To the theory of static magnetizations of ferrogels with heterogeneous clusters. Effect of dimers

Effect of clusters, consisting of two single-domain ferromagnetic nanoparticles (dimers) on magnetostatic properties of ferrogels is studied theoretically. The proposed model of the static magnetization of the motionless dimer is developed by using the mathematically regular saddle point method. A simple approximate formula for the dimer magnetization is derived and compared with the exact formula, following from the Boltzmann law of distribution over physically possible states of the dimer. For large value of parameters of the interparticle dipole–dipole interaction and the particles internal magnetic anisotropy, the approximate formula leads to good agreement with the exact formula and can be recommended for practical calculations to avoid numerical calculation of integrals of high multiplicity. The obtained results can serve as a robust basis for studying of magnetic and other physical properties of ferrogels with more complicated internal structures.