Testing the validity of the core-shell-surface layer model on the size dependence of effective magnetic anisotropy in magnetic nanoparticles

Abstract

The stability of the stored information in magnetic recording media depends on the anisotropy energy Ea (=KeffV) of nanoparticles (NPs) of volume V or diameter D. Therefore, it is important to know how the effective anisotropy constant Keff varies with size D of the NPs. In a recent paper [Appl. Phys. Lett. 110, 222409 (2017)], the observed Keff versus D variation in NPs of maghemite (γ-Fe2O3) was explained on the basis of the core-shell-surface layer (CSSL) model given by Eq.: Keff = Kb + (6KS/D) +Ksh{[1-(2d/D)]−3–1}, where Kb,KS, and Ksh are the anisotropy constants of spins in the core, surface layer, and a shell of thickness d, respectively. This CSSL model is an extension of an earlier core-surface layer (CSL) model described by Keff = Kb + (6KS/D) [Phys. Rev. Lett. 72, 282 (1994)] proposed to explain the Keff versus D variation in Fe NPs. For the NPs of γ-Fe2O3, the additional term of the CSSL model involving Ksh was found to be necessary to fit the data for sizes D < 5 nm. In this paper, we report the validity of the CSSL model for NPs of several other systems viz. Co, Ni, NiO, and Fe3O4 using the available data from literature. In selecting the data, care was taken to consider data only for non-interacting NPs since the interparticle interactions generally overshadow the actual value of Keff in NPs. It is shown that the new CSSL model describes very well the Keff vs. D variation for all particle sizes whereas the CSL model fails for smaller particles with the notable exception of Fe NPs. This validation of the CSSL model for the NPs of Co, Ni, NiO, Fe3O4, and γ-Fe2O3 suggests its general validity for magnetic NPs. Discussion is also presented on the comparative magnitudes of the parameters Kb, KS, and Ksh obtained from the fits to the CSSL model.