The thermodynamic properties of soft magnetic materials containing superparamagnetic nanoparticles frozen in the nodes of the regular cubic lattice

This work is devoted to the study of the thermodynamic properties of soft magnetic materials that are actively used in technology and medicine. The mathematical model assumes that magnetic nanoparticles are embedded in the nodes of a regular cubic lattice, so that the particle translational degrees of freedom are turned off and the mechanical Brownian rotation of particles is impossible. The response of the particles to the external magnetic field occurs by the Neel mechanism due to their magnetic moment rotation inside the nanoparticle. The easy axes are distributed according to the particular configuration: these are aligned (i) parallel or (ii) perpendicular to the direction of an external field. These models are investigated using both theory and computer simulation. The theoretical approach is based on a modification of the virial expansion method, which allows us to determine analytical expressions for the Helmholtz free energy, the static magnetization, and the initial magnetic susceptibility. These characteristics turned out in a good agreement with the numerical calculations in the region of low and moderate values of intensity of the dipole-dipole interparticle interactions and anisotropy energy barrier.