Domains and domain walls in multiferroics

Donald M. Evans (1) , Vincent Garcia (2) , Dennis Meier (1) , M. Bibes (2)

1 IMA NTNU - Department of Materials Science and Engineering [Trondheim]
2 Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales)

Multiferroics are materials combining several ferroic orders such as ferroelectricity, ferro-(or anti-ferro-) magnetism, ferroelasticity and ferrotoroidicity [1]. They are of interest both from a fundamental perspective , as they have multiple (coupled) non-linear functional responses-providing a veritable myriad of correlated phenomena, and because of the opportunity to apply these functionalities for new device applications. One application is, for instance, in no-volatile memory, which has led to special attention being devoted to ferroelectric and magnetic multiferroics. For this application, the vision is to combine the low writing power of ferroelectric information with the easy, non-volatile, reading of magnetic information to give a 'best of both worlds' computer memory: however, for this to be realised the two ferroic orders need to be intimately linked via the magnetoelec-tric effect. The magnetoelectric coupling-the way polarization and magnetization reverse-is manifested by the formation and interactions of domains and domain walls, and so to understand how to engineer future devices one must first understand the interactions of domains and domain walls. In this article, we provide a short introduction to the domain formation in ferroelectrics and ferromagnets, as well as different microscopy techniques that enable the visualization of such domains. We then review the recent research on multiferroic domains and domain walls, including their manipulation and intriguing properties, such as enhanced conductivity and anomalous magnetic order. Finally, we discuss future perspectives concerning the field of multiferroic domain walls and emergent topological structures such as ferroelectric vortices and skyrmions. 1 Domain structures in (multi-)ferroics 1.1 Introduction to ferroic domains and domain walls Ferroic materials are defined by the appearance of an order parameter (e.g., elastic, electric or magnetic) at a non-disruptive phase transition. This order parameter can point in at least two symmetrically equivalent directions (polarities) between which it can be switched by the application of an external field. When cooling through the phase transition in zero-field, the polarities have the same energy and, as a consequence, both polarities appear inside the ferroic material. These regions are called domains and the interfaces that separate them are call domain walls. While this shows, trivially, that multiple domains form naturally in ferroics, the details of how many domains, their size, and where they form, depend on several energy terms, as well as the local defect structure. In the following, we will give a brief outline of how ferroic domains and domain walls form, using a ferroelectric as an illustrative example; although, as we will see, analogous arguments can be made for the formation of domains and domains walls in ferromagnets. For a more complete and in-depth descriptions of the physics of ferroelectric and ferromagnetic domains we refer to, for instance, the textbooks by Tagantsev et al. [2] and by Hubert & Schäfer [3]. A proper ferroelectric is a material for which the spontaneous electric polarization plays the role of the primary symmetry breaking order parameter, which can completely describe the phase transition into the ferroic state [4],[5]. Practically, this means energy contributions related to this order parameter are very important in the system, particularly for the domain formation. For instance, in ferroelectrics, surfaces perpendicular to the ferroelectric polarization comprise bound charges that create a strong depolarizing field (Fig. 1a): this is a major driving force for domain formation. The depolar-izing field can be minimized by either (i) screening the surface charges of the ferroelectric with surface adsorbates or metallic electrodes (Fig. 1b), or (ii) the formation of ferroelectric domains, for example, 180° domains, so that the net polarization at the surface averages to zero (Fig. 1c). The number and size of the ferroelectric domains that form will

Mots clés: multiferroic; domains; domain walls; microscopy

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Donald M. Evans, Vincent Garcia, Dennis Meier, M. Bibes. Domains and domain walls in multiferroics. Physical Sciences Reviews, 2020, 5 (9), ⟨10.1515/psr-2019-0067⟩. ⟨hal-02984540⟩