Nonmonotonic field dependence of the zero-field cooled magnetization peak in some systems of magnetic nanoparticles

We have performed magnetic measurements on a diluted system of $\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles $\left(d\sim 7\hspace{0.5em}\mathrm{nm}\right)$, and on a ferritin sample. In both cases, the zero-field cooled (ZFC) peak presents a nonmonotonic field dependence, as has already been reported in some experiments, and discussed as possible evidence of resonant tunneling. Within simple assumptions, we derive expressions for the magnetization obtained in the usual ZFC, field cooled (FC) and thermoremanent magnetization (TRM) procedures. We point out that the ZFC-peak position is extremely sensitive to the width of the particle-size distribution, and give some numerical estimates of this effect. We propose to combine the FC magnetization with a modified TRM measurement, a procedure which allows a more direct access to the barrier distribution in a field. The typical barrier values that are obtained in this procedure show a monotonic decrease for increasing fields, as expected from the simple effect of anisotropy barrier lowering, in contrast with the ZFC results. From our measurements on $\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3$ particles, we show that the width of the effective barrier distribution is slightly increasing with the field, an effect that is sufficient for causing the observed initial increase of the ZFC-peak temperatures.