Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.