Interaction and collision of skyrmions in chiral antiferromagnets

TL;DR

The study analyzes head-on collisions of propagating skyrmions in a two-dimensional chiral antiferromagnet described by a sigma-model for the Néel vector, showing that collision outcomes depend on the initial speed: slow skyrmions shrink and bounce back, while fast ones shrink to a singular point and annihilate, with kinetic energy converting into exchange energy and spin waves. A two-parameter collective-coordinate model, with inter-skyrmion distance $X(t)$ and radius $R(t)$, coupled via a far-field interaction $V_{\rm int}(X,R)\approx 2\pi q(R)^2 K_0(X)$, reproduces the main collision dynamics and the breathing oscillations observed in full-field simulations. The reduced model yields Euler–Lagrange equations for $X$ and $R$ and fidelity with full simulations, highlighting skyrmion elasticity as a key factor in soliton collisions. Overall, the findings reveal distinctive AFM skyrmion collision behavior, provide a practical framework for predicting outcomes, and guide potential experimental studies of AFM skyrmions.

Abstract

Skyrmions in an antiferromagnet can travel as solitary waves in stark contrast to the situation in ferromagnets. Traveling skyrmion solutions have been found numerically in chiral antiferromagnets. We study head-on collision events between two skyrmions. We find that the result of the collision depends on the initial velocity of the skyrmions. For small velocities, the skyrmions shrink as they approach, then bounce back and eventually acquire almost their initial speed. For larger velocities, the skyrmions approach each other and shrink until they become singular points at some finite separation and are eventually annihilated. Considering skyrmion energetics, we can determine the regimes of the different dynamical behaviors. Using a collective co-ordinate approach, we reproduce the dynamics of the collisions including the variation of the size of the skyrmions and collapse above a critical velocity.

Figures (11)

• Figure 1: Energy $E$ of propagating skyrmions of the form \ref{['eq:travelingWave']} as a function of velocity $\upsilon$ for parameter value $\lambda=0.50$. The static skyrmion ($\upsilon=0$) has energy $E<4\pi$. The energy crosses the critical value $E=4\pi$ at $\upsilon\approx 0.53$.
• Figure 2: Simulation of a head-on collision of skyrmions place initially ($\tau=0$) at positions $(\pm 10.5,0)$ with velocities $\upsilon=\mp 0.2$. (a) At the time $\tau=30.0$, the skyrmions are at a distance, not yet interacting. (b) At $\tau=38.0$, their speed and size have decreased due to interaction. (c) At $\tau=\tau_{\rm crit}=46.2$, they stop ($\upsilon=0$) temporarily and have a minimum size. (d) At $\tau=60.8$, they have bounced back and they have acquired almost their initial speed and size.
• Figure 3: Simulation of a head-on collision of skyrmions placed initially ($\tau=0$) at positions $(\pm 10.5,0)$ with velocities $\upsilon=\mp 0.4$. The process is similar to Fig. \ref{['fig:Skyrm_scat_v02']}. We show snapshots at times (a) $\tau=17.1$, (b) $\tau=23.7$, (c) $\tau=\tau_{\rm crit}=27.1$, where the skyrmions have approached closer and their size is smaller compared to the corresponding picture in Fig. \ref{['fig:Skyrm_scat_v02']}, and at (d) $\tau=37.2$.
• Figure 4: The position of the two colliding skyrmions on the $x$ axis ($x_L, x_R$ for the skyrmions coming from the left and right, respectively) as a function of time for initial velocities (a) $\upsilon=0.2$, corresponding to the simulation in Fig. \ref{['fig:Skyrm_scat_v02']}, and (b) $\upsilon=0.4$, corresponding to the simulation in Fig. \ref{['fig:Skyrm_scat_v04']}. The skyrmions stop temporarily and bounce back after the collision.
• Figure 5: The radius $R$ of the skyrmions during the collision for the cases with initial velocities (a) $\upsilon=0.2$, shown in Fig. \ref{['fig:Skyrm_scat_v02']}, (b) $\upsilon=0.4$, shown in Fig. \ref{['fig:Skyrm_scat_v04']}. The skyrmion radius is reduced during collision. The breathing mode has been excited after the skymions bounce back.