Domains within domains and walls within walls: evidence for polar domains in cryogenic SrTiO3

Ferroelastic Twin-Wall-Mediated Ferroelectriclike Behavior and Bulk Photovoltaic Effect in SrTiO_{3}

Ferroelastic twin walls in nonpolar materials can give rise to a spontaneous polarization due to symmetry breaking. Nevertheless, the bistable polarity of twin walls and its reversal have not yet been demonstrated. Here, we report that the polarity of SrTiO_{3} twin walls can be switched by an ultralow strain gradient. Using first-principles-based machine-learning potential, we demonstrate that the twin walls can be deterministically rotated and realigned in specific directions under the strain gradient, which breaks the inversion symmetry of a sequence of walls and leads to a macroscopic polarization. The system can maintain polarity even after the constraint is removed. As a result, the polarization of twin walls can exhibit a ferroelectriclike hysteresis loop upon cyclic bending, namely flexoferroelectricity. Finally, we propose a scheme to experimentally detect the polarity of the twin wall by measuring the bulk photovoltaic responses. Our findings suggest a twin-wall-mediated flexoferroelectricity in SrTiO_{3}, which could be potentially exploited as functional elements in nanoelectronic devices design.

Designing spin and orbital sources of Berry curvature at oxide interfaces

Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as the Berry curvature (BC). Large BCs typically arise when electronic states with different spin, orbital or sublattice quantum numbers hybridize at finite crystal momentum. In all the materials known to date, the BC is triggered by the hybridization of a single type of quantum number. Here we report the discovery of the first material system having both spin- and orbital-sourced BC: LaAlO₃/SrTiO₃ interfaces grown along the [111] direction. We independently detect these two sources and probe the BC associated to the spin quantum number through the measurements of an anomalous planar Hall effect. The observation of a nonlinear Hall effect with time-reversal symmetry signals large orbital-mediated BC dipoles. The coexistence of different forms of BC enables the combination of spintronic and optoelectronic functionalities in a single material.

Two-Dimensional Ferroelasticity and Domain-Wall Flexoelectricity in HgX2 (X = Br or I) Monolayers

Electromechanical phenomena in two-dimensional (2D) materials can be related to sizable electric polarizations and switchable spontaneous ferroelasticity, allowing them to be used as miniaturized electronic and memory devices. Even in a parent centrosymmetric (nonpolar) ferroelastic (FE) material, non-zero polarization can be produced around the FE domain wall, owing to the strain-gradient-induced flexoelectricity. Compared with the negligibly weak flexoelectric effect in bulk compounds, significant electric polarizations can be expected in 2D FE materials that sustain a large elastic strain and a strain gradient. Using first-principles calculations, we predict that spontaneous 2D ferroelasticity and domain-wall flexoelectricity can be simultaneously realized in synthetic HgX₂ (X = Br or I) monolayers. The FE phase renders three oriented variants, which form FE domain walls with a large strain gradient and the associated domain-wall flexoelectric polarizations. Our thermodynamic stability analysis and kinetic barrier simulations allow us to manipulate the domain-wall flexoelectricity via applied mechanical stress, thereby enabling future electromechanical applications in nanoelectronics.

Octahedra-Tilted Control of Displacement Disorder and Dielectric Relaxation in Mn-Doped SrTiO3 Single Crystals

Strontium titanate SrTiO₃ (STO) is a canonical example of a quantum paraelectric, and its doping with manganese ions unlocks its potential as a quantum multiferroic candidate. However, to date, the specifics of incorporation of the manganese ion into the perovskite lattice and its impact on structure-property relationships are debatable questions. Herein, using high-precision X-ray diffraction of a Mn (2 atom %)-doped STO single crystal, clear fingerprints of the displacement disorder of Mn cations in the perovskite B-sublattice are observed. Moreover, near the temperature of the antiferrodistortive transition, the off-center Mn position splits in two, providing the unequal potential barrier's distribution for possible local atomic hopping. A link with this was found via analysis of the dielectric response that reveals two Arrhenius-type relaxation processes with similar activation energies (35 and 43 meV) and attempt frequencies (1 × 10¹¹ and ∼1.6 × 10¹⁰ Hz), suggesting similar dielectric relaxation mechanisms.

Anomalous transport in high-mobility superconducting SrTiO3 thin films

The study of subtle effects on transport in semiconductors requires high-quality epitaxial structures with low defect density. Using hybrid molecular beam epitaxy (MBE), SrTiO₃ films with a low-temperature mobility exceeding 42,000 cm² V^-1 s^-1 at a low carrier density of 3 × 10¹⁷ cm^-3 were achieved. A sudden and sharp decrease in residual resistivity accompanied by an enhancement in the superconducting transition temperature were observed across the second Lifshitz transition where the third band becomes occupied, revealing dominant intraband scattering. These films further revealed an anomalous behavior in the Hall carrier density as a consequence of the antiferrodistortive (AFD) transition and the temperature dependence of the Hall scattering factor. Using hybrid MBE growth, phenomenological modeling, temperature-dependent transport measurements, and scanning superconducting quantum interference device imaging, we provide critical insights into the important role of inter- versus intraband scattering and of AFD domain walls on normal-state and superconducting properties of SrTiO₃.

Precision Multi-Mode Dielectric Characterization of a Crystalline Perovskite Enables Determination of the Temperature-Dependent Phase Transitions

Simple perovskite crystals undergo structural phase transitions on cooling to low temperatures, which significantly change the material properties of the crystal. In this work, we rigorously characterize the temperature evolution of permittivity of a perovskite crystal as it undergoes phase transitions. In particular, we have undertaken precision measurements of a single crystal of Strontium Titanate from 294.6 to 5.6 K, by measuring the frequency of multiple microwave transverse electric (TE) and magnetic resonant modes simultaneously. The multi-mode microwave measurement technique of resonant frequency used in this work allows high precision determination of any induced anisotropy of the permittivity as the crystal undergoes structural phase transitions. Compared with previous results, we unequivocally show that the permittivity has an isotropic value of 316.3±2.2 at room temperature, consistent with its well-known cubic structure, and determine the onset of dielectric anisotropy as the crystal is cooled to lower temperatures. We show that the crystal exhibits uniaxial anisotropy in the permittivity below 105 K when the structure becomes tetragonal, and exhibits biaxial anisotropy in the permittivity below 51 K when the structure becomes orthorhombic.

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.

Observation of Zero-Field Transverse Resistance in AlO_{x}/SrTiO_{3} Interface Devices

Domain walls in AlO_{x}/SrTiO_{3} (AlO_{x}/STO) interface devices at low temperatures give a rise to a new signature in the electrical transport of two-dimensional carrier gases formed at the surfaces or interfaces of STO-based heterostructures: a finite transverse resistance observed in Hall bars in zero external magnetic field. This transverse resistance depends on the local domain wall configuration and hence changes with temperature, gate voltage, thermal cycling, and position along the sample and can even change sign as a function of these parameters. The transverse resistance is observed below ≃70  K but grows and changes significantly below ≃40  K, the temperature at which the domain walls become increasingly polar. Surprisingly, the transverse resistance is much larger in (111) oriented heterostructures in comparison to (001) oriented heterostructures. Measurements of the capacitance between the conducting interface and an electrode applied to the substrate, which reflect the dielectric constant of the STO, indicate that this difference may be related to the greater variation of the temperature-dependent dielectric constant with electric field when the electric field is applied in the [111] direction. The finite transverse resistance can be explained inhomogeneous current flow due to the preferential transport of current along domain walls that are askew to the nominal direction of the injected current.

The duration-energy-size enigma for acoustic emission

Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ A_max^x and A_max ~ D^χ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and ‘half-moon’ shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude A_max as predicted by MFT but scales linearly S ~ A_max. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.

Unveiling Temperature-Induced Structural Domains and Movement of Oxygen Vacancies in SrTiO3 with Graphene

Heterointerfaces coupling complex oxides exhibit coexisting functional properties such as magnetism, superconductivity, and ferroelectricity, often absent in their individual constituent. SrTiO₃ (STO), a canonical band insulator, is an active constituent of such heterointerfaces. Temperature-, strain-, or mechanical stress-induced ferroelastic transition leads to the formation of narrow domains and domain walls in STO. Such ferroelastic domain walls have been studied using imaging or transport techniques and, often, the findings are influenced by the choice and interaction of the electrodes with STO. In this work, we use graphene as a unique platform to unveil the movement of oxygen vacancies and ferroelastic domain walls near the STO surface by studying the temperature and gate bias dependence of charge transport in graphene. By sweeping the back gate voltage, we observe antihysteresis in graphene typically observed in conventional ferroelectric oxides. Interestingly, we find features in antihysteresis that are related to the movement of domain walls and of oxygen vacancies in STO. We ascertain this by analyzing the time dependence of the graphene square resistance at different temperatures and gate bias. Density functional calculations estimate the surface polarization and formation energies of layer-dependent oxygen vacancies in STO. This corroborates quantitatively with the activation energies determined from the temperature dependence of the graphene square resistance. Introduction of a hexagonal boron nitride (hBN) layer, of varying thicknesses, between graphene and STO leads to a gradual disappearance of the observed features, implying the influence of the domain walls onto the potential landscape in graphene.

Superconductivity mediated by polar modes in ferroelectric metals

The occurrence of superconductivity in doped SrTiO₃ at low carrier densities points to the presence of an unusually strong pairing interaction that has eluded understanding for several decades. We report experimental results showing the pressure dependence of the superconducting transition temperature, T_c, near to optimal doping that sheds light on the nature of this interaction. We find that T_c increases dramatically when the energy gap of the ferroelectric critical modes is suppressed, i.e., as the ferroelectric quantum critical point is approached in a way reminiscent to behaviour observed in magnetic counterparts. However, in contrast to the latter, the coupling of the carriers to the critical modes in ferroelectrics is predicted to be small. We present a quantitative model involving the dynamical screening of the Coulomb interaction and show that an enhancement of T_c near to a ferroelectric quantum critical point can arise due to the virtual exchange of longitudinal hybrid-polar-modes, even in the absence of a strong coupling to the transverse critical modes.

Superconductivity in doped SrTiO₃ near to a ferroelectric quantum critical point emerges due to a strong interaction driving the formation of Cooper pairs, the nature of which has remained elusive for several decades.  Here, the authors reveal that pairing is due to the exchange of longitudinal hybrid polar modes rather than transverse critical modes.

Order-Disorder Ferroelectric Transition of Strained SrTiO_{3}

SrTiO_{3} is an incipient ferroelectric that is believed to exhibit a prototype displacive, soft mode ferroelectric transition when subjected to mechanical stress or alloying. We use high-angle annular dark-field imaging in scanning transmission electron microscopy to reveal local polar regions in the room-temperature, paraelectric phase of strained SrTiO_{3} films, which undergo a ferroelectric transition at low temperatures. These films contain nanometer-sized domains in which the Ti columns are displaced. In contrast, these nanodomains are absent in unstrained films, which do not become ferroelectric. The results show that the ferroelectric transition of strained SrTiO_{3} is an order-disorder transition. We discuss the impact of the results on the nature of the ferroelectric transition of SrTiO_{3}.

Quantum critical phenomena in a compressible displacive ferroelectric

The dielectric and magnetic polarizations of quantum paraelectrics and paramagnetic materials have in many cases been found to initially increase with increasing thermal disorder and hence, exhibit peaks as a function of temperature. A quantitative description of these examples of "order-by-disorder" phenomena has remained elusive in nearly ferromagnetic metals and in dielectrics on the border of displacive ferroelectric transitions. Here, we present an experimental study of the evolution of the dielectric susceptibility peak as a function of pressure in the nearly ferroelectric material, strontium titanate, which reveals that the peak position collapses toward absolute zero as the ferroelectric quantum critical point is approached. We show that this behavior can be described in detail without the use of adjustable parameters in terms of the Larkin-Khmelnitskii-Shneerson-Rechester (LKSR) theory, first introduced nearly 50 y ago, of the hybridization of polar and acoustic modes in quantum paraelectrics, in contrast to alternative models that have been proposed. Our study allows us to construct a detailed temperature-pressure phase diagram of a material on the border of a ferroelectric quantum critical point comprising ferroelectric, quantum critical paraelectric, and hybridized polar-acoustic regimes. Furthermore, at the lowest temperatures, below the susceptibility maximum, we observe a regime characterized by a linear temperature dependence of the inverse susceptibility that differs sharply from the quartic temperature dependence predicted by the LKSR theory. We find that this non-LKSR low-temperature regime cannot be accounted for in terms of any detailed model reported in the literature, and its interpretation poses an empirical and conceptual challenge.

Unconventional Co-Existence of Insulating Nano-Regions and Conducting Filaments in Reduced SrTiO3: Mode Softening, Local Piezoelectricity, and Metallicity

Doped SrTiO3 becomes a metal at extremely low doping concentrations n and is even superconducting at n < 1020 cm−3, with the superconducting transition temperature adopting a dome-like shape with increasing carrier concentration. In this paper it is shown within the polarizability model and from first principles calculations that up to a well-defined carrier concentration nc transverse optic mode softening takes place together with polar nano-domain formation, which provides evidence of inhomogeneity and a two-component type behavior with metallicity coexisting with polarity. Beyond this region, a conventional metal is formed where superconductivity as well as mode softening is absent. For n ≤ nc the effective electron-phonon coupling follows the superconducting transition temperature. Effusion measurements, as well as macroscopic and nanoscopic conductivity measurements, indicate that the distribution of oxygen vacancies is local and inhomogeneous, from which it is concluded that metallicity stems from filaments which are embedded in a polar matrix as long as n ≤ nc.

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.

Non-Ohmic Variable-Range Hopping and Resistive Switching in SrTiO_{3} Domain Walls

We report observation of electric field driven conductivity with negative differential conductance and resistive switching in insulating SrTiO_{3} samples over a wide range of applied voltages at low temperatures. The observed current follows I=I_{0}exp[-(E^{*}/E)^{1/2}] at large applied electric field, corresponding to variable range hopping conduction with a Coulomb gap in domain walls. Our data are sufficient to discriminate unambiguously between Shklovskii and Mott hopping via their different electric field exponent. Under some conditions space-charge-limited currents are observed, and the charge mobility limit is determined to be in the range of 17 and 210  cm^{2}/Vs.

Phonon Thermal Hall Effect in Strontium Titanate

It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in the presence of a magnetic field. Recent studies of thermal Hall conductivity, κ_{xy}, in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of κ_{xy} in quantum paraelectric SrTiO_{3}, which is a nonmagnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as "giant." Remarkably, κ_{xy}(T) and κ(T) peak at the same temperature and the former decreases faster than the latter at both sides of the peak. Interestingly, in the case of La_{2}CuO_{4} and α-RuCl_{3}, κ_{xy}(T) and κ(T) peak also at the same temperature. We also studied KTaO_{3} and found a small signal, indicating that a sizable κ_{xy}(T) is not a generic feature of quantum paraelectrics. Combined to other observations, this points to a crucial role played by antiferrodistortive domains in generating κ_{xy} of this solid.

Domain Dynamics in Quantum-Paraelectric SrTiO_{3}

Twin dynamics forced by acoustic waves shows several linear and nonlinear response modes below T_{c}=106  K. In the quantum paraelectric state a "quantum domain glass" at 25  K<T<40  K shows intense relaxation and temperature hysteresis. Domains float collectively in a complex, smooth landscape with long relaxation times. In the "quantum domain solid" state below 25 K new phenomena occur. A temperature-dependent memory effect of the elastic response after anneal at 36 K depends on the lowest temperature reached in the quantum domain solid state below 25 K. The glassiness of twin boundary dynamics vanishes for temperatures approaching absolute zero.

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.

Glasslike Dynamics of Polar Domain Walls in Cryogenic SrTiO_{3}

Polar and highly mobile domain walls in SrTiO_{3} move under electric and elastic fields. Two vastly different timescales dominate their dynamical behavior. The previously observed fast changes lead to anomalies near 40 K where the elastic moduli soften and the polarity of the walls becomes strong. Keeping the sample under isothermal conditions leads to a new and unexpected phenomenon: The softening vanishes over timescales of days while the piezoelectricity of the sample remains unchanged. The hardening follows glass dynamics below an onset at T^{*}≈40  K. The timescale of the hardening is strongly temperature dependent and can be followed experimentally down to 34 K when the relaxation is not completed within two days. The relaxation time of a stretched exponential decay increases exponentially with the decreasing temperature. This relaxation process follows similar dynamics after zero-field cooling and after applying or removing an electric field. The sluggish behavior is attributed to collective interactions of domain patterns following overdamped glass dynamics rather than ballistic dynamics.

Dielectric Response of Quantum Critical Ferroelectric as a Function of Pressure

In this work we report for the first time measurements of the dielectric loss of single-crystal SrTiO₃ under the application of hydrostatic pressure up to 20 kbar and temperatures down to 200 mK which allow us to comment on the evolution of new fundamental material properties and their relationship with the recently discovered quantum critical phenomena in this material. The well known 18 K peak or shoulder was no longer observed after pressure was applied, even after subsequently removing it, suggesting it is associated with the twin walls formed at the 110 K cubic-tetragonal transition. The family of familiar peaks were all seen to increase in temperature linearly with pressure and the height of the 9.4 K peak was drastically suppressed by even the smallest pressures. This peak is discussed in the context of a postulated ferroelectric quantum critical point in SrTiO₃ and the behaviour of its size linked to the position of this point on the recently established phase diagram.

Low-Temperature Dielectric Anisotropy Driven by an Antiferroelectric Mode in SrTiO_{3}

Strontium titanate (SrTiO_{3}) is the quintessential material for oxide electronics. One of its hallmark features is the transition, driven by antiferrodistortive (AFD) lattice modes, from a cubic to a ferroelastic low-temperature phase. Here we investigate the evolution of the ferroelastic twin walls upon application of an electric field. Remarkably, we find that the dielectric anisotropy of tetragonal SrTiO_{3}, rather than the intrinsic domain wall polarity, is the main driving force for the motion of the twins. Based on a combined first-principles and Landau-theory analysis, we show that such anisotropy is dominated by a trilinear coupling between the polarization, the AFD lattice tilts, and a previously overlooked antiferroelectric (AFE) mode. We identify the latter AFE phonon with the so-called "R mode" at ∼440  cm^{-1}, which was previously detected in IR experiments, but whose microscopic nature was unknown.

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.

Link between the Superconducting Dome and Spin-Orbit Interaction in the (111) LaAlO_{3}/SrTiO_{3} Interface

We measure the gate voltage (V_{g}) dependence of the superconducting properties and the spin-orbit interaction in the (111)-oriented LaAlO_{3}/SrTiO_{3} interface. Superconductivity is observed in a dome-shaped region in the carrier density-temperature phase diagram with the maxima of superconducting transition temperature T_{c} and the upper critical fields lying at the same V_{g}. The spin-orbit interaction determined from the superconducting parameters and confirmed by weak-antilocalization measurements follows the same gate voltage dependence as T_{c}. The correlation between the superconductivity and spin-orbit interaction as well as the enhancement of the parallel upper critical field, well beyond the Chandrasekhar-Clogston limit, suggest that superconductivity and the spin-orbit interaction are linked in a nontrivial fashion. We propose possible scenarios to explain this unconventional behavior.

Vacancies and holes in bulk and at 180° domain walls in lead titanate

Domain walls (DWs) in ferroic materials exhibit a plethora of unexpected properties that are different from the adjacent ferroic domains. Still, the intrinsic/extrinsic origin of these properties remains an open question. Here, density functional theory calculations are used to investigate the interaction between vacancies and 180° DWs in the prototypical ferroelectric PbTiO₃, with a special emphasis on cationic vacancies and released holes. All vacancies are more easily formed within the DW than in the domains. This is interpreted, using a phenomenological model, as the partial compensation of an extra-tensile stress when the defect is created inside the DW. Oxygen vacancies are found to be always fully ionized, independently of the thermodynamic conditions, while cationic vacancies can be either neutral or partially ionized (oxygen-rich conditions), or fully ionized (oxygen-poor conditions). Therefore, in oxidizing conditions, holes are induced by neutral and partially ionized Pb vacancies. In the bulk PbTiO₃, these holes are more stable as delocalized rather than small polarons, but at DWs, the two forms are found to be possible.

Imaging and tuning polarity at SrTiO3 domain walls

Electrostatic fields tune the ground state of interfaces between complex oxide materials. Electronic properties, such as conductivity and superconductivity, can be tuned and then used to create and control circuit elements and gate-defined devices. Here we show that naturally occurring twin boundaries, with properties that are different from their surrounding bulk, can tune the LaAlO₃/SrTiO₃ interface 2DEG at the nanoscale. In particular, SrTiO₃ domain boundaries have the unusual distinction of remaining highly mobile down to low temperatures, and were recently suggested to be polar. Here we apply localized pressure to an individual SrTiO₃ twin boundary and detect a change in LaAlO₃/SrTiO₃ interface current distribution. Our data directly confirm the existence of polarity at the twin boundaries, and demonstrate that they can serve as effective tunable gates. As the location of SrTiO₃ domain walls can be controlled using external field stimuli, our findings suggest a novel approach to manipulate SrTiO₃-based devices on the nanoscale.

Prospects and applications near ferroelectric quantum phase transitions: a key issues review

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this key issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Empirically the sensitivity of the ferroelectric T _c's to external and to chemical pressure gives practical access to a broad range of temperature behavior over several hundreds of Kelvin. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.

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.

Macroscopic Polarization from Antiferrodistortive Cycloids in Ferroelastic SrTiO_{3}

Based on a first-principles based multiscale approach, we study the polarity P of ferroelastic twin walls in SrTiO_{3}. In addition to flexoelectricity, which was pointed out before, we identify two new mechanisms that crucially contribute to P: a direct "rotopolar" coupling to the gradients of the antiferrodistortive oxygen tilts, and a trilinear coupling that is mediated by the antiferroelectric displacement of the Ti atoms. Remarkably, the rotopolar coupling presents a strong analogy to the mechanism that generates a spontaneous polarization in cycloidal magnets. We show how this similarity allows for a breakdown of macroscopic inversion symmetry (and therefore a macroscopic polarization) in a periodic sequence of parallel twins. These results open new avenues towards engineering pyroelectricity or piezoelectricity in nominally nonpolar ferroic materials.

On the persistence of polar domains in ultrathin ferroelectric capacitors

The instability of ferroelectric ordering in ultra-thin films is one of the most important fundamental issues pertaining realization of a number of electronic devices with enhanced functionality, such as ferroelectric and multiferroic tunnel junctions or ferroelectric field effect transistors. In this paper, we investigate the polarization state of archetypal ultrathin (several nanometres) ferroelectric heterostructures: epitaxial single-crystalline BaTiO₃ films sandwiched between the most habitual perovskite electrodes, SrRuO₃, on top of the most used perovskite substrate, SrTiO₃. We use a combination of piezoresponse force microscopy, dielectric measurements and structural characterization to provide conclusive evidence for the ferroelectric nature of the relaxed polarization state in ultrathin BaTiO₃ capacitors. We show that even the high screening efficiency of SrRuO₃ electrodes is still insufficient to stabilize polarization in SrRuO₃/BaTiO₃/SrRuO₃ heterostructures at room temperature. We identify the key role of domain wall motion in determining the macroscopic electrical properties of ultrathin capacitors and discuss their dielectric response in the light of the recent interest in negative capacitance behaviour.

Stable charged antiparallel domain walls in hyperferroelectrics

Charge-neutral 180° domain walls that separate domains of antiparallel polarization directions are common structural topological defects in ferroelectrics. In normal ferroelectrics, charged 180° domain walls running perpendicular to the polarization directions are highly energetically unfavorable because of the depolarization field and are difficult to stabilize. We explore both neutral and charged 180° domain walls in hyperferroelectrics, a class of proper ferroelectrics with persistent polarization in the presence of a depolarization field, using density functional theory. We obtain zero temperature equilibrium structures of head-to-head and tail-to-tail walls in recently discovered ABC-type hexagonal hyperferroelectrics. Charged domain walls can also be stabilized in canonical ferroelectrics represented by LiNbO₃ without any dopants, defects or mechanical clamping. First-principles electronic structure calculations show that charged domain walls can reduce and even close the band gap of host materials and support quasi-two-dimensional electron(hole) gas with enhanced electrical conductivity.

Local Electrical Imaging of Tetragonal Domains and Field-Induced Ferroelectric Twin Walls in Conducting SrTiO_{3}

We demonstrate electrical mapping of tetragonal domains and electric field-induced twin walls in SrTiO_{3} as a function of temperature and gate bias utilizing the conducting LaAlO_{3}/SrTiO_{3} interface and low-temperature scanning electron microscopy. Conducting twin walls appear below 105 K, and new twin patterns are observed after thermal cycling through the transition or on electric field gating. The nature of the twin walls is confirmed by calculating their intersection angles for different substrate orientations. Numerous walls formed when a large side- or back-gate voltage is applied are identified as field-induced ferroelectric twin walls in the paraelectric tetragonal matrix. The walls persist after switching off the electric field and on thermal cycling below 105 K. These observations point to a new type of ferroelectric functionality in SrTiO_{3}, which could be exploited together with magnetism and superconductivity in a multifunctional context.

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.

Anisotropic Transport at the LaAlO3/SrTiO3 Interface Explained by Microscopic Imaging of Channel-Flow over SrTiO3 Domains

Oxide interfaces, including the LaAlO3/SrTiO3 interface, have been a subject of intense interest for over a decade due to their rich physics and potential as low-dimensional nanoelectronic systems. The field has reached the stage where efforts are invested in developing devices. It is critical now to understand the functionalities and limitations of such devices. Recent scanning probe measurements of the LaAlO3/SrTiO3 interface have revealed locally enhanced current flow and accumulation of charge along channels related to SrTiO3 structural domains. These observations raised a key question regarding the role these modulations play in the macroscopic properties of devices. Here we show that the microscopic picture, mapped by scanning superconducting quantum interference device, accounts for a substantial part of the macroscopically measured transport anisotropy. We compared local flux data with transport values, measured simultaneously, over various SrTiO3 domain configurations. We show a clear relation between maps of local current density over specific domain configurations and the measured anisotropy for the same device. The domains divert the direction of current flow, resulting in a direction-dependent resistance. We also show that the modulation can be significant and that in some cases up to 95% of the current is modulated over the channels. The orientation and distribution of the SrTiO3 structural domains change between different cooldowns of the same device or when electric fields are applied, affecting the device behavior. Our results, highlight the importance of substrate physics, and in particular, the role of structural domains, in controlling electronic properties of LaAlO3/SrTiO3 devices. Furthermore, these results point to new research directions, exploiting the STO domains' ability to divert or even carry current.

Insulating phase at low temperature in ultrathin La0.8Sr0.2MnO3 films

Metal-insulator transition is observed in the La0.8Sr0.2MnO3 thin films with thickness larger than 5 unit cells. Insulating phase at lower temperature appeared in the ultrathin films with thickness ranging from 6 unit cells to 10 unit cells and it is found that the Mott variable range hopping conduction dominates in this insulating phase at low temperature with a decrease of localization length in thinner films. A deficiency of oxygen content and a resulting decrease of the Mn valence have been observed in the ultrathin films with thickness smaller than or equal to 10 unit cells by studying the aberration-corrected scanning transmission electron microscopy and electron energy loss spectroscopy of the films. These results suggest that the existence of the oxygen vacancies in thinner films suppresses the double-exchange mechanism and contributes to the enhancement of disorder, leading to a decrease of the Curie temperature and the low temperature insulating phase in the ultrathin films. In addition, the suppression of the magnetic properties in thinner films indicates stronger disorder of magnetic moments, which is considered to be the reason for this decrease of the localization length.

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.

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.

Polar domain walls trigger magnetoelectric coupling

Interface physics in oxides heterostructures is pivotal in material’s science. Domain walls (DWs) in ferroic systems are examples of naturally occurring interfaces, where order parameter of neighboring domains is modified and emerging properties may develop. Here we show that electric tuning of ferroelastic domain walls in SrTiO₃ leads to dramatic changes of the magnetic domain structure of a neighboring magnetic layer (La_1/2Sr_1/2MnO₃) epitaxially clamped on a SrTiO₃ substrate. We show that the properties of the magnetic layer are intimately connected to the existence of polar regions at twin boundaries of SrTiO₃, developing at , that can be electrically modulated. These findings illustrate that by exploiting the responsiveness of DWs nanoregions to external stimuli, even in absence of any domain contribution, prominent and adjustable macroscopic reactions of neighboring layers can be obtained. We conclude that polar DWs, known to exist in other materials, can be used to trigger tunable responses and may lead to new ways for the manipulation of interfacial emerging properties.

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.

Static and dynamic strain coupling behaviour of ferroic and multiferroic perovskites from resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) provides a window on the pervasive influence of strain coupling at phase transitions in perovskites through determination of elastic and anelastic relaxations across wide temperature intervals and with the application of external fields. In particular, large variations of elastic constants occur at structural, ferroelectric and electronic transitions and, because of the relatively long interaction length provided by strain fields in a crystal, Landau theory provides an effective formal framework for characterizing their form and magnitude. At the same time, the Debye equations provide a robust description of dynamic relaxational processes involving the mobility of defects which are coupled with strain. Improper ferroelastic transitions driven by octahedral tilting in KMnF3, LaAlO3, (Ca,Sr)TiO3, Sr(Ti,Zr)O3 and BaCeO3 are accompanied by elastic softening of tens of % and characteristic patterns of acoustic loss due to the mobility of twin walls. RUS data for ferroelectrics and ferroelectric relaxors, including BaTiO3, (K,Na)NbO3,Pb(Mg1/3Nb2/3)O3 (PMN), Pb(Sc1/2Ta1/2)O3 (PST), (Pb(Zn1/3Nb2/3)O3)0.955(PbTiO3)0.045 (PZN-PT) and (Pb(In1/2Nb1/2)O3)0.26(Pb(Mg1/3Nb2/3)O3)0.44(PbTiO3)0.30 (PIN-PMN-PT) show similar patterns of softening and attenuation but also have precursor softening associated with the development of polar nano regions. Defect-induced ferroelectricity occurs in KTaO3, without the development of long range ordering. By way of contrast, spin-lattice coupling is much more variable in strength, as reflected in a greater range of softening behaviour for Pr0.48Ca0.52MnO3 and Sm0.6Y0.4MnO3 as well as for the multiferroic perovskites EuTiO3,BiFeO3, Bi0.9Sm0.1FeO3, Bi0.9Nd0.1FeO3, (BiFeO3)0.64(CaFeO2.5)0.36, (Pb(Fe0.5Ti0.5)O3)0.4(Pb(Zr0.53Ti0.47)O3)0.6. A characteristic feature of transitions in which there is a significant Jahn-Teller component is softening as the transition point is approached from above, as illustrated by PrAlO3, and this is suppressed by application of an external magnetic field in the colossal magnetoresistive manganite Pr0.48Ca0.52MnO3 or by reducing grain size in La0.5Ca0.5MnO3. Spin state transitions for Co(3+) in LaCoO3, NdCoO3 and GdCoO3 produce changes in the shear modulus that scale with a spin state order parameter, which is itself coupled with the order parameter(s) for octahedral tilting in a linear-quadratic manner. A new class of phase transitions in perovskites, due to orientational or conformational ordering of organic molecules on the crystallographic A-site of metal organic frameworks, is illustrated for [(CH3)2NH2]Co(HCOO)3 and [(CH2)3NH2]Mn(HCOO)3 which also display elastic and anelastic anomalies due to the influence of intrinsic and extrinsic strain relaxation behaviour.

Electric polarization of magnetic domain walls in magnetoelectrics

Two prominent magnetoelectrics MnWO4 and CuO possess low-temperature commensurate paraelectric magnetically ordered phase. Here using Monte Carlo simulations we show that the walls between the domains of this phase are ferroelectric with the same electric polarization direction and value as those in the magnetoelectric phases of these compounds. We also suggest that experimental observation of electric polarization of domain walls in MnWO4 should help to determine the macroscopic interactions responsible for its magnetoelectric properties.

Strain relaxation mechanisms of elastic softening and twin wall freezing associated with structural phase transitions in (Ca,Sr)TiO3 perovskites

Resonant ultrasound spectroscopy has been used to measure the bulk modulus (K), shearmodulus (G) and acoustic dissipation of polycrystalline perovskite samples across theCaTiO(3)–SrTiO(3) solid solution in the temperature range ∼10–1350 K. A remarkable pattern of up to ∼25% softening of G as a function of both temperature and composition is due to coupling of shear strain with order parameters for the Pm3m ↔ I 4/mcm, I 4/mcm↔Pnmaand I 4/mcm↔Pbcm transitions. Anomalies in K associated with the phase transitions are small, consistent with only weak coupling of octahedral tilting order parameter(s) with volume strain. A change from tricritical character for the Pm3m ↔ I 4/mcm transition towards second order character at Sr-rich compositions appears to be due to changing properties of the soft optic mode rather than to changes in magnitude of strain/order parameter coupling coefficients. Precursor softening of G ahead of the Pm3m ↔ I 4/mcm transition, due tof luctuations or clustering, occurs over a temperature interval of up to ∼200 K, and also changes character at the most Sr-rich compositions. The tetragonal structure with Sr-rich compositions is characterized by additional softening with falling temperature which is most likely related to the proximity of a ferroelectric instability. The I 4/mcm↔Pnma transition is accompanied by stiffening, which is attributed to the effects of strong coupling between order parameters for M-point and R-point tilting. The pattern of attenuation at RUS frequencies in the tetragonal phase can be understood in terms of the mobility of twin walls which be come pinned below ∼500 K, and the loss mechanism most likely involves local bowing of the walls by lateral motion of ledges rather than the advance and retraction of needle tips. Twin wall mobility is suppressed in the orthorhombic structure.

Twin boundary profiles with linear-quadratic coupling between order parameters

A new type of twin boundary was found when two order parameters interact by linear-quadratic coupling QP(2). In this solution, we find that a domain wall consists of two layers in which in one layer both order parameters Q and P are active while in the second layer only Q is active. The adjacent domains are equally asymmetric (Q, P) and (Q, 0) so that one phase could be polar and/or magnetic and contain a ferroelastic strain while the second layer is ferroelastic only without polar or magnetic properties. The two layers represent a stepwise transition between the two domains.We analyze the full phase diagram depending on the coupling constant and anisotropy of the gradient term, and show that in a certain regime the order parameter Q becomes activated only in the interfacial region. A common solution contains kinks and breathers whereby the width of the interface can be very wide in agreement with the first order character of the transition.

Ferroelectric transitions at ferroelectric domain walls found from first principles

We present a first-principles study of model domain walls (DWs) in prototypic ferroelectric PbTiO(3). At high temperature the DW structure is somewhat trivial, with atoms occupying high-symmetry positions. However, upon cooling the DW undergoes a symmetry-breaking transition characterized by a giant dielectric anomaly and the onset of a large and switchable polarization. Our results thus corroborate previous arguments for the occurrence of ferroic orders at structural DWs, providing a detailed atomistic picture of a temperature-driven DW-confined transformation. Beyond its relevance to the field of ferroelectrics, our results highlight the interest of these DWs in the broader areas of low-dimensional physics and phase transitions in strongly fluctuating systems.