# Paths to annihilation of first and second-order (anti)skyrmions via (anti)meron nucleation on the frustrated square lattice

## TL;DR

This paper investigates how small skyrmions and antiskyrmions on a frustrated square lattice annihilate through meron or antimeron nucleation, revealing complex energy landscapes and validating theoretical lifetime predictions with simulations.

## Contribution

It introduces detailed mechanisms of skyrmion and antiskyrmion annihilation on a frustrated lattice, including energy barriers and nucleation pathways, with validation against Langevin simulations.

## Key findings

- Annihilation occurs via meron or antimeron nucleation.
- Complex energy landscape with multiple stable and unstable states.
- Excellent agreement between transition state theory and simulations.

## Abstract

We study annihilation mechanisms of small first- and second-order skyrmions and antiskyrmions on the frustrated $J_1-J_2-J_3$ square lattice with broken inversion symmetry (DMI). We find that annihilation happens via the injection of the opposite topological charge in the form of meron or antimeron nucleation. Overall, the exchange frustration generates a complex energy landscape with not only many (meta)stable and unstable local energy solutions, but also many possible paths connecting them. Whenever possible, we compute the activation energy and attempt frequency for the annihilation of isolated topological defects. In particular, we compare the average lifetime of the antiskyrmion calculated with transition state theory with direct Langevin simulations, where an excellent agreement is obtained.