Melting Curve of ${}^4\mathrm{He}$: No Sign of a Supersolid Transition down to 10 mK

We have measured the melting curve of ${}^4\mathrm{He}$ in the temperature range from 10 to 400 mK with the accuracy of about $0.5\mu \mathrm{bar}$. Crystals of different quality show the expected $T^4$ dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid ${}^4\mathrm{He}$ and on the Debye temperature of solid ${}^4\mathrm{He}$. Below 80 mK, we have observed a small deviation from $T^4$ dependence, which, however, cannot be attributed to the supersolid transition, because instead of decrease the entropy of the solid rather remains constant, about $2.5\times {10}^{-6}$ $R$.

Figure 1

Melting pressure of ${}^4\mathrm{He}$ after substracting the $T^4$ term found from the fit of the data at $T>100$ mK. Data have been taken with the crystals grown at 1.4 and 1.1 K. Open symbols correspond to cooldowns and solid ones to warmups. Different symbols correspond to different runs. In the vicinity of the ${}^3\mathrm{He}$ melting curve minimum at 0.32 K, the scatter of experimental points is somewhat larger because of the smaller sensitivity of the melting curve thermometer. Note that the substracted $T^4$ term varies by about 1 mbar in this temperature range.

Figure 2

Melting pressure of ${}^4\mathrm{He}$ at low temperatures measured with the crystal grown at 1.1 K. Open symbols correspond to cooldowns and solid ones to warmups. Different symbols correspond to different runs. The solid line is the $T^4$ fit to the data at $T>100$ mK extended down to 0 K.