Dipolar interaction effects in core–shell magnetic nanoparticles

Dipolar interaction between magnetic nanoparticles (MNPs) affects their magnetization properties, and the effect is particularly significant for multi-core MNPs and high-concentration MNP samples. In this work, we performed numerical simulations using the Landau–Lifshitz–Gilbert equation to investigate the effect of dipolar interaction on magnetization properties. In these simulations, we introduced a cubic model with 10 00 MNPs whose core size d c ranges from 10 to 20 nm and whose easy axes are randomly oriented. The distance d g between two adjacent MNPs in the cubic model was varied from 10–70 nm. We quantified the critical interparticle distance d crit — defined as the minimum surface-to-surface distance between magnetic nanoparticles (MNPs) at which dipolar interaction becomes negligible. Assuming a uniform spherical coating layer, this corresponds to d crit = 2 t m , where t m is the minimum coating thickness required to eliminate dipolar effects for a given d c . Our results reveal that d crit varies with harmonic order: the values of d crit for the third M 3 and fifth M 5 harmonic components of magnetization are larger than that for the fundamental component M 1 , indicating that higher-order harmonics commonly used in MPI are more sensitive to dipolar interaction. Moreover, we found d