T² law for magnetite-based ferrofluids

The temperature dependence of the saturation magnetization of Fe₃O₄ surfacted nanoparticles does not follow the law in T² that corresponds to bulk ferrite: M_s (T) = M_s (0)[1 − BT² ] (where M_s (T) is the saturation magnetization at temperature T, M_s (0) is the saturation magnetization at 0 K and B is a constant that depends on the exchange integral). This abnormal behaviour was studied for a ferrofluid that contains magnetite particles covered in oleic acid (surfactant) in a carrier fluid (kerosene); the anomaly is attributed to modification of the superexchange interaction between the iron ions from the surface layer of the nanoparticles, a layer that is formed due to the presence of the surfactant. Taking into consideration the size distribution of the particles, according to magneto-granulometric measurements and transmission electron microscopy, we have shown that the thickness of the surface layer at a temperature of 300 K is ⟨η⟩ ∼ = 0.9 nm. By adopting the 'core–shell' model we have shown that the layer at the particles' surface is paramagnetic at room temperature and it gradually becomes ferrimagnetically ordered as the temperature decreases. The consequence of this change is the increase of the mean volume of the nanoparticles' magnetic core where the spins are aligned due to the superexchange interaction from 1280 to 1910 nm³ when the temperature decreases from 300 to 77 K.