  By measuring the nuclear magnetic resonance (NMR) 1/T_1 relaxation rate in
the Br (bond) doped DTN compound, Ni(Cl(1-x)Br_x)2-4SC(NH2)2 (DTNX), we show
that the low-energy spin dynamics of its high magnetic field "Bose-glass"
regime is dominated by a strong peak of spin fluctuations found at the nearly
doping-independent position H* = 13.6 T. From its temperature and field
dependence we conclude that this corresponds to a level crossing of the energy
levels related to the doping-induced impurity states. Observation of the local
NMR signal from the spin adjacent to the doped Br allowed us to fully
characterize this impurity state. We have thus quantified a microscopic
theoretical model that paves the way to better understanding of the Bose-glass
physics in DTNX, as revealed in the related theoretical study [M. Dupont, S.
Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017),
arXiv:1610.05136].
