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

This corrects the article DOI: 10.1038/ncomms15944.

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.

On the origin of the great rigidity of self-assembled diphenylalanine nanotubes.

The elastic properties of the nanotubes of self-assembled aromatic dipeptide diphenylalanine are investigated by means of Raman spectroscopy and a mass-in-mass 1D model. Analysis of nanotubes' lattice vibrations reveals the essential contribution of the water in the nanochannel core of the tubes to the Young's modulus and high water mobility along the channel. Direct measurements of the Young's modulus performed by nanoindentation confirm the obtained results.

Novel complex phenomena in ferroelectric nanocomposites.

A first-principles-based effective Hamiltonian is used to investigate finite-temperature properties of ferroelectric nanocomposites made of periodic arrays of ferroelectric nanowires embedded in a matrix formed by another ferroelectric material. Novel transitions and features related to flux-closure configurations are found. Examples include (i) a vortex core transition, that is characterized by the change of the vortex cores from being axisymmetric to exhibiting a 'broken symmetry'; (ii) translational mode of the vortex cores; (iii) striking zigzag dipolar chains along the vortex core axis; and (iv) phase-locking of ferroelectric vortices accompanied by ferroelectric antivortices. These complex phenomena are all found to coexist with a spontaneous electrical polarization aligned along the normal of the plane containing the vortices.

A simple law governing coupled magnetic orders in perovskites.

An energetic expression containing four different macroscopic terms is proposed to explain and understand coupled magnetic orders (and the directions of the simultaneously occurring ferromagnetic and/or antiferromagnetic vectors) in terms of anti-phase and/or in-phase tilting of oxygen octahedra in magnetic and multiferroic perovskites. This expression is derived from a suggested simple microscopic formula, and has its roots in the Dzyaloshinsky-Moriya interaction. Comparison with data available in the literature and with first-principles calculations we conduct here confirms the validity of such a simple and general law for any tested structural paraelectric and even ferroelectric phase, and for any chosen direction of any selected primary magnetic vector.

Phase transitions in epitaxial (-110) BiFeO3 films from first principles.

The effect of misfit strain on properties of epitaxial BiFeO3 films that are grown along the pseudocubic [110] direction, rather than along the usual [001] direction, is predicted from density-functional theory. These films adopt the monoclinic Cc space group for compressive misfit strains smaller in magnitude than ≃1.6% and for any investigated tensile strain. In this Cc phase, both polarization and the axis about which antiphase oxygen octahedra tilt rotate within the epitaxial plane as the strain varies. Surprisingly and unlike in (001) films, for compressive strain larger in magnitude than ≃1.6%, the polarization vanishes and two orthorhombic phases of Pnma and P2(1)2(1)2(1) symmetry successively emerge via strain-induced transitions. The Pnma-to-P2(1)2(1)2(1) transition is a rare example of a so-called pure gyrotropic phase transition, and the P2(1)2(1)2(1) phase exhibits original interpenetrated arrays of ferroelectric vortices and antivortices.

Critical behavior in ferroelectrics from first principles.

We report first-principles-based calculations, combined with an efficient Monte Carlo technique, that undoubtedly show that Pb(Zr0.5Ti0.5)O3, one of the most important ferroelectrics to date, adopts critical behavior that strongly deviates from the classical mean-field approach while being, in fact, consistent with the 3D-random Ising universality class.

Finite-temperature properties of multiferroic BiFeO3.

An effective Hamiltonian scheme is developed to study finite-temperature properties of multiferroic BiFeO3. This approach reproduces very well (i) the symmetry of the ground state, (ii) the Néel and Curie temperatures, and (iii) the intrinsic magnetoelectric coefficients (that are very weak). This scheme also predicts (a) an overlooked phase above Tc approximately 1100 K that is associated with antiferrodistortive motions, as consistent with our additional x-ray diffractions, (b) improperlike dielectric features above Tc, and (c) that the ferroelectric transition is of first order with no group-subgroup relation between the paraelectric and polar phases.

Phase diagram of pb(Zr,Ti)O3 solid solutions from first principles.

A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of Pb(Zr1-xTix)O3 solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.

Ferroelectricity of perovskites under pressure.

Ab initio simulations and experimental techniques are combined to reveal that, unlike what was commonly accepted for more than 30 years, perovskites and related materials enhance their ferroelectricity as hydrostatic pressure increases above a critical value. This unexpected high-pressure ferroelectricity is different in nature from conventional ferroelectricity because it is driven by an original electronic effect rather by long-range interactions.

Ultrathin films of ferroelectric solid solutions under a residual depolarizing field.

A first-principles-derived approach is developed to study the effects of depolarizing electric fields on the properties of Pb(Zr,Ti)O3 ultrathin films for different mechanical boundary conditions. A rich variety of ferroelectric phases and polarization patterns is found, depending on the interplay between strain and the amount of screening of surface charges. Examples include triclinic phases, monoclinic states with in-plane and/or out-of-plane components of the polarization, homogeneous and inhomogeneous tetragonal states, as well as peculiar laminar nanodomains.

Unusual thermodynamic properties and nonergodicity in ferroelectric superlattices.

The properties of [Pb(Zr(1-x(1))Ti(x(1)))O(3)](n)/[Pb(Zr(1-x(2))Ti(x(2)))O(3)](n) superlattices, with a 2n period, are simulated using an ab initio based approach. The x(1) and x(2) compositions are chosen to be located across the morphotropic phase boundary of the corresponding disordered alloys, while the (x(1)+x(2))/2 average composition lies inside this boundary. These superlattices exhibit an unusual thermodynamic phase transition sequence, including a triclinic ground state. They also have the kind of peculiar free-energy landscape yielding nonergodicity. The effects responsible for these anomalies are discussed.

Planar defects and incommensurate phases in highly ordered perovskite solid solutions.

A first-principles-derived approach is used to study the effects of planar defects on structural properties of a rocksalt-ordered Pb(Sc0.5Nb0.5)O3 alloy. These defects lead to unusual features, including a less symmetrical ground state with respect to the perfectly ordered material. We also propose that a simple and original mechanism, involving these defects, may be responsible for the existence and anomalous characteristics of the incommensurate phases observed in insulating perovskites.