Langevin simulation of thermally activated magnetization reversal in nanoscale pillars

Abstract

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 × 9 nm × 150 nm. Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be 1979 ± 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 ∼ 1 Oe, the interactions have a significant effect on the switching of the magnets.

A theory of magnetization reversal in nanowires

“…Since we do not take the L → ∞ limit, our expression for the metastable nucleus configuration is more complicated than Braun's. It involves elliptic functions [16] show that a droplet of reversed magnetization forms at one of the ends and spreads inward [19,20]. This reversal mode is in agreement with our analytic treatment.…”

Magnetization reversal in elongated Fe nanoparticles

“…Recent micromagnetic simulation of defect-free d=9 nm Fe nanopillars by Brown et al 26,27 showed that nucleation can start at both ends and propagate through the whole pillars in the time scale of nanoseconds. The calculated H sw is about 2 kOe for the fields applied parallel to the easy axis, which is close to our experimental value.…”

Angular dependence of switching properties in single Fe nanopillars

“…With the field and pillar aligned (0 • ), reversal initiates at the ends, as previously reported. 6 At 45…”

“…For such a large number of sites, direct calculation of the dipole-dipole interactions is impractical, and the Fast Multipole Method was employed, as described elsewhere. 6 The second model is a 5.2 nm×5.2 nm×88 nm Fe pillar discretized into a onedimensional chain of 17 spins. This model assumes that deviations of the magnetization from uniformity over the cross-section of the pillar are negligible, as has been observed in Monte Carlo simulations.…”