Size dependence of the effective magnetic anisotropy in Co, Ni, Fe, and magnetite nanoparticles: Testing the core-shell-surface-layer (CSSL) model

The stability of the stored information in recording media depends on the anisotropy energy Ea = KeffV of nanoparticles (NPs) of volume V or diameter D. Therefore, the knowledge of how the effective magnetic anisotropy Keff varies with D for a given system is important for technological applications. In a recent paper [Appl. Phys. Lett. 110 (22), 222409 (2017)], the variation of Keff versus D in NPs of maghemite ({\gamma}-Fe2O3) was best described by the 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 core-shell-surface layer (CSSL) model is an extension of the often used core-surface layer (CSL) model described by Keff = Kb + (6KS/D) [Phys. Rev. Lett. 72, 282 (1994)]. The additional term involving Ksh was found to be necessary to fit the data for smaller NPs of {\gamma}-Fe2O3 with D < 5 nm. Here we check the validity of the CSSL model for metallic magnetic NPs of Co, Ni, Fe and magnetite using Keff vs. D data from published literature. Care was taken in selecting data only for those NPs for which the effects of interparticle interactions has been taken into account in determining Keff. The importance of the new CSSL model is that it describes well the Keff vs. D variation for all particles sizes whereas the core-surface layer model often fails for smaller particles with the notable exception of Fe NPs. The verification of the CSSL model for metallic NPs of Co, Ni, and magnetite along with NPs of NiO and {\gamma}-Fe2O3 validates its general applicability.