Modelling the magnetization data of Fe3O4 nanoparticles above blocking temperature

Nanoparticles of Fe₃O₄ are prepared by simple co-precipitation method. The sample is characterized using an x-ray diffractometer, transmission electron microscope, and vibrating sample magnetometer. The x-ray diffraction pattern of the sample clearly shows that it is a single-phase magnetite. The transmission electron micrograph shows that the sample has a narrow distribution in particle size with average particle size of 9.9 nm. The SAED pattern only shows the diffraction planes correspond to magnetite and no other phase impurity is detected. The calculated thickness of the magnetic disordered shell due to the reduction in particle size is found to be 1.7 nm. The magnetization of the sample is measured as a function of temperature and applied magnetic field. The zero-field cooled and field cooled curves of the sample are measured in the presence of 250 Oe applied magnetic field and both the curves bifurcate at 170 K. The peak in the zero-field curve indicates that the sample has a blocking temperature of around 100 K. The magnetization as a function of applied magnetic field data at 200, 225, 250, 275 and 300 K are measured (up to ±20 kOe). These magnetization data are used for the fitting to analyze the magnetic behavior of Fe₃O₄ nanoparticles. . The magnetization of nanoparticles systems is influenced by several factors such as particle size distribution, disordered surface, magnetocrystalline anisotropy, magnetic moment distribution and magnetic interactions. The ignorance of such factors while analyzing the magnetization data leads to discrepancies in the results. The surface effects are sensitive to the reduction in particle size leading to the spin frustrations on the surface suggesting a magnetic disordered layer which affect the magnetic behavior of nanoparticles. This work presents the analysis of the magnetization data in an appropriate magnetization expression which takes into consideration the effect of magnetic moment distribution. This distribution in the magnetic moment is found to be significantly influenced the magnetization analysis and affected by the magnetic disordered surface which accounts for the presence of magnetic anisotropy and magnetic interactions on the particles surface. The results and observations are discussed in detail.