Onset of Superfluidity in ^{3}He Films

We elucidate, for the first time, the overall behavior of the onset temperature of superfluidity in ^{3}He films for a wide range of film thicknesses d between 0.06 and 10  μm by taking advantage of the tunability of d implemented using microfabricated devices. We observe a suppression of the onset temperature of superfluidity T_{c}^{f} in a film from the bulk transition temperature as d decreases. In particular, T_{c}^{f} is strongly suppressed when d approaches the coherence length (∼77  nm). The observed T_{c}^{f} as a function of d is similar to that expected from the quasiclassical theory, but it unexpectedly deviates from the theoretical value by several percent when 0.5≲d≲5  μm.