Getting saturation magnetization of superparamagnetic nanoparticles more accurately from room-temperature magnetization curve

The saturation magnetization (M-s) of a superparamagnetic (SPM) nanoparticle system is an important factor that affects the performance of nanoparticles and can reflect their other physical properties. In this work, we make a comparison between two functions that can be used to extrapolate the room temperature curve of magnetization versus the inverse magnetic field (M - 1/H curve) to get saturation magnetization. The functions are the common linear function and the Mittag-Leffler function. Simulated M - 1/H curves of various systems of SPM nanoparticles were fitted to the functions, and extrapolated M-s was obtained. For each fitting procedure, the average absolute deviations (AADs) were calculated. The systems include core-shell iron-oxide nanoparticles with mono-disperse, multi-disperse, log-normal, and bi-log-normal size distributions. The used magnetization fields were up to 20 kOe. The results showed that for each function and each system, the extrapolated M-s depends on the number of points of the M - 1/H curve used in the fitting procedure. However, there are characteristic marks on the diagrams of M-s and AAD versus the number of points from which the correct value of M-s can be determined. Moreover, for mono-disperse systems with 3nm nanoparticles, the linear function leads to a better result for extrapolated M-s than the Mittag-Leffler function. However, for log-normal and bi-log-normal with broad size distributions, the results of the Mittag-Leffler function are better. In the other cases, investigated here, both functions lead to similar and reasonable results. Exploration of M-s was also performed for eight samples of iron-oxide nanoparticles that were synthesized by the co-precipitation method. The obtained results from the two functions were compared. The correct value of M-s for each sample was determined according to the characteristic mark on the M-s and AAD curves versus the number of points. According to the results of this work, we suggest using both functions together to determine the saturation magnetization of magnetic nanoparticles in practical cases.