Journal of Nanomaterials

Volume 2015 (2015), Article ID 169874, 8 pages

http://dx.doi.org/10.1155/2015/169874

## Characterization of Multiferroic Domain Structures in Multiferroic Oxides

National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China

Received 25 April 2014; Accepted 27 September 2014

Academic Editor: Debasis Dhak

Copyright © 2015 Lizhi Liang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Multiferroic oxides have been received much attention due to that these materials exhibit multiple ferroic order parameters (e.g., electric polarization in ferroelectrics, magnetization in ferromagnetics, or spontaneous strain in ferroelastics) simultaneously in the same phase in a certain temperature range, which offer an exciting way of coupling between the ferroic order parameters. Thus, this provides a possibility for constructing new type of multifunctional devices. The multiferroic domain structures in these materials are considered to be an important factor to improve the efficiency and performance of future multiferroic devices. Therefore, the domain structures in multiferroic oxides are widely investigated. Recent developments in domain characterization techniques, particularly the aberration-corrected transmission electron microscopy (TEM), have enabled us to determine the domain structures at subangstrom scale, and the recent development of *in situ* TEM techniques allows ones to study the dynamic behaviors of multiferroic domains under applied fields or stress while the atomic structure is imaged directly. This paper provides a review of recent advances on the characterization of multiferroic domain structures in multiferroic oxides, which have been achieved by the notable advancement of aberration-corrected TEM.

#### 1. Introduction

In recent years multiferroic materials have attracted much interest because they possess more than one type of ferroic order parameters in the same phase, which brings out novel physical phenomena and offers the possibilities for developing new multiferroic devices [1–3]. The defining characteristic of a ferroic material is ferroic order parameter (e.g., electric polarization in ferroelectrics, magnetization in ferromagnets, or spontaneous strain in ferroelastics) that has different, energetically equivalent orientations; the orientation of which can be selected using an applied field. For example, in the magnetoelectric multiferroics there exists a coupling between the electric and magnetic fields, or named as magnetoelectric effect, which describes the induction of magnetization (*M*) by an electric field (*E*) or polarization (*P*) generated by a magnetic field (*H*). The multiferroic materials may have domains with differently oriented regions, separated by domain walls, coexisting in a sample. In the magnetoelectric multiferroics, both ferroelectric and magnetic domains exist simultaneously. In addition, “ferroelectric domain switching controlled by magnetic field” and “magnetic domain switching controlled by electric field” are also available, which lead to the possibilities for designing new multiferroic devices [4]. In the multiferroic oxides, the possible domain structures are much more complex than that in either ferroelectric or ferroelastic materials due to the multiple coupling between the primary ferroic order parameters. Aizu [5] analyzed the numbers of ferroic domain states in multiferroics, and found that the possible domain walls, was given by the ratio of the point group orders of the high- and low-symmetry phases, although Shuvalov et al. [6] argued that a higher number of domains (super-orientational states) could be permissible than given by the Aizu rule, as indeed observed in ferroelastic YBa_{2}Cu_{3} [7]. The muliferroic domain structures in these multiferroic oxides are considered to be important factors to improve the efficiency and performance of future magnetoelectric devices. Therefore, multiferroic domain structures in mutltiferroic oxides have been extensively investigated. Meanwhile, both the techniques and instruments of transmission electron microscopy (TEM), which is one of the most powerful tools of the domain analysis, have been much improved in the last decade. As advances in aberration-corrected TEM have enabled ones to determine three-dimensional structures of materials with subangstrom resolution, the recent development of* in situ* TEM techniques also allows ones to study the dynamic behaviors of multiferroic domains under applied fields or stress while the atomic structure is directly imaged simultaneously [8–10]. Therefore, the new generation high-resolution TEM (HRTEM) and scanning transmission electron microscopy (STEM) facilities equipped with Cs-corrector will benefit for the characterizations of multiferroic domain structures in multiferroic oxides. Recently, much progress in this direction has been achieved by the notable advancement of aberration-corrected TEM. In this paper, an overview of the characterizations of multiferroic domain structures in multiferroic oxides is presented, and the future challenges of the characterizations on the domain structures of multiferroic oxides are also discussed.

#### 2. Multiferroic Domain Structures in Multiferroic Oxides

Multiferroic oxides can be classified four categories based on their different microscopic nature for multiferroic behaviors [1]. The first type is lone pair multiferroics (examples such as BiFeO_{3}, BiMnO_{3}, and PbVO_{3}, in which the A-site cation (Bi^{3+}, Pb^{2+}) has a stereochemically active 6s^{2} lone-pair electrons, distorting the geometry of the BO_{3} anion, resulting in ferroelectricity); the second one is charge-ordered multiferroics (certain “noncentrosymmetric” arrangements of ions induce ferroelectricity in magnetic materials, one prominent example is LuFe_{2}O_{4}); the third one is magnetic-ordered multiferroics (as exemplified in DyMnO_{3}, TbMnO_{3}, and TbMn_{2}O_{4}, ferroelectricity is induced by magnetic long-range order in which the arrangement of magnetic dipoles lacks reflection symmetry); and the fourth one is geometrical frustration multiferroics (as exemplified in REMnO_{3} (RE = Y, Dy, Tb, etc.), in which long-range dipole-dipole interactions and rotations of oxygen atoms generate a stable ferroelectric state). In multiferroics, the possible domain structures are much more complex than that in either ferroelectric or ferroelastic materials due to the multiple coupling between the primary ferroic order parameters. In this work, we will focus on the multiferroic domain structures in mutltiferroics revealed by TEM and aberration-corrected HRTEM/STEM.

##### 2.1. Multiferroic Domain Structures in BiFeO_{3} Thin Films

Perovskite-type BiFeO_{3}, as one of the few known single-phase magnetoelectric multiferroics, exhibits a coexistence of simultaneous ferroelectric and magnetic order parameters above room temperature. Thus, it offers exciting potential for room temperature device integration and has been the topic of intensive studies as an interesting model multiferroics [11]. Structurally, BiFeO_{3} crystallizes in a rhombohedrally distorted perovskite structure with* R3c* space group at room temperature, of which the lattice constants were determined as* a*_{h} = 5.587 Å,* c*_{h} = 13.867 Å in the hexagonal unit cell containing six formula or* a*_{R} = 5.638 Å, *α* = 59.348° in the rhombohedral unit cell containing two formula units [11]. Three main distortions are responsible for the existence of spontaneous polarization along the direction (i.e., ). Therefore, in the BiFeO_{3} with a rhombohedral structure, there exists eight different polar domains, and three possible types of ferroelectric domain walls, namely as 71°, 109°, and 180° domain walls. Recently, a new kind of vortex-like nanodomain arrays (toroidal domain patterns) were reported in the epitaxial BiFeO_{3} thin films grown on TbScO_{3} substrates, which were revealed by aberration-corrected STEM [12]. Figure 1(a) is dark-field TEM image of the vortex nanodomain arrays formed at the interface between the BiFeO_{3} film and TbScO_{3} substrate, and Figure 1(b) is the plotting of the vectors ( defined as the atomic displacement in the image plane of the Fe cation from the center of the unit cell formed by its four Bi neighbors) for a 109° domain wall which forms a vortex domain by addition of a pair of 180° triangle domains, where the polarization rotates about the intersection of two 109° and two 180° domain walls to form a vortex domain structure. The formation of such complex domain structures tends to reduce the depolarization fields produced at the surface of the TbScO_{3} insulator substrates. And along with the interface epitaxy constraints, a local broadening of the walls is produced, which makes the polarization rotation quasicontinuous.