Ultrastrong Coupling between Polar Distortion and Optical Properties in Ferroelectric MoBr2O2.

Tuning the properties of materials by using external stimuli is crucial for developing versatile smart materials. Strong coupling among the order parameters within a single-phase material constitutes a potent foundation for achieving precise property control. However, cross-coupling is fairly weak in most single materials. Leveraging first-principles calculations, we demonstrate a layered mixed anion compound MoBr2O2 that exhibits electric-field switchable spontaneous polarization and ultrastrong coupling between polar distortion and electronic structures as well as optical properties. It offers feasible avenues of achieving tunable Rashba spin-splitting, electrochromism, thermochromism, photochromism, and nonlinear optics by applying an external electric field to a single domain sample and heating, as well as intense light illumination. Additionally, it exhibits an exceptionally large photostrictive effect. These findings not only showcase the feasibility of achieving multiple order parameter coupling within a single material but also pave the way for comprehensive applications based on property control, such as energy harvesting, information processing, and ultrafast control.

Spin disorder control of topological spin texture.

Stabilization of topological spin textures in layered magnets has the potential to drive the development of advanced low-dimensional spintronics devices. However, achieving reliable and flexible manipulation of the topological spin textures beyond skyrmion in a two-dimensional magnet system remains challenging. Here, we demonstrate the introduction of magnetic iron atoms between the van der Waals gap of a layered magnet, Fe3GaTe2, to modify local anisotropic magnetic interactions. Consequently, we present direct observations of the order-disorder skyrmion lattices transition. In addition, non-trivial topological solitons, such as skyrmioniums and skyrmion bags, are realized at room temperature. Our work highlights the influence of random spin control of non-trivial topological spin textures.

Revealing the three-dimensional arrangement of polar topology in nanoparticles.

In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.

Tunable and parabolic piezoelectricity in hafnia under epitaxial strain.

Piezoelectrics are a class of functional materials that have been extensively used for application in modern electro-mechanical and mechatronics technologies. The sign of longitudinal piezoelectric coefficients is typically positive but recently a few ferroelectrics, such as ferroelectric polymer poly(vinylidene fluoride) and van der Waals ferroelectric CuInP2S6, were experimentally found to have negative piezoelectricity. Here, using first-principles calculation and measurements, we show that the sign of the longitudinal linear piezoelectric coefficient of HfO2 can be tuned from positive to negative via epitaxial strain. Nonlinear and even parabolic piezoelectric behaviors are further found at tensile epitaxial strain. This parabolic piezoelectric behavior implies that the polarization decreases when increasing the magnitude of either compressive or tensile longitudinal strain, or, equivalently, that the strain increases when increasing the magnitude of electric field being either parallel or antiparallel to the direction of polarization. The unusual piezoelectric effects are from the chemical coordination of the active oxygen atoms. These striking piezoelectric features of positive and negative sign, as well as linear and parabolical behaviors, expand the current knowledge in piezoelectricity and broaden the potential of piezoelectric applications towards electro-mechanical and communications technology.

Dynamical Control of Topology in Polar Skyrmions via Twisted Light.

Twisted light carries a nonzero orbital angular momentum, that can be transferred from light to electrons and particles ranging from nanometers to micrometers. Up to now, the interplay between twisted light with dipolar systems has scarcely been explored, though the latter bear abundant forms of topologies such as skyrmions and embrace strong light-matter coupling. Here, using first-principles-based simulations, we show that twisted light can excite and drive dynamical polar skyrmions and transfer its nonzero winding number to ferroelectric ultrathin films. The skyrmion is successively created and annihilated alternately at the two interfaces, and experiences a periodic transition from a markedly "Bloch" to "Néel" character, accompanied with the emergence of a "Bloch point" topological defect with vanishing polarization. The dynamical evolution of skyrmions is connected to a constant jump of topological number between "0" and "1" over time. These intriguing phenomena are found to have an electrostatic origin. Our study thus demonstrates that, and explains why this unique light-matter interaction can be very powerful in creating and manipulating topological solitons in functional materials.

Low voltage-driven high-performance thermal switching in antiferroelectric PbZrO3 thin films.

Effective control of heat transfer is vital for energy saving and carbon emission reduction. In contrast to achievements in electrical conduction, active control of heat transfer is much more challenging. Ferroelectrics are promising candidates for thermal switching as a result of their tunable domain structures. However, switching ratios in ferroelectrics are low (<1.2). We report that high-quality antiferroelectric PbZrO3 epitaxial thin films exhibit high-contrast (>2.2), fast-speed (<150 nanoseconds), and long-lifetime (>107) thermal switching under a small voltage (<10 V). In situ reciprocal space mapping and atomistic modelings reveal that the field-driven antiferroelectric-ferroelectric phase transition induces a substantial change of primitive cell size, which modulates phonon-phonon scattering phase space drastically and results in high switching ratio. These results advance the concept of thermal transport control in ferroic materials.

The anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in hafnia.

The anti-symmetric and anisotropic symmetric exchange interactions between two magnetic dipole moments - responsible for intriguing magnetic textures (e.g., magnetic skyrmions) - have been discovered since last century, while their electric analogues were either hidden for a long time or still not known. It is only recently that the anti-symmetric exchange interactions between electric dipoles was proved to exist (with materials hosting such an interaction being still rare) and the existence of anisotropic symmetric exchange interaction between electric dipoles remains ambiguous. Here, by symmetry analysis and first-principles calculations, we identify hafnia as a candidate material hosting the non-collinear dipole alignments, the analysis of which reveals the anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in this material. Our findings can hopefully deepen the current knowledge of electromagnetism in condensed matter, and imply the possibility of discovering novel states of matter (e.g., electric skyrmions) in hafnia-related materials.

Toward Ultimate Memory with Single-Molecule Multiferroics.

The demand for high-density storage is urgent in the current era of data explosion. Recently, several single-molecule (-atom) magnets and ferroelectrics have been reported to be promising candidates for high-density storage. As another promising candidate, single-molecule multiferroics are not only small in size but also possess ferroelectric and magnetic orderings, which can sometimes be strongly coupled and used as data storage to realize the combination of electric writing and magnetic reading. However, they have been rarely proposed and have never been experimentally reported. Here, by building Hamiltonian models, we propose a new model of single-molecule multiferroics in which electric dipoles and magnetic moments are parallel and can rotate with the rotation of the single molecule. Furthermore, by performing spin-lattice dynamics simulations, we reveal the conditions (e.g., large enough single-ion anisotropy and an appropriate electric field) under which the new single-molecule multiferroic can arise. Based on this model, as well as first-principles calculations, a realistic example of Co(NH3)4N@SWCNT is constructed and numerically confirmed to demonstrate the feasibility of the new single-molecule multiferroic model. Our work not only sheds light on the discovery of single-molecule multiferroics but also provides a new guideline to design multifunctional materials for ultimate memory devices.

Dynamical Multiferroicity and Magnetic Topological Structures Induced by the Orbital Angular Momentum of Light in a Nonmagnetic Material.

Recent studies have revealed that chiral phonons resonantly excited by ultrafast laser pulses carry magnetic moments and can enhance the magnetization of materials. In this work, using first-principles-based simulations, we present a real-space scenario where circular motions of electric dipoles in ultrathin two-dimensional ferroelectric and nonmagnetic films are driven by orbital angular momentum of light via strong coupling between electric dipoles and optical field. Rotations of these dipoles follow the evolving pattern of the optical field and create strong on-site orbital magnetic moments of ions. By characterizing topology of orbital magnetic moments in each 2D layer, we identify the vortex type of topological texture-magnetic merons with a one-half topological charge and robust stability. Our study thus provides alternative approaches for generating magnetic fields and topological textures from light-matter interaction and dynamical multiferroicity in nonmagnetic materials.

Quantum criticality at cryogenic melting of polar bubble lattices.

Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are known to prevent the occurrence of polar phases in bulk incipient ferroelectrics down to 0 K. On the other hand, little is known about the effects of QFs on the recently discovered topological patterns in ferroelectric nanostructures. Here, by using an atomistic effective Hamiltonian within classical Monte Carlo (CMC) and path integral quantum Monte Carlo (PI-QMC), we unveil how QFs affect the topology of several dipolar phases in ultrathin Pb(Zr0.4Ti0.6)O3 (PZT) films. In particular, our PI-QMC simulations show that the ZPPVs do not suppress polar patterns but rather stabilize the labyrinth, bimeron and bubble phases within a wider range of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce a quantum critical point (QCP) separating a hexagonal bubble lattice from a liquid-like state characterized by spontaneous motion, creation and annihilation of polar bubbles at cryogenic temperatures. Finally, we show that the discovered quantum melting is associated with anomalous physical response, as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.

Ferroelectric solitons crafted in epitaxial bismuth ferrite superlattices.

In ferroelectrics, complex interactions among various degrees of freedom enable the condensation of topologically protected polarization textures. Known as ferroelectric solitons, these particle-like structures represent a new class of materials with promise for beyond-CMOS technologies due to their ultrafine size and sensitivity to external stimuli. Such polarization textures have scarcely been demonstrated in multiferroics. Here, we present evidence for ferroelectric solitons in (BiFeO3)/(SrTiO3) superlattices. High-resolution piezoresponse force microscopy and Cs-corrected high-angle annular dark-field scanning transmission electron microscopy reveal a zoo of topologies, and polarization displacement mapping of planar specimens reveals center-convergent/divergent topological defects as small as 3 nm. Phase-field simulations verify that some of these structures can be classed as bimerons with a topological charge of ±1, and first-principles-based effective Hamiltonian computations show that the coexistence of such structures can lead to non-integer topological charges, a first observation in a BiFeO3-based system. Our results open new opportunities in multiferroic topotronics.

Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films.

Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.

Spherical ferroelectric solitons.

Spherical ferroelectric domains, such as electrical bubbles, polar skyrmion bubbles and hopfions, share a single and unique feature-their homogeneously polarized cores are surrounded by a vortex ring of polarization whose outer shells form a spherical domain boundary. The resulting polar texture, typical of three-dimensional topological solitons, has an entirely new local symmetry characterized by a high polarization and strain gradients. Consequently, spherical domains represent a different material system of their own with emergent properties drastically different from that of their surrounding medium. Examples of new functionalities inherent to spherical domains include chirality, optical response, negative capacitance and giant electromechanical response. These characteristics, particularly given that the domains naturally have an ultrafine scale, offer new opportunities in high-density and low-energy nanoelectronic technologies. This Perspective gives an insight into the complex polar structure and physical origin of these spherical domains, which facilitates the understanding and development of spherical domains for device applications.

Size-Induced Ferroelectricity in Antiferroelectric Oxide Membranes.

Despite extensive studies on size effects in ferroelectrics, how structures and properties evolve in antiferroelectrics with reduced dimensions still remains elusive. Given the enormous potential of utilizing antiferroelectrics for high-energy-density storage applications, understanding their size effects will provide key information for optimizing device performances at small scales. Here, the fundamental intrinsic size dependence of antiferroelectricity in lead-free NaNbO3 membranes is investigated. Via a wide range of experimental and theoretical approaches, an intriguing antiferroelectric-to-ferroelectric transition upon reducing membrane thickness is probed. This size effect leads to a ferroelectric single-phase below 40 nm, as well as a mixed-phase state with ferroelectric and antiferroelectric orders coexisting above this critical thickness. Furthermore, it is shown that the antiferroelectric and ferroelectric orders are electrically switchable. First-principle calculations further reveal that the observed transition is driven by the structural distortion arising from the membrane surface. This work provides direct experimental evidence for intrinsic size-driven scaling in antiferroelectrics and demonstrates enormous potential of utilizing size effects to drive emergent properties in environmentally benign lead-free oxides with the membrane platform.

Zeeman Effect in Centrosymmetric Antiferromagnetic Semiconductors Controlled by an Electric Field.

Centrosymmetric antiferromagnetic semiconductors, although abundant in nature, seem less promising than ferromagnets and ferroelectrics for practical applications in semiconductor spintronics. As a matter of fact, the lack of spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these materials. Here, we propose a paradigm to harness electronic spin in centrosymmetric antiferromagnets via Zeeman spin splitting of electronic energy levels-termed as the spin Zeeman effect-which is controlled by an electric field. By symmetry analysis, we identify 21 centrosymmetric magnetic point groups that accommodate such a spin Zeeman effect. We further predict by first principles that two antiferromagnetic semiconductors, Fe_{2}TeO_{6} and SrFe_{2}S_{2}O, are excellent candidates showcasing Zeeman splittings as large as ∼55 and ∼30 meV, respectively, induced by an electric field of 6 MV/cm. Moreover, the electronic spin magnetization associated to the splitting energy levels can be switched by reversing the electric field. Our Letter thus sheds light on the electric-field control of electronic spin in antiferromagnets, which broadens the scope of application of centrosymmetric antiferromagnetic semiconductors.

Two-Dimensional Organic-Inorganic Room-Temperature Multiferroics.

Organic-inorganic multiferroics are promising for the next generation of electronic devices. To date, dozens of organic-inorganic multiferroics have been reported; however, most of them show a magnetic Curie temperature much lower than room temperature, which drastically hampers their application. Here, by performing first-principles calculations and building effective model Hamiltonians, we reveal a molecular orbital-mediated magnetic coupling mechanism in two-dimensional Cr(pyz)2 (pyz = pyrazine) and the role that the valence state of the molecule plays in determining the magnetic coupling type between metal ions. Based on these, we demonstrate that a two-dimensional organic-inorganic room-temperature multiferroic, Cr(h-fpyz)2 (h-fpyz = half-fluoropyrazine), can be rationally designed by introducing ferroelectricity in Cr(pyz)2 while keeping the valence state of the molecule unchanged. Our work not only reveals the origin of magnetic coupling in 2D organic-inorganic systems but also provides a way to design room-temperature multiferroic materials rationally.

Deterministic control of ferroelectric polarization by ultrafast laser pulses.

Ultrafast light-matter interactions present a promising route to control ferroelectric polarization at room temperature, which is an exciting idea for designing novel ferroelectric-based devices. One emergent light-induced technique for controlling polarization consists in anharmonically driving a high-frequency phonon mode through its coupling to the polarization. A step towards such control has been recently accomplished, but the polarization has been reported to be only partially reversed and for a short lapse of time. Such transient partial reversal is not currently understood, and it is presently unclear if full control of polarization, by, e.g., fully reversing it or even making it adopt different directions (thus inducing structural phase transitions), can be achieved by activating the high-frequency phonon mode via terahertz pulse stimuli. Here, by means of realistic simulations of a prototypical ferroelectric, we reveal and explain (1) why a transient partial reversal has been observed, and (2) how to deterministically control the ferroelectric polarization thanks to these stimuli. Such results can provide guidance for realizing original ultrafast optoferroic devices.

High-density switchable skyrmion-like polar nanodomains integrated on silicon.

Topological domains in ferroelectrics1-5 have received much attention recently owing to their novel functionalities and potential applications6,7 in electronic devices. So far, however, such topological polar structures have been observed only in superlattices grown on oxide substrates, which limits their applications in silicon-based electronics. Here we report the realization of room-temperature skyrmion-like polar nanodomains in lead titanate/strontium titanate bilayers transferred onto silicon. Moreover, an external electric field can reversibly switch these nanodomains into the other type of polar texture, which substantially modifies their resistive behaviours. The polar-configuration-modulated resistance is ascribed to the distinct band bending and charge carrier distribution in the core of the two types of polar texture. The integration of high-density (more than 200 gigabits per square inch) switchable skyrmion-like polar nanodomains on silicon may enable non-volatile memory applications using topological polar structures in oxides.

Assembling Diverse Skyrmionic Phases in Fe3 GeTe2 Monolayers.

Skyrmionic magnetic states are promising in advanced spintronics. This topic is experiencing recent progress in 2D magnets, with, for example, a near 300 K Curie temperature observed in Fe3 GeTe2 . However, despite previous studies reporting skyrmions in Fe3 GeTe2 , such a system remains elusive, since it has been reported to host either Néel-type or Bloch-type textures, while a net Dzyaloshinskii-Moriya interaction (DMI) cannot occur in this compound for symmetry reasons. It is thus desirable to develop an accurate model to deeply understand Fe3 GeTe2 . Here, a newly developed method adopting spin invariants is applied to build a first-principle-based Hamiltonian, which predicts colorful topological defects assembled from the unit of Bloch lines, and reveals the critical role of specific forms of fourth-order interactions in Fe3 GeTe2 . Rather than the DMI, it is the multiple fourth-order interactions, with symmetry and spin-orbit couplings considered, that stabilize both Néel-type and Bloch-type skyrmions, as well as antiskyrmions, without any preference for clockwise versus counterclockwise spin rotation. This study also demonstrates that spin invariants can be used as a general approach to study complex magnetic interactions.