Linear and Mittag-Leffler extrapolation to get saturation magnetization of superparamagnetic system from room temperature magnetization curve

Herein, we make a comparison between two functions that can be used to extrapolate the roomtemperature curve of magnetization versus inverse magnetic field (M-۱/H curve) to get the saturationmagnetization (Ms). The functions are the common linear function and Mittag-Leffler function.Simulated M-۱/H curves of various systems of superparamagnetic (SPM) nanoparticles were fitted tothe functions. The systems include core-shell magnetite nanoparticles with mono and multi-dispersesize distributions. The results showed that linear extrapolation is excellent for systems containedmoderate and big mono-disperse nanoparticles and poly disperse nanoparticles with narrow sizedistribution, but it leads to big errors in obtained Ms for very fine mono-disperse particles and the polydisperse particles that have wide size distribution. However, Mittag-Leffler function leads to theacceptable results for all of the systems considered here. Extrapolation of Ms was also performed for asample of iron-oxide nanoparticles that was synthesized by co-precipitation method and the obtainedresults from the two function were compared. The correct value of Ms was determined according to thecharacteristic mark on the Ms curves versus number of points.

Keywords:

super-paramagnetic nanoparticles , saturation magnetization , extrapolation