The numerous phenomenological equations used in the study of the behaviour of single-domain magnetic nanoparticles are described and some issues clarified by means of qualitative comparison. To enable a quantitative textit{application} of the model based on the Debye (exponential) relaxation and the torque driving the Larmor precession, we present analytical solutions for the steady states in presence of circularly and linearly polarized AC magnetic fields. Using the exact analytical solutions, we can confirm the insight that underlies Rosensweigs introduction of the chord susceptibility for an approximate calculation of the losses. As an important consequence, it can also explain experiments, where power dissipation for both fields were found to be identical in root mean square sense. We also find that this approximation provides satisfactory numerical accuracy only up to magnetic fields for which the argument of the Langevin function reaches the value 2.8.
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