Estimation of effective anisotropy constant distribution of magnetic nanoparticles based on magnetic particle spectroscopy

Magnetic nanoparticles (MNPs) have gained significant attention in biomedical applications such as magnetic particle imaging (MPI) and magnetic hyperthermia. The AC magnetization properties of MNPs, which are crucial for their performance, are influenced by factors such as the core size distribution, saturation magnetization, and effective anisotropy constant. In this study, we proposed a method to estimate an effective anisotropy constant distribution in a MNP sample, which is generally treated as a constant value. Experimental results of the AC magnetization for different MNP samples, including single-core and multi-core samples, were well described by the numerical simulation results in which the estimated effective anisotropy constant distribution was taken into consideration. Furthermore, we demonstrated that the effective anisotropy constant distribution obtained from 1-20 kHz harmonics of AC magnetization measured by magnetic particle spectroscopy (MPS) could be effectively applied to simulations at frequencies up to 40 kHz within 20% relative error, potentially extending the practical frequency range of MPS through simulations. Our findings provide a reliable approach for estimating an effective anisotropy constant distribution in a nano-sized magnetic particle sample, analyzing the AC magnetization properties of MNPs, and optimizing their applications in biomedical fields.