Inertial domain wall characterization in layered multisublattice antiferromagnets

TL;DR

This paper investigates the inertial and relativistic dynamics of domain walls in layered antiferromagnets under time-dependent spin-orbit fields, providing a detailed theoretical framework for understanding their motion and energy transformation.

Contribution

It introduces an effective nonlinear sigma-model that accurately captures the inertial and relativistic behavior of domain walls in layered antiferromagnets, extending understanding beyond quasistatic processes.

Findings

The model replicates atomistic spin dynamics results for quasistatic processes.

Stored exchange energy converts into translational mobility when external stimuli cease.

Predicts inertial travel distance based on relativistic mass in dynamic regimes.

Abstract

The motion of a N\'eel-like ${180}^{\circ}$ domain wall induced by a time-dependent staggered spin-orbit field in the layered collinear antiferromagnet Mn$_2$Au is explored. Through an effective version of the two sublattice nonlinear $\sigma$-model which does not take into account the antiferromagnetic exchange interaction directed along the tetragonal c-axis, it is possible to replicate accurately the relativistic and inertial traces intrinsic to the magnetic texture dynamics obtained through atomistic spin dynamics simulations for quasistatic processes. In the case in which the steady-state magnetic soliton motion is extinguished due to the abrupt shutdown of the external stimulus, its stored relativistic exchange energy is transformed into a complex translational mobility, being the rigid domain wall profile approximation no longer suitable. Although it is not feasible to carry out a detailed follow-up of its temporal evolution in this case, it is possible to predict the inertial-based distance travelled by the domain wall in relation to its steady-state relativistic mass. This exhaustive dynamical characterization for different time-dependent regimes of the driving force is of potential interest in antiferromagnetic domain wall-based device applications.