Magnetic irreversibility and relaxation in assembly of ferromagnetic nanoparticles

Measurements of the magnetic irreversibility line and time-logarithmic decay of the magnetization are described for three ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ samples composed of regular amorphous, acicular amorphous, and crystalline nanoparticles. The relaxation rate is the largest and the irreversibility temperature is the lowest for the regular amorphous nanoparticles. The crystalline material exhibits the lowest relaxation rate and the largest irreversibility temperature. We develop a phenomenological model to explain the details of the experimental results. The main new aspect of the model is the dependence of the barrier for magnetic relaxation on the instantaneous magnetization and therefore on time. The time-dependent barrier yields a natural explanation for the time-logarithmic decay of the magnetization. Interactions between particles as well as shape and crystalline magnetic anisotropies define an energy scale that controls the magnetic irreversibility. Introducing this energy scale yields a self-consistent explanation of the experimental data.