Fixed magnetic nanoparticles: Obtaining anisotropy energy density from high field magnetization

A simple method is proposed to obtain the effective anisotropy energy density Keff of an assembly of randomly oriented magnetic nanoparticles, from their hysteresis loops. It involves the fitting of a high field asymptotic expression of the magnetization in inverse powers of the applied field H, up to H−3. This is derived from the partition function formalism and the Stoner–Wohlfarth model for single domain nanoparticles. This method can be applied to ferrogels, frozen ferrofluids or magnetic nanoparticles powder (or any system where the nanoparticles are fixed in random directions, and not allowed to rotate), when dipolar interactions can be neglected. As a proof of concept, it is applied to a suspension of iron oxide nanoparticles in hexane, at different temperatures, obtaining the anisotropy energy density Keff as a function of temperature below the fusion point. •A method to obtain the effective anisotropy energy density of randomly oriented magnetic nanoparticles is proposed.•This method can be applied to any system where the nanoparticles are fixed and not allowed to rotate.•The method involves the fitting of a high field asymptotic expression of the magnetization.•It is applied to a suspension of iron oxide nanoparticles in hexane to obtain K as a function of temperature, below the fusion point.