# Annihilation of Domain Walls in a Ferromagnetic Wire

## TL;DR

This paper develops an effective theoretical framework for understanding the annihilation of topological solitons in a one-dimensional ferromagnetic wire, validated by micromagnetic simulations.

## Contribution

It introduces a four-collective-coordinate model capturing the key physics of soliton annihilation in ferromagnets, bridging theory and simulation.

## Key findings

- The model accurately describes the annihilation dynamics.
- Simulation results confirm the effectiveness of the collective coordinate approach.
- The approach provides insights into the role of symmetries and conserved quantities.

## Abstract

We study the annihilation of topological solitons in the simplest setting: a one-dimensional ferromagnet with an easy axis. We develop an effective theory of the annihilation process in terms of four collective coordinates: two zero modes of the translational and rotational symmetries $Z$ and $\Phi$, representing the average position and azimuthal angle of the two solitons, and two conserved momenta $\zeta$ and $\varphi$, representing the relative distance and twist. Comparison with micromagnetic simulations shows that our approach captures well the essential physics of the process.