AUTHOR=Singh Sobhit , Seehra Mohindar S. 

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

JOURNAL=Frontiers in Materials

VOLUME=9

YEAR=2022

URL=https://www.frontiersin.org/journals/materials/articles/10.3389/fmats.2022.1050600

DOI=10.3389/fmats.2022.1050600

ISSN=2296-8016

ABSTRACT=<p>The stability of the stored information in magnetic recording media depends on the anisotropy energy <italic>E</italic><sub><italic>a</italic></sub> (=<italic>K</italic><sub><italic>eff</italic></sub><italic>V</italic>) of nanoparticles (NPs) of volume <italic>V</italic> or diameter <italic>D</italic>. Therefore, it is important to know how the effective anisotropy constant <italic>K</italic><sub><italic>eff</italic></sub> varies with size <italic>D</italic> of the NPs. In a recent paper [Appl. Phys. Lett. 110, 222409 (2017)], the observed <italic>K</italic><sub><italic>eff</italic></sub> versus <italic>D</italic> variation in NPs of maghemite (γ-Fe<sub>2</sub>O<sub>3</sub>) was explained on the basis of the core-shell-surface layer (CSSL) model given by Eq.: <italic>K</italic><sub><italic>eff</italic></sub> = <italic>K</italic><sub><italic>b</italic></sub> + (6<italic>K</italic><sub><italic>S</italic></sub>/<italic>D</italic>) +<italic>K</italic><sub><italic>sh</italic></sub>{[1-(<italic>2d/D</italic>)]<sup>−3</sup>–1}, where <italic>K</italic><sub><italic>b,</italic></sub><italic>K</italic><sub><italic>S</italic></sub><italic>,</italic> and <italic>K</italic><sub><italic>sh</italic></sub> are the anisotropy constants of spins in the core, surface layer, and a shell of thickness <italic>d</italic>, respectively. This CSSL model is an extension of an earlier core-surface layer (CSL) model described by <italic>K</italic><sub><italic>eff</italic></sub> = <italic>K</italic><sub><italic>b</italic></sub> + (6<italic>K</italic><sub><italic>S</italic></sub>/<italic>D</italic>) [Phys. Rev. Lett. 72, 282 (1994)] proposed to explain the <italic>K</italic><sub><italic>eff</italic></sub> versus <italic>D</italic> variation in Fe NPs. For the NPs of γ-Fe<sub>2</sub>O<sub>3</sub>, the additional term of the CSSL model involving <italic>K</italic><sub><italic>sh</italic></sub> was found to be necessary to fit the data for sizes <italic>D</italic> &lt; 5 nm. In this paper, we report the validity of the CSSL model for NPs of several other systems viz. Co, Ni, NiO, and Fe<sub>3</sub>O<sub>4</sub> 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 <italic>K</italic><sub><italic>eff</italic></sub> in NPs. It is shown that the new CSSL model describes very well the <italic>K</italic><sub><italic>eff</italic></sub> vs. <italic>D</italic> 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, Fe<sub>3</sub>O<sub>4</sub>, and γ-Fe<sub>2</sub>O<sub>3</sub> suggests its general validity for magnetic NPs. Discussion is also presented on the comparative magnitudes of the parameters <italic>K</italic><sub><italic>b</italic></sub><italic>, K</italic><sub><italic>S</italic></sub><italic>,</italic> and <italic>K</italic><sub><italic>sh</italic></sub> obtained from the fits to the CSSL model.</p>