Although ammonia is an abundant molecule commonly observed towards the dense interstellar medium, it has not yet been established whether its main formation route is from gas-phase ion-molecule reactions or grain-surface hydrogen additions on adsorbed nitrogen atoms. Deuterium fractionation can be used as a tool to constrain formation mechanisms. High abundances of deuterated molecules are routinely observed in the dense interstellar medium, with the ratio between deuterated molecules and the main isotopologue enhanced by several orders of magnitude with respect to the elemental D/H ratio. In the case of ammonia, the detection of its triply deuterated isotopologue hints at high abundances of the deuterated intermediate nitrogen radicals, ND, NHD and ND$_2$. So far however, only ND has been detected in the interstellar medium. In this paper, to constrain the formation of ammonia, we aim at determining the NHD/NH$_2$ and ND$_2$/NHD abundance ratios, and compare them with the predictions of both pure gas-phase and grain-surface chemical models. We searched for the fundamental rotational transitions of NHD and ND$_2$ towards the class 0 protostar IRAS16293-2422, towards which NH, NH$_2$ and ND had been previously detected. Both NHD and ND$_2$ are detected in absorption towards the source. The relative abundance ratios NH$_2$ : NHD : ND$_2$ are close to 8 : 4 : 1. These ratios can be reproduced by our gas-phase chemical model within a factor of two-three. Statistical ratios as expected from grain-surface chemistry are also consistent with our data. Further investigations of the ortho-to-para ratio in ND$_2$ , both theoretical and observational, could bring new constraints to better understand nitrogen hydride chemistry.
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