  The main idea of magnetic hyperthermia is to increase locally the temperature
of the human body by means of injected superparamagnetic nanoparticles. They
absorb energy from a time-dependent external magnetic field and transfer it
into their environment. In the so-called superlocalization, the combination of
an applied oscillating and a static magnetic field gradient provides even more
focused heating since for large enough static field the dissipation is
considerably reduced. Similar effect was found in the deterministic study of
the rotating field combined with a static field gradient. Here we study
theoretically the influence of thermal effects on superlocalization and on
heating efficiency. We demonstrate that when time-dependent steady state
motions of the magnetisation vector are present in the zero temperature limit,
then deterministic and stochastic results are very similar to each other. We
also show that when steady state motions are absent, the superlocalization is
severely reduced by thermal effects. Our most important finding is that in the
low frequency range ($\omega \to 0$) suitable for hyperthermia, the oscillating
applied field is shown to result in two times larger intrinsic loss power and
specific absorption rate then the rotating one with identical superlocalization
ability which has importance in technical realisation.
