  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 difference 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,
excitation frequency, and so on. We proposed a compensation function for AC
magnetization harmonic with consideration of the key factors and the difference
between the Fokker-Planck equation and the Langevin function. Then a
temperature estimation model based on the compensation function and 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.
