Bulk ferroelectrics undergo structural phase transformations at low temperatures, giving multi-stable (that is, multiple-minimum) degenerate states with spontaneous polarization. Accessing these states by applying, and varying the direction of, an external electric field is a key principle for the operation of devices such as non-volatile ferroelectric random access memories (NFERAMs). Compared with bulk ferroelectrics, low-dimensional finite ferroelectric structures promise to increase the storage density of NFERAMs 10,000-fold. But this anticipated benefit hinges on whether phase transitions and multi-stable states still exist in low-dimensional structures. Previous studies have suggested that phase transitions are impossible in one-dimensional systems, and become increasingly less likely as dimensionality further decreases. Here we perform ab initio studies of ferroelectric nanoscale disks and rods of technologically important Pb(Zr,Ti)O3 solid solutions, and demonstrate the existence of previously unknown phase transitions in zero-dimensional ferroelectric nanoparticles. The minimum diameter of the disks that display low-temperature structural bistability is determined to be 3.2 nm, enabling an ultimate NFERAM density of 60 x 10(12) bits per square inch-that is, five orders of magnitude larger than those currently available. Our results suggest an innovative use of ferroelectric nanostructures for data storage, and are of fundamental value for the theory of phase transition in systems of low dimensionality.

A first-principles-derived approach is developed to study finite-temperature properties of Pb(Zr1−xTix)O3 (PZT) solid solutions near the morphotropic phase boundary (MPB). Structural and piezoelectric predictions are in excellent agreement with experimental data and direct firstprinciples results. A low-temperature monoclinic phase is confirmed to exist, and is demonstrated to act as a bridge between the well-known tetragonal and rhombohedral phases delimiting the MPB. A successful explanation for the large piezoelectricity found in PZT ceramics is also provided. High piezoelectric response is experimentally found in ceramics of PZT around the MPB. The origins of this large piezoelectric response are unclear. On the one hand, semi-empirical simulations predict that the large experimental value of the d 33 piezoelectric coefficient results mainly from the large value of d 33 that a single-crystal PZT would exhibit [4]. On the other hand, recent firstprinciples calculations [5,6] have found that the d 33 coefficient of a tetragonal single crystal of Pb(Zr 0.5 Ti 0.5 )O 3 are estimated to be three times smaller than the experimental value obtained for ceramics at low temperature.Furthermore, recent synchrotron x-ray powder diffraction studies have revealed the existence of an unexpected low-temperature monoclinic phase of PZT at x=0.48 [7], which implies that the phase diagram of PZT is more complex than previously thought. This monoclinic phase may act as a second-order transitional bridge between the tetragonal phase, for which the electrical polarization P lies along the pseudo-cubic [001] direction, and the rhombohedral phase, for which P is along the pseudo-cubic [111] direction. If this is indeed the case, the polarization of the monoclinic phase continuously rotates as the composition x decreases in the MPB region [7]. Such a continuous rotation has yet to be observed.Obviously, accurate simulations are needed to understand the properties of perovskite alloys in general, and of PZT in particular. Since the beginning of the present decade, first-principles methods have emerged as a powerful tool for investigating properties of ferroelectric systems theoretically (see [5,6,8,9] and references therein). However, these methods are essentially restricted to the study of the zero-temperature properties of small cells, while accurate and interesting predictions of alloy properties would require calculations on much larger cells at finite temperature. Ideally one desires a computational scheme with the capability of predicting the properties of "real" perovskite alloy systems at finite temperature, with the accuracy of the first-principles methods.The purpose of this letter is to demonstrate that it is possible to develop such a scheme, and to apply it to study the finite-temperature behavior of PZT in the vicinity of the MPB. Remarkably, we find that the existence of an intermediate monoclinic phase emerges naturally from this approach. Moreover, the theory provides a novel and successful explanation for the large ...

In the brain, learning is achieved through the ability of synapses to reconfigure the strength by which they connect neurons (synaptic plasticity). In promising solid-state synapses called memristors, conductance can be finely tuned by voltage pulses and set to evolve according to a biological learning rule called spike-timing-dependent plasticity (STDP). Future neuromorphic architectures will comprise billions of such nanosynapses, which require a clear understanding of the physical mechanisms responsible for plasticity. Here we report on synapses based on ferroelectric tunnel junctions and show that STDP can be harnessed from inhomogeneous polarization switching. Through combined scanning probe imaging, electrical transport and atomic-scale molecular dynamics, we demonstrate that conductance variations can be modelled by the nucleation-dominated reversal of domains. Based on this physical model, our simulations show that arrays of ferroelectric nanosynapses can autonomously learn to recognize patterns in a predictable way, opening the path towards unsupervised learning in spiking neural networks.

We present an approach to the implementation of the virtual crystal approximation (VCA) for the study of properties of solid solutions in the context of density-functional methods. Our approach can easily be applied to any type of pseudopotential, and also has the advantage that it can be used to obtain estimates of the atomic forces that would arise if the real atoms were present, thus giving insight into the expected displacements in the real alloy. We have applied this VCA technique within the Vanderbilt ultrasoft-pseudopotential scheme to predict dielectric and piezoelectric properties of the Pb(Zr0.5Ti0.5)O3 solid solution in its paraelectric and ferroelectric phases, respectively. Comparison with calculations performed on ordered alloy supercells and with data on parents compounds demonstrates the adequacy of using the VCA for perovskite solid solutions. In particular, the VCA approach reproduces the anomalous Born effective charges and the large value of the piezoelectric coefficients.

We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.

Multiferroics are compounds that show ferroelectricity and magnetism. BiFeO3, by far the most studied, has outstanding ferroelectric properties, a cycloidal magnetic order in the bulk, and many unexpected virtues such as conductive domain walls or a low bandgap of interest for photovoltaics. Although this flurry of properties makes BiFeO3 a paradigmatic multifunctional material, most are related to its ferroelectric character, and its other ferroic property--antiferromagnetism--has not been investigated extensively, especially in thin films. Here we bring insight into the rich spin physics of BiFeO3 in a detailed study of the static and dynamic magnetic response of strain-engineered films. Using Mössbauer and Raman spectroscopies combined with Landau-Ginzburg theory and effective Hamiltonian calculations, we show that the bulk-like cycloidal spin modulation that exists at low compressive strain is driven towards pseudo-collinear antiferromagnetism at high strain, both tensile and compressive. For moderate tensile strain we also predict and observe indications of a new cycloid. Accordingly, we find that the magnonic response is entirely modified, with low-energy magnon modes being suppressed as strain increases. Finally, we reveal that strain progressively drives the average spin angle from in-plane to out-of-plane, a property we use to tune the exchange bias and giant-magnetoresistive response of spin valves.

Magnetic anisotropy is crucially important for the stabilization of two-dimensional (2D) magnetism, which is rare in nature but highly desirable in spintronics and for advancing fundamental knowledge. Recent works on CrI 3 and CrGeTe 3 monolayers not only led to observations of the long-time-sought 2D ferromagnetism, but also revealed distinct magnetic anisotropy in the two systems, namely Ising behavior for CrI 3 versus Heisenberg behavior for CrGeTe 3 . Such magnetic difference strongly contrasts with structural and electronic similarities of these two materials, and understanding it at a microscopic scale should be of large benefits. Here, first-principles calculations are performed and analyzed to develop a simple Hamiltonian, to investigate magnetic anisotropy of CrI 3 and CrGeTe 3 monolayers. The anisotropic exchange coupling in both systems is surprisingly determined to be of Kitaev-1 arXiv:1811.05413v1 [cond-mat.mtrl-sci] 13 Nov 2018 type. Moreover, the interplay between this Kitaev interaction and single ion anisotropy (SIA) is found to naturally explain the different magnetic behaviors of CrI 3 and CrGeTe 3 . Finally, both the Kitaev interaction and SIA are further found to be induced by spin-orbit coupling of the heavy ligands (I of CrI 3 or Te of CrGeTe 3 ) rather than the commonly believed 3d magnetic Cr ions.

Topological defects in ferroic materials are attracting much attention both as a playground of unique physical phenomena and for potential applications in reconfigurable electronic devices. Here, we explore electronic transport at artificially created ferroelectric vortices in BiFeO 3 thin films. The creation of one-dimensional conductive channels activated at voltages as low as 1 V is demonstrated. We study the electronic as well as the static and dynamic polarization structure of several topological defects using a combination of first-principles and phase-field modelling. The modelling predicts that the core structure can undergo a reversible transformation into a metastable twist structure, extending charged domain walls segments through the film thickness. The vortex core is therefore a dynamic conductor controlled by the coupled response of polarization and electron-mobile-vacancy subsystems with external bias. This controlled creation of conductive one-dimensional channels suggests a pathway for the design and implementation of integrated oxide electronic devices based on domain patterning.