A simple and fast measurement method for the saturation magnetization of magnetic nanoparticles and biosensing application

The saturation magnetization (Ms) is a critical parameter for selecting and optimizing of magnetic materials for specific applications, including but not limited to medical imaging, biosensing, and hyperthermia. The Ms is often measured using a vibrating sample magnetometer (VSM). Although VSM is known for its accuracy, it typically requires strong excitation magnetic fields and is susceptible to background noise, especially when measuring weak signals. These factors limit its practicality in routine or rapid measurement scenarios. Aiming to solve this problem, a simple and fast measurement method for the Ms is reported in this study. We study the relationship between Ms and harmonic amplitude ratios of magnetic nanoparticles (MNPs) based on the Langevin function, and then construct an estimation model of the Ms, and calculate the Ms by using the Levenberg-Marquardt algorithm. Further, in the process of Taylor expansion of the Langevin function, it is found that when α is less than 0.6 and the Taylor expansion terms are greater than five, the error can be limited within the range required. Subsequently, we set up a simple magnetic particle spectroscopy with a temperature controller in the range of 297 K to 321 K, and carried out experiments for measuring the Ms of four MNP samples (SHP-15-1, SHP-25-2, SOR25, and EMG1300). The relationship between the Ms and temperature was explored, which still obeys the Bloch-Law approximately within the hyperthermia temperature range by parameter fitting. The fitting model may be used in MNPs hyperthermia.