# The Landau-Lifshitz-Bloch equation for domain wall motion in antiferromagnets

## TL;DR

This paper derives a finite-temperature Landau-Lifshitz-Bloch equation for antiferromagnetic materials, enabling analytical study of domain wall motion and its temperature dependence, advancing understanding in AFM spintronics.

## Contribution

It introduces a comprehensive analytical framework for AFM domain wall dynamics at finite temperature, validated against numerical results and applicable to various AFM systems.

## Key findings

- Analytical model reproduces numerical results on velocity saturation.
- Temperature influences static domain wall profiles.
- The theory applies to diverse AFM domain wall motions.

## Abstract

In this work, we derive the Landau-Lifshitz-Bloch equation accounting for the multi-domain antiferromagnetic (AFM) lattice at finite temperature, in order to investigate the domain wall (DW) motion, the core issue for AFM spintronics. The continuity equation of the staggered magnetization is obtained using the continuum approximation, allowing an analytical calculation on the domain wall dynamics. The influence of temperature on the static domain wall profile is investigated, and the analytical calculations reproduce well earlier numerical results on temperature gradient driven saturation velocity of the AFM domain wall, confirming the validity of this theory. Moreover, it is worth noting that this theory could be also applied to dynamics of various wall motions in an AFM system. The present theory represents a comprehensive approach to the domain wall dynamics in AFM materials, a crucial step toward the development of AFM spintronics.

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Source: https://tomesphere.com/paper/1812.00759