Dynamic single-domain particle model for magnetite particles with combined crystalline and shape anisotropy

The dynamical behaviour of superparamagnetic iron oxide nanoparticles (SPIONs) is not yet fully understood. In magnetic particle imaging (MPI) SPIONs are used to determine quantitative real-time medical images of a tracer material distribution. For reaching spatial resolution in the sub-millimetre range, MPI requires a well engineered instrumentation providing a magnetic field gradient exceeding 2 T m^-1. However, as the particle performance strongly affects the sensitivity of the imaging process, optimization of the particle parameters is a crucial factor, which is not easy to address. Today most simulations of MPI use the Langevin model to describe the particle behaviour. In equilibrium, the model matches the measured data. If alternating fields in the mid kHz frequency range are applied, the dynamic behaviour of the particles differs from the Langevin theory due to anisotropy effects, particle-particle-interactions and/or exchange interaction in case of multi-core particles. In this paper a model based on previous work is introduced, which was adopted to include crystal and shape anisotropy of immobilised mono-domain single-core particles. The model is applied to typical MPI frequencies and field strengths with different possible superposition of the anisotropy effects, leading to differences in the particle response. It is shown that, despite comparatively high anisotropy constants, the magnetocrystalline anisotropy energy does not quench the signal response for MPI. The constructive superposition of shape and crystal anisotropy leads to the best performance in terms of sensitivity and resolution of the associated imaging modality and slightly reduces the energy barriers compared to a sole-shape anisotropy.