Traveling antiferromagnetic domain walls in a magnetic field

TL;DR

This work analyzes one-dimensional antiferromagnetic domain walls under a magnetic field aligned with the easy axis, using a nonlinear sigma model for the Néel vector. By applying a traveling-wave ansatz, the authors derive closed-form wall profiles and reveal a maximum wall speed $v_c = \sqrt{1-h^2}$ and a wall width $\ell_w = \dfrac{1-v^2}{\sqrt{1-h^2-v^2}}$, which exhibits non-monotonic behavior and diverges at $v_c$. They extend the analysis to include a Dzyaloshinskii-Moriya interaction, finding that DM induces chirality and narrows the wall, while also allowing a propagating spiral to replace the wall when $v>v_c$, with a characteristic period $2\pi(1-v^2)/(hv)$. When $v>v_c$, a spiral state minimizes the effective energy, with DM modifying the spiral structure to involve all three magnetization components. These results illuminate high-velocity AFM-wall dynamics under external fields and DM interactions, with potential implications for fast domain-wall manipulation and spintronic devices.

Abstract

We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum $v_c$. The width of the domain wall is a non-monotonic function of the velocity and it diverges to infinity at $v_c$. Both features are in contrast to the case of the Lorentz invariant model in the absence of the field. We further study the modification of the wall profile when a Dzyaloshinskii-Moriya interaction is added. Finally, we present a propagating spiral expected to form when the system is forced at a velocity higher than the maximum velocity for domain walls and we give numerical results for the effect of the Dzyaloshinskii-Moriya interaction.

Figures (5)

• Figure 1: The Néel vector components for traveling domain wall solutions for an external field $h=0.5$ and velocities (a) $v=0.6$, (b) $v=0.8$. We have chosen $x_0=0$ in Eq. \ref{['eq:ThetaSol']} (center of wall at $t=0$) and also $x_1=0$ in Eq. \ref{['eq:PhiSol']}, although these two arbitrary constant need not, in general, be equal. (We consider here that $\Theta(x=-\infty)=\pi,\; \Theta(x=\infty)=0$.)
• Figure 2: The width $\ell_w$ given in Eq. \ref{['eq:ThetaSol']} of traveling domain walls vs velocity for two values of the external field (and $\lambda=0$). For $h < 1/\sqrt{2}$ (e.g., $h=0.5$), the width has a minimum at $v=\sqrt{1-2h^2}$ and it diverges to infinity at the maximum velocity $v_c=\sqrt{1-h^2}$. For values of the external field $h > 1/\sqrt{2}$ (e.g., $h=0.72$), the wall width increases monotonically.
• Figure 3: The Néel vector components for propagating chiral domain walls for DM parameter $\lambda=0.5$, external field $h=0.5$, and velocities (a) $v=0.6$ and (b) $v=0.8$. The $n_2$ component is smaller in magnitude and the wall width is smaller compared to the non-chiral walls in Fig. \ref{['fig:domainWalls']}. For the chiral wall, we necessarily have $x_0=x_1$, i.e., the center of the wall ($n_3=0$) is at $\Phi=0$. (We consider here that $\Theta(\xi=-\infty)=-\pi,\; \Theta(\xi=\infty)=0$.)
• Figure 4: The width $\ell_w$ for traveling domain walls vs velocity for $\lambda=0.1$ and field $h=0.5$ is shown by dots connected with a line. The dots for $\ell_w$ have been found by fitting a hyperbolic tangent to the numerical solutions. The corresponding curve for $\lambda=0$ is plotted for comparison (it is identical to the curve in Fig. \ref{['fig:chiralwallWidth']}).
• Figure 5: A spiral propagating with velocity $v=0.79$ for parameters $h=0.6$ and $\lambda=0.2$. This velocity is below $v_c=0.8$ which is the critical velocity for the transition to the spiral when $\lambda=0$.