Stability of magnetic skyrmions: Systematic calculations of the effect of size from nanometer scale to microns

Abstract

The lifetime of a magnetic skyrmion in a two-dimensional lattice is calculated as a function of size, from nanometer scale to microns, while the shape of the skyrmion remains the same. Values of the parameters in the extended Heisenberg Hamiltonian that includes exchange, anisotropy, Dzyaloshinskii-Moriya interaction, and the effect of an external field, are scaled in accordance with a continuous micromagnetic description. The lifetime increases dramatically with increased skyrmion size both because of a decrease in the entropy of the transition state with respect to that of the skyrmion state, resulting in an increase in the pre-exponential factor by four orders of magnitude, and because the activation energy increases towards an upper bound consistent with the energy of the Belavin-Polyakov soliton. While the calculated lifetime of the skyrmion for the Hamiltonian parameter values chosen here is less than a microsecond when the radius is 5 lattice constants, it reaches years when the radius is 100 lattice constants at a temperature of 200 K and an hour at room temperature. The calculations of the largest skyrmion studied here explicitly include over 20 000 000 spins.