Hysteresis model with dipole interaction: Devil’s staircase like shape of the magnetization curve

Magnetic properties of two-dimensional (2D) systems of magnetic nanoobjects (2D regular lattices of magnetic nanoparticles or magnetic nanostripes) are considered. Analytical calculations of the hysteresis curve of a system with interaction between nanoobjects are provided. It is shown that during a magnetization reversal the system undergoes a number of metastable states. The kinetic problem of the magnetization reversal was solved for three models. The following results have been obtained: (1) for a 1D system (T=0) with a long-range interaction with the energy proportional to r^-p, a staircaselike shape of the magnetization curve has a self-similar character (complete “devil’s staircase”). The nature of the steps is determined by the interplay of the interparticle interaction and the coercivity of a single nanoparticle; (2) The influence of thermal fluctuations on the kinetic process was examined in the framework of the nearest-neighbor interaction model. The thermal fluctuations lead to additional splitting of the steps on the magnetization curve. The influence of the coercivity dispersion in the system is also discussed. A simple method to experimentally distinguish the influence of interaction from the coercivity dispersion on the magnetization curve is proposed.