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.

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.

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.

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.

Magnetoelastic standing waves induced in UO2 by microsecond magnetic field pulses.

Magnetoelastic dilatometry of the piezomagnetic antiferromagnet UO2 was performed via the fiber Bragg grating method in magnetic fields up to 150 T generated by a single-turn coil setup. We show that in microsecond timescales, pulsed-magnetic fields excite mechanical resonances at temperatures ranging from 10 to 300 K, in the paramagnetic as well as within the robust antiferromagnetic state of the material. These resonances, which are barely attenuated within the 100-µs observation window, are attributed to the strong magnetoelastic coupling in UO2 combined with the high crystalline quality of the single crystal samples. They compare well with mechanical resonances obtained by a resonant ultrasound technique and superimpose on the known nonmonotonic magnetostriction background. A clear phase shift of π in the lattice oscillations is observed in the antiferromagnetic state when the magnetic field overcomes the piezomagnetic switch field H[Formula: see text] T. We present a theoretical argument that explains this unexpected behavior as a result of the reversal of the antiferromagnetic order parameter at Hc.

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.

Anisotropic epitaxial stabilization of a low-symmetry ferroelectric with enhanced electromechanical response.

Piezoelectrics interconvert mechanical energy and electric charge and are widely used in actuators and sensors. The best performing materials are ferroelectrics at a morphotropic phase boundary, where several phases coexist. Switching between these phases by electric field produces a large electromechanical response. In ferroelectric BiFeO3, strain can create a morphotropic-phase-boundary-like phase mixture and thus generate large electric-field-dependent strains. However, this enhanced response occurs at localized, randomly positioned regions of the film. Here, we use epitaxial strain and orientation engineering in tandem-anisotropic epitaxy-to craft a low-symmetry phase of BiFeO3 that acts as a structural bridge between the rhombohedral-like and tetragonal-like polymorphs. Interferometric displacement sensor measurements reveal that this phase has an enhanced piezoelectric coefficient of ×2.4 compared with typical rhombohedral-like BiFeO3. Band-excitation frequency response measurements and first-principles calculations provide evidence that this phase undergoes a transition to the tetragonal-like polymorph under electric field, generating an enhanced piezoelectric response throughout the film and associated field-induced reversible strains. These results offer a route to engineer thin-film piezoelectrics with improved functionalities, with broader perspectives for other functional oxides.

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.

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.

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.

Dzyaloshinskii-Moriya-like interaction in ferroelectrics and antiferroelectrics.

The Dzyaloshinskii-Moriya interaction (DMI) between two magnetic moments mi and mj is of the form [Formula: see text]. It originates from spin-orbit coupling, and is at the heart of fascinating phenomena involving non-collinear magnetism, such as magnetic topological defects (for example, skyrmions) as well as spin-orbit torques and magnetically driven ferroelectricity, that are of significant fundamental and technological interest. In sharp contrast, its electric counterpart, which is an electric DMI characterized by its [Formula: see text] strength and describing an interaction between two polar displacements ui and uj, has rarely been considered, despite the striking possibility that it could also generate new features associated with non-collinear patterns of electric dipoles. Here we report first-principles simulations combined with group theoretical symmetry analysis which not only demonstrate that electric DMI does exist and has a one-to-one correspondence with its magnetic analogue, but also reveals a physical source for it. These findings can be used to explain and/or design phenomena of possible technological importance in ferroelectrics and multiferroics.

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.

Coexistence and Coupling of Multiple Charge Orderings and Spin States in Hexagonal Ferrite.

The coupling between charge and spin orderings in strongly correlated systems plays a crucial role in fundamental physics and device applications. As a candidate of multiferroic materials, LuFe2O4 with a nominal Fe2.5+ valence state has the potential for strong charge-spin interactions; however, these interactions have not been fully understood until now. Here, combining complementary characterization methods with theoretical calculations, two types of charge orderings with distinct magnetic properties are revealed. The ground states of LuFe2O4 are decided by the parallel/antiparallel coupling of both charge and spin orderings in the adjacent FeO double layers. Whereas the ferroelectric charge ordering remains ferrimagnetic below 230 K, the antiferroelectric ordering undergoes antiferromagnetic-ferrimagnetic-paramagnetic transitions from 2 K to room temperature. This study demonstrates the unique aspects of strong spin-charge coupling within LuFe2O4. Our results shed light on the coexistence and competing nature of orderings in quantum materials.

Purely Cubic Spin Splittings with Persistent Spin Textures.

Purely cubic spin splittings in the band structure of bulk insulators have not been extensively investigated yet despite the fact that they may pave the way for novel spin-orbitronic applications and can also result in a variety of promising spin phenomena. By symmetry analysis and first-principles simulations, we report symmetry-enforced purely cubic spin splittings (SEPCSS) that can even lead to persistent spin textures. In particular, these SEPCSS can be thought to be complementary to the cubic Rashba and cubic Dresselhaus types of spin splittings. Strikingly, the presently discovered SEPCSS are expected to exist in the large family of materials crystallizing in the 6[over ¯]m2 and 6[over ¯] point groups, including the Ge_{3}Pb_{5}O_{11}, Pb_{7}Br_{2}F_{12}, and Pb_{7}Cl_{2}F_{12} compounds.

Photoinduced Phase Transitions in Ferroelectrics.

Ferroic materials naturally exhibit a rich number of functionalities, which often arise from thermally, chemically, or mechanically induced symmetry breakings or phase transitions. Based on density functional calculations, we demonstrate here that light can drive phase transitions as well in ferroelectric materials such as the perovskite oxides lead titanate and barium titanate. Phonon analysis and total energy calculations reveal that the polarization tends to vanish under illumination, to favor the emergence of nonpolar phases, potentially antiferroelectric, and exhibiting a tilt of the oxygen octahedra. Strategies to tailor photoinduced phases based on phonon instabilities in the electronic ground state are also discussed.

Ferroelectricity with Asymmetric Hysteresis in Metallic LiOsO_{3} Ultrathin Films.

Bulk LiOsO_{3} was experimentally identified as a "ferroelectric" metal where polar distortions coexist with metallicity [Shi et al., Nat. Mater. 12, 1024 (2013)NMAACR1476-112210.1038/nmat3754]. It is generally believed that polar displacements in a ferroelectric metal cannot be switched by an external electric field. Here, via comprehensive density functional theory calculations, we demonstrate that a two-unit cell-thick LiOsO_{3} thin film exhibits a ferroelectric ground state having an out-of-plane electric dipole moment that can be switched by an external electric field. Moreover, its dipole moment-versus-electric field hysteresis loop is asymmetric because only surface Li ions' displacements are reversed by the external electric field whereas the field-induced force on inner Li atoms is nearly fully screened by itinerant electrons. As a relevant by-product of our study, we also extend the concept of "Born effective charge" to finite metallic systems, and show its usefulness to rationalize the observed effects.

Uncompensated Polarization in Incommensurate Modulations of Perovskite Antiferroelectrics.

Complex polar structures of incommensurate modulations (ICMs) are revealed in chemically modified PbZrO_{3} perovskite antiferroelectrics using advanced transmission electron microscopy techniques. The Pb-cation displacements, previously assumed to arrange in a fully compensated antiparallel fashion, are found to be either antiparallel, but with different magnitudes, or in a nearly orthogonal arrangement in adjacent stripes in the ICMs. Ab initio calculations corroborate the low-energy state of these arrangements. Our discovery corrects the atomic understanding of ICMs in PbZrO_{3}-based perovskite antiferroelectrics.

Intrinsic Origin of Enhancement of Ferroelectricity in SnTe Ultrathin Films.

Previous studies showed that, as ferroelectric films become thinner, their Curie temperature (T_{c}) and polarization below T_{c} both typically decrease. In contrast, a recent experiment [Chang et al., Science 353, 274 (2016)SCIEAS0036-807510.1126/science.aad8609] observed that atomic-thick SnTe films have a higher T_{c} than their bulk counterpart, which was attributed to extrinsic effects. We find, using first-principles calculations, that the 0-K energy barrier for the polarization switching (which is a quantity directly related to T_{c}) is higher in most investigated defect-free SnTe ultrathin films than that in bulk SnTe, and that the 5-unit-cell (UC) SnTe thin film has the largest energy barrier as a result of an interplay between hybridization interactions and Pauli repulsions. Further simulations, employing a presently developed effective Hamiltonian, confirm that freestanding, defect-free SnTe thin films have a higher T_{c} than bulk SnTe, except for the 1-UC case. Our work, therefore, demonstrates the possibility to intrinsically enhance ferroelectricity of ultrathin films by reducing their thickness.

Topological Defects with Distinct Dipole Configurations in PbTiO_{3}/SrTiO_{3} Multilayer Films.

Distinct and novel features of nanometric electric topological defects, including dipole waves and dipole disclinations, are presently revealed in the PbTiO_{3} layers of PbTiO_{3}/SrTiO_{3} multilayer films by means of quantitative high-resolution scanning transmission electron microscopy. These original dipole configurations are confirmed and explained by atomistic simulations and have the potential to act as functional elements in future electronics.