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The mechanism of magnetization reversal in single-domain ferromagnetic particles is of interest in many applications, in most of which losses must be minimized. In cancer therapy by hyperthermia the opposite requirement prevails: the specific loss power should be maximized. Of the mechanisms of dissipation, here we study the effect of Néel relaxation on magnetic nanoparticles unable to move or rotate and compare the losses in linearly and circularly polarized fields. We present exact analytical solutions of the Landau-Lifshitz equation as derived from the Gilbert equation and use the calculated time-dependent magnetizations to find the energy loss per cycle. In frequencies lower than the Larmor frequency, linear polarization is found to be the better source of heat power, at high frequencies (beyond the Larmor frequency) circular polarization is preferable.