Evidence of the Monopolar-Dipolar Crossover Regime: A Multiscale Study of Ferroelastic Domains by In Situ Microscopy Techniques

The elastic interaction between kinks (and antikinks) within domain walls plays a pivotal role in shaping the domain structure, and their dynamics. In bulk materials, kinks interact as elastic monopoles, dependent on the distance between walls (d-1) and typically characterized by a rigid and straight domain configuration. In this work the evolution of the domain structure is investigated, as the sample size decreases, by the means of in situ heating microscopy techniques on free-standing samples. As the sample size decreases, a significant transformation is observed: domain walls exhibit pronounced curvature, accompanied by an increase in both domain wall and junction density. This transformation is attributed to the pronounced influence of kinks, inducing sample warping, where "dipole-dipole" interactions are dominant (d-2). Moreover, a critical thickness range that delineates a crossover between the monopolar and dipolar regimens is experimentally identified and corroborated by atomic simulations. These findings are relevant for in situ TEM studies and for the development of novel devices based on free-standing ferroic thin films and nanomaterials.

Direct Visualization of Distorted Twin Boundaries in Ce-Doped GdFeO3

Utilizing advanced transmission electron microscopy (TEM), the structure at the (110)-type twin boundary (TB) of Ce-doped GdFeO₃ (C-GFO) has been investigated with picometer precision. Such a TB is promising to generate local ferroelectricity within a paraelectric system, while precise knowledge about its structure is still largely missing. In this work, a direct measurement of the cation off-centering with respect to the neighboring oxygen is enabled by integrated differential phase contrast (iDPC) imaging, and up to 30 pm Gd off-centering is highly localized at the TB. Further electron energy loss spectroscopy (EELS) analysis demonstrates a slight accumulation of oxygen vacancies at the TB, a self-balanced behavior of Ce at the Gd sites, and a mixed occupation of Fe²⁺ and Fe³⁺ at the Fe sites. Our results provide an informative picture with atomic details at the TB of C-GFO, which is indispensable to further push the potential of grain boundary engineering.

Effect of Acoustic Oscillations on Non-Equilibrium State of Magnetic Domain Structure in Cubic Ni2MnGa Single Crystal

Magnetic hysteresis is a manifestation of non-equilibrium state of magnetic domain walls trapped in local energy minima. Using two types of experiments we show that, after application of a magnetic field to a ferromagnet, acoustic oscillations excited in the latter can "equilibrate" metastable magnetic domain structure by triggering the motion of domain walls into more stable configurations. Single crystals of archetypal Ni₂MnGa magnetic shape memory alloy in the cubic phase were used in the experiments. The magnetomechanical absorption of ultrasound versus strain amplitude was studied after step-like changes of a polarizing magnetic field. One-time hysteresis was observed in strain amplitude dependences of magnetomechanical internal friction after step-like variations of a polarizing field. We distinguish two ingredients of the strain amplitude hysteresis that are found in the ranges of linear and non-linear internal friction and show qualitatively different behavior for increasing and decreasing applied polarizing fields. The uncovered effect is interpreted in terms of three canonical magnetomechanical internal friction terms (microeddy, macroeddy and hysteretic) and attributed to "triggering" by acoustic oscillations of the irreversible motion of domain walls trapped in the metastable states. To confirm the suggested interpretation we determine the coercive field of magnetization hysteresis through the measurements of the reversible Villari effect. We show that the width of the hysteresis loops decreases when acoustic oscillations in the non-linear range of domain wall motion are excited in the crystal. The observed "equilibration" of the magnetic domain structure by acoustic oscillations is attributed to the periodic stress anisotropy field induced by oscillatory mechanical stress.

Dynamic domain boundaries: chemical dopants carried by moving twin walls

Domain walls and specifically ferroelastic twin boundaries are depositaries and fast diffusion pathways for chemical dopants and intrinsic lattice defects. Ferroelastic domain patterns act as templates for chemical structures where the walls are the device and not the bulk. Several examples of such engineered domain boundaries are given. Moving twin boundaries are shown to carry with them the dopants, although the activation of this mechanism depends sensitively on the applied external force. If the force is too weak, the walls remain pinned while too strong forces break the walls free of the dopants and move them independently. Several experimental methods and approaches are discussed.

Partially disordered pyrochlore: time-temperature dependence of recrystallization and dehydration

The comparison of the evolution of the mechanical properties (elastic modulus and hardness) after step-wise thermal annealing for 1 and 16 h up to 900 K of a radiation-damaged pyrochlore (∼35% amorphous fraction; 1.8 wt% ThO2) provides insights to the time-temperature dependence of the recrystallization behavior. Especially the elastic modulus, directly related to interatomic bonding, enables the correlation with the amount of amorphous fraction. From this a pronounced effect of the annealing time on percolation behavior could be deduced. Evolved gas analysis indicate dehydration in the course of the structural reorganization process.

The Third Dimension of Ferroelectric Domain Walls

Ferroelectric domain walls are quasi-2D systems that show great promise for the development of nonvolatile memory, memristor technology, and electronic components with ultrasmall feature size. Electric fields, for example, can change the domain wall orientation relative to the spontaneous polarization and switch between resistive and conductive states, controlling the electrical current. Being embedded in a 3D material, however, the domain walls are not perfectly flat and can form networks, which leads to complex physical structures. In this work, the importance of the nanoscale structure for the emergent transport properties is demonstrated, studying electronic conduction in the 3D network of neutral and charged domain walls in ErMnO₃ . By combining tomographic microscopy techniques and finite element modeling, the contribution of domain walls within the bulk is clarified and the significance of curvature effects for the local conduction is shown down to the nanoscale. The findings provide insights into the propagation of electrical currents in domain wall networks, reveal additional degrees of freedom for their control, and provide quantitative guidelines for the design of domain-wall-based technology.

Domain Wall Dynamics in a Ferroelastic Spin Crossover Complex with Giant Magnetoelectric Coupling

Pinned and mobile ferroelastic domain walls are detected in response to mechanical stress in a Mn³⁺ complex with two-step thermal switching between the spin triplet and spin quintet forms. Single-crystal X-ray diffraction and resonant ultrasound spectroscopy on [Mn^III(3,5-diCl-sal₂(323))]BPh₄ reveal three distinct symmetry-breaking phase transitions in the polar space group series Cc → Pc → P1 → P1_(1/2). The transition mechanisms involve coupling between structural and spin state order parameters, and the three transitions are Landau tricritical, first order, and first order, respectively. The two first-order phase transitions also show changes in magnetic properties and spin state ordering in the Jahn–Teller-active Mn³⁺ complex. On the basis of the change in symmetry from that of the parent structure, Cc, the triclinic phases are also ferroelastic, which has been confirmed by resonant ultrasound spectroscopy. Measurements of magnetoelectric coupling revealed significant changes in electric polarization at both the Pc → P1 and P1 → P1_(1/2) transitions, with opposite signs. All these phases are polar, while P1 is also chiral. Remanent electric polarization was detected when applying a pulsed magnetic field of 60 T in the P1→ P1_(1/2) region of bistability at 90 K. Thus, we showcase here a rare example of multifunctionality in a spin crossover material where the strain and polarization tensors and structural and spin state order parameters are strongly coupled.

Giant conductivity of mobile non-oxide domain walls

Atomically sharp domain walls in ferroelectrics are considered as an ideal platform to realize easy-to-reconfigure nanoelectronic building blocks, created, manipulated and erased by external fields. However, conductive domain walls have been exclusively observed in oxides, where domain wall mobility and conductivity is largely influenced by stoichiometry and defects. Here, we report on giant conductivity of domain walls in the non-oxide ferroelectric GaV₄S₈. We observe conductive domain walls forming in zig-zagging structures, that are composed of head-to-head and tail-to-tail domain wall segments alternating on the nanoscale. Remarkably, both types of segments possess high conductivity, unimaginable in oxide ferroelectrics. These effectively 2D domain walls, dominating the 3D conductance, can be mobilized by magnetic fields, triggering abrupt conductance changes as large as eight orders of magnitude. These unique properties demonstrate that non-oxide ferroelectrics can be the source of novel phenomena beyond the realm of oxide electronics.

Interconversion of multiferroic domains and domain walls

Systems with long-range order like ferromagnetism or ferroelectricity exhibit uniform, yet differently oriented three-dimensional regions called domains that are separated by two-dimensional topological defects termed domain walls. A change of the ordered state across a domain wall can lead to local non-bulk physical properties such as enhanced conductance or the promotion of unusual phases. Although highly desirable, controlled transfer of these properties between the bulk and the spatially confined walls is usually not possible. Here, we demonstrate this crossover by confining multiferroic Dy_0.7Tb_0.3FeO₃ domains into multiferroic domain walls at an identified location within a non-multiferroic environment. This process is fully reversible; an applied magnetic or electric field controls the transformation. Aside from expanding the concept of multiferroic order, such interconversion can be key to addressing antiferromagnetic domain structures and topological singularities.

Domains and domain walls can have distinctively different physical properties. Here, the authors show how to transfer domains into domain walls and vice versa while maintaining their physical properties. Thereby the authors tune a multiferroic state between three and two dimensions.

Driving magnetic domains at the nanoscale by interfacial strain-induced proximity

We investigate the local nanoscale changes of the magnetic anisotropy of a Ni film subject to an inverse magnetostrictive effect by proximity to a V2O3 layer. Using temperature-dependent photoemission electron microscopy (PEEM) combined with X-ray magnetic circular dichroism (XMCD), direct images of the Ni spin alignment across the first-order structural phase transition (SPT) of V2O3 were obtained. We find an abrupt temperature-driven reorientation of the Ni magnetic domains across the SPT, which is associated with a large increase of the coercive field. Moreover, angular dependent ferromagnetic resonance (FMR) shows a remarkable change in the magnetic anisotropy of the Ni film across the SPT of V2O3. Micromagnetic simulations based on these results are in quantitative agreement with the PEEM data. Direct measurements of the lateral correlation length of the Ni domains from XMCD images show an increase of almost one order of magnitude at the SPT compared to room temperature, as well as a broad spatial distribution of the local transition temperatures, thus corroborating the phase coexistence of Ni anisotropies caused by the V2O3 SPT. We show that the rearrangement of the Ni domains is due to strain induced by the oxide layers' structural domains across the SPT. Our results illustrate the use of alternative hybrid systems to manipulate magnetic domains at the nanoscale, which allows for engineering of coercive fields for novel data storage architectures.

Order-disorder, ferroelasticity and mobility of domain walls in multiferroic Cu-Cl boracite

Domain walls in Cu-Cl boracite develop as a consequence of an improper ferroelastic, improper ferroelectric transition, and have attracted close interest because some are conductive and all can be mechanically written and repositioned by application of an electric field. The phase transition and its associated dynamical properties have been analysed here from the perspective of strain and elasticity. Determination of spontaneous strains from published lattice parameter data has allowed the equilibrium long-range order parameter for F [Formula: see text]3c → Pca2₁ to be modelled simply as being close to the order-disorder limit. High acoustic loss in the cubic phase, revealed by resonant ultrasound spectroscopy, is consistent with the presence of dynamical microdomains of the orthorhombic structure with relaxation times in the vicinity of ∼10^-5-10^-6 s. Low acoustic loss in the stability field of the orthorhombic structure signifies, on the other hand, that ferroelastic twin walls which develop as a consequence of the order-disorder process are immobile on this time scale. A Debye loss peak accompanied by ∼1% elastic stiffening at ∼40 K is indicative of some freezing of defects which couple with strain or of some more intrinsic freezing process. The activation energy of ⩾∼0.01-0.02 eV implies a mechanism which could involve strain relaxation clouds around local ferroelectric dipoles or freezing of polarons that determine the conductivity of twin walls.

Layer number dependent ferroelasticity in 2D Ruddlesden-Popper organic-inorganic hybrid perovskites

Ferroelasticity represents material domains possessing spontaneous strain that can be switched by external stress. Three-dimensional perovskites like methylammonium lead iodide are determined to be ferroelastic. Layered perovskites have been applied in optoelectronic devices with outstanding performance. However, the understanding of lattice strain and ferroelasticity in layered perovskites is still lacking. Here, using the in-situ observation of switching domains in layered perovskite single crystals under external strain, we discover the evidence of ferroelasticity in layered perovskites with layer number more than one, while the perovskites with single octahedra layer do not show ferroelasticity. Density functional theory calculation shows that ferroelasticity in layered perovskites originates from the distortion of inorganic octahedra resulting from the rotation of aspherical methylammonium cations. The absence of methylammonium cations in single layer perovskite accounts for the lack of ferroelasticity. These ferroelastic domains do not induce non-radiative recombination or reduce the photoluminescence quantum yield.

Avalanche criticality during ferroelectric/ferroelastic switching

Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ contains complex domains with needles and junction patterns, while BaTiO₃ has parallel straight domains. Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field.

While classical approaches rely on the study of individual ferroelectric domain wall movement on long time scales, the authors consider collective movements of domain walls during short time scales, characterized by discrete jumps, as indicators of avalanches on a broad range of scales.

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.

Comportamiento de las Paredes de Dominio Ferroeléctricas en una Nanoesfera de Titanato de Plomo

El objetivo del presente trabajo fue estudiar el comportamiento de las paredes de dominio ferroeléctricas en una nanoesfera de titanato de plomo bajo diferentes condiciones térmicas, eléctricas y mecánicas. Para ello se ha hecho uso de la teoría fenomenológica de Ginzburg-Landau y para obtener el estado de equilibrio se utilizaron principios variacionales; las ecuaciones que aparecen en el desarrollo se resolvieron analíticamente. Los resultados obtenidos proveen un perfil de la polarización dentro de las paredes de dominio 180° de la nanoesfera de titanato de plomo, así como el espesor de dicha pared en función de la temperatura y para distintas condiciones de la nanoesfera. Se observa que, con el aumento de la temperatura, el perfil de la polarización se reduce y el espesor de la pared crece al acercarse a cierta temperatura; todo lo cual permitiría sintonizar la temperatura de transición ferroeléctrica mediante el control del tamaño de la nanoestructura, de la presencia de cargas libres y de la aplicación de esfuerzos mecánicos.

A Lattice Litany for Transition Metal Oxides

In this tribute to K Alex Müller, I describe how his early insights have influenced future decades of research on perovskite ferroelectrics and more broadly transition metal oxides (TMOs) and related quantum materials. I use his influence on my own research journey to discuss impacts in three areas: structural phase transitions, precursor structure, and quantum paraelectricity. I emphasize materials functionality in ground, metastable, and excited states arising from competitions among lattice, charge, and spin degrees of freedom, which results in highly tunable landscapes and complex networks of multiscale configurations controlling macroscopic functions. I discuss competitions between short- and long-range forces as particularly important in TMOs (and related materials classes) because of their localized and directional metal orbitals and the polarizable oxygen ions. I emphasize crucial consequences of elasticity and metal–oxygen charge transfer.

Enhancement of polar nature of domain boundaries in ferroelastic Pb3(PO4)2by doping divalent-metal ions

The effect of doping metal ions in ferroelastic Pb3(PO4)2(PPO) on the polar nature of domain boundaries (DBs) was investigated using a second harmonic generation (SHG) microscope. It has been already reported that (DBs) of non-doped PPO is SH active and polar. The present study reveals that DBs of Ca-doped and Mg-doped PPO show greatly enhanced SH activity. This indicates that doping by metal ions enhances the polar nature of the DBs of PPO. This is important for future applications of DB nanotechnology. The enhancement of SH intensity is explained by a larger displacement of Ca2+and Mg2+ions in DBs due to smaller ionic radii. Analyses of the SH anisotropy experiments reveal that the symmetry-adaptedW-wall belongs to monoclinicmand the non-adaptedW'-wall to monoclinic 2. Both point groups are classified as the polar classes, which coincides with the case of pure PPO.

Optical studies of ferroelectric and ferroelastic domain walls

Recent studies carried out with atomic force microscopy or high-resolution transmission electron microscopy reveal that ferroic domain walls can exhibit different physical properties than the bulk of the domains, such as enhanced conductivity in insulators, or polar properties in non-polar materials. In this review we show that optical techniques, in spite of the diffraction limit, also provide key insights into the structure and physical properties of ferroelectric and ferroelastic domain walls. We give an overview of the uses, specificities and limits of these techniques, and emphasize the properties of the domain walls that they can probe. We then highlight some open questions of the physics of domain walls that could benefit from their use.

Polaronic States and Superconductivity in WO3-x

Superconducting domain boundaries were found in WO3-x and doped WO3. The charge carriers in WO3-type materials were identified by Schirmer and Salje as bipolarons. Several previous attempts to determine the electronic properties of polarons in WO3 failed until Bousque et al. (2020) reported a full first principle calculation of free polarons in WO3. They confirmed the model of Schirmer and Salje that each single polaron is centred around one tungsten position with surplus charges smeared over the adjacent eight tungsten positions. Small additional charges are distributed further apart. Further calculations to clarify the coupling mechanism between polaron to form bipolarons are not yet available. These calculations would help to identify the carrier distribution in Magneli clusters, which were shown recently to contain high carrier concentrations and may indicate totally localized superconductivity in non-percolating clusters.

Imaging and quantification of charged domain walls in BiFeO3

Charged domain walls in ferroelectrics hold great promise for the design of novel electronic devices due to their enhanced local conductivity. In fact, charged domain walls show unique properties including the possibility of being created, moved and erased by an applied voltage. Here, we demonstrate that the charged domain walls are constituted by a core region where most of the screening charge is localized and such charge accumulation is responsible for their enhanced conductivity. In particular, the link between the local structural distortions and charge screening phenomena in 109° tail-to-tail domain walls of BiFeO3 is elucidated by a series of multiscale analysis performed by means of scanning probe techniques, including conductive atomic force microscopy (cAFM) and atomic resolution differential phase contrast scanning transmission electron microscopy (DPC-STEM). The results prove that an accumulation of oxygen vacancies occurs at the tail-to-tail domain walls as the leading charge screening process. This work constitutes a new insight in understanding the behavior of such complex systems and lays down the fundaments for their implementation into novel nanoelectronic devices.

Ferroelectric switching in ferroelastic materials with rough surfaces

Electric switching of non-polar bulk crystals is shown to occur when domain walls are polar in ferroelastic materials and when rough surfaces with steps on an atomic scale promote domain switching. All domains emerging from surface nuclei possess polar domain walls. The progression of domains is then driven by the interaction of the electric field with the polarity of domain boundaries. In contrast, smooth surfaces with higher activation barriers prohibit effective domain nucleation. We demonstrate the existence of an electrically driven ferroelectric hysteresis loop in a non-ferroelectric, ferroelastic bulk material.

Polaronic Emergent Phases in Manganite-based Heterostructures

Transition metal functional oxides, e.g., perovskite manganites, with strong electron, spin and lattice correlations, are well-known for different phase transitions and field-induced colossal effects at the phase transition. Recently, the interfaces between dissimilar perovskites were shown to be a promising concept for the search of emerging phases with novel functionalities. We demonstrate that the properties of manganite films are effectively controlled by low dimensional emerging phases at intrinsic and extrinsic interfaces and appeared as a result of symmetry breaking. The examples include correlated Jahn–Teller polarons in the phase-separated (La1−yPry)0.7Ca0.3MnO3, electron-rich Jahn–Teller-distorted surface or “dead” layer in La0.7Sr0.3MnO3, electric-field-induced healing of “dead” layer as an origin of resistance switching effect, and high-TC ferromagnetic emerging phase at the SrMnO3/LaMnO3 interface in superlattices. These 2D polaronic phases with short-range electron, spin, and lattice reconstructions could be extremely sensitive to external fields, thus, providing a rational explanation of colossal effects in perovskite manganites.

Ferroelasticity, anelasticity and magnetoelastic relaxation in Co-doped iron pnictide: Ba(Fe0.957Co0.043)2As2

The hypothesis that strain has a permeating influence on ferroelastic, magnetic and superconducting transitions in 122 iron pnictides has been tested by investigating variations of the elastic and anelastic properties of a single crystal of Ba(Fe_0.957Co_0.043)₂As₂ by resonant ultrasound spectroscopy as a function of temperature and externally applied magnetic field. Non-linear softening and stiffening of C ₆₆ in the stability fields of both the tetragonal and orthorhombic structures has been found to conform quantitatively to the Landau expansion for a pseudoproper ferroelastic transition which is second order in character. The only exception is that the transition occurs at a temperature (T _S  ≈  69 K) ~10 K above the temperature at which C ₆₆ would extrapolate to zero ([Formula: see text]  ≈  59 K). An absence of anomalies associated with antiferromagnetic ordering below T _N  ≈  60 K implies that coupling of the magnetic order parameter with shear strain is weak. It is concluded that linear-quadratic coupling between the structural/electronic and antiferromagnetic order parameters is suppressed due to the effects of local heterogeneous strain fields arising from the substitution of Fe by Co. An acoustic loss peak at ~50-55 K is attributed to the influence of mobile ferroelastic twin walls that become pinned by a thermally activated process involving polaronic defects. Softening of C ₆₆ by up to ~6% below the normal-superconducting transition at T _c  ≈  13 K demonstrates an effective coupling of the shear strain with the order parameter for the superconducting transition which arises indirectly as a consequence of unfavourable coupling of the superconducting order parameter with the ferroelastic order parameter. Ba(Fe_0.957Co_0.043)₂As₂ is representative of 122 pnictides as forming a class of multiferroic superconductors in which elastic strain relaxations underpin almost all aspects of coupling between the structural, magnetic and superconducting order parameters and of dynamic properties of the transformation microstructures they contain.

Layer-by-Layer Resistive Switching: Multistate Functionality due to Electric-Field-Induced Healing of Dead Layers

Materials exhibiting reversible resistive switching in electrical fields are highly demanded for functional elements in oxide electronics. In particular, multilevel switching effects allow for advanced applications like neuromorphic circuits. Here, we report a structurally driven switching mechanism involving the so-called "dead" layers of perovskite manganite surfaces. Forming a tunnel barrier whose thickness can be changed in monolayer steps by electrical fields, the switching effect exhibits well-defined and robust resistive states.

Temperature Chaos, Memory Effect, and Domain Fluctuations in the Spiral Antiferromagnet Dy

The spiral antiferromagnetic phase of polycrystalline dysprosium between 140 K and the Néel temperature at 178 K and its domain wall (DW) dynamics were investigated using high-resolution ultrasonic spectroscopy. Two kinetic processes of quasi-static DW motion occur under non-isothermal and isothermal conditions. A “fast” process is proportional to the rate of the temperature change and results in a new category of anelastic phenomena: magnetic transient ultrasonic internal friction (IF). This IF, related to fast moving magnetic DWs, decays rapidly after interruptions of cooling/heating cycles. A second, “slow” kinetic process is seen as logarithmic IF relaxation under isothermal conditions. This second process is glass-like and results in memory and temperature chaos effects. Low-frequency thermal fluctuations of DWs, previously detected by X-ray photon correlation spectroscopy, are related to critical fluctuations with Brownian motion-like dynamics of DWs.

Observation of Uncompensated Bound Charges at Improper Ferroelectric Domain Walls

Low-temperature electrostatic force microscopy (EFM) is used to probe unconventional domain walls in the improper ferroelectric semiconductor Er_0.99Ca_0.01MnO₃ down to cryogenic temperatures. The low-temperature EFM maps reveal pronounced electric far fields generated by partially uncompensated domain-wall bound charges. Positively and negatively charged walls display qualitatively different fields as a function of temperature, which we explain based on different screening mechanisms and the corresponding relaxation time of the mobile carriers. Our results demonstrate domain walls in improper ferroelectrics as a unique example of natural interfaces that are stable against the emergence of electrically uncompensated bound charges. The outstanding robustness of improper ferroelectric domain walls in conjunction with their electronic versatility brings us an important step closer to the development of durable and ultrasmall electronic components for next-generation nanotechnology.

Advances in magnetoelectric multiferroics

The manipulation of magnetic properties by an electric field in magnetoelectric multiferroic materials has driven significant research activity, with the goal of realizing their transformative technological potential. Here, we review progress in the fundamental understanding and design of new multiferroic materials, advances in characterization and modelling tools to describe them, and the exploration of devices and applications. Focusing on the translation of the many scientific breakthroughs into technological innovations, we identify the key open questions in the field where targeted research activities could have maximum impact in transitioning scientific discoveries into real applications.

Avalanche mixing and the simultaneous collapse of two media under uniaxial stress

Avalanches in coal and sandstone samples under common uniaxial stress serve as a model for mixing of avalanche exponents in ceramics, multiferroics, and alloys. The two media are sandwiched together and subjected to common uniaxial stress using high- and low-stress compression. Each medium collapses individually through avalanches that often coincide with secondary avalanches into the other medium. The total avalanche time sequence allows a detailed investigation of the mixing by superposition and delayed coincidence. Correlations can be described by an inter-media Båth's law.

Frequency-dependent decoupling of domain-wall motion and lattice strain in bismuth ferrite

Dynamics of domain walls are among the main features that control strain mechanisms in ferroic materials. Here, we demonstrate that the domain-wall-controlled piezoelectric behaviour in multiferroic BiFeO₃ is distinct from that reported in classical ferroelectrics. In situ X-ray diffraction was used to separate the electric-field-induced lattice strain and strain due to displacements of non-180° domain walls in polycrystalline BiFeO₃ over a wide frequency range. These piezoelectric strain mechanisms have opposing trends as a function of frequency. The lattice strain increases with increasing frequency, showing negative piezoelectric phase angle (i.e., strain leads the electric field), an unusual feature so far demonstrated only in the total macroscopic piezoelectric response. Domain-wall motion exhibits the opposite behaviour, it decreases in magnitude with increasing frequency, showing more common positive piezoelectric phase angle (i.e., strain lags behind the electric field). Charge redistribution at conducting domain walls, oriented differently in different grain families, is demonstrated to be the cause.

Conductive domain walls of ferroelectric materials are considered for device applications demanding a fundamental understanding of their dynamics. Here, frequency-dependent decoupling of strains upon electric field cycling in BiFeO₃ is demonstrated to arise from conductive domain walls.

Electrical half-wave rectification at ferroelectric domain walls

Domain walls in ferroelectric semiconductors show promise as multifunctional two-dimensional elements for next-generation nanotechnology. Electric fields, for example, can control the direct-current resistance and reversibly switch between insulating and conductive domain-wall states, enabling elementary electronic devices such as gates and transistors. To facilitate electrical signal processing and transformation at the domain-wall level, however, an expansion into the realm of alternating-current technology is required. Here, we demonstrate diode-like alternating-to-direct current conversion based on neutral ferroelectric domain walls in ErMnO₃. By combining scanning probe and dielectric spectroscopy, we show that the rectification occurs at the tip-wall contact for frequencies at which the walls are effectively pinned. Using density functional theory, we attribute the responsible transport behaviour at the neutral walls to an accumulation of oxygen defects. The practical frequency regime and magnitude of the direct current output are controlled by the bulk conductivity, establishing electrode-wall junctions as versatile atomic-scale diodes.

Nearly Diffraction-Free Nonlinear Imaging of Irregularly Distributed Ferroelectric Domains

Second-harmonic generation is used experimentally for the nonlinear imaging of two-dimensional irregular domain structures. Analytical solutions and simulation results for the Fresnel distribution of domain walls are obtained. The results show that the domain wall plays an important role in the imaging process and the corresponding diffraction effect is greatly suppressed (we call it a nearly diffraction-free effect), thus providing a simple way to realize high-resolution imaging for ferroelectric domains.

Raman signatures of ferroic domain walls captured by principal component analysis

Ferroic domain walls are currently investigated by several state-of-the art techniques in order to get a better understanding of their distinct, functional properties. Here, principal component analysis (PCA) of Raman maps is used to study ferroelectric domain walls (DWs) in LiNbO₃ and ferroelastic DWs in NdGaO₃. It is shown that PCA allows us to quickly and reliably identify small Raman peak variations at ferroelectric DWs and that the value of a peak shift can be deduced-accurately and without a priori-from a first order Taylor expansion of the spectra. The ability of PCA to separate the contribution of ferroelastic domains and DWs to Raman spectra is emphasized. More generally, our results provide a novel route for the statistical analysis of any property mapped across a DW.

Re-entrant spin glass transitions: new insights from acoustic absorption by domain walls

Re-entrant spin glass (RSG) transitions in Ni-Mn and Au-Fe have been reassessed by acoustic measurements of the magneto-mechanical damping by domain walls. Stress-induced non-thermally activated domain wall dynamics is progressively replaced by an intense thermally activated relaxational response when the temperature approaches the RSG freezing point. A “frozen” state with negligible motion of domain walls on atomic and mesoscopic scales occurs in the RSG. We propose that RSG freezing has its origin in intrinsic properties of domain walls.

Statistics of twinning in strained ferroelastics

In this review, we show that the evolution of the microstructure and kinetics of ferroelastic crystals under external shear can be explored by computer simulations of 2D model materials. We find that the nucleation and propagation of twin boundaries in ferroelastics depend sensitively on temperature. In the plastic regime, the evolution of the ferroelastic microstructure under strain deformation maintains a stick-and-slip mechanism in all temperature regimes, whereas the dynamic behavior changes dramatically from power-law statistics at low temperature to a Kohlrausch law at intermediate temperature, and then to a Vogel-Fulcher law at high temperature. In the yield regime, the distribution of jerk energies follows power-law statistics in all temperature regimes for a large range of strain rates. The non-spanning avalanches in the yield regime follow a parabolic temporal profile. The changes of twin pattern and twin boundaries density represent an important step towards domain boundary engineering.

Large and accessible conductivity of charged domain walls in lithium niobate

Ferroelectric domain walls are interfaces between areas of a material that exhibits different directions of spontaneous polarization. The properties of domain walls can be very different from those of the undisturbed material. Metallic-like conductivity of charged domain walls (CDWs) in nominally insulating ferroelectrics was predicted in 1973 and detected recently. This important effect is still in its infancy: The electric currents are still smaller than expected, the access to the conductivity at CDWs is hampered by contact barriers, and stability is low because of sophisticated domain structures or proximity of the Curie point. Here, we report on large, accessible, and stable conductivity at CDWs in lithium niobate (LN) crystals - a vital material for photonics. Our results mark a breakthrough: Increase of conductivity at CDWs by more than 13 orders of magnitude compared to that of the bulk, access to the effect via ohmic and diode-like contacts, and high stability for temperatures T ≤ 70 °C are demonstrated. A promising and now realistic prospect is to combine CDW functionalities with linear and nonlinear optical phenomena. Our findings allow new generations of adaptive-optical elements, of electrically controlled integrated-optical chips for quantum photonics, and of advanced LN-semiconductor hybrid optoelectronic devices.

Resonant electron tunnelling assisted by charged domain walls in multiferroic tunnel junctions

The peculiar features of domain walls observed in ferroelectrics make them promising active elements for next-generation non-volatile memories, logic gates and energy-harvesting devices. Although extensive research activity has been devoted recently to making full use of this technological potential, concrete realizations of working nanodevices exploiting these functional properties are yet to be demonstrated. Here, we fabricate a multiferroic tunnel junction based on ferromagnetic La_0.7Sr_0.3MnO₃ electrodes separated by an ultrathin ferroelectric BaTiO₃ tunnel barrier, where a head-to-head domain wall is constrained. An electron gas stabilized by oxygen vacancies is confined within the domain wall, displaying discrete quantum-well energy levels. These states assist resonant electron tunnelling processes across the barrier, leading to strong quantum oscillations of the electrical conductance.

Non-Ising and chiral ferroelectric domain walls revealed by nonlinear optical microscopy

The properties of ferroelectric domain walls can significantly differ from those of their parent material. Elucidating their internal structure is essential for the design of advanced devices exploiting nanoscale ferroicity and such localized functional properties. Here, we probe the internal structure of 180° ferroelectric domain walls in lead zirconate titanate (PZT) thin films and lithium tantalate bulk crystals by means of second-harmonic generation microscopy. In both systems, we detect a pronounced second-harmonic signal at the walls. Local polarimetry analysis of this signal combined with numerical modelling reveals the existence of a planar polarization within the walls, with Néel and Bloch-like configurations in PZT and lithium tantalate, respectively. Moreover, we find domain wall chirality reversal at line defects crossing lithium tantalate crystals. Our results demonstrate a clear deviation from the ideal Ising configuration that is traditionally expected in uniaxial ferroelectrics, corroborating recent theoretical predictions of a more complex, often chiral structure.

Ferroelasticity in palmierite-type(1 - x)Pb3(PO4)2 - xPb3(AsO4)2

Lead phosphate-arsenate Pb₃(P_1-x As _x O₄)₂ undergoes an improper ferroelastic phase transition from a rhombohedral paraphase [Formula: see text] to a monoclinic ferrophase [Formula: see text] leading to distinct twin boundary patterns. On cooling compounds with x larger than 0.8 undergo further transitions to monoclinic low-temperature phases, whereas the composition with x  =  0.8 shows order-parameter coupling phenomena. The transformation [Formula: see text]-[Formula: see text] was described on the basis of a three-state Potts model and the existence of precursors of monoclinic clusters in the rhombohedral paraphase. The system is one of the best studied improper ferroelastics. Due to its two-mode phonon behaviour the solid solution exhibits multistep temperature- as well as pressure-driven structural transformations with different length and time scales. Relevant investigations and findings of this palmierite-type material have been made by Prof E K H Salje. Some of the most prominent results from x-ray diffraction, optical microscopy and Raman scattering are reviewed, and the potential implications for domain-wall structures and engineering are discussed.

Functional electronic inversion layers at ferroelectric domain walls

Ferroelectric domain walls hold great promise as functional two-dimensional materials because of their unusual electronic properties. Particularly intriguing are the so-called charged walls where a polarity mismatch causes local, diverging electrostatic potentials requiring charge compensation and hence a change in the electronic structure. These walls can exhibit significantly enhanced conductivity and serve as a circuit path. The development of all-domain-wall devices, however, also requires walls with controllable output to emulate electronic nano-components such as diodes and transistors. Here we demonstrate electric-field control of the electronic transport at ferroelectric domain walls. We reversibly switch from resistive to conductive behaviour at charged walls in semiconducting ErMnO₃. We relate the transition to the formation-and eventual activation-of an inversion layer that acts as the channel for the charge transport. The findings provide new insight into the domain-wall physics in ferroelectrics and foreshadow the possibility to design elementary digital devices for all-domain-wall circuitry.

Computer vision distortion correction of scanning probe microscopy images

Since its inception, scanning probe microscopy (SPM) has established itself as the tool of choice for probing surfaces and functionalities at the nanoscale. Although recent developments in the instrumentation have greatly improved the metrological aspects of SPM, it is still plagued by the drifts and nonlinearities of the piezoelectric actuators underlying the precise nanoscale motion. In this work, we present an innovative computer-vision-based distortion correction algorithm for offline processing of functional SPM measurements, allowing two images to be directly overlaid with minimal error – thus correlating position with time evolution and local functionality. To demonstrate its versatility, the algorithm is applied to two very different systems. First, we show the tracking of polarisation switching in an epitaxial Pb(Zr_0.2Ti_0.8)O₃ thin film during high-speed continuous scanning under applied tip bias. Thanks to the precise time-location-polarisation correlation we can extract the regions of domain nucleation and track the motion of domain walls until the merging of the latter in avalanche-like events. Secondly, the morphology of surface folds and wrinkles in graphene deposited on a PET substrate is probed as a function of applied strain, allowing the relaxation of individual wrinkles to be tracked.

Assessing the amorphousness and periodicity of common domain boundaries in silica bilayers on Ru(0 0 0 1)

Domain boundaries are hypothesized to play a role in the crystalline to amorphous transition. Here we examine domain boundary structures in comparison to crystalline and amorphous structures in bilayer silica grown on Ru(0 0 0 1). Atomically resolved scanning probe microscopy data of boundaries in crystalline bilayer films are analyzed to determine structural motifs. A rich variety of boundary structures including rotational, closed-loop, antiphase, and complex boundaries are identified. Repeating units with ring sizes of 558 and 57 form the two most common domain boundary types. Quantitative metrics are utilized to assess the structural composition and degree of order for the chemically equivalent crystalline, domain boundary, and amorphous structures. It is found that domain boundaries in the crystalline phase show similarities to the amorphous phase in their ring statistics and, in some cases, in terms of the observed ring neighborhoods. However, by assessing order and periodicity, domain boundaries are shown to be distinct from the glassy state. The role of the Ru(0 0 0 1) substrate in influencing grain boundary structure is also discussed.

Unique magnetostriction of Fe68.8Pd31.2 attributable to twinning

Fe68.8Pd31.2 exhibits an anomalously large magnetostriction of ~400 ppm at room temperature as well as linear, isotropic, and hysteresis free magnetization behavior. This near perfectly reversible magnetic response is attributable to the presence of a large number of premartensitic magnetoelastic twin clusters present in the system made possible through the elastic softening that occurs near a martensitic transformation temperature of 252 K. It is proposed that the twin clusters in the material reduce both internal elastic and magnetic energy, causing the elastic and magnetic behavior of the material to be intimately linked. In such a framework, the anisotropy energy becomes extremely low causing the material to bear no crystalline dependence on magnetization, and application of a magnetic field causes simultaneous magnetic and twin domain movement which relaxes the system.

Controlled creation and displacement of charged domain walls in ferroelectric thin films

Charged domain walls in ferroelectric materials are of high interest due to their potential use in nanoelectronic devices. While previous approaches have utilized complex scanning probe techniques or frustrative poling here we show the creation of charged domain walls in ferroelectric thin films during simple polarization switching using either a conductive probe tip or patterned top electrodes. We demonstrate that ferroelectric switching is accompanied - without exception - by the appearance of charged domain walls and that these walls can be displaced and erased reliably. We ascertain from a combination of scanning probe microscopy, transmission electron microscopy and phase field simulations that creation of charged domain walls is a by-product of, and as such is always coupled to, ferroelectric switching. This is due to the (110) orientation of the tetragonal (Pb,Sr)TiO₃ thin films and the crucial role played by the limited conduction of the LSMO bottom electrode layer used in this study. This work highlights that charged domain walls, far from being exotic, unstable structures, as might have been assumed previously, can be robust, stable easily-controlled features in ferroelectric thin films.

Direct observation of polar tweed in LaAlO3

Polar tweed was discovered in mechanically stressed LaAlO₃. Local patches of strained material (diameter ca. 5 μm) form interwoven patterns seen in birefringence images, Piezo-Force Microscopy (PFM) and Resonant Piezoelectric Spectroscopy (RPS). PFM and RPS observations prove unequivocally that electrical polarity exists inside the tweed patterns of LaAlO₃. The local piezoelectric effect varies greatly within the tweed patterns and reaches magnitudes similar to quartz. The patterns were mapped by the shift of the E_g soft-mode frequency by Raman spectroscopy.

Flexoelectricity, incommensurate phases and the Lifshitz point

The solutions for the minimizers of the energy density f (q, p)  =  Aq² + Bq⁴ + p² + gA,B + β(q'p - p'q)+ |q'|² +κ|p'|²] describe the flexoelectric effect with a flexoelectric coupling coefficient β. The order parameters q and p can be visualized as strain and polarisation, respectively. The parameter κ denotes the ratio of intrinsic length scales for q and p. We show that the structural ground-states include 3 phases, namely the paraelastic state q  =  p  =  0, the ferroelastic state where polarization exists inside and near twin boundaries, and the incommensurate (modulated) phases with a very rich array of structural modulations ranging from nearly pure sine waves to kink arrays and ripple states. The phases coincide in the multicritical Lifshitz point. Linear flexoelectricity p~q' is encountered only approximately inside the ferroelastic phase and near the phase boundary between the paraelastic phase and the incommensurate phase. The relationship between the polarisation and the strain gradient is highly non-linear in all other states. The spatial profiles and energy distributions are discussed in detail.

Influence of defects and domain walls on dielectric and mechanical resonances in LiNbO3

Monodomain and periodically poled LiNbO3 crystals (congruent composition) show dielectric and piezoelectric resonances between 100 K and 900 K. Dielectric measurements show resonances in some samples between 10-100 kHz. These resonances vanish under thermal anneal in monodomain crystals while they remain stable in periodically poled samples with high domain wall densities. The low activation energy of 0.18 eV suggests their electronic (bi-polaronic) origin. Resonant piezoelectric spectroscopy, RPS, shows two features in virgin samples: a relaxation peak at 420 K and a rapid hardening when the sample was slowly heated to ~500 K. The dynamic relaxation and the hardening are related to excitations and reorientations of Li defects. The relaxations and hardening are irreversibly suppressed by high temperature anneal. We do not observe domain wall related RPS resonances in annealed samples, which excludes the existence of highly charged walls. We suggest that domain walls stabilize polaronic states with (bi-)polarons located inside or near to the ferroelectric domain walls.

Breakdown of Shape Memory Effect in Bent Cu-Al-Ni Nanopillars: When Twin Boundaries Become Stacking Faults

Bent Cu-Al-Ni nanopillars (diameters 90-750 nm) show a shape memory effect, SME, for diameters D > 300 nm. The SME and the associated twinning are located in a small deformed section of the nanopillar. Thick nanopillars (D > 300 nm) transform to austenite under heating, including the deformed region. Thin nanopillars (D < 130 nm) do not twin but generate highly disordered sequences of stacking faults in the deformed region. No SME occurs and heating converts only the undeformed regions into austenite. The defect-rich, deformed region remains in the martensite phase even after prolonged heating in the stability field of austenite. A complex mixture of twins and stacking faults was found for diameters 130 nm < D < 300 nm. The size effect of the SME in Cu-Al-Ni nanopillars consists of an approximately linear reduction of the SME between 300 and 130 nm when the SME completely vanishes for smaller diameters.

Hidden magnetism in the paramagnetic phase of EuTiO₃

EuTiO3 is investigated experimentally by temperature dependent conductivity and dielectric constant measurements. Both data sets evidence a crossover behavior in their temperature dependence around T * ~ 200 K indicating a change of the electrical and magnetic behavior of EuTiO3 as already observed by muon spin rotation (μSR) measurements. Around T '  =  80 K an additional anomaly appears which is consistent with previous resonant ultrasound spectroscopy (RUS) data. By applying a magnetic field (1.2 T at room temperature) the bulk conductivity is anomalously enhanced by more than one order of magnitude. The bulk dielectric constant ε(r) decreases with increasing temperature and is enhanced by the magnetic field by up to 22%. All data reveal a substantial hysteresis which is diminished in a magnetic field. The unusual magnetic field dependence of all quantities is suggested to stem from magnetically active domain walls which are mobile between the structural phase transition temperature (T(S)  =  282 K) and T * and are pinned below it.

Modulated minerals as potential ferroic materials

A list of potential (multi-) ferroic systems is derived based on the idea that structure gradients can generate ferroic distortions. Structure gradients are restricted here to structural modulations, which are commonly observed in natural minerals. These minerals contain transition metals and are prone to Jahn-Teller distortions and magnetic instabilities. The list contains mineral groups, which are often available in mineralogical collections.