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.

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.

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.

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2.

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl_{3} and Na_{2}IrO_{3}, having an effective S=1/2 spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe_{3}, that rather possess a S=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3d transition metal compounds.

ABINIT: Overview and focus on selected capabilities.

abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe-Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the "temperature-dependent effective potential" approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned.

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.

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.

Freestanding Ferroelectric Bubble Domains.

Bubble-like domains, typically a precursor to the electrical skyrmions, arise in ultrathin complex oxide ferroelectric-dielectric-ferroelectric heterostructures epitaxially clamped with flat substrates. Here, it is reported that these specially ordered electric dipoles can also be retained in a freestanding state despite the presence of inhomogeneously distributed structural ripples. By probing local piezo and capacitive responses and using atomistic simulations, this study analyzes these ripples, sheds light on how the bubbles are stabilized in the modified electromechanical energy landscape, and discusses the difference in morphology between bubbles in freestanding and as-grown states. These results are anticipated to be the starting point of a new paradigm for the exploration of electric skyrmions with arbitrary boundaries and physically flexible topological orders in ferroelectric curvilinear space.

Ferroelectric phase-transition frustration near a tricritical composition point.

Phase transition describes a mutational behavior of matter states at a critical transition temperature or external field. Despite the phase-transition orders are well sorted by classic thermodynamic theory, ambiguous situations interposed between the first- and second-order transitions were exposed one after another. Here, we report discovery of phase-transition frustration near a tricritical composition point in ferroelectric Pb(Zr1-xTix)O3. Our multi-scale transmission electron microscopy characterization reveals a number of geometrically frustrated microstructure features such as self-assembled hierarchical domain structure, degeneracy of mesoscale domain tetragonality and decoupled polarization-strain relationship. Associated with deviation from the classic mean-field theory, dielectric critical exponent anomalies and temperature dependent birefringence data unveil that the frustrated transition order stems from intricate competition of short-range polar orders and their decoupling to long-range lattice deformation. With supports from effective Hamiltonian Monte Carlo simulations, our findings point out a potentially universal mechanism to comprehend the abnormal critical phenomena occurring in phase-transition materials.

Microscopic origins of the large piezoelectricity of leadfree (Ba,Ca)(Zr,Ti)O3.

In light of directives around the world to eliminate toxic materials in various technologies, finding lead-free materials with high piezoelectric responses constitutes an important current scientific goal. As such, the recent discovery of a large electromechanical conversion near room temperature in (1-x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 compounds has directed attention to understanding its origin. Here, we report the development of a large-scale atomistic scheme providing a microscopic insight into this technologically promising material. We find that its high piezoelectricity originates from the existence of large fluctuations of polarization in the orthorhombic state arising from the combination of a flat free-energy landscape, a fragmented local structure, and the narrow temperature window around room temperature at which this orthorhombic phase is the equilibrium state. In addition to deepening the current knowledge on piezoelectricity, these findings have the potential to guide the design of other lead-free materials with large electromechanical responses.

Nanoscale Bubble Domains and Topological Transitions in Ultrathin Ferroelectric Films.

Observation of a new type of nanoscale ferroelectric domains, termed as "bubble domains"-laterally confined spheroids of sub-10 nm size with local dipoles self-aligned in a direction opposite to the macroscopic polarization of a surrounding ferroelectric matrix-is reported. The bubble domains appear in ultrathin epitaxial PbZr0.2 Ti0.8 O3 /SrTiO3 /PbZr0.2 Ti0.8 O3 ferroelectric sandwich structures due to the interplay between charge and lattice degrees of freedom. The existence of the bubble domains is revealed by high-resolution piezoresponse force microscopy (PFM), and is corroborated by aberration-corrected atomic-resolution scanning transmission electron microscopy mapping of the polarization displacements. An incommensurate phase and symmetry breaking is found within these domains resulting in local polarization rotation and hence impart a mixed Néel-Bloch-like character to the bubble domain walls. PFM hysteresis loops for the bubble domains reveal that they undergo an irreversible phase transition to cylindrical domains under the electric field, accompanied by a transient rise in the electromechanical response. The observations are in agreement with ab-initio-based calculations, which reveal a very narrow window of electrical and elastic parameters that allow the existence of bubble domains. The findings highlight the richness of polar topologies possible in ultrathin ferroelectric structures and bring forward the prospect of emergent functionalities due to topological transitions.

Corrigendum: Microscopic origins of the large piezoelectricity of leadfree (Ba,Ca)(Zr,Ti)O3.

This corrects the article DOI: 10.1038/ncomms15944.