Two-Dimensional Magnetic Vortices

In the proposed review, the structure of peculiar topological excitations of magnetically ordered media, the so-called two-dimensional magnetic vortices, is described as completely and in detail as possible. Magnetic vortices represent a distinct category of defects within the field of condensed matter physics. Accordingly, the structure of vortices in hydrodynamics and superfluids, as well as dislocations in solid-state physics, is presented at the beginning of the review. A specific section of the review is dedicated to elucidating the structural characteristics of plane vortices, instantons, spiral vortices, magnetic "targets," vortex stripes, and their interactions employing analytical methods. A general solution of a two-dimensional isotropic ferromagnetic system is presented using methods of differential geometry. The discussion encompasses two-dimensional vortices with anisotropic exchange interactions. A substantial portion of the review is devoted to helicoidal structures and vortices (skyrmions) in chiral magnets, encompassing their theoretical characterization based on a functional incorporating the DMI, as well as the outcomes of the early experiments on the detection of one-dimensional helical structures. A theoretical description of skyrmions and two-dimensional skyrmion lattices in bulk crystals is provided. It is observed that the DMI significantly alters the morphology of skyrmions with an arbitrary topological charge. Such structures can be represented as a "sack" with the shell comprised of k pi-skyrmions. The observed Archimedean spiral vortices are described, and a hexagonal lattice of Archimedean spiral is predicted to represent a new equilibrium phase.