Author Correction: Spatially resolved steady-state negative capacitance.

In this Letter, the first name of author Bhagwati Prasad was misspelled Bhagawati. This error has been corrected online.

Spatially resolved steady-state negative capacitance.

Negative capacitance is a newly discovered state of ferroelectric materials that holds promise for electronics applications by exploiting a region of thermodynamic space that is normally not accessible1-14. Although existing reports of negative capacitance substantiate the importance of this phenomenon, they have focused on its macroscale manifestation. These manifestations demonstrate possible uses of steady-state negative capacitance-for example, enhancing the capacitance of a ferroelectric-dielectric heterostructure4,7,14 or improving the subthreshold swing of a transistor8-12. Yet they constitute only indirect measurements of the local state of negative capacitance in which the ferroelectric resides. Spatial mapping of this phenomenon would help its understanding at a microscopic scale and also help to achieve optimal design of devices with potential technological applications. Here we demonstrate a direct measurement of steady-state negative capacitance in a ferroelectric-dielectric heterostructure. We use electron microscopy complemented by phase-field and first-principles-based (second-principles) simulations in SrTiO3/PbTiO3 superlattices to directly determine, with atomic resolution, the local regions in the ferroelectric material where a state of negative capacitance is stabilized. Simultaneous vector mapping of atomic displacements (related to a complex pattern in the polarization field), in conjunction with reconstruction of the local electric field, identify the negative capacitance regions as those with higher energy density and larger polarizability: the domain walls where the polarization is suppressed.

Emergent chirality in the electric polarization texture of titanate superlattices.

Chirality is a geometrical property by which an object is not superimposable onto its mirror image, thereby imparting a handedness. Chirality determines many important properties in nature-from the strength of the weak interactions according to the electroweak theory in particle physics to the binding of enzymes with naturally occurring amino acids or sugars, reactions that are fundamental for life. In condensed matter physics, the prediction of topologically protected magnetic skyrmions and related spin textures in chiral magnets has stimulated significant research. If the magnetic dipoles were replaced by their electrical counterparts, then electrically controllable chiral devices could be designed. Complex oxide BaTiO3/SrTiO3 nanocomposites and PbTiO3/SrTiO3 superlattices are perfect candidates, since "polar vortices," in which a continuous rotation of ferroelectric polarization spontaneously forms, have been recently discovered. Using resonant soft X-ray diffraction, we report the observation of a strong circular dichroism from the interaction between circularly polarized light and the chiral electric polarization texture that emerges in PbTiO3/SrTiO3 superlattices. This hallmark of chirality is explained by a helical rotation of electric polarization that second-principles simulations predict to reside within complex 3D polarization textures comprising ordered topological line defects. The handedness of the texture can be topologically characterized by the sign of the helicity number of the chiral line defects. This coupling between the optical and novel polar properties could be exploited to encode chiral signatures into photon or electron beams for information processing.

Interplay of couplings between antiferrodistortive, ferroelectric, and strain degrees of freedom in monodomain PbTiO3/SrTiO3 superlattices.

We report first-principles calculations on the coupling between epitaxial strain, polarization, and oxygen octahedra rotations in monodomain (PbTiO(3))(n)/(SrTiO(3))(n) superlattices. We show how the interplay between (i) the epitaxial strain and (ii) the electrostatic conditions can be used to control the orientation of the main axis of the system. The electrostatic constrains at the interface facilitate the polarization rotation and, as a consequence, we predict large piezoelectric responses at epitaxial strains smaller than those required considering only strain effects. In addition, ferroelectric (FE) and antiferrodistortive (AFD) modes are strongly coupled. Usual steric arguments cannot explain this coupling and a covalent model is proposed to account for it. The energy gain due to the FE-AFD coupling decreases with the periodicity of the superlattice, becoming negligible for n ≥ 3.

Atomic scale crystal field mapping of polar vortices in oxide superlattices.

Polar vortices in oxide superlattices exhibit complex polarization topologies. Using a combination of electron energy loss near-edge structure analysis, crystal field multiplet theory, and first-principles calculations, we probe the electronic structure within such polar vortices in [(PbTiO3)16/(SrTiO3)16] superlattices at the atomic scale. The peaks in Ti [Formula: see text]-edge spectra shift systematically depending on the position of the Ti4+ cations within the vortices i.e., the direction and magnitude of the local dipole. First-principles computation of the local projected density of states on the Ti [Formula: see text] orbitals, together with the simulated crystal field multiplet spectra derived from first principles are in good agreement with the experiments.

Anomalous Motion of Charged Domain Walls and Associated Negative Capacitance in Copper-Chlorine Boracite.

During switching, the microstructure of a ferroelectric normally adapts to align internal dipoles with external electric fields. Favorably oriented dipolar regions (domains) grow at the expense of those in unfavorable orientations and this is manifested in a predictable field-induced motion of the walls that separate one domain from the next. Here, the discovery that specific charged 90°domain walls in copper-chlorine boracite move in the opposite direction to that expected, increasing the size of the domain in which polarization is anti-aligned with the applied field, is reported. Polarization-field (P-E) hysteresis loops, inferred from optical imaging, show negative gradients and non-transient negative capacitance, throughout the P-E cycle. Switching currents (generated by the relative motion between domain walls and sensing electrodes) confirm this, insofar as their signs are opposite to those expected conventionally. For any given bias, the integrated switching charge due to this anomalous wall motion is directly proportional to time, indicating that the magnitude of the negative capacitance component should be inversely related to frequency. This passes Jonscher's test for the misinterpretation of positive inductance and gives confidence that field-induced motion of these specific charged domain walls generates a measurable negative capacitance contribution to the overall dielectric response.

Effect of intrinsic defects on the thermal conductivity of PbTe from classical molecular dynamics simulations.

Despite being the archetypal thermoelectric material, still today some of the most exciting advances in the efficiency of these materials are being achieved by tuning the properties of PbTe. Its inherently low lattice thermal conductivity can be lowered to its fundamental limit by designing a structure capable of scattering phonons over a wide range of length scales. Intrinsic defects, such as vacancies or grain boundaries, can and do play the role of these scattering sites. Here we assess the effect of these defects by means of molecular dynamics simulations. For this we purposely parametrize a Buckingham potential that provides an excellent description of the thermal conductivity of this material over a wide temperature range. Our results show that intrinsic point defects and grain boundaries can reduce the lattice conductivity of PbTe down to a quarter of its bulk value. By studying the size dependence we also show that typical defect concentrations and grain sizes realized in experiments normally correspond to the bulk lattice conductivity of pristine PbTe.

Ferromagneticlike closure domains in ferroelectric ultrathin films: first-principles simulations.

We simulate from first principles the energetic, structural, and electronic properties of ferroelectric domains in ultrathin SrRuO_{3}/BaTiO_{3}/SrRuO_{3} ferroelectric capacitors in short circuit. The domains are stabilized down to two unit cells at zero temperature, adopting the form of a domain of closure, common in ferromagnetic thin films. The domains are closed by the in-plane relaxation of the atoms in the first SrO layer of the electrode, which behaves more like SrO in highly polarizable SrTiO3 than in metallic SrRuO3. Even if small, these lateral displacements are very important to stabilize the domains and might provide some hints to explain why some systems break into domains while others remain in a monodomain configuration. An analysis of the electrostatic potential reveals preferential points of pinning for charged defects at the ferroelectric-electrode interface, possibly playing a major role in film fatigue.