Methods of investigating the demagnetization factors within assemblies of superparamagnetic nanoparticles

Three-dimensional distributions of demagnetization factors Nd within assemblies of magnetic nanoparticles have been investigated along the axes of cuboid containing vessels. From the results of a numerical polar-based model, a significant skew toward high values in the number distribution is observed and often overlooked by the assumed uniformity of the conventional analytical approach. To enable comparison with experiment, new transverse susceptibility techniques have been developed, which are also applicable to superparamagnetic assemblies that do not have the magnetization features normally required using conventional methods. Applying the two techniques to a system of ∼13 nm magnetite (Fe3O4) particles resulted in the difference between the in-plane and out-of-plane Nd factors of (0.21 ± 0.03) and (0.201 ± 0.009), respectively, which shows closest agreement with the simulation value for the mode of (0.19 ± 0.02). The median and mean results of the model move further away from the experimental result, yielding values of (0.17 ± 0.02) and (0.16 ± 0.02), respectively, which is consistent with the skewed distributions observed here. In all cases, the sum of the Nd factors from each orthogonal axis was equal to 1, giving further confidence in the model. The new methods allow measurements on the superparamagnetic systems often found at this scale, and the agreement with the model means that the spatial distribution of Nd factors may now be taken into account in studies on any nanoscale material that considers the whole structure as a distribution of magnetic elements.