is connected with the fact that the results of Figure 4 were obtained in samples treated by the Joule heating effect. This kind of annealing could induce some inhomogeneous magnetic anisotropy, which could be responsible for this significant change of the grain size dependence of the coercive field. This argument is supported by the remanence ratio, which is achieved by these samples of values around 0.50. As a consequence, it can be assumed that the presence of more long-range uniaxial anisotropies are larger than the average magnetocrystalline anisotropy (K1). It should also be noted that Eq. (5) can, interestingly, account for the occurrence of dipolar and deteriorated exchange intergrain interaction and thus can be more realistic than the simple anisotropy averaging, since those features are involved in the accomplishment of a nanocrystallization process.

An interesting study can be one related with the dependencies of the magnetization in partially crystallized samples. Figure 5 displays such dependencies. In Table 1, the evolution with the annealing time of the average grain size, D, the Si atomic percentage diffused in the Fe crystalline lattice, and the crystalline phase percentage are listed. It has been mentioned that in samples annealed with short times (0.5 to 5 minutes), there was no evidence of crystallization. In samples treated for long times, the Si content was of the order of 20% at and slightly larger in the samples having a larger grain size.

On the other hand, the current density dependence of the coercivity for Finemet-type alloys results in a very interesting study (illustrated by the Fig. 6). Such dependencies exhibit a peak of coercivity in nanocrystallized samples (treated for 60-720 minutes). This peak of coercivity occurs above the Curie point of the residual amorphous phase. The intensity and the width of the peak strongly depend on the annealing current density. It must be mentioned that the current density above the Curie point of the amorphous matrix being paramagnetic and with its thickness is high enough to avoid exchange interactions between the grains, the nanocrystalline sample can be magnetically considered

Table 1. Evolution with the annealing time of the percentage of crystalline phase, percentage of Si content inside bcc phase, and average grain size of Fe^C^N^Si^^ amorphous alloy ribbon treated by current annealing at 40 A/mm2.
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