  We introduce a novel method for local structure determination with a spatial
resolution of the order of 0.01 Angstroem. 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={\alpha} (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 CsMnxMg1 xBr3 (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.
