A new model to describe the crossover from superparamagnetic to blocked magnetic nanoparticles

A new model that considers the thermal probability of uniform magnetization inversion in magnetic nanoparticles is presented. We included the temporal window in consideration of the thermal average, which allowed us to take into account the hysteretic behavior, leading to a more clear description of the passage from one regime to another. From this formalism appears a superparamagnetic probability L that indicated the fraction of superparamagnetic particles we find on the ensemble at a given T, H and experimental time window. We have performed numerical simulations, including different time windows and considering the high- and low-temperature regimes. We compare our model with the analytic solution in zero and high-temperature limits and find that the proposed model agrees with the simulations. Measurements of field-cooling and zero-filed-cooling magnetization as well as hysteresis loops were simulated applying this model, from which relevant considerations regarding the importance, applicability and limitations of this treatment could be obtained.