The core size distribution is an important physical characteristic of magnetic nanoparticles (MNPs) because it seriously affects biomedical and biological applications. In this study, we proposed an improved method for estimating the distributions, which optimizes the excitation frequency based on AC susceptibility to avoid the effects of Brownian relaxation. Moreover, the first, third, and fifth magnetization harmonics under different excitation field strengths are used for estimating core size distributions to avoid measuring higher harmonics. The experiment results show that the improved AC harmonic method can accurately and quickly estimate the distribution of large core sizes compared with the method of static magnetization (M–H) curves, which is a competitive advantage in MNP immunoassays.

This paper presents a novel method for estimating the temperature of magnetic nanoparticles (MNPs) based on AC magnetization harmonics of MNPs dominated by Brownian relaxation. The disparity in the AC magnetization response and magnetization harmonic between the Fokker-Planck equation and the Langevin function was analyzed, and we studied the relationship between the magnetization harmonic and the key factors, such as Brownian relaxation time, temperature, magnetic field strength, core size and hydrodynamic size of MNPs, and excitation frequency. We proposed a compensation function for AC magnetization harmonic with consideration of the key factors and the disparity between the Fokker-Planck equation and the Langevin function. Then a temperature estimation model based on the compensation function and the analytical harmonic expression of the Langevin function was established. By employing the least squares algorithm, the temperature was successfully calculated. The experimental results show that the temperature error is less than 0.035 K in the temperature range from 310 K to 320 K. The temperature estimation model is expected to improve the performance of the magnetic nanoparticle thermometer and be applied to magnetic nanoparticle-mediated hyperthermia.

Thermometry is essential in laboratory and industry settings. We propose a noninvasive temperature measurement method based on the superparamagnetic properties of nickel-plated films. When the nickel (Ni) film is uniformly heated from 100 K to 300 K, we observe that the polarization angle of the reflected polarized light decreases correspondingly. Compared with optical temperature measurement, this method introduces magnetic physical quantity, which increases the penetration of temperature measurement. Compared with magnetic temperature measurement, this method introduces optical physical quantity, which greatly increases the amount of information contained in the measurement channel. On this basis, we introduce the characteristic matrix of membrane system, and the improved the mean field theory which can interpret superparamagnetism. Our experiment has demonstrated that the above theoretical model is feasible from low temperature to normal temperature. The thin film sensor element provides the necessary temperature information for cryogenic wind tunnel design and hypersonic vehicle surface model design in real time

The Fokker–Planck equation accurately describes AC magnetization dynamics of magnetic nanoparticles (MNPs). However, the model for describing AC magnetization dynamics of MNPs based on Fokker-Planck equation is very complicated and the numerical calculation of Fokker-Planck function is time consuming. In the stable stage of AC magnetization response, there are differences in the harmonic phase and amplitude between the stable magnetization response of MNPs described by Langevin and Fokker–Planck equation. Therefore, we proposed an empirical model for AC magnetization harmonics to compensate the attenuation of harmonics amplitude induced by a high frequency excitation field. Simulation and experimental results show that the proposed model accurately describes the AC M–H curve. Moreover, we propose a harmonic amplitude–temperature model of a magnetic nanoparticle thermometer (MNPT) in a high-frequency excitation field. The simulation results show that the temperature error is less than 0.008 K in the temperature range 310–320 K. The proposed empirical model is expected to help improve MNPT performance.

In this study, a temperature imaging method based on a magnetic nanoparticle thermometer is proposed and evaluated. We first constructed a new model for finding the single temperature of magnetic nanoparticles with core size distribution. Specifically, we employed an air-core coil as a magnetic probe, which measured the magnetization of magnetic nanoparticles (MNPs). We then constructed a relation between the output signal of an air-core coil in the direction of the geometric center axis and the magnetization of the MNPs in a 2-D imaging area based on the magnetic dipole theory. Once this was achieved, we established a temperature imaging model by utilizing Green function as the convolution kernel, which describes the distance relationship between MNPs and the geometric center axis of the air-cored coil. After this, we calculated the harmonic distribution by a deconvolution algorithm and determined the temperature of the MNPs at different positions based on the model of harmonic amplitude and temperature, resulting in the 2-D temperature distribution. The simulation proved that the model and method of 2-D temperature distribution measurement could theoretically be acceptable. In the experiment, the 2-D temperature distribution of multi-chip power LEDs was measured accurately by a homemade system, thus demonstrating the feasibility of the proposed method for temperature imaging. This method is expected to provide a new solution for measuring the internal temperature distribution of opaque objects under extreme conditions.

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.