# Direct Observation of Attractive Skyrmions and Skyrmion Clusters in the Cubic Helimagnet Cu$_2$OSeO$_3$

## TL;DR

This paper reports the direct observation of attractive skyrmions and their clusters in the cubic helimagnet Cu$_2$OSeO$_3$, revealing a new type of three-dimensional magnetic solitons with potential implications for magnetic materials.

## Contribution

It provides the first real-space images of attractive skyrmion clusters in Cu$_2$OSeO$_3$ and introduces a phenomenological theory describing these non-standard skyrmions.

## Key findings

- Observation of attractive skyrmions in Cu$_2$OSeO$_3$
- Visualization of skyrmion clusters via transmission electron microscopy
- Development of a theoretical model for these skyrmions

## Abstract

We report the discovery of attractive magnetic skyrmions and their clusters in non-centrosymmetric ferromagnets. These three-dimensional solitons have been predicted to exist in the cone phase of chiral ferromagnets (J. Phys: Condens. Matter 28 (2016) 35LT01) and are fundamentally different from the more common repulsive axisymmetric skyrmions that occur in the magnetically saturated state. We present real-space images of these skyrmion clusters in thin (~70 nm) single-crystal samples of Cu$_2$OSeO$_3$ taken using transmission electron microscopy and develop a phenomenological theory describing this type of skyrmion.