Magnetic properties of nanoparticles in the Bethe-Peierls approximation

In this work we present a new method to calculate the classical properties of magnetic nanoparticles. Based on the Bethe-Peierls (pair) approximation, we developed a simple system of equations for the classical magnetization of spins at any position within the nanoparticle. The nearest neightbor pair correlations are treated exactly for Ising spins, and the method can be generalized for various lattice symmetries. The master equation is solved for the Glauber dynamics (single-spin-flip) in order to obtain the time evolution of the magnetization. The capabilities of the model are demonstrated through the calculation of hysteresis loops as well as field cooling (FC) and zero field cooling (ZFC) magnetization curves of heterogeneous nanoparticles. The present method can be an alternative to the usually complex and time consuming methods employed in micromagnetism.