The sample was made using a graded composition technique which allows to obtain the Fe/Rh stoechiometry required for the presence of an antiferromagnetic-ferromagnetic transition. We show that the low-field microwave absorption (LFMA) signal can be well modelled by simply introducing the hysteresis of the static magnetization in the dynamic magnetic susceptibility. Finally, previous observations of LFMA on a cobalt thin film are also reproduced by this model. 55 Up to now, none of these studies had explored the low-field 56 range necessary to evidence LFMA experimentally. We fill 57 this gap by performing field-swept FMR at various temper-58 atures. Clear LFMA signals are obtained up to 25 GHz. We 59 show that taking into account the hysteresis in the usual Polder 60 susceptibility is sufficient to reproduce the important features 61 of our data, as well as that of previous authors[24]. This pro-62 vides a definitive explanation for the up-to-now elusive origins 63 of the LFMA phenomenon.