Modeling the Dipolar Interaction Field distributions in Random Superparamagnetic System

Dipolar interactions in a system of superparamagnetic nanoparticles play an important role in the magnetic response of the system, where it is well known that they depress the magnetisation. In this study, we simulate a system of 5000 interacting nanoparticles using Metropolis Monte Carlo method. In such system, it is known that the dipolar interactions adopt Gaussian distribution with approximately zero mean and with varying standard deviation depending on the external applied field and the packing density. In this study we comprehensively investigate the effect of the packing density on the standard deviation of the interaction fields at different applied fields. We provide an empirical formula that combines the two factors and show that it gives magnetisation curves that are in a very good agreement to actual Monte Carlo simulations. Furthermore, the individual effects of the interaction fields along each direction are investigated using the developed empirical formula. Our results show that the longitudinal and the transverse components do not contribute linearly to the overall depression of magnetisation (i.e., the sum of the individual reductions in magnetisation of each component does not add up to the total reduction due to the combined effect of all components). We tried to explain this by showing theoretically that the reduction in magnetisation due to the longitudinal components is, to a first order approximation, directly proportional to the curvature of the magnetisation curve of the noninteracting system. However, the reduction due to the transverse components does not show this behaviour.