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

TL;DR

This paper introduces an extended core-shell-surface layer model to better explain the size dependence of magnetic anisotropy in nanoparticles, especially for particles smaller than 5 nm, validated across three different magnetic systems.

Contribution

The paper proposes a new model incorporating a shell layer to improve understanding of magnetic anisotropy in small nanoparticles, surpassing traditional models.

Findings

The extended model fits experimental data for particles smaller than 5 nm.

Validation across three different magnetic nanoparticle systems.

The model suggests a universal applicability for 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 ({\gamma}-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 {\gamma}-Fe2O3, ferromagnetic Ni and antiferromagnetic NiO suggests its possible applicability for all magnetic nanoparticles.