# Skyrmion knots in frustrated magnets

## TL;DR

This paper predicts through numerical simulations that magnetic Skyrmions in frustrated magnets can form stable three-dimensional knotted structures, opening new avenues for experimental research and potential spintronic applications.

## Contribution

It introduces the concept of stable knotted Skyrmion structures in three dimensions within frustrated magnets, a novel theoretical prediction.

## Key findings

- Skyrmions can form stable knots with integer Hopf charge
- Low Hopf charge Skyrmions tend to be ring-shaped
- Higher Hopf charge Skyrmions favor links and knots

## Abstract

A magnetic Skyrmion is a stable two-dimensional nanoparticle describing a localized winding of the magnetization in certain magnetic materials. Skyrmions are the subject of intense experimental and theoretical investigation and have potential technological spintronic applications. Here we show that numerical computations of frustrated magnets predict that Skyrmions can be tied into knots to form new stable three-dimensional nanoparticles. These stable equilibria of twisted loops of Skyrmion strings have an integer-valued topological charge, known as the Hopf charge, that counts the number of particles. Rings are formed for low values of this charge, but for higher values it is energetically favourable to form links and then knots. This computational study provides a novel impetus for future experimental work on these nanoknots and an exploration of the potential technological applications of three-dimensional nanoparticles encoding knotted magnetization.