Theory of the Lifetime of Metastable Skyrmions in Chiral Magnets

Understanding the lifetime of metastable skyrmions in chiral magnetic materials is both of fundamental interest and of practical importance. We use the Landau-Lifshitz-Gilbert equation with thermal noise to derive the activated rate for an isolated metastable skyrmion to decay into the stable ferromagnetic state. Our formalism includes damping as well as the effects of entropic corrections to the energy barrier within a Gaussian approximation. We show that the nature of the saddle point that needs to be crossed for the decay of a skyrmion changes from a Bloch point singularity in 2D systems to a chiral bobber in films with thickness L > L_D=2π J/D. We will present numerical and variational results as a function of ferromagnetic exchange J, Dzyaloshinskii-Moriya interaction D, effective anisotropy K, and the external field B, and discuss the relation between the size and lifetime of metastable skyrmions.