A glimpse at topological structures in multiferroic materials

Abstract

It is with great pleasure that we present this special issue focused on topological structures in ferroic materials. It is composed of invited contributions from the International Workshop on Topological Structures in Ferroic Materials held at the University of South Wales, Sydney, Australia from 19–21st May 2015. The aim of the workshop was to capture current research interests regarding interfaces, domains, domain walls, vortices and skyrmions in ferroics as an emerging and highly active field in solid state physics and materials science. Significant emphasis was placed on understanding the fundamental commonalities that bridge topological defects across various types of ferroic materials, and therefore lessons learned on how new and groundbreaking functionalities afforded by the aforementioned concepts could be translated into emerging technologies. Topological defects see widespread study in a number of vastly different fields, ranging from cosmology to liquid crystals and magnetoelectrics.1-4 In ferroic materials, the topological defect is typically associated with a change in structure and/or order parameter, leading to different properties at the defect that can be exploited to provide new functionalities in materials, including properties that are not at all present in the bulk. These changes within the order parameter typically occur over a length scale ranging from a few atoms to several microns. With the advent of both, precise atomic scale nanofabrication and measurements, we now stand in an era where not only direct imaging of such defects is possible5 but also we can characterize the response of a single defect and utilizing sophisticated nanoscale probes. We begin our journey into the fascinating world of topological defects with a review by Vasudevan et al (article number 1500292). The authors present a review of topological structures in multiferroic materials, which have become prominent in the last decade. The authors give direct examples of how advances in synthesis, imaging and characterization techniques have allowed access and controlled writing of topological defects at the nanometer scale. The review encompasses discussions on domain walls, vortices and skyrmions in multiferroic compounds, highlighting how the altered structure at the defect directly impacts a relevant material property, such as electronic conductivity. Following this we turn to the complexities and intrigue of the world of complex oxide epitaxy. In particular, the role of symmetry mismatch in the growth and nucleation of an oxide material on a non-isostructural surface (i.e. orthorhombic film on a cubic substrate) has recently gained attention. In article number 1500201 Meyer et al. provide detailed analysis of the interfacial and bulk microstructure of the orthorhombic brownmillerite, SrCoO2.5, grown epitaxially on the cubic perovskite, SrTiO3. SrCoO2.5 is known for its demonstrated catalytic behavior, and it can also be topotactically oxidized into the ferromagnetic metal, SrCoO3.6 Thus, the authors cover a critical component based on understanding the nucleation and structural details of this versatile compound and its specific interface structure. The work is of importance as it provides useful information regarding the growth and development of other layered oxide materials. One of the defining features of a ferroic material are domains associated with the specific order parameter and the interfaces that separate domains, i.e. domain walls. Traditionally domain morphology (i.e. size, shape, periodicity etc.) and kinetics (i.e. mobility, pinning and propagation) were believed to fundamentally govern the physical properties of all ferroics. This notion changed dramatically, when in a landmark report in Nature Materials, Seidel et al. demonstrated that certain types of domain walls in an insulating multiferroic show room-temperature conductivity.7 The finding put domain walls in a completely new light by establishing that properties of domain walls can be radically different from the domains they delineate. This exciting discovery opened up a new avenue to design functional materials where, given a sufficiently large volume density of such domain walls, the functional behavior of a ferroic is dominated not by the atomic structure of the domains but by the domain walls themselves. This would make it possible to design new functionalities not by changing the bulk material composition and structure, as has been done in the past, but by using nanofabrication to artificially engineer domain walls.8 The paper by Meier et al. (article number 1500195) is a beautiful example of this hypothesis. They explore the idea of point defect-driven modulation of domain wall properties, where they dope specific acceptor or donor atoms in order to control electronic behavior, just like conventional semiconductors. They demonstrate the optimization of electronic domain-wall properties in a ferroelectric semiconductor by aliovalent cation substitution. They modify the domain-wall conductance by replacing trivalent Er3+ for divalent Ca2+ (0 ≤ x ≤ 0.01) in Er1-xCaxMnO3. A doping level of 1% is found to enhance the local electronic conductance by a factor of ∼50. In addition, leakage effects at the domain walls are suppressed, reducing the effective width of these conducting nano-channels by about 50%. The higher conductance, together with the reduced domain-wall width, lead to a significant enhancement of the current density carried by the walls. On similar grounds of domain structure tuning, Everhardt et al. follow a more traditional approach in article number 1500214. Ferroelectric BaTiO3 has been predicted to undergo a variety of phase transformations and adopt lower-symmetry domain configurations when grown under low strain on low mismatched substrates. However, very few experimental investigations of that region of the phase diagram exist until now. Everhardt et al. demonstrate very high quality BaTiO3 thin films on NdScO3 substrates that impose a low (∼0.1%) strain. Using high-resolution synchrotron X-ray diffraction and systematic piezoresponse force microscopy they provide experimental evidence of a phase transition close to room temperature, a low symmetry ca1/ca2 phase and the formation of periodic domains. The work thus is an example of domain engineering in order to enhance the piezoelectric performance utilizing low crystal symmetries and a high density of domain walls. One of the central factors that affect the domain and domain wall structure in ferroics is the presence of a force field opposite to the direction of the order parameter. Such a field (either demagnetization or depolarization field) fundamentally appears in order to lower the energy. Simply put, unless there is an effective screening mechanism, it is energetically unfavorable for a ferroic material to be in a single domain or so-called monodomain state. A direct consequence of the depolarization field in ferroelectrics is thus oppositely poled domains such that the net polarization is almost close to zero. However, in ultra-thin (or nanoscale) ferroelectrics, the energy cost to create a domain wall may be quite large and thus a more efficient option can be either to smear out or even completely eliminate the ferroelectric polarization. Thus an uncompensated depolarization field can even completely eliminate the ferroelectric phase at room temperature and it is for this reason, the community has always looked at ways to suppress its influence. In article number 1500288, Chen and co-workers turn this concept on its head and pose the following challenge – can the depolarization field be exploited to enhance ferroelectric polarization switching? Indeed, they show that by intentionally enhancing depolarization effects in a ferroelectric heterostructure (through the introduction of a semiconducting STO dielectric spacer layer) it is possible to control the nanoscale domain structure in the PZT layers. The presence of a spacer promotes the formation of irregular 180° domains, as evidenced by piezoresponse force microscopy (PFM). Critically, when compared to a reference sample without this spacer, the introduction of the spacer reduces the measured coercive voltage, decreases the built-in voltage (imprint) by ∼80% and shortens the nucleation time for a written domain under a biased PFM tip by two orders of magnitude. Thus at right length scale, depolarization phenomena can result in a large improvement of ferroelectric properties, such as lower measured coercive voltages, faster nucleation speed, reduced imprint, and reduced leakage current. Following these experimental papers based on domain and domain wall driven phenomena, the next set of articles look at the important features of topological defects from a theoretical perspective. The first is a paper by Walter et al. (article number 1500218) on electrical control of chiral phases in toroidal (or vortex-like) defects. In ferroelectric nanostructures, size effects can induce the formation of topological defects in the polarization field not present in bulk systems. The most important of these topological defects are electrical vortices, which are characterized by order parameter of electrical toroidal moment. Their existence was predicted theoretically in the early 2000's by Bellaiche et al.9 Compared to magnetic vortices, electrical vortices have not yet received as much attention, although they promise to be better suited for high-density, ultra- fast memory due to their smaller scale and THz dynamics. A more recent promising concept is the potential optical application of such vortices. Theoretical contributions made in recent work10 show that electrotoroidic (or ferrotoroidic) systems, i.e. those with electrical vortices, naturally exhibit gyrotropy, or rotation of the plane of polarization of linearly polarized light. Therefore, there are very exciting prospects for devices such as nanoscale optical circulators. Gyrotropy occurs provided that the electrical toroidal moment responds linearly in applied electric field, which occurs if the electrical toroidal moment couples to a spontaneous electrical polarization parallel to it. Walter et al. shed light on the optimization of the magnitude of the gyrotropic coefficient with respect to temperature and applied DC electric fields. Combined molecular dynamics and Monte Carlo simulations are used to construct a temperature-electric field phase diagram which can be useful to predict the factors under which a ferroelectric/paraelectric or ferrotoroidic/paratoroidic phase transition can occur. Next, we look at the creation of skyrmions, i.e. nanometric spin vortices characterized by a quantized topological number, by electric field in magnetic insulators. The paper by Mochizuki (article number 1500180) theoretically proposes that magnetic skyrmions can be electrically created in a thin film specimen of a chiral-lattice magnetic insulator within a few nanoseconds by applying an electric field via an electrode tip. This concept takes advantage of the coupling between noncollinear skyrmion spins and electric polarizations in these materials. The author shows that the applied electric field induces twisting of the magnetization alignment and eventually a 180° flop of the local magnetization through modulation of the spatial distribution of Dzyaloshinskii-Moriya interaction energy as well as the local polarization orientation via magnetoelectric coupling. The skyrmion spin structure then grows around the flopped magnetization after switching off the electric field. This finding will pave a route to utilizing multiferroic skyrmions as information carriers for low-energy-consuming magnetic storage devices without Joule-heating energy losses. The interplay between the various spin interactions and the resultant wall structure is discussed by Borys et al. in article number 1500202. When Dzyaloshinskii-Moriya interactions (DMI) are active, due to the broken spatial inversion symmetry, a rotating spin alignment is favored. In contrast the ferromagnetic-exchange interactions favor a parallel spin alignment. While in Bloch-type walls spin waves are not reflected and only acquire a phase shift, the authors argue that the DMI leads to scattering of the spin waves and their reflection at specific DMI domain walls. They propose a periodic array of domain walls to test the reflection phenomenon in experiments. Interestingly, the band structure of the array associated with these walls is expected to exhibit gaps that resemble the ones found in magnonic crystals, allowing, in principle, for tunable devices through externally applied magnetic fields. The last paper, article number 1500196, covers newly discovered inversion symmetry breaking and hence piezoelectricity in the family of layered perovskites (LiRTiO4 (R = rare earths)). Gupta et al. reveal that the improper mechanism for breaking inversion symmetry and thus inducing piezoelectricity arises from TiO6 octahedral rotation. This family of materials is shown to have a very high Tc (up to 1200K) with a predicted piezoelectric coefficient (d36) of -15 pC/N. Piezoelectric force microscopy along with optical second harmonic response confirms inversion symmetry breaking. The fundamental idea behind the development of these materials is that the oxygen octahedral rotations (OOR) can break inversion symmetry in layered perovskites. Previous theoretical work11, 12 first proposed that the OOR represented by a−a−c+ in the Glazer notation can remove inversion centers in Ruddlesden-Popper phases and perovskite superlattices, respectively. This idea of breaking inversion symmetry by OOR has now been demonstrated in a wide family of oxide perovskites. The approach presented by the authors here opens a gateway for careful examination of OOR-induced symmetry breaking in other classes of layered oxides such as Ruddlesden Popper phases, perovskite superlattices, Aurivillius perovskites, and others. In conclusion, this special issue addresses a range of fascinating concepts of topological structures and issues relevant to this rapidly moving field in ferroic materials. We hope that the workshop and this special issue will motivate and spur deep discussions and hearty debates on addressing the further development of topological structures as nanoscale electronic and magnetic device elements. Furthermore, the similarities between various families of ferroics (and multiferroics) as shown by the workshop presentations should be exploited and promote cross-pollination of theory and experimental ideas across the various sub-communities. In this sense we sincerely hope this special issue will be an important step towards bringing the scientists working at the forefront of this topic together and promote a tradition of regular annual/biennial meetings. Finally we would like to extend our sincere thanks to the students and research associates from our research groups, School of Materials Science and Engineering staff at UNSW, our sponsors (Attocube systems, Oxford Instruments and ANFF UNSW node) and the editorial staff at Advanced Electronic Materials (in particular Dr. Hakim Meskine), without whose support none of this endeavor would have been possible. Jan Seidel is an Associate Professor at the School of Materials Science and Engineering at UNSW Australia. He received his doctorate in physics from the University of Technology Dresden in 2005. From 2006 to 2007, he was a Feodor Lynen Fellow (Alexander von Humboldt Foundation) at the University of California, Berkeley. From 2008 to 2011, he worked at Lawrence Berkeley National Laboratory. His main interests are in materials physics of complex oxide materials, especially fundamental electronic, optical and magnetic properties of interfaces and topological structures. Nagarajan (Nagy) Valanoor received his B. Engg in Metallurgy from the University of Pune (1997) and Ph.D from the University of Maryland (2001) under supervision of Prof. Ramesh in Materials Science and Engineering respectively. In 2005 he was offered a lectureship at the School of Materials Science and Engineering, where he is currently Professor and Research Director. His research interests include understanding nanoscale phenomena in functional oxide interfaces and the synthesis of novel interfaces based on these understandings.