Size dependence of magnetic parameters and surface disorder in magnetite nanoparticles

Magnetic properties of oleic acid/oleylamine coated magnetite nanoparticles of average diameter D=4, 6, 8, 10, and 12nm are reported. The samples were characterized by transmission electron microscopy and x-ray diffraction (XRD) with XRD showing increasing disorder with decreasing D. Magnetization M vs temperature T data show the blocking temperature TB decreasing with decreasing D from TB=38K for 12nm to TB=6.5K for D=4nm. The saturation magnetization Ms at 2K also decreases from Ms=62emu∕g for 12nm to Ms=17emu∕g for 4nm but the coercivity at 2K increases with a decrease in D. It is shown that Ms fits Ms=92(1−2d∕D)3 with d=0.68nm for D>4nm and d=0.86 for D=4nm. This equation is derived assuming a core-shell model with shell of thickness d consisting of disordered spins not contributing to Ms.