Relaxation processes and thermodynamic equilibrium in nanoparticle powder heated from very low temperatures in the presence of a magnetic field

The thermal dependence of the magnetization of a nanoparticles powder heated from very low temperatures 1–400 K for both cases of cooling in the absence (zfc) and in presence (fc) of a constant magnetic field was studied. In the presence of the magnetic field, the uniaxial anisotropy generates asymmetric double well energy landscapes. The changes with temperature and time of the particles distribution between the two energy minima was examined, and calculations based on particles distribution were developed. At low temperatures, the relaxation time is very long, the transitions between the two energy minima are extremely rare and the particle distribution on the minima does not change. Close to the blocking temperature T_B, the relaxation time becomes much shorter and a significant increase in the transition number takes place, the particle distribution changes and so does the magnetization. Above this temperature, the relaxation time decreases faster, the transitions in both directions come to balance and the particle distribution becomes stable: the magnetization values will correspond to successive thermodynamic equilibrium states, verified by the zfc, fc and td curves superposition. The theoretical results are in good agreement with the experimental data reported by many authors.