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Decoherence in many solid-state systems is anomalously high, frustratingefforts to make solid-state qubits. We show that in nanomagnetic insulators inlarge transverse fields, there can be a fairly narrow field region in whichboth phonon and nuclear spin-mediated decoherence are drastically reduced. Asexamples 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 thedecoherence, compared to low field rates, can exceed 6 orders of magnitude. Theresults also give limitations on the observability of macroscopic coherenceeffects in magnetic systems.Comment: 5 LaTeX pages, 3 figure

Coherence window in the dynamics of quantum nanomagnets