More than 50 years ago, Russian physicist Dzyaloshinsky has proposed the specific interaction in some kinds of magnets to explain weak ferromagnetic behavior of them, and soon after that, Professor Moriya has identified its microscopic origin as the spin-orbit coupling. That interaction, now called the Dzyaloshinskii–Moriya (DM) interaction, is one of the most important topics in both experimental and theoretical study of magnetism. This is because it induces novel inhomogeneously ordered states in spin systems such as a chiral soliton lattice and Skyrmion crystal. These interesting states support non-vanishing "topological" charges and have been experimentally observed in some magnetic materials. In this paper, focussing on one-dimensional antiferromagnetic spin chains with the DM interaction, we exhaustively construct instanton solutions with topological excitations and elucidate their properties based on the field theoretical (nonlinear sigma model) description of spin chains. As shown in Fig, the resulting spin configurations show helical ordering due to the DM interaction.

Masaru Hongo, Toshiaki Fujimori, Tatsuhiro Misumi, Muneto Nitta, Norisuke Sakai
"Instantons in Chiral Magnets"
arXiv: 1907.02062