"Polymerization" of Bimerons in Quasi-Two-Dimensional Chiral Magnets with Easy-Plane Anisotropy

We re-examine the internal structure of bimerons, which are stabilized in easy-plane chiral magnets and represent coupled states of two merons with the same topological charge |1/2| but with opposite vorticity and the polarity. We find that, in addition to the vortices and antivortices, bimerons feature circular regions which are located behind the anti-vortices and bear the rotational sense opposite to the rotational sense chosen by the Dzyaloshinskii-Moriya interaction. In an attempt to eliminate these wrong-twist regions with an excess of positive energy density, bimerons assemble into chains, and as such exhibit an attracting interaction potential. As an alternative to chains, we demonstrate the existence of ring-shaped bimeron clusters of several varieties. In some rings, bimeron dipoles are oriented along the circle and swirl clockwise and/or counterclockwise (dubbed "roundabouts"). Moreover, a central meron encircled by the outer bimerons may possess either positive or negative polarity. In other rings, the bimeron dipoles point towards the center of a ring and consequently couple to the central meron (dubbed "crossings"). We point out that the ringlike solutions for baryons obtained within the Skyrme model of pions, although driven by the same tendency of the energy reduction, yield only one type of bimeron rings. The conditions of stability applied to the described bimeron rings are additionally extended to bimeron networks when bimerons fill the whole space of two-dimensional samples and exhibit combinations of rings and chains dispersed with different spatial density (dubbed bimeron "polymers"). In particular, bimeron crystals with hexagonal and the square bimeron orderings are possible when the sides of the unit cells represent chains of bimerons joined in intersections with three or four bimerons, respectively; otherwise, bimeron networks represent disordered bimeron structures. Moreover, we scrutinize the inter-transformations between hexagonal Skyrmion lattices and disordered bimeron polymers occuring via nucleation and mutual annihilation of merons within the cell boundaries. Our theory provides clear directions for experimental studies of bimeron orderings in different condensed-matter systems with quasi-two-dimensional geometries.