This book provides a state-of-the art overview of a highly interesting emerging research field in solid state physics/nanomaterials science, topological structures in ferroic materials. Topological structures in ferroic materials have received strongly increasing attention in the last few years. Such structures include domain walls, skyrmions and vortices, which can form in ferroelectric, magnetic, ferroelastic or multiferroic materials. These topological structures can have completely different properties from the bulk material they form in. They also can be controlled by external fields (electrical, magnetic, strain) or currents, which makes them interesting from a fundamental research point of view as well as for potential novel nanomaterials applications. To provide a comprehensive overview, international leading researches in these fields contributed review-like chapters about their own work and the work of other researchers to provide a current view of this highly interesting topic.

This book focuses on the characterisation of the chiral and topological nature of magnetic skyrmions in noncentrosymmetric helimagnets. In these materials, the skyrmion lattice phase appears as a long-range-ordered, close-packed grid of nearly millimetre-level correlation length, while the size of a single skyrmion is 3–100 nm. This is a very challenging range of length scales (spanning 5 orders of magnitude from tens of nm to mm) for magnetic characterisation techniques, and, to date, extensive information on this fascinating, magnetically ordered state has remained elusive. In response, this work develops novel resonant elastic x-ray scattering (REXS) techniques, which allow the magnetic structure, including the long-range order and domain formation, as well as microscopic skyrmion parameters, to be measured across the full range of length scales. Most importantly, using circular dichroism in REXS, the internal structure of a given skyrmion, the topological winding number, and the skyrmion helicity angle can all be unambiguously determined. These new techniques are applicable to many materials systems, and allow us to retrieve information on modulated spin structures, multiferroic order, spin-density-waves, and other forms of topological magnetic order.

Topological structures in multiferroic materials have recently received considerable attention because of their potential use as nanoscale functional elements. Their reduced size in conjunction with exotic arrangement of the ferroic order parameter and potential order parameter coupling allows for emergent and unexplored phenomena in condensed matter and functional materials systems. This will lead to exciting new fundamental discoveries as well as application concepts that exploit their response to external stimuli such as mechanical strain, electric and magnetic fields. In this review we capture the current development of this rapidly moving field with specific emphasis on key achievements that have cast light on how such topological structures in multiferroic materials systems can be exploited for use in complex oxide nanoelectronics and spintronics.

This book presents both experimental and theoretical aspects of topology in magnetism. It first discusses how the topology in real space is relevant for a variety of magnetic spin structures, including domain walls, vortices, skyrmions, and dynamic excitations, and then focuses on the phenomena that are driven by distinct topology in reciprocal momentum space, such as anomalous and spin Hall effects, topological insulators, and Weyl semimetals. Lastly, it examines how topology influences dynamic phenomena and excitations (such as spin waves, magnons, localized dynamic solitons, and Majorana fermions). The book also shows how these developments promise to lead the transformative revolution of information technology.