# Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes

## TL;DR

This study visualizes and analyzes skyrmion clusters with orthogonal orientations in chiral liquid crystals and ferromagnets, revealing interaction mechanisms and forming complex superstructures.

## Contribution

It provides the first direct visualization of orthogonal skyrmion clusters and develops a phenomenological theory of their interactions and configurations.

## Key findings

- Identification of attractive and repulsive skyrmion interactions
- Observation of skyrmion windings forming superstructures
- Validation of simulations in cubic helimagnets' A-phase

## Abstract

We report the discovery and direct visualization of skyrmion clusters with mutually-orthogonal orientations of constituent isolated skyrmions in chiral liquid crystals and ferromagnets. We show that the nascent conical state underlies attracting inter-skyrmion potential, whereas an encompassing homogeneous state leads to the repulsive skyrmion-skyrmion interaction. The crossover between different regimes of skyrmion interaction could be identified upon changing layer thickness and/or the surface anchoring. We develop a phenomenological theory describing two types of skyrmions and the underlying mechanisms of their interaction. We show that isolated horizontal skyrmions with the same polarity may approach a vertical isolated skyrmion from both sides and thus constitute two energetically-different configurations which are also observed experimentally. In an extreme regime of mutual attraction, the skyrmions wind around each other forming compact superstructures with undulations. We also indicate that our numerical simulations on skyrmion clusters are valid in a parameter range corresponding to the A-phase region of cubic helimagnets.