Relevance of magnetic moment distribution and scaling law methods to study the magnetic behavior of antiferromagnetic nanoparticles: Application to ferritin

The analysis of magnetization of antiferromagnetic nanoparticles is not straightforward due to the presence of a linear component, ${\ensuremath{\chi}}_{\mathit{AF}}H$ superimposed on the saturation and the inexistence of a simple relation between size and magnetic moment $\ensuremath{\mu}$. We present a method, based on scaling laws, to determine the variation of ${\ensuremath{\chi}}_{\mathit{AF}}$ with temperature and to find the temperature dependence of $⟨\ensuremath{\mu}⟩$, without any assumption on both the magnetization dependence on the magnetic field and the moment distribution function. We have applied this method to ferritin nanoparticles (with very narrow size distribution) and found that, independently of the magnetization law, $⟨\ensuremath{\mu}⟩$ decreases with increasing temperature and that a magnetic moment distribution function cannot be ignored. The fit of the magnetization data with Langevin and lognormal moment distribution functions yielded $⟨\ensuremath{\mu}⟩=120\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ (at $30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$), decreasing to about 70% of this value at $T=250\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, in agreement with the scaling method estimations, and a log(\ensuremath{\mu}) variance ${s}^{2}=1$. This result shows that in ferritin there is no direct relation between size and moment distribution and that disorder should play a major role in the moment distribution. In general, if a moment distribution is ignored, the fitted magnetic moment presents an artificial systematic increase with temperature, similar to some previous reports in the literature. This highlights the need for evaluating the effect of such a distribution before drawing conclusions about the physical nature of the parameters variation.