Superparamagnetic state magnetization

At high temperatures, a nanoparticle is in a superparamagnetic state with thermal equilibrium properties as described in the previous section. At low temperatures, the magnetic moment is blocked in one potential well with a small probability to overcome the energy barrier, while at intermediate temperatures, where the relaxation time of a spin is comparable to the observation time, dynamical properties can be observed, including magnetic relaxation and a frequency-dependent ac susceptibility. 

Firstly, at room temperature the low-x composites display low complex magnetic permeability (compare Figs. 1 and 2 at x Xq)- These samples also reveal high DC resistance and lack of hysteresis for the magnetization curves and sextet component in the Mossbauer spectra that can evidence a superparamagnetic state. 

A shape of the ZFC and FC magnetization curves in Fig. 3 is typical of superparamagnetic state of materials. 

F.2. Field-Cooled and Zero-Field-Cooled Magnetizations and Susceptibility in the Superparamagnetic State at Low Field... 

F.2.2. Field-Cooled Magnetization (Mp ) Experiments F.2.3. Magnetization in the Superparamagnetic State... 

Let us recall the usual process. The sample is cooled at once without applied field from a temperature where all the particles are in the superparamagnetic state until the lowest temperature Afterward a field is applied and the measurement is performed increasing the temperature. In fact, if the magnetization in the superparamagnetic state has to be studied, the above condition on the initial temperature must be fulfilled. But if only Tg is of interest, it is sufficient that the magnetic moments m of the particles are frozen in random orientation at This can easily be checked from the zero field magnetization value, which must be equal to zero. 

Finally, a last property has been evidenced very recently. The magnetization in the superparamagnetic state has been studied vs. H pp on y-Fe203 particles in a polymer. The effect of H pp is the same for samples with Q = 0.008 and = 0.20, independently of the H pp direction, which means that it does not depend on the interparticle interactions and is only related to the properties of a single particle. A small increase in Qp vs. H pp is observed while a strong shift of d p toward negative value (Fig. F.2.9) approximately proportional to H pp is observed. At the present no definite explanation is proposed. 

In conclusion we want to underline that the magnetization in the superparamagnetic state depends strongly on different parameters such as the shape of the sample, the direction of H pp, the volumic concentration. 

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