Measuring magnetic correlations in nanoparticle assemblies

We illustrate how to extract correlations between magnetic moments in assemblies of nanoparticles from, e. g., electron holography data providing the combined knowledge of particle size distribution, inter-particle distances, and magnitude and orientation of each magnetic moment within a nanoparticle superstructure, We show, based on simulated data, how to build a radial/angular pair distribution function f(r, theta) encoding the spatial and angular difference between every pair of magnetic moments. A scatter-plot of f(r, theta) reveals the degree of structural and magnetic order present, and hence provides a measure of the strength and range of magnetic correlations.