Magnetization of immobilized multi-core particles with varying internal structures

This work is devoted to the study of the static magnetization of immobilized multi-core particles (MCPs) and their ensembles. These objects model aggregates of superparamagnetic nanoparticles that are taken up by biological cells and subsequently used, for example, as magnetoactive agents for cell imaging. In this study, we derive an analytical formula that allows us to predict the static magnetization of MCPs consisting of immobilized granules, in which the magnetic moment rotates freely via the N'{e}el mechanism. The formula takes into account intergranule dipole-dipole interactions at the level of pair correlations and is suitable for determining the magnetization of MCPs with any structure. The theory is tested using Monte Carlo computer simulations on a series of MCP samples with 4 and 7 superparamagnetic granules. The results demonstrate that the formulas accurately describe the magnetization of MCPs with the intergranule dipolar coupling constant $\lambda \leq 2$. We propose a method for determining the magnetization of an ensemble of non-interacting immobilized MCPs with interacting granules by identifying this system with an ensemble of single-core immobilized non-interacting superparamagnetic particles for which the effective magnetic anisotropy parameter is determined. The results obtained in this work represent a significant step towards predicting the magnetic response of MCPs in biological media, such as biological cells.