We have studied the Ho3+ spin dynamics for LiY0.998Ho0.002F4 through the positive muon (mu+) transverse field depolarization rate lambda_TF as a function of temperature and magnetic field. We find sharp reductions in lambda_TF(H) at fields of 23, 46 and 69 mT, for which the Ho3+ ion system has field-induced (avoided) level crossings. The reduction scales with calculated level repulsions, suggesting that mu+ depolarization by slow fluctuations of non-resonant Ho3+ spin states is partially suppressed when resonant tunneling opens new fluctuation channels at frequencies much greater than the muon precession frequency.
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