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 nm x 9 nm x 150 nm. Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 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 Oe, the interactions have a significant effect on the switching of the magnets.