Domains and domain walls in multiferroics

Multiferroics are gathering solid-state matter in which several types of orders are simultaneously allowed, as ferroelectricity, ferromagnetism (or antiferromagnetism), ferroelasticity, or ferrotoroidicity. Among all, the ferroelectric/ferromagnetic couple is the most intensively studied because of potential applications in novel low-power magnetoelectric devices. Switching of one order thanks to the other necessarily proceeds via the nucleation and growth of coupled domains. This review is an introduction to the basics of ferroelectric/ferromagnetic domain formation and to the recent microscopy techniques devoted to domains imaging, providing new insights into the archetypal multiferroic domain morphologies. Some relevant examples are also given to illustrate some of the unexpected properties of domain walls, as well as the way these domain walls can be manipulated altogether thanks to various types of magnetoelectric coupling.     

Magnetotransport at domain walls in BiFeO3

Domain walls in multiferroics can exhibit intriguing behaviors that are significantly different from the bulk of the material. We investigate strong magnetoresistance in domain walls of the model multiferroic BiFeO3 by probing ordered arrays of 109° domain walls with temperature- and magnetic-field-dependent transport. We observe temperature-dependent variations in the transport mechanism and magnetoresistances as large as 60%. These results suggest that by locally breaking the symmetry of a material, such as at domain walls and structural interfaces, one can induce emergent behavior with properties that deviate significantly from the bulk.     

The role of homophase and heterophase interfaces on transport properties in structured materials

In structured or self-organized materials spatial confinement effects lead to structure- and interface-controlled modifications of the bulk transport properties. In part, such modifications can be accounted for by a classical master equation approach for the transport of the different charge carrier species. The rather large quantity of parameters, which enter such an approach, can more or less easily be adjusted to the dimensional characteristics, local potential changes at interfaces, and the electronic settings of the system as well as to temperature effects. On the other hand, a microscopically more detailed and mostly parameter-free picture is obtained from a quantum-mechanical treatment on the basis of the density-functional theory. An extension by a Green’s function formalism allows the determination and analysis of electronic transport through contacted nanostructures. Examples will be given to demonstrate the applicability of the different approaches for dissipative and hopping transport through a regular array of nanostructures, for a mechanically triggered metal-insulator transition in nanowires, and for the enhanced conductivity at multiferroic domain walls.     

Direct observation of ferroelectric domain switching in varying electric field regimes using in situ TEM

In situ Transmission Electron Microscopy (TEM) techniques can potentially fill in gaps in the current understanding interfacial phenomena in complex oxides. Select multiferroic oxide materials, such as BiFeO(3) (BFO), exhibit ferroelectric and magnetic order, and the two order parameters are coupled through a quantum-mechanical exchange interaction. The magneto-electric coupling in BFO allows control of the ferroelectric and magnetic domain structures via applied electric fields. Because of these unique properties, BFO and other magneto-electric multiferroics constitute a promising class of materials for incorporation into devices such as high-density ferroelectric and magnetoresistive memories, spin valves, and magnetic field sensors. The magneto-electric coupling in BFO is mediated by volatile ferroelastically switched domains that make it difficult to incorporate this material into devices. To facilitate device integration, an understanding of the microstructural factors that affect ferroelastic relaxation and ferroelectric domain switching must be developed. In this article, a method of viewing ferroelectric (and ferroelastic) domain dynamics using in situ biasing in TEM is presented. The evolution of ferroelastically switched ferroelectric domains in BFO thin films during many switching cycles is investigated. Evidence of partial domain nucleation, propagation, and switching even at applied electric fields below the estimated coercive field is revealed. Our observations indicate that the occurrence of ferroelastic relaxation in switched domains and the stability of these domains is influenced the applied field as well as the BFO microstructure. These biasing experiments provide a real time view of the complex dynamics of domain switching and complement scanning probe techniques. Quantitative information about domain switching under bias in ferroelectric and multiferroic materials can be extracted from in situ TEM to provide a predictive tool for future device development.     

Giant effect of uniaxial pressure on magnetic domain populations in multiferroic bismuth ferrite

Neutron diffraction is used to show that small (～7 MPa, or 70 bar) uniaxial pressure produces significant changes in the populations of magnetic domains in a single crystal of 2% Nd-doped bismuth ferrite. The magnetic easy plane of the domains converted by the pressure is rotated 60° relative to its original position. These results demonstrate extreme sensitivity of the magnetic properties of multiferroic bismuth ferrite to tiny (less than 10(-4)) elastic strain, as well as weakness of the forces pinning the domain walls between the cycloidal magnetic domains in this material.     

Domain boundary engineering – recent progress and many open questions

Some domain boundaries contain functionalities which do not exist in the bulk. Typical examples are (super-) conducting twin walls in WO₃, highly conducting walls in BiFeO₃ and in structural interfaces between SrTiO₃ and LaAlO₃, and ferroelectric walls in CaTiO₃. The emerging field of ‘Domain Boundary Engineering’ endeavors to generate such functional interfaces in a multitude of materials for applications in device materials. Some of the recent successes are reviewed together with suggestions for further research.     

Strain control of domain-wall stability in epitaxial BiFeO3 (110) films

We have studied the stability of domains and domain walls in multiferroic BiFeO3 thin films using a combination of piezoelectric force microscopy and phase-field simulations. We have discovered that a film-substrate misfit strain may result in a drastically different thermodynamic stability of two parallel domain walls with the same orientation. A fundamental understanding of the underlying physics, the stress distribution in a domain structure, leads to a novel approach to control the ferroelastic domain stability in the multiferroic BiFeO3 system.     

Effect of magnetoelectrical interactions on the multiferroic domain walls

The antiferromagnetic domain structure of a multiferroic has been investigated in the presence of a ferroelectric domain structure. It has been demonstrated that an inhomogeneous magnetoelectric (flexomagnetoelectric) interaction leads to pinning of antiferromagnetic domain walls at the walls of the ferroelectric domains and to a change in the structure of antiferromagnetic domain walls.     

Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3

Domains in ferroelectric films are usually smooth, stripelike, very thin compared with magnetic ones, and satisfy the Landau-Lifshitz-Kittel scaling law (width proportional to square root of film thickness). However, the ferroelectric domains in very thin films of multiferroic BiFeO3 have irregular domain walls characterized by a roughness exponent 0.5-0.6 and in-plane fractal Hausdorff dimension H||=1.4+/-0.1, and the domain size scales with an exponent 0.59+/-0.08 rather than 1/2. The domains are significantly larger than those of other ferroelectrics of the same thickness, and closer in size to those of magnetic materials, which is consistent with a strong magnetoelectric coupling at the walls. A general model is proposed for ferroelectrics, ferroelastics or ferromagnetic domains which relates the fractal dimension of the walls to domain size scaling.     

钙钛矿型氧化物非常规铁电研究进展

钙钛矿型氧化物因具有丰富的磁性、铁电、力学和光学等诸多功能属性,在电子信息通信材料器件领域中有广阔的应用前景.在各种物理性质之中,铁电极化因其产生机制多样,并能与磁性和晶格应变相互耦合形成多铁性等特点,近十多年来一直被作为凝聚态物理研究的国际热点问题.与以自发极化作为初级序参量的常规铁电材料不同,非常规铁电材料中的铁电极化是被其他的序参量诱导而产生的.本综述围绕无机钙钛矿型氧化物非常规铁电体的研究进展进行了总结.回顾了该体系经典唯象理论和原子尺度的微观模型,有序排列的人工钙钛矿超晶格型结构,以及稀土正铁氧体单晶的反铁磁畴壁结构中非常规铁电的极化强度大小及其诱导机制,为系统理解非常规铁电提供了理论途径.     

Interplay between elasticity,ferroelectricity and magnetism at the domain walls of bismuth ferrite

Multiferroic domain walls have recently been proposed as the active element in devices related to spintronics, data storage, and magnetic logic. Among multiferroics, BiFeO₃ is by far the most studied material. Its domain walls have shown rich behaviours that include conductivity in an otherwise insulating crystal, and magnetotransport properties that are markedly different from those of the bulk. In this article we summarize the experimental evidence and the current models used to understand the interplay between elastic, electric, and magnetic properties of the domain walls. Starting from the considera‐ tion of antiferromagnetic domain structures on a background of ferroelectric domains, and emphasizing pinning effects, we proceed to discuss the microscopic behavior of ferroelectricity and magnetism at the walls. We describe how domain organization in BiFeO₃ is caused by structural transformations, and scrutinize modelling works pinpointing their characteristic features. Finally, we summarize the recent progress and list open questions for future study on BiFeO₃ domain structures. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Functional twin boundaries

Functional interfaces are at the core of research in the emerging field of ‘domain boundary engineering’ where polar, conducting, chiral, and other interfaces and twin boundaries have been discovered. Ferroelectricity was found in twin walls of paraelectric CaTiO₃. We show that the effect of functional interfaces can be optimized if the number of twin boundaries is increased in densely twinned materials. Such materials can be produced by shear in the ferroelastic phase rather than by rapid quench from the paraelastic phase.     

Conduction of topologically protected charged ferroelectric domain walls

We report on the observation of nanoscale conduction at ferroelectric domain walls in hexagonal HoMnO(3) protected by the topology of multiferroic vortices using in situ conductive atomic force microscopy, piezoresponse force microscopy, and Kelvin-probe force microscopy at low temperatures. In addition to previously observed Schottky-like rectification at low bias [Phys. Rev. Lett. 104, 217601 (2010)], conductance spectra reveal that negatively charged tail-to-tail walls exhibit enhanced conduction at high forward bias, while positively charged head-to-head walls exhibit suppressed conduction at high reverse bias. Our results pave the way for understanding the semiconducting properties of the domains and domain walls in small-gap ferroelectrics.     

Ferroelastic domain structure of (CH3)4N CdCl3 (TMCC) crystal

The ferroelastic domain structure and the phase boundaries of TMCC have been studied in the temperature range 114-90 K by direct observation under polarised light. By applying an external, compressive and unidirectional mechanical stress the ferroelastic character of the domain structure has been confirmed. The orientation of the domain walls and phase boundaries are analysed. To characterise quantitatively the observed domain wall distribution the classical symmetry approach, based on the criterion of spontaneous strain compatibility, has to be extended to allow small rotations of the domain walls with respect to their ideal orientation. The observed switching process among the different domains can be understood as a mechanism that minimises the elastic energy. Received 21 July 2000     

Kittel law in BiFeO₃ ultrathin films: a first-principles-based study

A first-principles-based effective Hamiltonian is used to investigate the thickness dependency of the size of straight-walled domains in ultrathin films made of the multiferroic BiFeO? (BFO) material. It is found that the Kittel law is followed, as in ferroelectric or ferromagnetic films. However, an original real-space decomposition of the different energetic terms of this effective Hamiltonian allows the discovery that the microscopic origins of such a law in BFO films dramatically differ from those in ferroelectric or ferromagnetic films. In particular, interactions between tilting of oxygen octahedra around the domain walls and magnetoelectric couplings near the surface (and away from the domain walls) play an important role in the observance of the Kittel law in the studied BFO films.     

激发态电荷转移有机体的多铁性研究

随着人们对多铁性的深入了解,越来越多不同类型的有机多铁材料被合成出来.激发态电荷转移有机体的电荷转移网络是由一个提供电子的分子(给体donor,D~+)和一个接受电子的分子(受体acceptor,A~-)有序排列后构成的.D~+A~-长程有序排列,其激发态(激子)具有较长寿命和±1/2自旋,这是产生室温铁电性和铁磁性的根本原因.激发态容易受外场刺激,因此光照、磁场、电场、应力等能够很好地调控这类材料的铁电极化、磁矩和相应的磁电耦合系数.激发态电荷转移有机体不仅大大丰富了室温多铁材料体系,而且可以为开发新型多功能电子器件提供材料基础和技术储备.     

Magnetic properties of BiFeO3 micro-cubes synthesized by microwave agitation

In this article, we present results of field cooled (FC) and zero field cooled (ZFC) magnetization measurements and investigation of aging and memory effect in bismuth ferrite (BFO) multiferroic micro-cubes obtained by means of simple microwave synthesis procedure. It is found that difference between FC and ZFC magnetizations appear at the temperature of freezing of ferromagnetic domain walls. The decay of the magnetic moment versus time described by power-law relation and the absence of memory effect are caused by domain growth mechanism rather than by the spin-glass phase. The negligible value of remnant magnetic moment indicates that BFO compound exhibits low concentration of ferromagnetic domains and can be close to ferromagnetic to spin-glass transition.     

Investigation of the domain structure of sintered Nd-Fe-B permanent magnets by Bitter-pattern method

The conventional Bitter-pattern technique and the colloid-scanning electron microscopy (colloid-SEM) method were used to study the domain structure of polycrystalline sintered Nd-Fe-B permanent magnets. In the thermally demagnetized state most of the grains are multidomain and the domain structures resemble those observed in bulk uniaxial crystals with strong magnetocrystalline anisotropy. Investigations of the magnetic microstructure during magnetizing cycle showed that the domain walls can easily be moved within the grains and that the magnetization reversal in sintered Nd-Fe-B magnets occurs predominantly by the nucleation and expansion of reverse domains at structural imperfections near the grain boundaries. It is also shown that the colloid-SEM method is more surface sensitive and reveals the domain structure with better resolution than the conventional Bitter technique. Thanks to the application of digital image processing systems, clear and high contrast domain images were obtained. The work was supported by the Lódź University within Research Grant 505/694 (2004).     

多铁性钙钛矿薄膜的氧空位调控研究进展

精确调控ABO_3钙钛矿结构中氧空位的位置与浓度已被证明可调控多铁性薄膜的不同物理性质,包括输运特性、光学特性和多铁性质等.本文回顾了多种典型的多铁性材料,从氧空位形成机理、氧八面体结构、应变-氧空位关系和具体物性调控效应(多铁、超导和电化学性能)等角度介绍了该体系中氧空位调控效应.同时依托氧空位调控的最新研究进展,尤其是对氧空位调控单相材料多铁性质方面工作的分析,为探索新型磁电功能性材料与器件提供了重要参考.     

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed ‘splitting.’ We discuss far-field ‘splitting’ in the full field and near-horizon ‘splitting’ in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the ‘splitting’ behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field ‘splitting’ is explained by competition between projected modes. The near-horizon ‘splitting’ is due to excitation of lower multipole modes that back excite the multipole mode for which ‘splitting’ is observed. In both cases ‘splitting’ is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter-mode excitation effect that we study.