Estimation of Core Size Distribution of Magnetic Nanoparticles using High-<i>T</i>_c SQUID Magnetometer and Particle Swarm Optimizer-based Inversion Technique

In this work, the core size estimation technique of magnetic nanoparticles (MNPs) using the static magnetization curve obtained from a high-Tc SQUID magnetometer and a metaheuristic inversion technique based on the Particle Swarm Optimizer (PSO) algorithm is presented. The high-Tc SQUID magnetometer is constructed from a high-Tc SQUID sensor coupled by a flux transformer to sense the modulated magnetization signal from a sample. The magnetization signal is modulated by the lateral vibration of the sample on top of a planar differential detection coil of the flux transformer. A pair of primary and excitation coils are utilized to apply an excitation field parallel to the sensitive axis of the detection coil. Using the high-Tc SQUID magnetometer, the magnetization curve of a commercial MNP sample (Resovist) was measured in a logarithmic scale of the excitation field. The PSO inverse technique is then applied to the magnetization curve to construct the magnetic moment distribution. A multimodal normalized log-normal distribution was used in the minimization of the objective function of the PSO inversion technique, and a modification of the PSO search region is proposed to improve the exploration and exploitation of the PSO particles. As a result, a good agreement on the Resovist magnetic core size was obtained between the proposed technique and the non-negative least square (NNLS) inversion technique. The estimated core sizes of 8.0484 nm and 20.3018 nm agreed well with the values reported in the literature using the commercial low-Tc SQUID magnetometer with the SVD and NNLS inversion techniques. Compared to the NNLS inversion technique, the PSO inversion technique had merits in exploring an optimal core size distribution freely without being regularized by a parameter and facilitating an easy peak position determination owing to the smoothness of the constructed distribution. The combination of the high-Tc SQUID magnetometer and the PSO-based reconstruction technique offers a powerful approach for characterizing the MNP core size distribution, and further improvements can be expected from the recent state-of-the-art optimization algorithm to optimize further the computation time and the best objective function value.