Skyrmion clusters and chains in bulk and thin-layered cubic helimagnets

I overview the properties of nonaxisymmetric isolated skyrmions (ISs), which arise within a cone phase of cubic helimagnets. The nascent conical state is shown to shape skyrmion internal structure and to substantiate the attracting skyrmion-skyrmion interaction. In bulk cubic helimagnets, skyrmion cluster formation with the hexagonal arrangement of constituent skyrmions is explained by the reduction of the total energy due to the overlap of skyrmion shells-circular domain boundaries with the positive energy density formed with respect to the surrounding host phase. In thin layers, however, such a shell localizes within two bags on the opposite sides from the skyrmion cores, which underlies the formation of polar skyrmion chains with the most effective suppression of the shell energy. A systematic analysis of skyrmion trio-clusters and trio-chains reveals that their thickness-dependent advantage rests on a subtle energetic balance between the lost negative energy of the skyrmion rings and the gained energy due to the suppressed shells. Such a polar ordering of nonaxisymmetric skyrmions was recently observed within the schools of liquid-crystal skyrmions powered into motion by an applied electric field [Nat. Commun. 10, 4744 (2019)]. Thus, the fundamental insights provided by this work imply deep physical relations and common physical features of skyrmions in different condensed-matter systems such as chiral liquid crystals and chiral magnets.

Automated summary

The properties of nonaxisymmetric isolated skyrmions (ISs) in a cone phase of cubic helimagnets are overviewed. The shape of the nascent conical state influences the internal structure and interaction of skyrmions. In bulk cubic helimagnets, hexagonal cluster formation is explained by the overlap of skyrmion shells with positive energy density. In thin layers, shell localization leads to the formation of polar skyrmion chains. Recent observations in liquid-crystal skyrmions have revealed the polar ordering of nonaxisymmetric skyrmions, indicating common physical features in different condensed-matter systems.