Magnetization process of noninteracting ferromagnetic cobalt nanoparticles in the superparamagnetic regime: Deviation from Langevin law

Magnetization measurements were performed and analyzed on two systems of noninteracting superparamagnetic cobalt nanoparticles displaying narrow size distributions. The experiments were carried out above the blocking temperature, i.e., in the superparamagnetic regime. Several deviations from classical Langevin behavior were pointed out, in particular, at high field and near the blocking temperature. These deviations were interpreted in terms of anisotropy effects on the magnetization process and analyzed using theoretical expressions including uniaxial anisotropy energy. The effect of the anisotropy on the theoretical magnetization curves plotted versus applied field divided by the temperature are characterized by: (i) superposition at low fields, (ii) deviations in the approach to saturation area, and (iii) decrease of the magnetization when lowering the temperature. These three characteristics are present in our experimental curves. It allows us to determine the magnetic moment of the particle in the low-field region, and then the effective anisotropy from the approach to the saturation area for each sample, validating therefore, our theoretical expressions. A more detailed analysis of the experimental magnetization curves showed that the magnetization process proceeds in two steps: orientation of the magnetic moment of the particle, and orientation of the canted spins in the particle along the applied field. Finally, the values of the effective anisotropy are compared with those determined by other techniques.