Nonlinear magnetization relaxation of superparamagnetic nanoparticles in superimposed ac and dc magnetic bias fields

The nonlinear ac response of the magnetization $\mathbf{M}\left(t\right)$ of a uniaxially anisotropic superparamagnetic nanoparticle subjected to both ac and dc bias magnetic fields of arbitrary strengths and orientations is determined by averaging Gilbert’s equation augmented by a random field with Gaussian white-noise properties in order to calculate exactly the relevant statistical averages. It is shown that the magnetization dynamics of the uniaxial particle driven by a strong ac field applied at an angle to the easy axis of the particle (so that the axial symmetry is broken) alters drastically leading to different nonlinear effects due to coupling of the thermally activated magnetization reversal mode with the precessional modes of $\mathbf{M}\left(t\right)$ via the driving ac field.

Figure 1

(Color online) $-\text{Im}\left[{\chi }_1^1\left(\omega \right)\right]$ vs $\omega {\tau }_N$ for various values of the angle $\psi$ and (a) ${\xi }_0=0$ (no dc bias field) and (b) ${\xi }_0=3$ (strong dc bias field). Solid lines: matrix continued fraction solution; filled circles: Eq. (9) with $\tau$ calculated using the method of Ref. 20.

Figure 2

(Color online) $-\text{Im}\left[{\chi }_1^1\left(\omega \right)\right]$ vs $\omega {\tau }_N$ (a) for various values of the ac field parameter $\xi$ and (b) for various values of damping $\alpha$.