Determination of the blocking temperature of magnetic nanoparticles: The good, the bad and the ugly

In a magnetization vs. temperature (M vs. T) experiment, the blocking region of a magnetic nanoparticle (MNP) assembly is the interval of T values were the system begins to respond to an applied magnetic field H when heating the sample from the lower reachable temperature. The location of this region is determined by the anisotropy energy barrier depending on the applied field H, the volume V, the magnetic anisotropy constant K of the MNPs and the observing time of the technique. In the general case of a polysized sample, a representative blocking temperature value $T_B$ can be estimated from ZFC-FC experiments as a way to determine the effective anisotropy constant. In this work, a numerical solved Stoner-Wolfharth two level model with thermal agitation is used to simulate ZFC-FC curves of monosized and polysized samples and to determine the best method for obtaining a representative $T_B$ value of polysized samples. The results corroborate a technique based on the T derivative of the difference between ZFC and FC curves proposed by Micha et al(the good) and demonstrate its relation with two alternative methods: the ZFC maximum (the bad) and inflection point (the ugly). The derivative method is then applied to experimental data, obtaining the $T_B$ distribution of a polysized $Fe_3O_4$ MNP sample suspended in hexane with an excellent agreement with TEM characterization.