Reversal time of the magnetization of antiferromagnetic nanoparticles

The reversal time of the magnetization $\tau$ of antiferromagnetic nanoparticles is evaluated for a uniform magnetic field applied at an arbitrary angle $\psi$ to the easy axis by using the adaptation of the Kramers escape rate theory to fine ferromagnetic particles given by Coffey et al. [Adv. Chem. Phys. 117, 483 (2001); Phys. Rev. E 63, 021102 (2001)]. The resulting analytic formula yields an accurate approximation to the reversal time $\tau$ for all values of the damping and agrees favorably with the numerically exact solution of the corresponding Fokker-Planck equation for the evolution of the probability density function of magnetization orientations.

Figure 1

(Color online) Three-dimensional plot of the potential Eq. (4) for $\sigma =10$, $h=0.15$, $\zeta =0.15$, and $\psi =\pi /3$.

Figure 2

(Color online) ${\lambda }_1{\tau }_N$ vs the anisotropy (or the inverse temperature) parameter $\sigma$ for $\alpha =0.01$, $\zeta =0.05$, $\psi =\pi /4$, and various values of the field parameter $h$. Solid lines: matrix continued fraction solution. Symbols: the universal Eq. (5).

Figure 3

(Color online) ${\lambda }_1{\tau }_N$ vs $\sigma$ for $h=0.2$, $\psi =\pi /4$, $\alpha =0.005$, and various values of the antiferromagnetic parameter $\zeta$. Solid lines: matrix continued fraction solution. Symbols: the universal Eq. (5).

Figure 4

(Color online) ${\lambda }_1{\tau }_N$ vs the oblique angle $\psi$ for $\zeta =0.3$, $\sigma =10$, $\alpha =0.1$, and various values of $h$. Solid lines: matrix continued fraction solution. Symbols: the universal Eq. (5).

Figure 5

(Color online) ${\lambda }_1{\tau }_N$ vs the antiferromagnetic parameter $\zeta$ for $h=0.1$, $\psi =\pi /6$, $\sigma =15$, and various values of $\alpha$. Solid lines: matrix continued fraction solution. Symbols: the universal Eq. (5).

Figure 6

(Color online) ${\lambda }_1{\tau }_N$ vs the damping parameter $\alpha$ for $\zeta =0.1$, $\psi =\pi /4$, $\sigma =10$, and various values of the field parameter $h=0.05$, 0.10, 0.15, and 0.20. Solid lines: matrix continued fraction solution. Symbols: the universal Eq. (5). Dashed lines: the IHD Eq. (6).

Figure 7

(Color online) ${\lambda }_1{\tau }_N$ vs the damping parameter $\alpha$ for $h=0.2$, $\psi =\pi /4$, $\sigma =10$, and various values of the antiferromagnetic parameter $\zeta =0$, 0.1, 0.2, and 0.3. Solid lines: matrix continued fraction solution. Symbols: the universal Eq. (5). Dashed lines: the IHD Eq. (6).