We introduce a novel method for local structure determination with a spatial resolution of the order of 0.01 Å. It can be applied to materials containing clusters of exchange-coupled magnetic atoms. We use neutron spectroscopy to probe the energies of the cluster excitations which are determined by the interatomic coupling strength J. Since for most materials J is related to the interatomic distance R through a linear relation dJ/dR=α (for dR/R≪1), we can directly derive the local distance R from the observed excitation energies. This is exemplified for the mixed one-dimensional paramagnetic compound CsMn(x)Mg(1-x)Br3 (x=0.05,0.10) containing manganese dimers oriented along the hexagonal c axis. Surprisingly, the resulting Mn-Mn distances R do not vary continuously with increasing internal pressure but lock in at some discrete values.