  The spin coherence phenomena and the possibility of their observation in
nanomagnetic insulators attract more and more attention in the last several
years. Recently it has been shown that in these systems in large transverse
magnetic field there can be a fairly narrow "coherence window" for phonon and
nuclear spin-mediated decoherence. What kind of spin dynamics can then be
expected in this window in a crystal of magnetic nanomolecules coupled to
phonons, to nuclear spin bath and it to each other via dipole-dipole
interactions? Studying multispin correlations, we determine the region of
parameters where "coherent clusters" of collective spin excitations can appear.
Although two particular systems, namely crystals of $Fe_8$-triazacyclonane and
$Mn_{12}$-acetate molecules, are used in this work to illustrate the results,
here we are not trying to predict an existence of collective coherent dynamics
in some particular system. Instead, we discuss the way how any crystalline
system of dipole-dipole coupled nanomolecules can be analyzed to decide whether
this system is suitable for attempts to observe coherent dynamics. The
presented analysis can be useful in the search for magnetic systems showing the
spin coherence phenomena.
