Pair interaction of localized topological structures in confined chiral media

We study pairwise interactions between localized topological structures in chiral magnetic and cholesteric liquid crystal (CLC) systems confined in the planar geometry. Our calculations for magnetics are based on the lattice model that takes into account the bulk and surface anisotropies along with the exchange and the Dzyaloshinskii-Moriya interactions. In CLC cells, these anisotropies describe the energy of interaction with an external magnetic or electric field and the anchoring energy assuming that the magnetic or electric anisotropy is negative and the boundary conditions are homeotropic. We have selected the region of the phase diagram, where various localized solitonlike structures, including skyrmion tubes, torons, and leeches, embedded in the ground state of the z-cone (conical phase) coexist, and carried out numerical analysis of the distance dependencies of the effective intersoliton interaction potentials. For skyrmions and torons, the potentials are found to be attractive in the large separation region. It turned out that for these potentials, the effects of axial asymmetry are negligible. By contrast, it turned out that for the intermediate structures between the skyrmions and torons known as the leeches, the leech-leech potentials generally depend on the orientation of the intersoliton separation vector and their large distance parts may become repulsive at certain directions of the vector. All the potentials have the short distance repulsive parts and the local minima located at the equilibrium separations. It is found that the skyrmion-skyrmion potential has an additional metastable configuration shifted towards the short-distance region.