Abstract
A detailed numerical simulation of quasistatic hysteresis loops of dense clusters of interacting magnetic nanoparticles is carried out. Both clusters of magnetically soft and magnetically hard nanoparticles are considered. The clusters are characterized by an average particle diameter D, the cluster radius Rc, the particle saturation magnetization Ms, and the uniaxial anisotropy constant K. The number of particles in the cluster varies between Np = 30 - 120. The particle centers are randomly distributed within the cluster, their easy anisotropy axes being randomly oriented. It is shown that a dilute assembly of identical random clusters of magnetic nanoparticles can be characterized by two dimensionless parameters: 1) the relative strength of magneto-dipole interaction, K/Ms2, and the average particle concentration within the cluster, η = V Np/Vc. Here V is the nanoparticle volume, and Vc is the volume of the cluster, respectively. In the strong interaction limit, Msη/Ha > > 1, where Ha = 2K/Ms is the anisotropy field, the ultimate hysteresis loops of dilute assemblies of clusters have been constructed. In the variables (M/Ms, H/Ms) these hysteresis loops depend only on the particle volume fraction η. In the weak interaction limit, Msη/Ha < < 1, the assembly hysteresis loops in the variables (M/Ms, H/Ha) are close to the standard Stoner-Wohlfarth hysteresis loop.
Highlights
Dense assemblies of magnetic nanoparticles show very rich and complex behavior because their properties depend on several important factors, such as the geometrical structure of the assembly, the nature of magnetic anisotropy of isolated nanoparticles, the presence of exchange and magneto- dipole interaction among the nanoparticles, etc
It is shown that a dilute assembly of identical random clusters of magnetic nanoparticles can be characterized by two dimensionless parameters: 1) the relative strength of magnetodipole interaction, K/Ms2, and the average particle concentration within the cluster, η = VN p/Vc
To check the hypothesis stated above it is necessary to analyze the shape of the averaged hysteresis loops of a dilute assembly of nanoparticle clusters depending on the set of dimensionless parameters (η, K/Ms2)
Summary
Dense assemblies of magnetic nanoparticles show very rich and complex behavior because their properties depend on several important factors, such as the geometrical structure of the assembly, the nature of magnetic anisotropy of isolated nanoparticles, the presence of exchange and magneto- dipole interaction among the nanoparticles, etc. In spite of the constraints assumed, this model seems to be able to describe adequately the behavior the experimentally investigated assemblies of clusters with strong magneto- dipole interaction.[35,36,37,38,39,40] Note that even with the simplifications adopted, there are 5 independent parameters of the model, i.e. the saturation magnetization Ms, the uniaxial anisotropy constant K, the particle radius R, the cluster radius Rcl, and the total number of the nanoparticles in the cluster Np. In this paper, based on the detailed numerical simulations, a unified description of the quasi-static hysteresis loops of the assembly of dense clusters of nanoparticles is obtained.
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