Topological Phenomena in Spin Systems: Textures and Waves

Abstract

This chapter reviews the implications of topology in the static and dynamics of magnetic systems. Our focus is twofold. In the first part, we describe how the application of topology allows an understanding of the structure and dynamics of magnetic textures that separate different magnetic domains in magnetic materials. Topological textures are rationalized in terms of elementary topological defects that determine complex magnetic orders and magnetization dynamics processes in the underlying magnetic systems. The second part studies topological phases and topological phenomena associated with the band theory of linear magnetic excitations. Topological spin waves are usually accompanied by exotic phenomena in magnetic materials such as the emergence of chiral edge states and the magnon Hall effect.