A core-shell-surface layer model to explain the size dependence of effective magnetic anisotropy in magnetic nanoparticles

Abstract

The particle size (D) dependence of the effective magnetic anisotropy Keff of magnetic nanoparticles (NPs) usually shows Keff increasing with decreasing D. This dependence is often interpreted using the Eq.: Keff = Kb + (6Ks/D) where Kb and Ks are the anisotropy constants of the spins in the bulk-like core and surface layer, respectively. Here, we show that this model is inadequate to explain the observed size-dependency of Keff for smaller nanoparticles with D < 5 nm. Instead the results in NPs of maghemite (γ-Fe2O3), NiO and Ni are best described by an extension of the above model leading to the variation given by Keff = Kb + (6Ks/D) +Ksh{[1-(2d/D)]^(-3) -1}, where the last term is due to the spins in a shell of thickness d with anisotropy Ksh. The validation of this core-shell-surface layer (CSSL) model for three different magnetic NPs systems viz. ferrimagnetic γ-Fe2O3, ferromagnetic Ni and antiferromagnetic NiO suggests its possible applicability for all magnetic nanoparticles.

5 pages, 6 figures

References in corpus (6)

• Magnetic Nanoparticles for Neural Engineering
• Effective anisotropies and energy barriers of magnetic nanoparticles with Neel surface anisotropy
• Finite-size versus Surface effects in nanoparticles
• Role of dipolar interactions in a system of Ni nanoparticles studied by magnetic susceptibility measurements
• Magnetic dynamics of single domain Ni nanoparticles
• Unusual enhancement of effective magnetic anisotropy with decreasing particle size in maghemite nanoparticles