Finding the magnetic size distribution of magnetic nanoparticles from magnetization measurements via the iterative Kaczmarz algorithm

The characterization of the size distribution of magnetic nanoparticles is an important step for the evaluation of their suitability for many different applications like magnetic hyperthermia, drug targeting or Magnetic Particle Imaging. We present a new method based on the iterative Kaczmarz algorithm that enables the reconstruction of the size distribution from magnetization measurements without a priori knowledge of the distribution form. We show in simulations that the method is capable of very exact reconstructions of a given size distribution and, in that, is highly robust to noise contamination. Moreover, we applied the method on the well characterized FeraSpin™ series and obtained results that were in accordance with literature and boundary conditions based on their synthesis via separation of the original suspension FeraSpin R. It is therefore concluded that this method is a powerful and intuitive tool for reconstructing particle size distributions from magnetization measurements.