Fractal Dimension Effect on the Magnetization Curves of Exchange-Coupled Clusters of Magnetic Nanoparticles

The effect of the fractal dimension of exchange-coupled clusters of magnetic nanoparticles on their magnetization curves is predicted by scaling estimates. These predictions form the basis for the experimental technique used for determining the fractal dimension of nanoparticle clusters from the magnetization curves. We estimate the reliability of determining the dimension by such methods with the help of micromagnetic simulation. It is shown that the effective dimension of magnetic correlation volumes, which is determined from analysis of the magnetization approaching saturation, is in conformity with the dimension of fractal clusters determined from analysis of their morphology. The dimension estimated from analysis of the coercive field on the particle size in a physically natural situation of the dipole–dipole interaction between nanoparticles provides estimates of the cluster dimension, which strongly differs from estimates obtained from analysis of their morphology.