# Spin texture motion in antiferromagnetic and ferromagnetic nanowires

## TL;DR

This paper develops a Hamiltonian formalism for modeling current and magnetic field-driven domain wall dynamics in ferromagnetic and antiferromagnetic nanowires, providing new insights into their motion and control mechanisms.

## Contribution

It introduces a Hamiltonian dynamics approach based on Poisson brackets for analyzing domain wall motion, including dissipative effects, in both ferromagnetic and antiferromagnetic systems.

## Key findings

- Derived Hamilton equations of motion for domain walls.
- Predicted magnetic moment induction in antiferromagnetic domain walls.
- Proposed an orientation switch mechanism for antiferromagnetic domain walls.

## Abstract

We propose a Hamiltonian dynamics formalism for the current and magnetic field driven dynamics of ferromagnetic and antiferromagnetic domain walls in one dimensional systems. To demonstrate the power of this formalism, we derive Hamilton equations of motion via Poisson brackets based on the Landau-Lifshitz-Gilbert phenomenology, and add dissipative dynamics via the evolution of the energy. We use this approach to study current induced domain wall motion and compute the drift velocity. For the antiferromagnetic case, we show that a nonzero magnetic moment is induced in the domain wall, which indicates that an additional application of a magnetic field would influence the antiferromagnetic domain-wall dynamics. We consider both cases of the magnetic field being parallel and transverse to the N{\'e}el field. Based on this formalism, we predict an orientation switch mechanism for antiferromagnetic domain walls which can be tested with the recently discovered N{\'e}el spin orbit torques.