Subterahertz collective dynamics of polar vortices.

The collective dynamics of topological structures1-6 are of interest from both fundamental and applied perspectives. For example, studies of dynamical properties of magnetic vortices and skyrmions3,4 have not only deepened our understanding of many-body physics but also offered potential applications in data processing and storage7. Topological structures constructed from electrical polarization, rather than electron spin, have recently been realized in ferroelectric superlattices5,6, and these are promising for ultrafast electric-field control of topological orders. However, little is known about the dynamics underlying the functionality of such complex extended nanostructures. Here, using terahertz-field excitation and femtosecond X-ray diffraction measurements, we observe ultrafast collective polarization dynamics that are unique to polar vortices, with orders-of-magnitude higher frequencies and smaller lateral size than those of experimentally realized magnetic vortices3. A previously unseen tunable mode, hereafter referred to as a vortexon, emerges in the form of transient arrays of nanoscale circular patterns of atomic displacements, which reverse their vorticity on picosecond timescales. Its frequency is considerably reduced (softened) at a critical strain, indicating a condensation (freezing) of structural dynamics. We use first-principles-based atomistic calculations and phase-field modelling to reveal the microscopic atomic arrangements and corroborate the frequencies of the vortex modes. The discovery of subterahertz collective dynamics in polar vortices opens opportunities for electric-field-driven data processing in topological structures with ultrahigh speed and density.

Publisher Correction: Enhanced ferroelectricity in ultrathin films grown directly on silicon.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Enhanced ferroelectricity in ultrathin films grown directly on silicon.

Ultrathin ferroelectric materials could potentially enable low-power perovskite ferroelectric tetragonality logic and nonvolatile memories1,2. As ferroelectric materials are made thinner, however, the ferroelectricity is usually suppressed. Size effects in ferroelectrics have been thoroughly investigated in perovskite oxides-the archetypal ferroelectric system3. Perovskites, however, have so far proved unsuitable for thickness scaling and integration with modern semiconductor processes4. Here we report ferroelectricity in ultrathin doped hafnium oxide (HfO2), a fluorite-structure oxide grown by atomic layer deposition on silicon. We demonstrate the persistence of inversion symmetry breaking and spontaneous, switchable polarization down to a thickness of one nanometre. Our results indicate not only the absence of a ferroelectric critical thickness but also enhanced polar distortions as film thickness is reduced, unlike in perovskite ferroelectrics. This approach to enhancing ferroelectricity in ultrathin layers could provide a route towards polarization-driven memories and ferroelectric-based advanced transistors. This work shifts the search for the fundamental limits of ferroelectricity to simpler transition-metal oxide systems-that is, from perovskite-derived complex oxides to fluorite-structure binary oxides-in which 'reverse' size effects counterintuitively stabilize polar symmetry in the ultrathin regime.

Pure Chiral Polar Vortex Phase in PbTiO3/SrTiO3 Superlattices with Tunable Circular Dichroism.

Nontrivial polarization textures have been demonstrated in ferroelectric/dielectric superlattices, where the electrostatic, elastic, and different gradient energies compete in a delicate balance. When PbTiO3/SrTiO3 superlattices are grown on DyScO3, the coexistence of ferroelectric domains and vortex structure is observed for n = 12-20 unit cells. Here, we report an approach to achieve single-phase vortex structures in superlattices by controlling the epitaxial strain using Sr1.04Al0.12Ga0.35Ta0.50O3 substrates. The domain width follows Kittel's law with the thickness of the ferroelectric PbTiO3 layers. A phase transition from vortex to a disordered phase with temperature is characterized by the correlation length. Resonant soft X-ray diffraction circular dichroism at the titanium L-edge reveals enhanced chirality with the thickness of the ferroelectric layer. These results are supported by second-principles simulations, which demonstrate that the integrated helicity increases with n. The stabilization of chiral single-phase polar vortices in ferroelectric/dielectric superlattices can enable novel optoelectronic devices with enhanced ferroelectric-light interaction.

Inherent Spin-Polarization Coupling in a Magnetoelectric Vortex.

Solid-state materials are currently being explored as a platform for the manipulation of spins for spintronics and quantum information science. More broadly, a wide spectrum of ferroelectric materials, spanning from inorganic oxides to polymeric systems such as PVDF, present a different approach to explore quantum phenomena in which the spins are set and manipulated with electric fields. Using dilute Fe3+-doped ferroelectric PbTiO3-SrTiO3 superlattices as a model system, we demonstrate intrinsic spin-polarization control of spin directionality in complex ferroelectric vortices and skyrmions. Electron paramagnetic resonance (EPR) spectra show that the spins in the Fe3+ ion are strongly coupled to the local polarization and preferentially aligned perpendicular to the ferroelectric polar c axis in this complex vortex structure. The effect of polarization-spin directionality is corroborated by first-principles calculations, demonstrating the variation of the spin directionality with the polar texture and offering the potential for future quantum analogues of macroscopic magnetoelectric devices.

Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering.

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Electric field control of chirality.

Polar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation­based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of nonchiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field-controllable order parameter.

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering.

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO3/SrTiO3 superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.

Emergence of the Vortex State in Confined Ferroelectric Heterostructures.

The manipulation of charge and lattice degrees of freedom in atomically precise, low-dimensional ferroelectric superlattices can lead to exotic polar structures, such as a vortex state. The role of interfaces in the evolution of the vortex state in these superlattices (and the associated electrostatic and elastic boundary conditions they produce) has remained unclear. Here, the toroidal state, arranged in arrays of alternating clockwise/counterclockwise polar vortices, in a confined SrTiO3 /PbTiO3 /SrTiO3 trilayer is investigated. By utilizing a combination of transmission electron microscopy, synchrotron-based X-ray diffraction, and phase-field modeling, the phase transition as a function of layer thickness (number of unit cells) demonstrates how the vortex state emerges from the ferroelectric state by varying the thickness of the confined PbTiO3 layer. Intriguingly, the vortex state arises at head-to-head domain boundaries in ferroelectric a1 /a2 twin structures. In turn, by varying the total number of PbTiO3 layers (moving from trilayer to superlattices), it is possible to manipulate the long-range interactions among multiple confined PbTiO3 layers to stabilize the vortex state. This work provides a new understanding of how the different energies work together to produce this exciting new state of matter and can contribute to the design of novel states and potential memory applications.

Epitaxial Strain Control of Relaxor Ferroelectric Phase Evolution.

Understanding and ultimately controlling the large electromechanical effects in relaxor ferroelectrics requires intimate knowledge of how the local-polar order evolves under applied stimuli. Here, the biaxial-strain-induced evolution of and correlations between polar structures and properties in epitaxial films of the prototypical relaxor ferroelectric 0.68PbMg1/3 Nb2/3 O3 -0.32PbTiO3 are investigated. X-ray diffuse-scattering studies reveal an evolution from a butterfly- to disc-shaped pattern and an increase in the correlation-length from ≈8 to ≈25 nm with increasing compressive strain. Molecular-dynamics simulations reveal the origin of the changes in the diffuse-scattering patterns and that strain induces polarization rotation and the merging of the polar order. As the magnitude of the strain is increased, relaxor behavior is gradually suppressed but is not fully quenched. Analysis of the dynamic evolution of dipole alignment in the simulations reveals that, while, for most unit-cell chemistries and configurations, strain drives a tendency toward more ferroelectric-like order, there are certain unit cells that become more disordered under strain, resulting in stronger competition between ordered and disordered regions and enhanced overall susceptibilities. Ultimately, this implies that deterministic creation of specific local chemical configurations could be an effective way to enhance relaxor performance.

Three-State Ferroelastic Switching and Large Electromechanical Responses in PbTiO3 Thin Films.

Leveraging competition between energetically degenerate states to achieve large field-driven responses is a hallmark of functional materials, but routes to such competition are limited. Here, a new route to such effects involving domain-structure competition is demonstrated, which arises from strain-induced spontaneous partitioning of PbTiO3 thin films into nearly energetically degenerate, hierarchical domain architectures of coexisting c/a and a1 /a2 domain structures. Using band-excitation piezoresponse force microscopy, this study manipulates and acoustically detects a facile interconversion of different ferroelastic variants via a two-step, three-state ferroelastic switching process (out-of-plane polarized c+ → in-plane polarized a → out-of-plane polarized c- state), which is concomitant with large nonvolatile electromechanical strains (≈1.25%) and tunability of the local piezoresponse and elastic modulus (>23%). It is further demonstrated that deterministic, nonvolatile writing/erasure of large-area patterns of this electromechanical response is possible, thus showing a new pathway to improved function and properties.