Modelization of Superferromagnetism in Soft Nanocrystalline Materials Based on an Accurate Description of Magnetostatic Interactions

At high temperature, Fe–Si nanograins obtained by partial crystallization of amorphous Fe–Si–Cu–Nb–B precursor are superparamagnetic, due to the disappearance of the magnetism of the residual amorphous matrix. At a transition temperature
$T_{\rm tr}$
above the amorphous Curie temperature, a spontaneous polarization
$J_{S}^{\rm sf}$
appears, despite a much lower blocking temperature. Dipolar interactions, or a residual ferromagnetic coupling between grains, have been invoked to explain this effect. We investigate here the dipolar hypothesis. The Lorentz field (L.f.) model is improved the idea being that the field acting on a nanograin is screened by a surrounding soft shell. The attenuation factor is calculated, leading to a decrease of
$T_{\rm tr}$
compared with the L.f. approximation. Moreover, a description of the spontaneous magnetization curve
$J_{S}^{\rm sf}(T)/J_{S}(T)$
is obtained, with a slope near
$T_{\rm tr}$
much sharper than predicted by the
$(T_{\rm tr}-T)^{1/2}$
law associated to an invariant molecular field factor. Comparison with the experiments shows good agreement.