# Tunable skyrmion-skyrmion binding on the surface of a topological insulator

## TL;DR

This paper demonstrates that skyrmions on the surface of a magnetic topological insulator can attract and form bound states, with the interaction tunable via chemical potential, magnetic field, and anisotropy, unlike in conventional ferromagnets.

## Contribution

It introduces a mechanism for skyrmion binding based on electronic orbital hybridization and shows how this can be controlled in topological insulator systems.

## Key findings

- Skyrmions can form bound states due to electronic hybridization.
- Binding can be tuned by chemical potential, magnetic field, and anisotropy.
- Phase diagram includes stable, unstable, and metastable skyrmion pairs.

## Abstract

We show that skyrmions on the surface of a magnetic topological insulator may experience an attractive interaction that leads to the formation of a skyrmion-skyrmion bound state. This is in contrast to the case of skyrmions in a conventional chiral ferromagnet, for which the intrinsic interaction is repulsive. The origin of skyrmion binding in our model is the molecular hybridization of topologically protected electronic orbitals associated with each skyrmion. Attraction between the skyrmions can therefore be controlled by tuning a chemical potential that populates/depopulates the lowest-energy molecular orbital. We find that the skyrmion-skyrmion bound state can be made stable, unstable, or metastable depending on the chemical potential, magnetic field, and easy-axis anisotropy of the underlying ferromagnet, resulting in a rich phase diagram. Finally, we discuss the possibility to realize this effect in a recently synthesized Cr doped ${\left(\mathrm{Bi}_{2-y}\mathrm{Sb}_{y}\right)}_{2}\mathrm{Te}_3$ heterostructure.