# Magnetic Skyrmions coupled to fermions

## TL;DR

This paper explores how fermionic states localized on magnetic Skyrmions influence their interactions, revealing stable Skyrmion configurations mediated by fermion-induced dipole forces.

## Contribution

It demonstrates the existence of localized fermionic modes on Skyrmions and shows these modes lead to stable Skyrmion systems through attractive interactions.

## Key findings

- Sequences of fermionic modes localized on Skyrmions
- Existence of stable Skyrmion configurations
- Fermion-mediated attractive dipole interactions

## Abstract

The index theorem implies that there are fermionic states localized on a soliton. Presence of these modes may significantly alter the pattern of interaction between the solitons. As a particular example we investigate the chiral magnetic Skyrmions coupled to spin-isospin fermions. It is shown that there are sequences of fermionic modes localized on the Skyrmions. We investigate the pattern of interaction between the soltions with localized modes and proved the existence of stable system of magnetic Skyrmions bounded by the strong attractive dipole interaction mediated by the chargeless fermionic modes.