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Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation isused to study dynamic processes in single-domain nanoscale magnets at nonzerotemperatures. Special attention is given to including thermal fluctuations as aLangevin term, and the Fast Multipole Method is used to calculate dipole-dipoleinteractions. It is feasible to simulate these dynamics on the nanosecond timescale for spatial discretizations that involve on the order of 10000 nodesusing a desktop workstation. The nanoscale magnets considered here are singlepillars with large aspect ratio. Hysteresis-loop simulations are employed tostudy the stable and metastable configurations of the magnetization. Eachpillar has magnetic end caps. In a time-dependent field the magnetization ofthe pillars is observed to reverse via nucleation, propagation, and coalescenceof the end caps. In particular, the end caps propagate into the magnet and meetnear the middle. A relatively long-lived defect is formed when end caps withopposite vorticity meet. Fluctuations are more important in the reversal of themagnetization for fields weaker than the zero-temperature coercive field, wherethe reversal is thermally activated. In this case, the process must bedescribed by its statistical properties, such as the distribution of switchingtimes, averaged over a large number of independent thermal histories.

Micromagnetic simulations of thermally activated magnetization reversal of nanoscale magnets