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.
@article{arxiv.1707.07241,
title = {A core-shell-surface layer model to explain the size dependence of effective magnetic anisotropy in magnetic nanoparticles},
author = {Sobhit Singh and Kelly L. Pisane and Mohindar S. Seehra},
journal= {arXiv preprint arXiv:1707.07241},
year = {2017}
}