Size dependence of ferromagnetism in gold nanoparticles: Mean field results

Abstract

In this paper, a simple spin-spin Ising interaction model for the surface ferromagnetism is combined with the bulk Au diamagnetic response to model the size dependence of the magnetization of a Au nanoparticle. Using the maximum entropy formalism, we obtain the average temperature dependent magnetization within a mean field model. Our results qualitatively reproduce recent experimental observations of size-dependent magnetization of Au nanoparticles in which the ferromagnetic moment of thiol-capped nanoparticles is seen to increase for diameters larger than $0.7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, peaking at approximately $3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and subsequently decreasing as the particle diameter increases further.