Second-order modified mean-field theory for textured immobilized magnetic nanoparticles

A second-order modified mean-field theory has been developed to predict the static magnetization and initial magnetic susceptibility of textured ensembles of immobilized interacting superparamagnetic nanoparticles with uniaxial anisotropy. The theory takes into account the orientational texture of the easy magnetization axes and interparticle dipole-dipole interactions, including three-particle correlations. Simple analytical expressions are proposed for calculating the magnetization and initial magnetic susceptibility of ensembles of interacting immobilized particles with random, parallel, and perpendicular texturing of the easy magnetization axes with respect to the applied magnetic field. It is shown that texture manipulation allows the collective magnetic response to be controlled: parallel orientation of the axes leads to a rapid increase in susceptibility, whereas perpendicular orientation leads to its suppression. The results of the theory demonstrate quantitative agreement with the data of computer modeling performed using the Monte Carlo method, significantly exceeding the accuracy of known theories. The theory developed in this work is a tool for predicting and purposeful designing the magnetic properties of modern magnetically active materials.