Dependence of hysteresis loss of immobilized magnetic nanoparticles on the easy-axis angle: Effect of easy-axis alignment

Magnetic nanoparticles (MNPs) have been widely studied for hyperthermia applications. We studied the hysteresis loss of immobilized MNPs with partially aligned easy axes. For this purpose, we investigated how the AC magnetization (M-H) curve of MNP depended on the easy-axis angle of magnetization, β, via numerical simulations of the Fokker-Planck equation. We clarified the dependences of the coercive field, Hc, and the hysteresis loss, A, on β. We, thus, obtained analytical expressions for Hc(β) and A(β) that explain simulation results for a wide range of MNP parameters and excitation conditions. The angle dependences were also discussed on the basis of magnetic moment reversal over the anisotropy energy barrier. We then examined the hysteresis loss of an MNP sample with partial alignment of the easy axes and obtained an expression for the loss by combining A(β) and a distribution function for β. We quantitatively clarified the relationship between the loss and the degree of easy-axis alignment. The loss of immobilized MNPs can be increased by a factor of 2.2 by using easy-axis alignment relative to the case of randomly oriented easy axes. Finally, we examined the alignment of easy axes induced by an AC field in suspended MNPs and showed that the loss of immobilized MNPs with partially aligned easy axes can be used to estimate the loss for suspended MNPs.