  Decoherence in many solid-state systems is anomalously high, frustrating
efforts to make solid-state qubits. We show that in nanomagnetic insulators in
large transverse fields, there can be a fairly narrow field region in which
both phonon and nuclear spin-mediated decoherence are drastically reduced. As
examples we calculate decoherence rates for the $Fe$-8 nanomolecule, for $Ni$
particles, and for $Ho$ ions in $LiHo_xY_{1-z}F_4$. The reduction in the
decoherence, compared to low field rates, can exceed 6 orders of magnitude. The
results also give limitations on the observability of macroscopic coherence
effects in magnetic systems.
