Induced magnetization and power loss for a periodically driven system of ferromagnetic nanoparticles with randomly oriented easy axes

Abstract

We study the effect of an elliptically polarized magnetic field on a system of non-interacting, single-domain ferromagnetic nanoparticles characterized by a uniform distribution of easy axis directions. Our main goal is to determine the average magnetization of this system and the power loss in it. In order to calculate these quantities analytically, we develop a general perturbation theory for the Landau-Lifshitz-Gilbert (LLG) equation and find its steady-state solution for small magnetic field amplitudes. On this basis, we derive the second-order expressions for the average

Efficiency of magnetic hyperthermia in the presence of rotating and static fields

“…Since our findings (even the above analytical formula) are based on numerical results it is useful to follow Ref. [32] where an analytical solution of the LLG equation in case of uniaxial anisotropy is presented in the framework of perturbation theory. The goal of this appendix is to show whether the method of Ref.…”

“…Therefore, the analytical method presented in Ref. [32] cannot be applied to verify our numerical results.…”

“…The findings discussed in this section are based on the approach of fixed nanoparticle which is an approximation where neither the thermal fluctuations, nor the motion of the particle has been taken into account and the direction of the static field is also fixed. Thus, an escape from the negative results of this section could be (i) the case when the direction of the static field is chosen arbitrarily, similarly to a randomly oriented anisotropy field [32], (ii) the inclusion of thermal effects which allows the magnetic moment to jump between the two steady state solutions [33,34], (iii) the description when the motion of the particle as a whole [1] is taken into account.…”

“…Finally, let us note that new findings of the present work where enhancement effect is found are based on numerical solution of the deterministic LLG equation. Analytical solutions are available in the literature based on perturbation theory, see [32], but unfortunately it cannot be used to verify the enhancement effect of this work since it requires very large anisotropy (and also very high frequencies), see Appendix A. However, our numerical results are verified by an analytical formula in the limit of vanishing static and anisotropy fields, b 0 = λ eff = 0, where the steady state solution ( 4) is used and we found perfect agreement.…”

Drift of suspended ferromagnetic particles due to the Magnus effect

“…Therefore, if the condition a ∈ (a 1 , a 2 ) holds, then the ferromagnetic core is single-domain and the magnetization dynamics is deterministic (for more details see Refs. [18,19]). As to the translational and rotational Brownian motions, they can be neglected if the shell radius b exceeds the critical one b 1 (b 1 is usually of the order of a few hundreds of nanometers).…”