Piezoelectric materials, which convert mechanical to electrical energy and vice versa, are typically characterized by the intimate coexistence of two phases across a morphotropic phase boundary. Electrically switching one to the other yields large electromechanical coupling coefficients. Driven by global environmental concerns, there is currently a strong push to discover practical lead-free piezoelectrics for device engineering. Using a combination of epitaxial growth techniques in conjunction with theoretical approaches, we show the formation of a morphotropic phase boundary through epitaxial constraint in lead-free piezoelectric bismuth ferrite (BiFeO3) films. Electric field-dependent studies show that a tetragonal-like phase can be reversibly converted into a rhombohedral-like phase, accompanied by measurable displacements of the surface, making this new lead-free system of interest for probe-based data storage and actuator applications.

We analyze the coupling between the ferroelectric and magnetic order parameters in the magnetoelectric multiferroic BiFeO 3 using density functional theory within the local spin density approximation ͑LSDA͒ and the LSDA+ U method. We show that weak ferromagnetism of the Dzyaloshinskii-Moriya type occurs in this material, and we analyze the coupling between the resulting magnetization and the structural distortions. We explore the possibility of electric-field-induced magnetization reversal and show that, although it is unlikely to be realized in BiFeO 3 , it is not in general impossible. Finally, we outline the conditions that must be fulfilled to achieve switching of the magnetization using an electric field. There has been increasing recent interest in magnetoelectric multiferroics, 1-5 which are materials that show spontaneous magnetic and electric ordering in the same phase. In addition to the fascinating physics resulting from the independent existence of two or more ferroic order parameters in one material, 6 the coupling between magnetic and electric degrees of freedom gives rise to additional phenomena. The linear and quadratic magnetoelectric ͑ME͒ effects, in which a magnetization linear or quadratic in the applied field strength is induced by an electric field ͑or an electric polarization is induced by a magnetic field͒, are already well established. 5 Recently, more complex coupling scenarios have been investigated. Examples are the coupling of the antiferromagnetic and ferroelectric domains in hexagonal YMnO 3 , 1 or the large magnetocapacitance near the ferromagnetic Curie temperature in ferroelectric BiMnO 3 . 3 Especially interesting are scenarios where the direction of the magnetization or electric polarization can be modified by an electric or magnetic field, respectively. Such a coupling would open up entirely new possibilities in data storage technologies, such as ferroelectric memory elements that could be read out nondestructively via the accompanying magnetization. Some progress has been made in this direction. Recently, the small ͑0.08 C/cm 2 ͒ electric polarization in perovskite TbMnO 3 was rotated by 90°using a magnetic field at low temperatures ͑ϳ10-20 K͒. 4 Conversely, early work on nickel-iodine boracite 7 showed that, below ϳ60 K, reversal of the spontaneous electric polarization rotates the magnetization by 90°, indicating that the axis of the magnetization, but not its sense, can be controlled by an electric field. In fact, it was believed 8,9 that electric-field-induced 180°switching of the magnetization should be impossible, because a reversal of the magnetization corresponds to the operation of time inversion, whereas the electric field is invariant under this operation. In this work we show that such behavior is not generally impossible by using multiferroic bismuth ferrite, BiFeO 3 , as a test case to analyze the coupling between magnetism and ferroelectricity.BiFeO 3 has long been known to be, in its bulk form, an antiferromagnetic, ferroelectric multiferroic, 10,11 with anti...

Multiferroic materials, which offer the possibility of manipulating the magnetic state by an electric field or vice versa, are of great current interest. In this work, we demonstrate the first observation of electrical control of antiferromagnetic domain structure in a single-phase multiferroic material at room temperature. High-resolution images of both antiferromagnetic and ferroelectric domain structures of (001)-oriented multiferroic BiFeO3 films revealed a clear domain correlation, indicating a strong coupling between the two types of order. The ferroelectric structure was measured using piezo force microscopy, whereas X-ray photoemission electron microscopy as well as its temperature dependence was used to detect the antiferromagnetic configuration. Antiferromagnetic domain switching induced by ferroelectric polarization switching was observed, in agreement with theoretical predictions.

The ground-state structural and electronic properties of ferroelectric BiFeO 3 are calculated using density functional theory within the local spin-density approximation ͑LSDA͒ and the LSDA+ U method. The crystal structure is computed to be rhombohedral with space group R3c, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90-100 C/cm 2 is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differing by an order of magnitude from early experiments. One possible explanation is that the latter may have suffered from large leakage currents. However, both past and contemporary measurements are shown to be consistent with the modern theory of polarization, suggesting that the range of reported polarizations may instead correspond to distinct switching paths in structural space. Modern measurements on well-characterized bulk samples are required to confirm this interpretation.

Epitaxial strain can substantially enhance the spontaneous polarizations and Curie temperatures of ferroelectric thin films compared to the corresponding bulk materials. In this Letter we use first principles calculations to calculate the effect of epitaxial strain on the spontaneous polarization of the ferroelectrics BaTiO 3 , PbTiO 3 , and LiNbO 3 , and the multiferroic material BiFeO 3 . We show that the epitaxial strain dependence of the polarization varies considerably for the different systems, and in some cases is, in fact, very small. We discuss possible reasons for this different behavior and show that the effect of epitaxial strain can easily be understood in terms of the piezoelectric and elastic constants of the unstrained materials. Our results provide a computational tool for the quantitative prediction of strain behavior in ferroelectric thin films. DOI: 10.1103/PhysRevLett.95.257601 PACS numbers: 77.84.Dy, 77.22.Ej, 77.55.+f, 77.65.ÿj The possible application of ferroelectric materials in microelectronic devices has led to strong interest in the properties of thin film ferroelectrics [1]. One important question in this context is how epitaxial strain, which is incorporated in the ferroelectric material due to the lattice mismatch with the substrate, affects the ferroelectric characteristics of the thin film. It has been demonstrated that epitaxial strain can have drastic effects, such as inducing ferroelectricity at room temperature in otherwise paraelectric SrTiO 3 [2] or increasing the ferroelectric Curie temperature of BaTiO 3 by nearly 500 C and the remanent polarization by 250% compared with the corresponding bulk values [3]. Based on these observations, it is often assumed that the strong sensitivity to epitaxial strain is a common feature of all ferroelectrics.Indeed, this assumption has been supported by first principles calculations for several simple ABO 3 perovskite ferroelectrics [4 -7]. Strain is introduced in these calculations by fixing the lattice constants corresponding to the lateral directions of the substrate while relaxing all remaining structural parameters, according to the minimum of the total energy under the epitaxial constraint. This makes it possible to isolate the pure strain effect from other effects present in real thin film samples such as structural defects, chemical inhomogeneities, and interface effects. For example, in Refs. [6,7] the change in phase stability due to epitaxial strain was investigated by first principles techniques for several simple perovskite systems including the prototype ferroelectrics BaTiO 3 and PbTiO 3 . It was shown that for these systems a series of consecutive phase transitions occur that effectively rotate the polarization from ''out-of-plane'' for compressive epitaxial strain to ''inplane'' for tensile epitaxial strain. Also, the magnitude of the spontaneous polarization within the different phases was shown to be strongly strain dependent. In contrast, we have recently shown that in BiFeO 3 , a multiferroic system where ferroel...

We calculate the effect of epitaxial strain on the structure and properties of multiferroic bismuth ferrite, BiFeO 3 , using first-principles density functional theory. We investigate epitaxial strain corresponding to an (001)-oriented substrate and find that, while small strain causes only quantitative changes in behavior from the bulk material, compressive strains of greater than 4% induce an isosymmetric phase transition accompanied by a dramatic change in structure. In striking contrast to the bulk rhombohedral perovskite, the highly strained structure has a c/a ratio of ∼1.3 and five-coordinated Fe atoms. We predict a rotation of polarization from [111] (bulk) to nearly [001], accompanied by an increase in magnitude of ∼50%, and a suppression of the magnetic ordering temperature. Our calculations indicate critical strain values at which the two phases might be expected to coexist and shed light on recent experimental observation of a morphotropic phase boundary in strained BiFeO 3 .

We present a theoretical analysis of magnetic toroidal moments in periodic systems, in the limit in which the toroidal moments are caused by a time and space reversal symmetry breaking arrangement of localized magnetic dipole moments. We summarize the basic definitions for finite systems and address the question of how to generalize these definitions to the bulk periodic case. We define the "toroidization" as the toroidal moment per unit cell volume, and we show that periodic boundary conditions lead to a multivaluedness of the toroidization, which suggests that only differences in toroidization are meaningful observable quantities. Our analysis bears strong analogy to the "modern theory of electric polarization" in bulk periodic systems, but we also point out some important differences between the two cases. We then discuss the instructive example of a one-dimensional chain of magnetic moments, and we show how to properly calculate changes of the toroidization for this system. Finally, we evaluate and discuss the toroidization ͑in the local dipole limit͒ of four important example materials:

We present results of an ab initio density-functional theory study of three bismuth-based multiferroics, BiFeO 3 , Bi 2 FeCrO 6 , and BiCrO 3 . We disuss differences in the crystal and electronic structure of the three systems and show that the application of the LDA+ U method is essential to obtain realistic structural parameters for Bi 2 FeCrO 6 . We calculate the magnetic nearest-neighbor coupling constants for all three systems and show how Anderson's theory of superexchange can be applied to explain the signs and relative magnitudes of these coupling constants. From the coupling constants we then obtain a mean-field approximation for the magnetic ordering temperatures. Guided by our comparison of these three systems, we discuss the possibilities for designing a multiferroic material with large magnetization above room temperature.