Curie temperature reduction in SiO$_{2}$-coated ultrafine Fe$_{3}$O$_{4}$ nanoparticles: Quantitative agreement with a finite-size scaling law

We report high-temperature magnetic measurements for SiO$_{2}$-coated ultrafine Fe$_{3}$O$_{4}$ nanoparticles. The Curie temperatures of the ultrafine Fe$_{3}$O$_{4}$ nanoparticles are significantly reduced and follow a finite-size scaling law predicted from Monte Carlo simulations. Our current result provides the first quantitative confirmation of the finite-size scaling law for quasi-zero-dimensional magnetic systems.