Langevin simulation of thermally activated magnetization reversal in nanoscale pillars

Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model incorporating thermal fluctuations and dipole-dipole interactions (calculated by the fast multipole method) are presented for systems composed of nanoscale iron pillars of dimension $9\mathrm{nm}\times 9\mathrm{nm}\times 150\mathrm{nm}.$ Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be $1979\pm 14\hspace{0.5em}\mathrm{Oe}$ using linear field sweeps at $T=0\mathrm{}\hspace{0.5em}\mathrm{K}.$ Thermal effects are essential to the relaxation of magnetization trapped in a metastable orientation, such as happens after a rapid reversal of an external magnetic field less than the coercive value. The distribution of switching times is compared to a simple analytic theory that describes reversal with nucleation at the ends of the nanomagnets. Results are also presented for arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a separation of 300 nm, where the field from neighboring pillars is only $\sim 1\hspace{0.5em}\mathrm{Oe},$ the interactions have a significant effect on the switching of the magnets.