# Gauge fields and related forces in antiferromagnetic solitons

## TL;DR

This paper develops a theoretical framework to describe how topological solitons in antiferromagnets respond to external perturbations, revealing effective forces and fields that influence their dynamics.

## Contribution

It introduces a formalism for the equations of motion of antiferromagnetic solitons under combined magnetic and electrical perturbations, including gyrotropic and electric field effects.

## Key findings

- Antiferromagnetic vortices can be moved by magnetic fields and electric currents.
- Perturbations generate effective magnetic and electric fields affecting soliton motion.
- The formalism applies to domain walls and vortices, predicting their dynamics under external stimuli.

## Abstract

We derive equations of motion for topological solitons in antiferromagnets under the combined action of perturbations such as an external magnetic field and torque-generating electrical current. Aside from conservative forces, such perturbations generate an effective "magnetic field" exerting a gyrotropic force on the soliton and an induced "electric field" if the perturbation is time-dependent. We apply the general formalism to the cases of a domain wall and of a vortex. An antiferromagnetic vortex can be effectively moved by combined applications of a magnetic field and an electric current.