Relevance of a magnetic moment distribution and scaling law methods to study the magnetic behavior of antiferromagnetic nanoparticles

In antiferromagnetic nanoparticles magnetization the linear component, $\chi_{AF}$H superposed to the saturation one usually complicates the fit of experimental data. We present a method based on scaling laws to determine the variation of $\chi_{AF}$ with temperature and to find the temperature dependence of the average magnetic moment $<\mu>$, without any assumption on both the magnetization dependence on field or the moment distribution function, whose relevance can also be estimated. We have applied this method to ferritin and found that $<\mu>$ decreases with increasing temperature and that a distribution function cannot be ignored. The fit with Langevin magnetization law and lognormal moment distribution functions yielded parameters close to those estimated with the scaling method. We also show that in general if the distribution is ignored, and a single particle moment $\mu_p$ is used, $\mu_p$ presents an artificial systematic increase with temperature. This calls the attention to the necessity of evaluating the effect of a size distribution before concluding about the physical nature of the parameters variation.