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

In this work, we derive the Landau-Lifshitz-Bloch equation accounting for the multidomain antiferromagnetic (AFM) lattice at finite temperature, in order to investigate the domain wall motion, the core issue for AFM spintronics. The continuity equation of the staggered magnetization is obtained using the continuum approximation, allowing an analytical calculation of the domain wall dynamics. The influence of temperature on the static domain wall profile is investigated, and the analytical calculations agree well with the numerical simulations on temperature-gradient-driven domain wall motion, confirming the validity of this theory. Furthermore, the decrease of the acceleration and the increase of the saturation velocity of the domain wall with the increase of temperature are uncovered for a fixed gradient. 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.