Interaction Between Three-Dimensional Topological Spin Textures With Layer-Dependent Sign Change Tunes Lattice Symmetry.

Abstract

Three-dimensional (3D) topological spin textures host rich internal structures in thickness dimensions and enable emergent topological phenomena. However, whether their layer-resolved textures and internal singularities fundamentally modify intralayer interactions lies beyond rigid-tube interaction models and remains unexplored. Here we show that, in 3D hybrid skyrmion-antiskyrmion strings, the layer-dependent topology gives rise to interactions with a sign change across the film thickness, producing a switch between attraction and repulsion both among different layers within each texture and between neighboring 3D strings. This vertically asymmetric attractive-repulsive interaction drives a tunable transition between square and triangular string lattices, in agreement with our experiment. Computational simulations identify quadrupolar Bloch points as internal topological junctions whose vertical migration mediates the intralayer competition between repulsive skyrmion segments near the surfaces and attractive antiskyrmion segments in the interior. We further show that the averaged topological charge quantifies the relative thickness fractions of the two competing topological segments and robustly captures the lattice phase boundary over a broad range of magnetic parameters. These findings highlight the importance of the surface-bulk difference in topological materials and establish vertically asymmetric interactions as an intrinsic mechanism for topological phase control in 3D magnetic systems.