  In this study, we proposed a temperature model of magnetic nanoparticle
relaxation and a phase measurement method under a mixing-frequency excitation
field, which can improve the temperature accuracy of magnetic nanothermometry.
According to the Debye-based magnetization model for magnetic nanoparticles,
the phases at the mixing frequencies are used to solve the relaxation phase
delay to the magnetic field with the higher frequency. The method could improve
the signal-to-noise ratio of the magnetic response signal, and also weaken the
phase shift of the detection coils caused by temperature changes. Experimental
results show that the method can achieve static temperature measurement error
less than 0.1K and dynamic temperature measurement error less than 0.2K.
