Effects of $^4$He film on quartz tuning forks in $^3$He at ultra-low temperatures

In pure superfluid $^3$He-B at ultra-low temperatures, quartz tuning fork oscillator response is expected to saturate when the dissipation caused by the superfluid medium becomes substantially smaller than the internal dissipation of the oscillator. However, even with small amount of $^4$He covering the surfaces, we have observed saturation already at significantly higher temperatures than anticipated, where we have other indicators to prove that the $^3$He liquid is still cooling. We found that this anomalous behavior has a rather strong pressure dependence, and it practically disappears above the crystallization pressure of $^4$He. We also observed a maximum in the fork resonance frequency at temperatures where the transition in quasiparticle flow from the hydrodynamic to the ballistic regime is expected. We suggest that such anomalous features derive from the superfluid $^4$He film on the oscillator surface.