Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature

Skyrmions are topologically protected entities in magnetic materials which have the potential to be used in spintronics for information storage and processing. However, Skyrmions in ferromagnets have some intrinsic difficulties which must be overcome to use them for spintronic applications, such as the inability to move straight along current. We show that Skyrmions can also be stabilized and manipulated in antiferromagnetic materials. An antiferromagnetic Skyrmion is a compound topological object with a similar but of opposite sign spin texture on each sublattice, which, e.g., results in a complete cancellation of the Magnus force. We find that the composite nature of antiferromagnetic Skyrmions gives rise to different dynamical behavior due to both an applied current and temperature effects.

Figure 1

The spin texture of a $G$-type AFM Skyrmion. (a) Top view of the Skyrmion, white lines show contours of constant $n_z$. The radius is 2.1 nm. (b) Cross section of the Skyrmion. The core is not a single spin but a compensated structure combining the two sublattices.

Figure 2

Current induced AFM Skyrmion dynamics ($j=200\mathrm{m}/\mathrm{s}$). (a) longitudinal velocity for different combinations of $\alpha$ and $\beta$. Points are calculated numerically and the lines are Eq. (3) based on Thiele’s equations for an AFM. Inset shows the mass term is small and the Skyrmion reaches terminal velocity after 2 ps. (b) Transverse velocities calculated from the same simulations show there is no transverse motion. (c) The AFM Skyrmion is composed of two topological objects with opposite topological charge; hence, the Magnus force acts in opposite directions. The strong coupling between the sublattices leads to a perfect cancellation of the two opposing forces, and so, the AFM Skyrmion has no transverse motion.

Figure 3

(a) Brownian motion of the AFM Skyrmion for Gilbert damping constants $\alpha =0.1$ and 0.01 at $T/T_c=0.25$. (b) Diffusion coefficient of the AFM Skyrmion as a function of $\alpha$. Points are calculated from the mean squared displacement $⟨r^2⟩$ (inset), the solid line is $\mathcal{D}=\lambda k_{B}T/(2\alpha s\sigma )$.

Figure 4

AFM and FM Skyrmion radii $R_s$ as a function of reduced temperature $T/T_{\mathrm{C}}$. The error bars represent the magnitude of the thermally induced radius fluctuations. The solid line is the simple scaling theory, Eq. (4), dashed lines are power law fits $R_s(T)\propto m^{-0.86}$ and $R_s(T)\propto n^{-2.09}$.