The nonlinear dynamics of magnetic nanoparticles: A thermometry in complex magnetic fields

In this Letter, we propose a thermometry method for magnetic nanoparticles in complex magnetic fields. Complex magnetic fields result in intricate magnetization that can be influenced by temperature and relaxation mechanisms. We derive a set of approximate equations from the results of a numerical simulation of the nonlinear dynamic magnetic response to describe the relationship between particle temperature and the cubic susceptibility phase under complex magnetic fields. The thermometry of various magnetic nanoparticles in suspended or immobilized states is achieved with measured susceptibility. The experimental results show that the temperature measurement accuracy is less than 0.1 K for temperatures ranging from 309 to 333 K. Furthermore, the combination of complex magnetic fields and suspension samples typically dominated by Brown relaxation leads to errors of less than 0.05 K, suggesting that the significant relaxation process improves the accuracy of the temperature measurements. The method also has potential for noninvasive and quantitative temperature monitoring in magnetic particle imaging with complex magnetic fields.