Thermally induced vortex nucleation in permalloy elements

Vortex nucleation and vortex motion are the main mechanisms of magnetization reversal in micrometer-sized magnetic elements. The critical field required to nucleate a vortex depends on the temperature. We propose a method that combines standard Landau-Lifshitz-Gilbert (LLG) micromagnetics and an elastic band method to simulate nonzero temperature hysteresis curves of magnetic thin film elements. Whereas the LLG simulations gives the equilibriums states before and after a vortex enters the element, the elastic band method gives the height of the energy barrier between these two states. Thus temperature-dependent nucleation fields can be computed without the need to perform stochastic LLG simulations.