Nonlinear response of superparamagnets with finite damping: An analytical approach

The strongly damping-dependent nonlinear dynamical response of classical superparamagnets is investigated by means of an analytical approach. Using rigorous balance equations for the spin occupation numbers a simple approximate expression is derived for the nonlinear susceptibility. The results are in good agreement with those obtained from the exact (continued-fraction) solution of the Fokker-Planck equation. The formula obtained could be of assistance in the modeling of the experimental data and the determination of the damping coefficient in superparamagnets.

Figure 1

Nonlinear susceptibility ${\chi }^{\left(3\right)}$ of classical spins with randomly distributed anisotropy axes vs frequency. The temperature is $k_{\mathrm{B}}T∕D=0.05\left(\sigma =20\right)$ and $\lambda =1,0.1,0.03$, and $0.01$ (bottom to top). The lines are the approximate formula (38) and the symbols the exact continued-fraction solution (Ref. 7). The upper and lower panels display, respectively, the real and imaginary parts of ${\chi }^{\left(3\right)}\left(\omega \right)$.