Empirical Expression for AC Magnetization Harmonics of Magnetic Nanoparticles under High-Frequency Excitation Field for Thermometry.

Zhongzhou Du,Yuki Noguchi,Takashi Yoshida,Dandan Wang,Shi Bai,Yi Sun

doi:10.3390/nano10122506

Zhongzhou Du, Yuki Noguchi + Show 4 more

Open Access

https://doi.org/10.3390/nano10122506

Copy DOI

Abstract

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.

Highlights

Magnetic nanoparticles (MNPs) have been widely studied for use in biomedical applications [1,2,3,4,5,6]
We investigated the stable AC magnetization described by the Fokker-Planck equation and the Langevin function, and found that there are differences in the harmonic phase and amplitude between the stable magnetization response of MNPs described by Langevin and Fokker–Planck equation
We investigated the difference in AC magnetization between the Fokker–Planck equation and Langevin function to obtain an empirical model for MNP magnetization harmonics

Summary

Introduction

Magnetic nanoparticles (MNPs) have been widely studied for use in biomedical applications [1,2,3,4,5,6]. The magnetic nanoparticle sample moves between the heating and exciting coils through a mechanical device, making the MNPT setup complicated. In these previous studies, the theoretical models for temperature measurement were based on the Langevin function, which describes the static magnetization of an MNP ensemble. The Langevin function is only valid in an equilibrium (or static) state and does not accurately describe MNP magnetization dynamics when MNP relaxation cannot be neglected These are problematic in an MNPT; i.e., MNPT application is restricted to a low-frequency excitation field, and an additional and complicated temperature setup is necessary. We investigate the temperature error on the basis of the proposed empirical harmonic model for an MNPT in a high-frequency excitation field

Langevin Function

Fokker–Planck Equation for Néel Relaxation

Compensation Expression for MNP Magnetization Harmonics

Magnetic Nanoparticle Thermometry at High Frequency

Conclusions