Abstract
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> above the amorphous Curie temperature, a spontaneous polarization J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sf</sup> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> compared with the L.f. approximation. Moreover, a description of the spontaneous magnetization curve J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sf</sup> (T)/J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> (T) is obtained, with a slope near T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> much sharper than predicted by the (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> - T) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> law associated to an invariant molecular field factor. Comparison with the experiments shows good agreement.
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