  Measurements of the magnetic irreversibility line and time-logarithmic decay
of the magnetization are described for three $Fe_{2}O_{3}$ 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 to
the time-logarithmic decay of the magnetization. Interactions between particles
as well as shape and crystalline magnetic anisotropies define a new energy
scale that controls the magnetic irreversibility. Introducing this energy scale
yields a self-consistent explanation of the experimental data.
