Multiscale Simulations of Domains in Ferroelectrics

This chapter focuses on recent studies of ferroelectrics, where large-scale molecular dynamics (MD) simulations using first-principles-based force fields played a central role in revealing important physics inaccessible to direct density functional theory (DFT) calculations but critical for developing physically-based free energy functional for coarse-grained phase-field-type simulations. After reviewing typical atomistic potentials of ferroelectrics for MD simulations, the chapter describes a progressive theoretical framework that combines DFT, MD, and a mean-field theory. It then focuses on relaxor ferroelectrics. By examining the spatial and temporal polarization correlations in prototypical relaxor ferroelectrics with million-atom MD simulations and novel analysis techniques, this chapter shows that the widely accepted model of polar nanoregions embedded in a non-polar matrix is incorrect for Pb-based relaxors. Rather, the unusual properties of theses relaxor ferroelectrics stem from the presence of a multi-domain state with extremely small domain sizes (2–10 nanometers), giving rise to a greater flexibility for polarization rotations and the ultrahigh dielectric and piezoelectric responses. Finally, this chapter discusses the challenges and opportunities for multiscale simulations of ferroelectric materials.

Fundamental Properties of Ferroelectric Domain Walls from Ginzburg–Landau Models

This chapter discusses the contemporary possibilities, prospects, and limitations of phase-field simulations and Ginzburg-Landau-Devonshire models of DWs. It focuses on the most studied ferroelectric oxides BaTiO3, KNbO3, PbTiO3, as well as in various complex perovskite oxides like lead zirconate titanate (PZT) and lead-based relaxor ferroelectrics. In the past decade, there have been multiple important results published in the field of perovskite ferroelectrics with a support of phase-field simulations. Certain predictions, like existence of Bloch walls in BaTiO3 or vortex structures in PbTiO3-SrTiO3 superlattices have been verified by atomistic or ab-initio calculations. The chapter resumes their available model potentials and the key predictions reported in the last decade. It is complemented by original data allowing comparisons and an outlook.

First-Principles Studies of Structural Domain Walls

This chapter discusses representative first-principles studies of structural domain walls in ferroics, focusing on the compounds that have received most attention by the simulations community so far: perovskite oxides. It describes in some detail a reduced number of case studies that come handy to illustrate different effects and to highlight the added value of the first-principles investigations. As regards the simulation methods, the chapter focuses on applications of density functional theory (DFT), typically employing an approximation for an effective treatment of ionic cores. A discussion on the application to domain-wall problems of first-principles-based methods for large-scale simulations of ferroelectrics and ferroelastics is also included. Finally, this chapter briefly on the opportunities and challenges for first-principles research in this field.

Physical Properties inside Domain Walls

This chapter explains that the field of domain wall (DW) nanoelectronics is predicated on the premise that the distinct physical properties of domain walls offer new conceptual possibilities for devices. It first deals with basic physics of domain wall properties, and in particular the cross-coupling that allows domain walls to display properties and order parameters different from those of the parent bulk material. The chapter then turns to scanning probe techniques for measuring some of these domain wall properties, and specifically atomic force microscopy (AFM). Together with transmission electron microscopy, AFM is one of the most important tools currently available to probe and manipulate the individual position and physical properties of domain walls. Finally, the chapter focuses on two recent developments that allow investigating hitherto overlooked properties of domain walls: their magnetotransport and their mechanical response.

Electronics Based on Domain Walls

This chapter reviews some of the initial developments and recently introduced potential application concepts related to domain walls in ferroelectrics and multiferroics. It gives a special (non-exclusive) focus on the heavily investigated bismuth ferrite BiFeO3 system as one of the rare examples of a single phase room-temperature multiferroic system that can be widely tailored in application relevant epitaxial thin films. Here, DWs as well as other topological structures reveal new ways to novel tailored states of matter with a wide range of electronic properties. Domain wall electronics, particularly with ferroelectrics and multiferroics, provides new nanotechnological concepts for identifying, understanding, and designing new material properties. However, this chapter observes that there has been very little work done on controlling electronic correlations.

Transmission Electron Microscopy Study of Ferroelectric Domain Walls in BiFeO3 Thin Films: Structures and Switching Dynamics

This chapter presents a review on the recent progress in transmission electron microscopy (TEM) studies of ferroelectric DWs in one of the most widely studied ferroelectric systems — BiFeO3 thin films. This system has been chosen representative for a much wider range of ferroelectric perovskites with functional DWs, due to its strong spontaneous polarization, coexistence of ferroelectricity, ferroelasticity and antiferromagnetism, and numerous functionalities at the DWs. Here, the chapter first briefly introduces the instrumentation, experimental procedures, imaging mechanisms, and analytical methods of the state-of-the-art TEM-based techniques. The application of these techniques to the study of DW structures and switching behaviors is demonstrated, with particular emphasis on the critical roles of interfaces and defects, and interplay between different types of DWs. The phenomena and mechanism discovered in the model system of BiFeO3 are also applicable to many other ferroelectric materials with similar DW structures. The results not only advance the fundamental understanding of static and dynamic properties of ferroelectric DWs, but also form the basis for designing of practical ferroelectric-DW-based devices.

Three-Dimensional Optical Analysis of Ferroelectric Domain Walls

This chapter presents the latest results demonstrating the flexibility and sensitivity of optical methods for the investigation of the physical properties of DWs in 3D. Domain walls in ferroelectric materials are nanoscale interfaces separating regions with different orientation of the polarization. They have long been considered as imperfections affecting the overall macroscopic properties of ferroelectrics. However, the recently discovered rich and diverse local physical properties of ferroelectric DWs have transformed these domain boundary regions into individual nanostructures with significant fundamental interest and potentially viable application in nanoelectronic device components. This chapter emphasizes the important contribution of both nonlinear and linear optical microscopy in different geometries (transmission, reflection, and non-collinear geometry) to access the detailed morphology of ferroelectric domain walls, obtain their 3D profile, access their internal structure, and establish correlations with their electronic properties.

Improper Ferroelectric Domain Walls

This chapter focuses on the specific physical properties at domain walls in ferroelectric materials where the spontaneous electric polarization appears as a by-product of a structural or magnetic phase transition, and not as its primary order parameter. The chapter begins with a short introduction to the fundamentals of improper ferroelectricity, followed by a discussion of emergent functional domain wall properties in different improper ferroelectric model systems. It then covers the broad variety of electronic states and application opportunities associated with improper ferroelectric domain walls in hexagonal manganites. Next, this chapter addresses the electronic transport and manipulation of domain walls in boracites, and presents additional magnetoelectric coupling phenomena that arise when the interaction of magnetic spins and electric charges gives rise to improper ferroelectricity. A perspective regarding future research and application opportunities of improper ferroelectric domain walls is given last.

Control of Ferroelectric Domain Wall Motion using Electrodes with Limited Conductivity

This chapter addresses the experimental control of ferroelectric DW motion in thin films using electron-beam induced deposition (EBID) electrodes with limited conductivity which governs the supply of charges required for DW nucleation and propagation. The problem of a moving domain boundary, addressed in this chapter, belongs to the general class of free-boundary problems, or Stefan problems, after Josef Stefan who mathematically described ice formation and then demonstrated generality of his approach by applying the same technique to describe diffusion. In the frame of this approach the position of the boundary is determined from the transport of a physical quantity, flowing through and partially consumed at the boundary. Nowadays mathematical modelling of Stefan problems has developed into a rich field of knowledge where both analytical and numerical methods are applied to solve various important applied tasks. In this chapter, the process is described by analogy to the classical Stefan model, historically applied to the motion of phase boundaries under propagation of heat but which is here applied to precisely describe DW motion under linear electrodes and the 2D growth of a circular domain.

Landau–Ginzburg–Devonshire Theory for Domain Wall Conduction and Observation of Microwave Conduction of Domain Walls

This chapter concerns DW electrical conduction. It first addresses the phenomenology of charged domain walls in the context of a Landau-Ginzburg-Devonshire (LGD) model for the ferroelectric semiconductor with analysis of the DW conductivity associated with accumulation of charge carriers near domain walls. It is revealed that there exists an interplay between the wall type — head-to-head or tail-to-tail — and conduction type of the semiconductor ferroelectric with a strong dependence of the domain wall conductivity on the wall orientation. The chapter then reviews observations of high-frequency — in the gigahertz frequency range — ac conductivity along the nominally uncharged 180-degree domain walls in a uniaxial Pb(Zr0.2Ti0.8)O3 epitaxial film. Measurements of the conduction at high frequencies are insensitive to presence of a Schottky barrier and the electrode-ferroelectric interface.