Equilibrium magnetization of a quasispherical cluster of single-domain particles

Abstract

Equilibrium magnetization curve of a rigid finite-size spherical cluster of single-domain particles is investigated both numerically and analytically. The spatial distribution of particles within the cluster is random. Dipole-dipole interactions between particles are taken into account. The particles are monodisperse. It is shown, using the stochastic Landau-Lifshitz-Gilbert equation, that the magnetization of such clusters is generally lower than predicted by the classical Langevin model. In a broad range of dipolar coupling parameters and particle volume fractions, the cluster magnetization in the weak field limit can be successfully described by the modified mean-field theory, which was originally proposed for the description of concentrated ferrofluids. In moderate and strong fields, the theory overestimates the cluster magnetization. However, predictions of the theory can be improved by adjusting the corresponding mean-field parameter. If magnetic anisotropy of particles is additionally taken into account and if the distribution of the particles' easy axes is random and uniform, then the cluster equilibrium response is even weaker. The decrease of the magnetization with increasing anisotropy constant is more pronounced at large applied fields. The phenomenological generalization of the modified mean-field theory, that correctly describes this effect for small coupling parameters, is proposed.

Force acting on a cluster of magnetic nanoparticles in a gradient field: A Langevin dynamics study

“…However, for noninteracting particles with the random easy-axis distribution, the initial slope of the magnetization curve does not depend on the anisotropy energy, it is always exactly the same as in the case of isotropic particles [20,21]. As for interacting uniaxial particles, our recent simulation study [22] also did not find any significant dependency between the weak-field magnetization and the anisotropy energy. The last important dimensionless parameter is the volume fraction (volume concentration) of nanoparticles inside the cluster:…”

“…It was shown in Refs. [22,34] that MMFT is able to successfully describe the initial susceptibility of nanoparticles embedded in a solid nonmagnetic matrix. According to MMFT, the susceptibility of an ensemble of single-domain nanoparticles is given by…”

Magnetic structure factor of correlated moments in small-angle neutron scattering

“…This finding is an indication that the superparamagnetic relaxations (i.e., Néel relaxation) of the particle moments is slowed down by dipole-dipole interactions [47][48][49][50] . The magnetic characteristics of the ensembles hence significantly depend on local the magnetostatic stray fields felt by the clustered nanoparticles [51][52][53][54] and reflects the subtle interplay between dipolar interactions, local magnetic anisotropy and sample homogeneity 55 .…”

Static magnetization of immobilized, weakly interacting, superparamagnetic nanoparticles

“…Note that R 1 (0, σ) = R(σ), and the function A k (σ) coincides with the corresponding value introduced by Raikher and Shliomis. 54 For magnetically soft particles, A k (0) = 1, and then eqn (35) and (37) coincide with (26). The limit of magnetically hard particles (σ → ∞) gives A k → 3 and the largest value of the initial magnetic susceptibility, χ k → 3χ L (1 + χ L ).…”

“…[24][25][26][27][28][29] The effects of interactions between magnetic nanoparticles have been investigated experimentally [30][31][32] and in computer simulations. [33][34][35][36][37] The links between the basic magnetic propertiessuch as the dynamic magnetic susceptibility spectrumand power dissipation 38 have been explored in the context of medical applications, such as hyperthermia treatments. [39][40][41] The effects of the carrier liquid on heat dissipation have also been investigated.…”