Thermal stability of metastable magnetic skyrmions, Entropic narrowing and significance of internal eigenmodes

L. Desplat, D. Suess, J-V. Kim, R. L. Stamps

Published 2018-02-19Version 1

We compute annihilation rates of metastable magnetic skyrmions using a form of Langer's theory in the intermediate-to-high damping (IHD) regime. We look at three possible paths to annihilation: isotropic collapse of an isolated skyrmion, isotropic collapse induced by another skyrmion and annihilation at a boundary. We find that the skyrmion's internal modes play a dominant role in the thermally activated transitions compared to the spin-wave excitations and that the relative contribution of internal modes depends on the nature of the transition process. Additionally, the eigenmodes at saddle point configurations are characterized by broken symmetries. Our calculations for a small skyrmion stabilized at zero-field show that the annihilation is largely dominated by the mechanism at the boundary, even though in this case the activation energy is higher than that of isotropic collapses. The potential source of stability of metastable skyrmions is therefore found not to lie in high activation energies, nor in the dynamics at the transition state, but comes from entropic narrowing in the saddle point region which leads to low attempt frequencies. This narrowing effect is found to be primarily associated with the skyrmion's internal modes. Isotropic collapse induced by another skyrmion exhibits the same internal energy barrier as a single skyrmion, but with a different entropic barrier. The probability of induced isotropic collapse is expected to increase with the number of skyrmions present on a racetrack.