Size-dependent magnetic properties of MnFe2O4 fine particles synthesized by coprecipitation.

Manganese ferrite, ${\mathrm{MnFe}}_{2}$${\mathrm{O}}_{4}$, fine particles in the size range 5\char21{}15 nm have been prepared by an aqueous phase coprecipitation method. The freshly prepared particles are in a metastable state with regard to the cation distribution between the A and B sites of the spinel lattice. Thermomagnetic, differential scanning calorimetry and M\"ossbauer spectroscopy show that heat treatment under inert gas to 670 K irreversibly changes the cation distribution to a stable state. Heat treatment of freshly prepared samples in air to 470 K both changes the cation site distribution somewhat and, most importantly, oxidizes the ${\mathrm{Mn}}^{2+}$ to ${\mathrm{Mn}}^{3+}$. The Curie temperature is modified in association with these changes. With this knowledge, we create a series of samples with various sizes but the same microstructure. We find the following. (1) The Curie temperature decreases relative to the bulk as size decreases. The decrease is consistent with finite size scaling. (2) The fit of the spontaneous magnetization to the Bloch ${\mathit{T}}^{3/2}$ law yields a Bloch constant larger than the bulk increasing with decreasing size in proportion to the specific surface area of the particles. We find a better fit is obtained if the exponent of the temperature is increased to be in the range 1.6 to 1.8. (3) The saturation magnetization decreases with decreasing size also in proportion to the specific surface area of the particles. \textcopyright{} 1996 The American Physical Society.