A micromagnetic theory of skyrmion lifetime in ultrathin ferromagnetic films

Abstract

We use the continuum micromagnetic framework to derive the formulas for compact skyrmion lifetime due to thermal noise in ultrathin ferromagnetic films with relatively weak interfacial Dzyaloshinskii-Moriya interaction. In the absence of a saddle point connecting the skyrmion solution to the ferromagnetic state, we interpret the skyrmion collapse event as "capture by an absorber" at microscale. This yields an explicit Arrhenius collapse rate with both the barrier height and the prefactor as functions of all the material parameters, as well as the dynamical paths to collapse.

Keywords: magnetic skyrmions; rare events; stochastic dynamics; topological protection.

Fig. 1.

(A) Skyrmion equilibrium radius ${\mathcal{l}}_{\text{ex}}{\rho }_0$ in nanometers, with ${\mathcal{l}}_{\text{ex}}=8.4$ nm and ρ₀ from Eq. 8. (B and C) Skyrmion lifetime ${\tau }_0/J_{\delta }$ for ${\tau }_0=7.8\times {10}^{-12}$ s, $\alpha =0.3,\hspace{0.17em}\delta =0.0475$, with $J_{\delta }$ from Eq. 23 for $\epsilon =0.0046$ (T = 4 K) in B and $J_{\delta }$ from Eq. 26 for $\epsilon =0.337$ (T = 293 K) in C. In A and B, only the region $\kappa /\sqrt{Q-1}<\frac{1}{2}$ is shown. (B, Inset) The optimal collapse path ${\overline{z}}_{\text{opt}}(t)$ from Eq. 28.