This article reports on the influence of the magnetization damping on dynamic hysteresis loops in single-domain particles with uniaxial anisotropy. The approach is based on the Néel–Brown theory and the hierarchy of differential recurrence relations, which follow from averaging over the realizations of the stochastic Landau–Lifshitz equation. A new method of solution is proposed, where the resulting system of differential equations is solved directly using optimized algorithms to explore its sparsity. All parameters involved in uniaxial systems are treated in detail, with particular attention given to the frequency dependence. It is shown that in the ferromagnetic resonance region, novel phenomena are observed for even moderately low values of the damping. The hysteresis loops assume remarkably unusual shapes, which are also followed by a pronounced reduction of their heights. Also demonstrated is that these features remain for randomly oriented ensembles and, moreover, are approximately independent of temperature and particle size.

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