Dependence of the Magnetization Response on the Driving Field Amplitude for Magnetic Particle Imaging and Spectroscopy

To predict the response of magnetic nanoparticles to changes in the external magnetic field in magnetic particle imaging (MPI) and magnetic particle spectroscopy, it is important to understand the relaxation mechanisms and relaxation times. Often, the zero-field formulas for Brownian and Néel relaxation are employed when theoretically estimating the relaxation times. However, as reported previously, the relaxation times depend on the magnetic field strength. The Néel relaxation time can change by many orders of magnitude even for magnetic field strengths typically used in MPI. Here, we report on numerical simulations of the Fokker-Planck equations governing Brownian and Néel relaxation for an externally driven system. We find that when only Néel relaxation is present-as occurs if the particles are embedded in a solid-a strong magnetization response can occur even if the zero-field equation predicts a weak response. For a system of particles suspended in a fluid, the dominate relaxation mechanism, either Brownian or Néel, depends on the magnetic field strength, the driving frequency, and the phase of the magnetization relative to the driving field. In addition, some analytical expressions for the relaxation times are evaluated.