromagnetism, multiferroicity, and photoelectricity. Finally, through discussions on the prospects and challenges associated with strain engineering in the materials, this review aims to stimulate the development of new methods for strain regulation and performance boosting in functional materials, transcending the boundaries of ferroelectrics.

Ultrafast Optically Induced Perturbation of Oxygen Octahedral Rotations in Multiferroic BiFeO3 Thin Films

The functional properties of complex oxides, including magnetism and ferroelectricity, are closely linked to subtle structural distortions. Ultrafast optical excitations provide the means to manipulate structural features and ultimately to affect the functional properties of complex oxides with picosecond-scale precision. We report that the lattice expansion of multiferroic BiFeO3 following above-bandgap optical excitation leads to distortion of the oxygen octahedral rotation (OOR) pattern. The continuous coupling between OOR and strain was probed using time-resolved X-ray free-electron laser diffraction with femtosecond time resolution. Density functional theory calculations predict a relationship between the OOR and the elastic strain consistent with the experiment, demonstrating a route to employing this approach in a wider range of systems. Ultrafast control of the functional properties of BiFeO3 thin films is enabled by this approach because the OOR phenomena are related to ferroelectricity, and via the Fe-O-Fe bond angles, the superexchange interaction between Fe atoms.

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.

Magnetoelectric coupling in multiferroics probed by optical second harmonic generation

Magnetoelectric coupling, as a fundamental physical nature and with the potential to add functionality to devices while also reducing energy consumption, has been challenging to be probed in freestanding membranes or two-dimensional materials due to their instability and fragility. In this paper, we report a magnetoelectric coupling probed by optical second harmonic generation with external magnetic field, and show the manipulation of the ferroelectric and antiferromagnetic orders by the magnetic and thermal fields in BiFeO₃ films epitaxially grown on the substrates and in the freestanding ones. Here we define an optical magnetoelectric-coupling constant, denoting the ability of controlling light-induced nonlinear polarization by the magnetic field, and found the magnetoelectric-coupling was suppressed by strain releasing but remain robust against thermal fluctuation for freestanding BiFeO₃.

Ferroelectric Proximity Effect and Topological Hall Effect in SrRuO3/BiFeO3 Multilayers

Interfaces between complex oxides provide a unique opportunity to discover novel interfacial physics and functionalities. Here, we fabricate the multilayers of itinerant ferromagnet SrRuO₃ (SRO) and multiferroic BiFeO₃ (BFO) with atomically sharp interfaces. Atomically resolved transmission electron microscopy reveals that a large ionic displacement in BFO can penetrate into SRO layers near the BFO/SRO interfaces to a depth of 2-3 unit cells, indicating the ferroelectric proximity effect. A topological Hall effect is indicated by hump-like anomalies in the Hall measurements of the multilayer with a moderate thickness of the SRO layer. With magnetic measurements, it can be further confirmed that each SRO layer in the multilayers can be divided into interfacial and middle regions, which possess different magnetic ground states. Our work highlights the key role of functional heterointerfaces in exotic properties and provides an important guideline to design spintronic devices based on magnetic skyrmions.

A Highly Strained Phase in PbZr0.2Ti0.8O3 Films with Enhanced Ferroelectric Properties

Although epitaxial strain imparted by lattice mismatch between a film and the underlying substrate has led to distinct structures and emergent functionalities, the discrete lattice parameters of limited substrates, combined with strain relaxations driven by film thickness, result in severe obstructions to subtly regulate electro-elastic coupling properties in perovskite ferroelectric films. Here a practical and universal method to achieve highly strained phases with large tetragonal distortions in Pb-based ferroelectric films through synergetic effects of moderately (≈1.0%) misfit strains and laser fluences during pulsed laser deposition process is demonstrated. The phase possesses unexpectedly large Poisson's ratio and negative thermal expansion, and concomitant enhancements of spontaneous polarization (≈100 µC cm-2) and Curie temperature (≈800 °C), 40% and 75% larger than that of bulk counterparts, respectively. This strategy efficiently circumvents the long-standing issue of limited numbers of discrete substrates and enables continuous regulations of exploitable lattice states in functional oxide films with tightly elastic coupled performances beyond their present levels.

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.

Tailoring the photovoltaic effect in (1 1 1) oriented BiFeO3/LaFeO3 superlattices

Ferroelectric and photovoltaic properties of (BiFeO₃)_(1-x)Λ/(LaFeO₃) _xΛ superlattices grown by pulsed laser deposition have been investigated (Λ being the bilayer thickness). For a high concentration of BiFeO₃ a ferroelectric state is observed simultaneously with a switchable photovoltaic response. In contrast for certain concentration of LaFeO₃ a non-switchable photovoltaic effect is evidenced. Such modulation of the PV response in the superlattices is attributed to the ferroelectric to paraelectric phase transition which is controlled with the increase of x. Remarkably, concomitant to this change of PV mechanism, a change of the conduction mechanism also seems to take place from a bulk-limited to an interface-limited transport as x increases.

Real-time studies of ferroelectric domain switching: a review

Ferroelectric materials have been utilized in a broad range of electronic, optical, and electromechanical applications and hold the promise for the design of future high-density nonvolatile memories and multifunctional nano-devices. The applications of ferroelectric materials stem from the ability to switch polarized domains by applying an electric field, and therefore a fundamental understanding of the switching dynamics is critical for design of practical devices. In this review, we summarize the progress in the study of the microscopic process of ferroelectric domain switching using recently developed in situ transmission electron microscopy (TEM). We first briefly introduce the instrumentation, experimental procedures, imaging mechanisms, and analytical methods of the state-of-the-art in situ TEM techniques. The application of these techniques to studying a wide range of complex switching phenomena, including domain nucleation, domain wall motion, domain relaxation, domain-defect interaction, and the interplay between different types of domains, is demonstrated. The underlying physics of these dynamic processes are discussed.

Crystal Growth Mechanisms of BiFeO3 Nanoparticles

A wet-chemical synthesis process was designed to obtain reproducible single-phase multiferroic BiFeO₃ nanoparticles. The phase purity, single crystallinity, and size of the nanoparticles are confirmed through the analysis of X-ray diffraction patterns, Raman spectroscopy, and high resolution transmission electron microscopy experiments. Crystal nucleation happens within the amorphous-rich area in multiple seeds, leading to the formation of single crystalline nanoparticles with no preferential faceting. Crystallization mechanisms of BiFeO₃ nanoparticles were investigated following the Kissinger-Akahira-Sunose approach, indicating that two crystallization steps are responsible of the complete BiFeO₃ nanoparticle formation. The first crystallization step involves a maximum of 70% of the final crystal volume, arising from nanocrystal nucleation and growth. The second step occurs above this threshold crystal volume fraction, and it is related to the nanocrystallite coalescence process. Analysis of the thermodynamic process of the crystallization of BiFeO₃ nanoparticles following Ostwald rules suggests a relatively low energy barrier for crystal nucleation, highlighting that phase pure, single crystalline BiFeO₃ nanoparticles are obtained using the present optimized wet-chemical synthesis process, with temperatures as low as 450 °C.

Structures and electronic properties of domain walls in BiFeO3 thin films

Domain walls (DWs) in ferroelectrics are atomically sharp and can be created, erased, and reconfigured within the same physical volume of ferroelectric matrix by external electric fields. They possess a myriad of novel properties and functionalities that are absent in the bulk of the domains, and thus could become an essential element in next-generation nanodevices based on ferroelectrics. The knowledge about the structure and properties of ferroelectric DWs not only advances the fundamental understanding of ferroelectrics, but also provides guidance for the design of ferroelectric-based devices. In this article, we provide a review of structures and properties of DWs in one of the most widely studied ferroelectric systems, BiFeO₃ thin films. We correlate their conductivity and photovoltaic properties to the atomic-scale structure and dynamic behaviors of DWs.

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.

Control of Domain Structures in Multiferroic Thin Films through Defect Engineering

Domain walls (DWs) have become an essential component in nanodevices based on ferroic thin films. The domain configuration and DW stability, however, are strongly dependent on the boundary conditions of thin films, which make it difficult to create complex ordered patterns of DWs. Here, it is shown that novel domain structures, that are otherwise unfavorable under the natural boundary conditions, can be realized by utilizing engineered nanosized structural defects as building blocks for reconfiguring DW patterns. It is directly observed that an array of charged defects, which are located within a monolayer thickness, can be intentionally introduced by slightly changing substrate temperature during the growth of multiferroic BiFeO₃ thin films. These defects are strongly coupled to the domain structures in the pretemperature-change portion of the BiFeO₃ film and can effectively change the configuration of newly grown domains due to the interaction between the polarization and the defects. Thus, two types of domain patterns are integrated into a single film without breaking the DW periodicity. The potential use of these defects for building complex patterns of conductive DWs is also demonstrated.

Single-Crystal BiFeO3 Nanoplates with Robust Antiferromagnetism

Freestanding and single-crystal BiFeO₃ (BFO) nanoplates have been successfully synthesized by a fluoride ion-assisted hydrothermal method, and the thickness of the nanoplates can be effectively tailored from 80 to 380 nm by the concentration of fluoride ions. It is revealed that BFO nanoplates grew via an oriented attachment of layer by layer, giving rise to the formation of the inner interface within the nanoplates. In particular, antiferromagnetic (AFM) phase-transition temperature (Néel temperature, T_N) of the BFO nanoplates is significantly enhanced from typical 370 to ∼512 °C, whereas the Curie temperature (T_C) of the BFO nanoplates is determined to be ∼830 °C, in good agreement with a bulk value. The combination of scanning transmission electron microscopy, electron energy loss spectroscopy, and the first-principle calculations reveals that the interfacial tensile strain remarkably improves the stability of AFM ordering, accounting for the significant enhancement in T_N of BFO plates. Correspondingly, the tensile strain induced the polarization and oxygen octahedral tilting has been observed near the interface. The findings presented here suggest that single-crystal BFO nanoplate is an ideal system for exploring an intrinsic magnetoelectric property, where a tensile strain can be a very promising approach to tailor AFM ordering and polarization rotation for an enhanced coupling effect.

B-site ordering and strain-induced phase transition in double-perovskite La2NiMnO6 films

The magnetic and electrical properties of complex oxide thin films are closely related to the phase stability and cation ordering, which demands that we understand the process-structure-property relationships microscopically in functional materials research. Here we study multiferroic thin films of double-perovskite La₂NiMnO₆ epitaxially grown on SrTiO₃, KTaO₃, LaAlO₃ and DyScO₃ substrates by pulsed laser deposition. The effect of epitaxial strains imposed by the substrate on the microstructural properties of La₂NiMnO₆ has been systematically investigated by means of advanced electron microscopy. It is found that La₂NiMnO₆ films under tensile strain exhibit a monoclinic structure, while under compressive strain the crystal structure of La₂NiMnO₆ films is rhombohedral. In addition, by optimizing the film deposition conditions a long-range ordering of B-site cations in La₂NiMnO₆ films has been obtained in both monoclinic and rhombohedral phases. Our results not only provide a strategy for tailoring phase stability by strain engineering, but also shed light on tuning B-site ordering by controlling film growth temperature in double-perovskite La₂NiMnO₆ films.

A Strain-Driven Antiferroelectric-to-Ferroelectric Phase Transition in La-Doped BiFeO3 Thin Films on Si

A strain-driven orthorhombic (O) to rhombohedral (R) phase transition is reported in La-doped BiFeO₃ thin films on silicon substrates. Biaxial compressive epitaxial strain is found to stabilize the rhombohedral phase at La concentrations beyond the morphotropic phase boundary (MPB). By tailoring the residual strain with film thickness, we demonstrate a mixed O/R phase structure consisting of O phase domains measuring tens of nanometers wide within a predominant R phase matrix. A combination of piezoresponse force microscopy (PFM), transmission electron microscopy (TEM), polarization-electric field hysteresis loop (P-E loop), and polarization maps reveal that the O-R structural change is an antiferroelectric to ferroelectric (AFE-FE) phase transition. Using scanning transmission electron microscopy (STEM), an atomically sharp O/R MPB is observed. Moreover, X-ray absorption spectra (XAS) and X-ray linear dichroism (XLD) measurements reveal a change in the antiferromagnetic axis orientation from out of plane (R-phase) to in plane (O-phase). These findings provide direct evidence of spin-charge-lattice coupling in La-doped BiFeO₃ thin films. Furthermore, this study opens a new pathway to drive the AFE-FE O-R phase transition and provides a route to study the O/R MPB in these films.

Multi-stimuli manipulation of antiferromagnetic domains assessed by second-harmonic imaging

Among the variety of magnetic textures available in nature, antiferromagnetism is one of the most 'discrete' because of the exact cancellation of its staggered internal magnetization. It is therefore very challenging to probe. However, its insensitivity to external magnetic perturbations, together with the intrinsic sub-picosecond dynamics, make it very appealing for tomorrow's information technologies. Thus, it is essential to understand the microscopic mechanisms governing antiferromagnetic domains to achieve accurate manipulation and control. Using optical second-harmonic generation, a unique and laboratory-available tool, we succeeded in imaging with sub-micrometre resolution both electric and antiferromagnetic orders in the model multiferroic BiFeO₃. We show here that antiferromagnetic domains can be manipulated with low power consumption, using sub-coercive electric fields and sub-picosecond light pulses. Interestingly, we also show that antiferromagnetic and ferroelectric domains can behave independently, thus revealing that magneto-electric coupling can lead to various arrangements of the two orders.

Direct atomic scale determination of magnetic ion partition in a room temperature multiferroic material

The five-layer Aurivillius phase Bi₆Ti_xFe_yMn_zO₁₈ system is a rare example of a single-phase room temperature multiferroic material. To optimise its properties and exploit it for future memory storage applications, it is necessary to understand the origin of the room temperature magnetisation. In this work we use high resolution scanning transmission electron microscopy, EDX and EELS to discover how closely-packed Ti/Mn/Fe cations of similar atomic number are arranged, both within the perfect structure and within defect regions. Direct evidence for partitioning of the magnetic cations (Mn and Fe) to the central three of the five perovskite (PK) layers is presented, which reveals a marked preference for Mn to partition to the central layer. We infer this is most probably due to elastic strain energy considerations. The observed increase (>8%) in magnetic cation content at the central PK layers engenders up to a 90% increase in potential ferromagnetic spin alignments in the central layer and this could be significant in terms of creating pathways to the long-range room temperature magnetic order observed in this distinct and intriguing material system.

Strain and Magnetic Field Induced Spin-Structure Transitions in Multiferroic BiFeO3

The magnetic-field-dependent spin ordering of strained BiFeO₃ films is determined using nuclear resonant scattering and Raman spectroscopy. The critical field required to destroy the cycloidal modulation of the Fe spins is found to be significantly lower than in the bulk, with appealing implications for field-controlled spintronic and magnonic devices.

New modalities of strain-control of ferroelectric thin films

Ferroelectrics, with their spontaneous switchable electric polarization and strong coupling between their electrical, mechanical, thermal, and optical responses, provide functionalities crucial for a diverse range of applications. Over the past decade, there has been significant progress in epitaxial strain engineering of oxide ferroelectric thin films to control and enhance the nature of ferroelectric order, alter ferroelectric susceptibilities, and to create new modes of response which can be harnessed for various applications. This review aims to cover some of the most important discoveries in strain engineering over the past decade and highlight some of the new and emerging approaches for strain control of ferroelectrics. We discuss how these new approaches to strain engineering provide promising routes to control and decouple ferroelectric susceptibilities and create new modes of response not possible in the confines of conventional strain engineering. To conclude, we will provide an overview and prospectus of these new and interesting modalities of strain engineering helping to accelerate their widespread development and implementation in future functional devices.

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.

Multiferroic Heterostructures Integrating Ferroelectric and Magnetic Materials

Multiferroic heterostructures can be synthesized by integrating monolithic ferroelectric and magnetic materials, with interfacial coupling between electric polarization and magnetization, through the exchange of elastic, electric, and magnetic energy. Although the nature of the interfaces remains to be unraveled, such cross coupling can be utilized to manipulate the magnetization (or polarization) with an electric (or magnetic) field, known as a converse (or direct) magnetoelectric effect. It can be exploited to significantly improve the performance of or/and add new functionalities to many existing or emerging devices such as memory devices, tunable microwave devices, sensors, etc. The exciting technological potential, along with the rich physical phenomena at the interface, has sparked intensive research on multiferroic heterostructures for more than a decade. Here, we summarize the most recent progresses in the fundamental principles and potential applications of the interface-based magnetoelectric effect in multiferroic heterostructures, and present our perspectives on some key issues that require further study in order to realize their practical device applications.

Magnetic ordering induced giant optical property change in tetragonal BiFeO3

Magnetic ordering could have significant influence on band structures, spin-dependent transport, and other important properties of materials. Its measurement, especially for the case of antiferromagnetic (AFM) ordering, however, is generally difficult to be achieved. Here we demonstrate the feasibility of magnetic ordering detection using a noncontact and nondestructive optical method. Taking the tetragonal BiFeO₃ (BFO) as an example and combining density functional theory calculations with tight-binding models, we find that when BFO changes from C1-type to G-type AFM phase, the top of valance band shifts from the Z point to Γ point, which makes the original direct band gap become indirect. This can be explained by Slater-Koster parameters using the Harrison approach. The impact of magnetic ordering on band dispersion dramatically changes the optical properties. For the linear ones, the energy shift of the optical band gap could be as large as 0.4 eV. As for the nonlinear ones, the change is even larger. The second-harmonic generation coefficient d₃₃ of G-AFM becomes more than 13 times smaller than that of C1-AFM case. Finally, we propose a practical way to distinguish the two AFM phases of BFO using the optical method, which is of great importance in next-generation information storage technologies.

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.

BiFeO3 epitaxial thin films and devices: past, present and future

The celebrated renaissance of the multiferroics family over the past ten years has also been that of its most paradigmatic member, bismuth ferrite (BiFeO3). Known since the 1960s to be a high temperature antiferromagnet and since the 1970s to be ferroelectric, BiFeO3 only had its bulk ferroic properties clarified in the mid-2000s. It is however the fabrication of BiFeO3 thin films and their integration into epitaxial oxide heterostructures that have fully revealed its extraordinarily broad palette of functionalities. Here we review the first decade of research on BiFeO3 films, restricting ourselves to epitaxial structures. We discuss how thickness and epitaxial strain influence not only the unit cell parameters, but also the crystal structure, illustrated for instance by the discovery of the so-called T-like phase of BiFeO3. We then present its ferroelectric and piezoelectric properties and their evolution near morphotropic phase boundaries. Magnetic properties and their modification by thickness and strain effects, as well as optical parameters, are covered. Finally, we highlight various types of devices based on BiFeO3 in electronics, spintronics, and optics, and provide perspectives for the development of further multifunctional devices for information technology and energy harvesting.

Effects of Interfaces on the Structure and Novel Physical Properties in Epitaxial Multiferroic BiFeO₃ Ultrathin Films

In functional oxide films, different electrical/mechanical boundaries near film surfaces induce rich phase diagrams and exotic phenomena. In this paper, we review some key points which underpin structure, phase transition and related properties in BiFeO₃ ultrathin films. Compared with the bulk counterparts, we survey the recent results of epitaxial BiFeO₃ ultrathin films to illustrate how the atomic structure and phase are markedly influenced by the interface between the film and the substrate, and to emphasize the roles of misfit strain and depolarization field on determining the domain patterns, phase transformation and associated physical properties of BiFeO₃ ultrathin films, such as polarization, piezoelectricity, and magnetism. One of the obvious consequences of the misfit strain on BiFeO₃ ultrathin films is the emergence of a sequence of phase transition from tetragonal to mixed tetragonal & rhombohedral, the rhombohedral, mixed rhombohedral & orthorhombic, and finally orthorhombic phases. Other striking features of this system are the stable domain patterns and the crossover of 71° and 109° domains with different electrical boundary conditions on the film surface, which can be controlled and manipulated through the depolarization field. The external field-sensitive enhancements of properties for BiFeO₃ ultrathin films, including the polarization, magnetism and morphotropic phase boundary-relevant piezoelectric response, offer us deeper insights into the investigations of the emergent properties and phenomena of epitaxial ultrathin films under various mechanical/electrical constraints. Finally, we briefly summarize the recent progress and list open questions for future study on BiFeO₃ ultrathin films.

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.

Orientation-tuning in self-assembled heterostructures induced by a buffer layer

Anisotropic nano-plate structures in self-assembled perovskite-spinel thin films, BiFeO3-NiFe2O4 and BiFeO3-CoFe2O4, which were deposited on (001)c SrRuO3/SrTiO3 and DyScO3 substrates, respectively, have been demonstrated using transmission electron microscopy combined with strain analysis. Unlike the unitary cube-on-cube orientation relationship reported widely, the growth direction of the CoFe2O4 and NiFe2O4 plates was tuned to [011]c while the BiFeO3 matrix kept [001]c in both systems. In particular, a thin stress-sensitive BiFeO3 buffer layer between the spinel nanostructure and the substrate was introduced for providing a complex strain state in both film systems. The novel orientation tuning and the pattern configuration of the heterostructures are mainly attributed to the strain imposed on the films and the anisotropic ledge growth mechanism of spinels.

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.

Effect of strain on voltage-controlled magnetism in BiFeO₃-based heterostructures

Voltage-modulated magnetism in magnetic/BiFeO₃ heterostructures can be driven by a combination of the intrinsic ferroelectric-antiferromagnetic coupling in BiFeO₃ and the antiferromagnetic-ferromagnetic exchange interaction across the heterointerface. However, ferroelectric BiFeO₃ film is also ferroelastic, thus it is possible to generate voltage-induced strain in BiFeO₃ that could be applied onto the magnetic layer across the heterointerface and modulate magnetism through magnetoelastic coupling. Here, we investigated, using phase-field simulations, the role of strain in voltage-controlled magnetism for these BiFeO₃-based heterostructures. It is predicted, under certain condition, coexistence of strain and exchange interaction will result in a pure voltage-driven 180° magnetization reversal in BiFeO₃-based heterostructures.

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.

Heteroepitaxy of tetragonal BiFeO(3) on hexagonal sapphire(0001)

Highly elongated BiFeO3 is epitaxially grown on hexagonal sapphire(0001) substrate within a rather narrow synthesis window. Both X-ray reciprocal space maps and Raman characterizations reveal that it is of true tetragonal symmetry but not the commonly observed MC type monoclinic structure. The tetragonal BiFeO3 film exhibits an island growth mode, with the island edges oriented parallel to the ⟨10-10⟩ and ⟨12-30⟩ directions of the sapphire substrate. With increasing deposition time, a transition from square island to elongated island and then to a continuous film is observed. The metastable tetragonal phase can remain on the substrate without relaxation to the thermally stable rhombohedral phase up to a critical thickness of 450 nm, providing an exciting opportunity for practicable lead-free ferroelectrics. These results facilitate a better understanding of the phase stability of BiFeO3 polymorphs and enrich the knowledge about the heteroepitaxial growth mechanism of functional oxides on symmetry-mismatched substrates.

A facile route for producing single-crystalline epitaxial perovskite oxide thin films

We report how a low vacuum pressure process followed by a few-minute annealing enables epitaxial stabilization, producing high-quality, phase-pure, single-crystalline epitaxial, and misfit dislocation-free BiFeO3(001) thin films on SrTiO3(001) at ∼450 °C less than current routes. These results unambiguously challenge the widely held notion that atomic layer deposition (ALD) is not appropriate for attaining high-quality chemically complex oxide films on perovskite substrates in single-crystalline epitaxial form, demonstrating applicability as an inexpensive, facile, and highly scalable route.

First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides

We present a scheme to construct model potentials, with parameters computed from first principles, for large-scale lattice-dynamical simulations of materials. We mimic the traditional solid-state approach to the investigation of vibrational spectra, i.e., we start from a suitably chosen reference configuration of the compound and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a form of the potential-energy surface is general, trivial to formulate for any material, and physically transparent. Further, such models involve clear-cut approximations, their precision can be improved in a systematic fashion, and their simplicity allows for convenient and practical strategies to compute/fit the potential parameters. We illustrate our scheme with two challenging cases in which the model potential is strongly anharmonic, namely, the ferroic perovskite oxides PbTiO3 and SrTiO3. Studying these compounds allows us to better describe the connection between the so-called effective-Hamiltonian method and ours (which may be seen as an extension of the former), and to show the physical insight and predictive power provided by our approach-e.g., we present new results regarding the factors controlling phase-transition temperatures, novel phase transitions under elastic constraints, an improved treatment of thermal expansion, etc.

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.

Ferroelectric domains in multiferroic BiFeO3 films under epitaxial strains

First-principles calculations are performed to investigate energetic and atomistic characteristics of ferroelectric domains walls (DWs) of BiFeO(3) (BFO) films subject to compressive strain. Significantly lower DW energies than those previously reported, and a different energetic hierarchy between the various DW types, are found for small strains. In all investigated cases (corresponding to ideal angles of 71°, 109°, and 180° formed by the domain polarizations), the DW energy reaches its maximum value for misfit strains that are around the critical strain at which the transition between the R-like and T-like phases occurs in single-domain BFO. Near these strains, several quantities depend strongly on the type of domain wall; such distinct behavior is associated with an elastic difference and a large out-of-plane polarization at the DW in the 180° case. A further increase of the magnitude of the strain leads to (i) a change of hierarchy of the DW energies, (ii) large out-of-plane polarizations inside each up and down domain, and (iii) novel atomic arrangements at the domain walls. Our study can thus initiate a new research direction, namely strain engineering of domain-wall functionalities.

Non-volatile ferroelastic switching of the Verwey transition and resistivity of epitaxial Fe3O4/PMN-PT (011)

A central goal of electronics based on correlated materials or 'Mottronics' is the ability to switch between distinct collective states with a control voltage. Small changes in structure and charge density near a transition can tip the balance between competing phases, leading to dramatic changes in electronic and magnetic properties. In this work, we demonstrate that an electric field induced two-step ferroelastic switching pathway in (011) oriented 0.71Pb(Mg1/3Nb2/3)O3-0.29PbTiO3 (PMN-PT) substrates can be used to tune the Verwey metal-insulator transition in epitaxial Fe3O4 films in a stable and reversible manner. We also observe robust non-volatile resistance switching in Fe3O4 up to room temperature, driven by ferroelastic strain. These results provides a framework for realizing non-volatile and reversible tuning of order parameters coupled to lattice-strain in epitaxial oxide heterostructures over a broad range of temperatures, with potential device applications.

Thickness-dependent polarization of strained BiFeO3 films with constant tetragonality

We measure the ferroelectric polarization of BiFeO3 films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5-7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultrathin films, the energetics of near open circuit electrical boundary conditions, i.e., an unscreened depolarizing field, drive the system through a phase transition from single out-of-plane polarization to nanoscale stripe domains. It gives rise to an average polarization close to zero as measured by the electron microscopy while maintaining the relatively large tetragonal distortion imposed by the nonzero polarization state of each individual domain.

Orthorhombic BiFeO3

A new orthorhombic phase of the multiferroic BiFeO3 has been created via strain engineering by growing it on a NdScO(3)(110)(o) substrate. The tensile-strained orthorhombic BiFeO3 phase is ferroelectric and antiferromagnetic at room temperature. A combination of nonlinear optical second harmonic generation and piezoresponse force microscopy revealed that the ferroelectric polarization in the orthorhombic phase is along the in-plane {110}(pc) directions. In addition, the corresponding rotation of the antiferromagnetic axis in this new phase was observed using x-ray linear dichroism.

Nanoscale phase boundaries: a new twist to novel functionalities

In functional materials, nanoscale phase boundaries exhibit exotic phenomena that are notably absent in their parent phases. Over the past two decades, much of the research into complex oxides (such as cuprate superconductors, CMR manganites and relaxor ferroelectrics) has demonstrated the key role that nanoscale inhomogeneities play in controlling the electronic and/or ionic structure of these materials. One of the key characteristics in such systems is the strong susceptibility to external perturbations, such as magnetic, electric and mechanical fields. A direct consequence of the accommodation of a large number of cationic substitutions in complex oxides is the emergence of a number of physical phenomena from essentially the same crystal framework. Recently, multiferroic behavior, which is characterized by the co-existence and potential coupling of multiple ferroic order parameters, has captured considerable worldwide research interest. The perovskite, BiFeO(3), exhibits robust ferroelectricity coupled with antiferromagnetism at room temperature. A rather unique feature of this material system is its ability to "morph" its ground state when an external mechanical constraint is imposed on it. A particularly striking example is observed when a large (~4 to 5%) compressive strain is imposed on a thin film through the epitaxial constraint from the underlying substrate. Under these conditions, the ground state rhombohedral phase transforms into a tetragonal-like (or a derivative thereof) phase with a rather large unit cell (c/a ratio of ~1.26). When the epitaxial constraint is partially relaxed by increasing the film thickness, this tetragonal-like phase evolves into a "mixed-phase" state, consisting of a nanoscale admixture of the rhombohedral-like phase embedded in the tetragonal-like phase. Such a system gives us a new pathway to explore a variety of mechanical, magnetic and transport phenomena in constrained dimensions. This article reviews our progress to date in this direction and also captures some possible areas of future research. We use the electromechanical response and the magnetic properties as examples to illustrate that its novel functionalities are intrinsically due to the phase boundaries and not the constituent phases. The possible origin of the giant piezoelectric response and enhanced magnetic moment across the boundaries is proposed based on the flexoelectric and flexomagnetic effects.

Atomistic molecular dynamic simulations of multiferroics

A first-principles-based approach is developed to simulate dynamical properties, including complex permittivity and permeability in the GHz-THz range, of multiferroics at finite temperatures. It includes both structural degrees of freedom and magnetic moments as dynamic variables in Newtonian and Landau-Lifshitz-Gilbert (LLG) equations within molecular dynamics, respectively, with the couplings between these variables being incorporated. The use of a damping coefficient and of the fluctuation field in the LLG equations is required to obtain equilibrated magnetic properties at any temperature. No electromagnon is found in the spin-canted structure of BiFeO3. On the other hand, two magnons with very different frequencies are predicted via the use of this method. The smallest-in-frequency magnon corresponds to oscillations of the weak ferromagnetic vector in the basal plane being perpendicular to the polarization while the second magnon corresponds to magnetic dipoles going in and out of this basal plane. The large value of the frequency of this second magnon is caused by static couplings between magnetic dipoles with electric dipoles and oxygen octahedra tiltings.

Revisiting properties of ferroelectric and multiferroic thin films under tensile strain from first principles

First-principles calculations are performed to revisit properties of (001) epitaxial BiFeO(3) (BFO) and PbTiO(3) thin films under tensile strain. While these two films possess different ground states when experiencing no misfit strain, they both exhibit the same, previously unknown phase for tensile strains above ≃5% at T = 0 K. This novel state is of orthorhombic Pmc2(1) symmetry and is macroscopically characterized by a large in-plane polarization coexisting with oxygen octahedra tilting in-phase about the out-of-plane direction. On a microscopic point of view, this Pmc2(1) state exhibits short atomic bonds and zigzag cation displacement patterns, unlike conventional ferroelectric phases and typical domains. Such unusual inhomogeneous patterns originate from the coexistence of polar and antiferroelectric distortions having the same magnitude and lead BFO films to be the first known material for which orbital ordering coexists with a large polarization. Furthermore, this Pmc2(1) state is also found in other perovskite films under tensile strain, which emphasizes its generality.

Strain dependence of polarization and piezoelectric response in epitaxial BiFeO3 thin films

Epitaxial strain has recently emerged as a powerful means to engineer the properties of ferroelectric thin films, for instance to enhance the ferroelectric Curie temperature (T(C)) in BaTiO(3). However, in multiferroic BiFeO(3) thin films an unanticipated strain-driven decrease of T(C) was reported and ascribed to the peculiar competition between polar and antiferrodistortive instabilities. Here, we report a systematic characterization of the room-temperature ferroelectric and piezoelectric properties for strain levels ranging between -2.5% and +1%. We find that polarization and the piezoelectric coefficient increase by about 20% and 250%, respectively, in this strain range. These trends are well reproduced by first-principles-based techniques.

Multiferroic phase transition near room temperature in BiFeO3 films

In multiferroic BiFeO(3) thin films grown on highly mismatched LaAlO(3) substrates, we reveal the coexistence of two differently distorted polymorphs that leads to striking features in the temperature dependence of the structural and multiferroic properties. Notably, the highly distorted phase quasiconcomitantly presents an abrupt structural change, transforms from a standard to a nonconventional ferroelectric, and transitions from antiferromagnetic to paramagnetic at 360±20 K. These coupled ferroic transitions just above room temperature hold promises of giant piezoelectric, magnetoelectric, and piezomagnetic responses, with potential in many applications fields.

Linear–quadratic order parameter coupling and multiferroic phase transitions

The coupling between order parameters in systems with several instabilities has been analysed within Landau theory. The dominant term considered in this paper is linear in one order parameter and quadratic in the second order parameter ~QP²; other coupling terms have been treated previously. Typical examples for Q are proper or pseudo-proper ferroelastic instabilities, while P might be octahedral tilting in a perovskite, (anti-)ferromagnetic ordering or (anti-)ferroelectric soft modes. Coupling of this type is common in fluorites, Verwey transitions, Jahn-Teller systems, pnictide superconductors, etc. Analytical solutions and characteristic phase diagrams of the stable configurations are compiled. The coupling can lead to stepwise phase transitions even when the uncoupled systems would show continuous transitions. Mixed phases are common, so that many 'intermediate phases' described in the literature may be the result of this linear-quadratic coupling.

Prediction of the magnetotoroidic effect from atomistic simulations

An effective Hamiltonian technique is used to investigate the effect of applying curled electric fields on physical properties of stress-free BiFeO(3) dots being under open-circuit electrical boundary conditions. It is discovered that such fields can lead to a control of not only the magnitude but also the direction of the magnetization. Such control originates from the field-induced transformation or switching of electrical vortices and their couplings with oxygen octahedral tilts and magnetic dipoles. This control involves striking intermediate states and constitutes a novel phenomenon that can be termed a "magnetotoroidic" effect.

Phase transitions in epitaxial (-110) BiFeO3 films from first principles

The effect of misfit strain on properties of epitaxial BiFeO3 films that are grown along the pseudocubic [110] direction, rather than along the usual [001] direction, is predicted from density-functional theory. These films adopt the monoclinic Cc space group for compressive misfit strains smaller in magnitude than ≃1.6% and for any investigated tensile strain. In this Cc phase, both polarization and the axis about which antiphase oxygen octahedra tilt rotate within the epitaxial plane as the strain varies. Surprisingly and unlike in (001) films, for compressive strain larger in magnitude than ≃1.6%, the polarization vanishes and two orthorhombic phases of Pnma and P2(1)2(1)2(1) symmetry successively emerge via strain-induced transitions. The Pnma-to-P2(1)2(1)2(1) transition is a rare example of a so-called pure gyrotropic phase transition, and the P2(1)2(1)2(1) phase exhibits original interpenetrated arrays of ferroelectric vortices and antivortices.

BiFeO3 films under tensile epitaxial strain from first principles

Density-functional calculations are performed to predict structural and magnetic properties of (001) BiFeO(3) films under tensile epitaxial strain. These films remain monoclinic (Cc space group) for misfit strains between 0% and ≈8%, with the polarization, tilt axis and magnetization all rotating when varying the strain. At a tensile strain ≈8%, these films undergo a first-order phase transition towards an orthorhombic phase (Ima2 space group). In this novel phase, the polarization and tilt axis lie in the epitaxial plane, while the magnetization is along the out-of-plane direction and the direction of the antiferromagnetic vector is unchanged by the phase transition. An unexpected additional degree of freedom, namely, an antiphase arrangement of Bi atoms, is also found for all tensile strains.

Epitaxial Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions

The temperature-versus-misfit-strain phase diagram of Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions is simulated via the use of an effective Hamiltonian. Two novel phases, both exhibiting dipolar nanodomains and oxygen octahedral tilting, are discovered. The interplay between dipolar, antiferrodistortive, alloying, and strain degrees of freedom induces several striking features in these two phases, such as the chemical pinning of domain walls, the enhancement of oxygen octahedral tilting near the domain walls, and the existence of dipolar waves and cylindrical dipolar chiral bubbles.