Efficiency of magnetic hyperthermia in the presence of rotating and static fields

Single-domain ferromagnetic nanoparticle systems can be used to transfer energy from a time-dependent magnetic field into their environment. This local heat generation, i.e., magnetic hyperthermia, receives applications in cancer therapy which requires the enhancement of the energy loss. A possible way to improve the efficiency is to chose a proper type of applied field, e.g., a rotating instead of an oscillating one. The latter case is very well studied and there is an increasing interest in the literature to investigate the former although it is still unclear under which circumstances the rotating applied field can be more favourable than the oscillating one. The goal of this work is to incorporate the presence of a static field and to perform a systematic study of the non-linear dynamics of the magnetisation in the framework of the deterministic Landau-Lifshitz-Gilbert equation in order to calculate energy losses. Two cases are considered: the static field is either assumed to be perpendicular to the plane of rotation or situated in the plane of rotation. In the latter case a significant increase in the energy loss/cycle is observed if the magnitudes of the static and the rotating fields have a certain ratio (e.g. it should be one for isotropic nanoparticles). It can be used to "super-localise" the heat transfer: in case of an inhomogeneous applied static field, tissues are heated up only where the magnitudes of the static and rotating fields reach the required ratio.