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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 &lt;; 5 nm. Instead the results in NPs of maghemite (&#x03B3;-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-(2rf/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 &#x03B3;-Fe2O3, ferromagnetic Ni and antiferromagnetic NiO suggests its possible applicability for all magnetic nanoparticles.

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