The magnetization spectrum and reversal time of uniaxial single-domain ferromagnetic particles driven by an ac magnetic field of arbitrary strength applied along the easy axis are evaluated by solving the infinite hierarchy of recurrence equations for the Fourier components of the relaxation functions governing the frequency dependence of the magnetization. A simple analytic equation for the reversal time is also obtained via the mean first passage time method exhibiting pronounced nonlinear effects such as a rapid decrease in the reversal time as the strength of the ac field increases. For weak ac fields, the results agree with perturbation theory.

The effect of long range dipole-dipole interactions on the thermal fluctuations of the magnetization of an assembly of single-domain ferromagnetic particles is considered. If orientational correlations between the particles are neglected, the evolution of the magnetization orientations may be described by a nonlinear Fokker-Planck equation (FPE) reducing to the usual linear one in the limit of infinite dilution [W.F. Brown Jr, Phys. Rev. 130, 1677 (1963)]. The thermally activated relaxation time scale of the assembly is estimated, leading to a simple modification of the axially symmetric asymptotes for the superparamagnetic relaxation time. PACS number(s) : 75.60.Jk, 75.50.Tt, 76.20.+q, 05.40.-a * 0ˆ4 J i J J

Dynamic magnetic hysteresis in uniaxial superparamagnetic nanoparticles in superimposed ac and dc magnetic fields of arbitrary amplitude is considered using Brown’s model of coherent rotation of the magnetization. The dependence of the area of the dynamic hysteresis loop on the temperature, frequency, and ac and dc bias fields is analyzed. In particular, the dynamic hysteresis loop of a single-domain ferromagnetic particle is substantially altered by applying a relatively weak dc field. Furthermore, it is shown that at intermediate to low ac field amplitudes, the dc bias field permits tuning of the magnetic power absorption of the particles, while for strong ac field amplitudes the effect becomes entirely analogous to that produced by the exchange biased anisotropy. Simple analytical formulas are provided in the linear response regime for the steady-state magnetization and loop area, exhibiting perfect agreement with the numerical solution of Brown’s Fokker–Planck equation. Comparison with previous results is also given.

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

The nonlinear effects arising from the first and second hyperpolarizabilities on the Kerr effect relaxation response of an ensemble of polar and anisotropically polarizable molecules in a strong dc electric field are studied by solving the infinite hierarchy of differential-recurrence relations underlying the noninertial Fokker–Planck (Smoluchowski) equation. The step-on solution is obtained by using the matrix continued fraction methods. An expression for the Kerr effect relaxation time is derived as well following the procedure of Kalmykov, Déjardin, and Coffey [Phys. Rev. E 55, 2509 (1997)] which is in full agreement with the matrix continued fraction expression. For small values of the electric field, it is shown that the first hyperpolarizability contributes to increasing the Kerr effect relaxation time while the second hyperpolarizability shifts the maximum of the relaxation time toward the lowest electric fields on increasing the value of this maximum. The dual nature of essentially two relaxation processes is also emphasized by plotting the Kerr effect relaxation spectra for various values of the first and second hyperpolarizability parameters.

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An analytical formula for the linear complex susceptibility of dipolar assemblies subjected to thermal agitation, long range interactions and an externally applied uniform sinusoidal field of weak amplitude is derived using the forced rotational diffusion equation of Cugliandolo et al. [Phys. Rev. E 91, 032139 (2015)] in the virial approximation. If the Kirkwood correlation factor of the dipolar assembly K g exceeds unity, a thermally activated process arising from the interaction-specific component arises while for 1 K g  , the susceptibility spectrum normalized by its static value is practically unaltered with respect to that of the ideal gas phase.

The relaxation rate and temperature-dependent switching field curve of a spherical magnetic nanocluster are calculated by including the effect of surface anisotropy via an effective anisotropy model. In particular, it is shown that surface anisotropy may change the thermally activated magnetization reversal by more than an order of magnitude, and that temperature-dependent switching field curves noticeably deviate from the Stoner-Wohlfarth astroid. With recent and future µ-SQUID measurements in mind, we indicate how comparison of our results with experimental data on isolated clusters may allow one to obtain valuable information on surface anisotropy.