Damping dependence of the reversal time of the magnetization of single-domain ferromagnetic particles for the Néel-Brown model: Langevin dynamics simulations versus analytic results

The damping dependence of the thermally activated reversal time of the magnetization of noninteracting uniaxial single-domain ferromagnetic particles is determined using Langevin dynamics simulations and the analytic Néel-Brown theory with the latter given both in the form of the exact matrix-continued fraction solution of the governing Fokker-Planck equation and its accompanying asymptotes for the escape rate. The reversal time from Langevin dynamics simulations is extremely sensitive to the initial and switching conditions used. Thus if the latter are chosen inappropriately the simulation result may markedly disagree with the analytic one particularly for low damping, where the precessional effects dominate, so that complete agreement can only be obtained by correctly choosing these conditions.

Figure 1

(Color online) $\tau \gamma H_K$ vs $\alpha$ for $\sigma =15$, $h=0.42$, and $\psi =\pi /4$. Solid line: MCF solution of the Landau-Lifshitz-Gilbert equation. Symbols: simulation results using different initial and switching conditions indicated in the figure. Dashed line: ${\tau }_{\text{IHD}}$ given by Eq. (10). The switching time is divided by two for the switching condition $m_z<-0.9$.

Figure 2

(Color online) $\tau \gamma H_K$ vs $\alpha$ for $\sigma =15$, $h=0.42$, and various values of $\psi =0$, $\pi /4$, and $\pi /2$, Solid lines: MCF solution. Symbols: simulation results starting with initial conditions distributed according to the Boltzmann distribution around the magnetization minimum. The switching condition is indicated for each curve and the switching time is divided by two for the switching condition $m_z<-0.9$.